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Cross country convergence of gross domestic products and associated factors

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Cross country convergence of gross domestic products and associated factors a cointegration approach
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Weatherspoon, Dave D
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x, 220 leaves : ill. ; 29 cm.

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Countries ( jstor )
Employment ( jstor )
Financial investments ( jstor )
Government expenditures ( jstor )
Gross domestic product ( jstor )
Income inequality ( jstor )
Investment income ( jstor )
Mathematical variables ( jstor )
Prices ( jstor )
Public investments ( jstor )
Dissertations, Academic -- Food and Resource Economics -- UF
Food and Resource Economics thesis Ph. D
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Thesis:
Thesis (Ph. D.)--University of Florida, 1993.
Bibliography:
Includes bibliographical references (leaves 211-219).
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Typescript.
General Note:
Vita.
Statement of Responsibility:
by Dave D. Weatherspoon.

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CROSS COUNTRY CONVERGENCE OF GROSS DOMESTIC
PRODUCTS AND ASSOCIATED FACTORS:
A COINTEGRATION APPROACH


















By

DAVE D. WEATHERSPOON


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1993














ACKNOWLEDGEMENTS

First, I would like to thank my wife for her support and

encouragement throughout this process. She provided me with

the incentives and assistance necessary to complete this

degree. I appreciate the standards of excellence expected and

portrayed by my parents. The supportive discussions with them

as well as my in-laws and siblings made this process somewhat

easier. I will always be indebted to my forefathers who stood

up for their rights so that people like myself can enter and

finish at any higher educational institution in the United

States.

The many hours of individual attention Dr. James Seale,

Jr., provided me during my course of study are much

appreciated. I would also like to acknowledge the extra

efforts of Dr. Charles Moss in helping me complete this

degree. The additional suggestions during the preparation of

this dissertation by Dr. Jong-Ying Lee, Dr. Gary Fairchild,

Dr. Douglas Waldo, Dr. M. Langham, and Dr. Henri Theil are

much appreciated.

The financial support as a McKnight Doctoral Fellow from

the Florida Endowment Fund for Higher Education made this all

possible. The additional financial support by Dr. James

Seale, Jr., and Dr. Henri Theil is much appreciated.

















TABLE OF CONTENTS



page

ACKNOWLEDGEMENTS . ... ii


LIST OF TABLES


. . vi


LIST OF FIGURES .. .

ABSTRACT . .


* viii

. ix


CHAPTERS


1 INTRODUCTION . .

2 CONVERGENCE . .


2.1
2.2
2.3
2.4
2.5
2.6


Overview of Convergence .
Historical Evidence .
Kuznets-Type Studies .
LDC Growth and Poverty .
Human Capital .
Contemporary Evidence ..


. 1

*6


S6
S8
. 11
. 15
. 24
. 27


3 THE INTERNATIONAL COMPARISON PROJECT AND ITS'
USEFULNESS IN EXAMINING CONVERGENCE .

3.1 Overview of the Construction of the ICP
3.2 The Geographic Expansion of the ICP:
Phases I to IV .
3.3 The Data . .

3.3.1 The Methodology of Calculating
Purchasing Power Parity .
3.3.2 Country-Product-Dummy Method .
3.3.3 Elteto-Koves-Szulc Method .. ...


3.4
3.5
3.6


Estimating Purchasing Power Parity .
The Geary-Khamis Method .
Calculating PPP's for Comparison
Resistant Goods .


3.7 Regionalism .. .
3.8 Phase III Results Compared with
Exchange Rates .
3.9 Phase IV Further Considered. .


. 33

. 33

* 34
. 36


S. 40
S. 41
. 42

. 46
. 52

S. 55
. 56

* 59
* 62


"'



r










3.9.1 Other Methods Used in Phase IV .
3.9.2 Linking the Regions of Phase IV .

4 EXTRAPOLATIONS. . .

4.1 The Beginning of Extrapolations with
ICP Data . .
4.2 Mark 1 . .
4.3 Mark 3 . .
4.4 Mark 4 . .
4.5 Mark 5 . .
4.6 The Centrally Planned Economies ...

5 INEQUALITY IN THE G-7 AND OECD. .

5.1 Inequality Measures. .

5.1.1 Graphical Inequality. .
5.1.2 Inequality Indices. .
5.1.3 Properties of an Inequality Index .

5.2 Income Inequality in the G-7 .
5.3 Variables of Interest .

5.3.1 Inequality in Government Expenditure. .
5.3.2 Inequality in Investment Expenditure. .
5.3.3 Inequality in Industrial Employment .

5.4 Inequality in Selected OECD Countries .

5.4.1 Income Inequality in the
OECD Countries. .
5.4.2 Inequality of Government Expenditure
in the OECD .
5.4.3 Investment Inequality in the OECD .
5.4.4 OECD Inequality in Industrial
Employment. .

5.5 Summary of the Inequality Results. .

6 COINTEGRATION . .

6.1 An Overview of Cointegration .
6.2 Unit Root Tests .

6.2.1 Augmented Dickey-Fuller (ADF) Test. .
6.2.2 Phillips Test .
6.2.3 Unit Root Results .

6.3 Pairwise Cointegration .

6.3.1 Durban Watson .

iv


. 63
* 65

. 70


. 70
. 76
. 77
. 82
. 87
. 93

. 96

. 96

. 96
. 97
.100

.102
.106

.107
.111
.113

.114


.115

.119
.122

.124

.125

.127

.127
.131

.132
.137
.139

.141

.141









6.3.2 Augmented Dickey-Fuller
Cointegration Test ..142
6.3.3 Pairwise Cointegration Results. ... ..143

6.4 Johansen's Multiple Cointegration Test ... .146

6.4.1 I(1) Procedure. .146
6.4.2 1(2) Procedure. .154
6.4.3 G-7 Multiple Cointegration Results. .161
6.4.4 OECD Multiple Cointegration Results .170
6.4.5 Other 7 Multiple Cointegration
Results ... .178

6.5 Summary and Interpretation ... .182

7 SUMMARY AND CONCLUSION. .190

APPENDICES

A PRICES PER KILOGRAM OF FRESH VEGETABLES AND
ESTIMATED PPP'S IN 10 COUNTRIES FOR 1970. .197

B SUPERCOUNTRY WEIGHTING. .199

C EKS CALCULATIONS .. 202

D FIXITY. . ... ... .205

E DATA AVAILABILITY .. ... 207

F EXTRAPOLATIONS OF INDUSTRIAL DATA .... .... .209

REFERENCES . .. .. .. 211

BIOGRAPHICAL SKETCH. . .220
















LIST OF TABLES


Table

3.1 Countries Represented in the International
Comparison Project. .

3.2 Fresh Vegetables for 4 Countries and Items
in 1970 . .

3.3 Mini-Laspeyres Price Ratio Matrix .

3.4 Mini-Fisher Ratios .

3.5 Transitive PPP's from the EKS Method. .

3.6 GDP Per Capita for 34 Countries in 1975 .

3.7 The Organizations that Performed the
Calculations and the Countries Involved
in Each Group for Phase IV. .

5.1 Income Per Capita and Income Inequality
(G-7 Countries) .

5.2 Government, Investment, and the Number of
People Employed in Industry Inequalities
(G-7 Countries) .

5.3 Investment Expenditure per Capita, and
the Rate of Investment Expenditures
for the G-7 .

5.4 Income Per Capita and Income Inequality
(OECD Countries) .

5.5 Government, Investment, and the Number of
People Employed in Industry Inequalities
(OECD Countries) .

5.6 Investment Expenditure per Capita, and the
Rate of Investment Expenditure for the
OECD. . .

6.1 Unit Root Tests .

vi


page


S 35


S 47

S 49

S 50

S. .. 51

S. .. 60



S 64


. .103



. .108



. .112


S .117



S .120



. .123

. .140








6.2

6.3

6.4


6.5

6.6

6.7


6.8

6.9

6.10


vii


Pairwise Tests for Cointegration. .

Johansen's Multiple Cointegration Test. .

Cointegrating Vectors and Adjustment
Coefficients from the G-7 .

Estimates of Gamma from the G-7 .

Johansen's Multiple Cointegration Test (OECD) .

Cointegrating Vectors and Adjustment
Coefficients from the OECD. .

Estimates of Gamma from the OECD. .

Johansen's Multiple Cointegration Test (Other 7).

Summary of Integration and Cointegration
Analysis. . .


. .144

. .162


. .165

. .169

. .172


. .174

. .177

. .179


. .183















LIST OF FIGURES


Figure

6.1 Total Income Inequality for the G-7 .

6.2 Total Government Inequality for the G-7 .

6.3 Total Investment Inequality for the G-7 .

6.4 Total Industrial Employment Inequality
for the G-7 .

6.5 Total Income Inequality for the G-7
Second Differenced. .

6.6 Total Government Inequality for the G-7
Second Differenced. .

6.7 Total Investment Inequality for the G-7
Second Differenced. .

6.8 Total Industrial Employment Inequality
for the G-7 Second Differenced .


page

. 133

S. .. 133

S. .. 134


. 134


. 135


. 135


. 136


. 136


viii














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

CROSS COUNTRY CONVERGENCE OF GROSS DOMESTIC
PRODUCTS AND ASSOCIATED FACTORS:
A COINTEGRATION APPROACH

By

Dave D. Weatherspoon

December 1993

Chairman: James L. Seale, Jr.,
Major Department: Food and Resource Economics

The convergence of income in the G-7 and selected OECD

countries was tested using Theil's inequality (entropy) index

between the years of 1950 to 1988. Theil's inequality index

was also applied to three potential factors of influence on

economic growth. These factors were government expenditure,

investment expenditure, and the number of people employed in

industry. The financial indicator variables were adjusted for

purchasing power parity based on Summers and Heston's 1991

data series. The derivation of this data set is also

discussed in this dissertation.

The results of the convergence test confirmed that all

four inequality indices were declining. This suggested that

income, government expenditure, investment expenditure, and

industrial employment are converging within the G-7 and within

the selected OECD countries. The inequality indices were then

tested to determine if they move together over time.








Pairwise and multiple cointegration tests were conducted

on the inequality indices that were found to be 1(2). In

general, there was support for pairwise cointegration of all

the variables for the G-7 and the selected OECD countries.

Johansen's 1(2) method was used to test multiple

cointegration. Multiple cointegration was supported for three

of the four variables for the G-7 sample, suggesting that

there exists a long-run equilibrium among the inequality in

income, investment expenditure, and the number of people

employed in industry. The OECD selected sample supported

multiple cointegration of all four variables. It was also

determined that industrial employment was the primary factor

in the sample that adjusts to return the four inequality

indices to their long-run equilibrium when innovations occur.

The G-7 equilibrium was stable without government

expenditure while the OECD sample was stable with government

expenditure. This may suggest that the OECD countries

excluding the G-7 rely on government expenditures for economic

growth and stabilization of their economies.














CHAPTER 1
INTRODUCTION

Cross-country economic convergence means that a group of

countries are becoming closer in terms of income. This

definition is usually operationalized as the faster rate of

productivity growth by less productive countries (Barro and

Sala-i-Martin, 1992). The result of which is the faster rate

of income growth of relatively poor countries than relatively

rich countries. Worldwide income growth and the factors that

influence this growth have been of interest for quite some

time. The interest in the economic welfare of current and

future trading partners is one reason why the U.S. in

particular is concerned with the area of economic growth and

convergence.

The literature has supported the idea that the high

income countries are converging (Grier and Tullock, 1989 and

Goa et al., 1992). However, none of the studies can

definitively state the factors in these economies that are

causing convergence. Therefore, the objective of this study

is to determine a method of measuring convergence, test the

method on a group of countries, and determine the factors that

influence convergence over time.

There are two hypotheses being tested in this

dissertation. First, it is hypothesized that the G-7 and the

1








2

selected OECD countries are converging in terms of income.'

Theil's inequality measure is used to test this hypothesis.

The second hypothesis is that the inequality of income has a

long-run relationship with the inequality of other factors in

the economy. The factors considered to influence the

convergence of income across countries are the inequalities in

government expenditure, investment expenditure, and the number

of people employed in industry. This hypothesis is tested by

using pairwise cointegration analysis and Johansen's multiple

cointegration technique.

The G-7 and OECD countries were chosen for this study for

several reasons. The most important factor is the

availability and the superior quality of their data. The fact

that the G-7 and OECD countries are some of the most powerful

countries economically in the world also influenced this

decision. The growth rate of per capital income for the G-7

and OECD has been sustained at a positive rate for a long time

period. In fact, per capital income in both groups increased

almost threefold during the 38-year period from 1950 to 1988.

These positive growth rates are not considered to be a random

process but are believed to be systematically related to other

factors in the economy (Grossman and Helpman, 1991).





'The G-7 countries are Canada, W. Germany, Italy, Japan, the
U.K., the U.S., and France. The selected 14 OECD countries are
Austria, Belgium, Denmark, the Netherlands, Norway, Ireland, Spain,
and the G-7 countries.








3
This analysis is not the first attempt to associate

economic growth and convergence to specific factors in an

economy. One of the models that influenced the way economists

approached the idea of convergence was put forth by Solow

(1956). Solow (1956) and the generalized neoclassical growth

model by Brock and Mirman (1972) implied that economies with

identical technology and preferences will converge regardless

of initial conditions. The driving force in both models was

technology. Several empirical studies have shown that the

world is not converging in terms of income and only recently

have the theoretical models begun to challenge the cross-

country implications of Solow's model (Romer, 1986; and Lucas,

1989).

Another approach was put forth by Kuznets (1955). He

approached convergence in an indirect manner by relating

personal income to economic development. Specifically,

Kuznets' (1955) hypothesis was that income inequality within

a country first increased then decreased as development

proceeded (divergence-convergence theory). This theory has

since been expanded to cross-country analysis where the

hypothesis is that countries first diverge then converge in

terms of income inequality as development occurs (Wright 1978,

Branco and Williamson 1988, and Ram 1988 and 1989a). The

cross-country interpretation of Kuznets hypothesis is not

directly tested in this dissertation. However, if the G-7 and

the OECD countries are found to be converging, then the








4
results may support Kuznets cross-country hypothesis since the

G-7 and OECD countries are developed countries. The

literature concerning the convergence or divergence of the

countries around the world is discussed in Chapter 2.

There are two main reasons why the topic of convergence

and economic growth are important. First, the factors that

cause convergence or economic growth have not been exclusively

identified. Second, the quality of international data have

been improved recently.

The problem in the past with output and income data from

different countries was that international comparisons require

the data to be converted to a common currency by using

official exchange rates. Official exchange rates do not

reflect the relative purchasing powers of different

currencies. For example, the official exchange rate does not

reflect domestic services since they are not traded

internationally (i.e. haircuts, house cleaning, etc.) (Kravis

et al. 1975, 1978a, and 1982). Hence, errors are introduced

into international comparisons when exchange rates are used.

This problem has been addressed and much improved by

Summers and Heston (1988 and 1991). They developed a data

series that is based on purchasing power parity. This data

set along with others are used to test the hypotheses stated

above.

The format of this dissertation is as follows. Chapter

2 includes a literature review on convergence while Chapters








5
3 and 4 include a discussion on the methodology used to

calculate gross domestic product without using exchange rates.

Specifically, the international comparison project (ICP)

methodology is addressed in Chapter 3. Then the data series

by Summers and Heston, which is based on the ICP, is

addressed.

The convergence of income, government expenditure,

investment expenditure, and the number of people employed in

industry is tested using Theil's inequality index in Chapter

5. Theil's decomposable index allows one to determine which

countries are driving the convergence. Then, these four

inequality indices are tested for cointegration using pairwise

cointegration and Johansen's 1(2) multiple cointegration test

in Chapter 6. This method determines if there exists a long-

run equilibrium among the four indices. If the series are

cointegrated, then the four inequality indices cannot drift

apart in the long-run given that there are no structural

changes. Chapter 7 presents the summary and conclusion of

this dissertation.














CHAPTER 2
CONVERGENCE


2.1 Overview of Convergence

The meaning of cross-country convergence in its simplest

form is that the income level of countries are becoming

closer. To get this result the less productive countries must

increase their productivity growth rate at a faster rate than

the more productive countries (Barro and Sala-i-Martin, 1992).

The result is that income grows at a faster rate in relatively

poor countries than in relatively rich countries. There has

been an interest in reducing the income gap (convergence)

between the developed countries (DCs) and the lesser developed

countries (LDCs) for some time (Berry et al., 1991). The

Pearson Commission (1969) was set up to address the income gap

problem. Specifically, the commission was to identify ways to

reduce the income gap between the developed and the developing

countries (Berry et al., 1991).

Kuznets (1955) influenced many researchers to explore

convergence through his hypothesis. Kuznets' hypothesis (also

known as the divergence-convergence theory) basically states

that income inequality within a country increases in the early

stages of economic development, stabilizes at some peak level,

then declines as the latter stages of development occur.








7

Kuznets was writing about a single country; however, this

hypothesis was quickly expanded to address international

development. Many studies attempt to directly and indirectly

prove or disprove Kuznets' hypothesis with income inequality

measures (Wright, 1978; Branco and Williamson, 1988; Ram,

1988, 1989a) or with regression analysis (Grier and Tullock,

1989; Barro, 1991; Barro and Sali-i-Martin, 1992; and

Baradaran-Shoraka, 1992). However, the results of all of

these studies have been inconclusive.

Three observations about economic growth in the world

economy frame the phenomenon examined in this study. First,

the growth of per capital income has been sustained at a

positive rate for many countries for a long time period.

Second, the performance of countries has varied across

countries and time. These two observations lead to the

conjecture that growth in income is not a random process.

They are believed to be systematically related to other

factors in the economy (Grossman and Helpman, 1991).

The third observation deals with the ability to study the

growth patterns around the world. Convergence of the world

cannot be thoroughly studied over long periods of time due to

data constraints. However, there are data available for many

countries starting in the 1950s. These data are largely due

to the efforts of Summers and Heston (1991) who developed a

time-series for several economic indicators for most of the








8

world for the years 1950 through 1988.' In the studies

mentioned above, the data of Summers and Heston as well as

other sources are used to analyze convergence from a

historical point of view. The international comparison

studies conducted prior to this data set were misspecified due

to the use of exchange rates (Kravis et al. 1975, 1978a, and

1982).

There have been two main approaches to studying

convergence, inequality measures and regression analysis.2

The review of the studies that follow represent both

approaches. The first section covers studies that analyze

what happened in the past.


2.2 Historical Evidence

Machinery investment and productivity growth have been

strongly associated over the past century in countries where

adequate data exist (Canada, Germany, Italy, Japan, the United

Kingdom, and the United States). In the recent past, the same

association holds for more countries (De Long, 1992). The

real question is whether high machinery investment causes

rapid growth?

Baumol (1986) showed that industrialized market economies

supported convergence using data from 1870 to 1979 (the data



'The development of the Summers and Heston data series is
discussed in the next two chapters.

2A summary of the inequality measures is given in
Chapter 5.








9

are not time-series). Baumol analyzed the G-7 countries along

with Australia for this time period. To extend his analysis

to a larger number of countries, he used the Summers and

Heston data from 1950 to 80. In this data set, the variable

used was output per capital. The results showed that

convergence is not supported when LDCs are included in the

analysis. The results of a similar study conducted by Dollar

and Wolff (1988) supported Baumol's 1986 results of

convergence.

In a follow up article criticizing Baumol's (1986)

findings, De Long (1988) showed that Baumol's study was

flawed. He commented that Baumol only used successful

countries (selection bias). In response to De Long's article,

Baumol and Wolff (1988) admitted to data mining in previous

studies. When they re-examined the results, it appeared that

a small group of countries began to converge in 1860. Since

then, more countries have joined the group according to

Baumol.

De Long (1992) reviewed the issue of productivity growth

and machinery investment similar to that done by Baumol. De

Long studied six countries (Canada, Germany, Italy, Japan, the

United Kingdom, and the United States) from 1870 to 1980, and

then a large number of countries on all six continents from

1950 to 1980. He divided up his study into 15 year periods to

offset any cycles and the effects of wars. This study showed

a strong positive relationship between growth and machinery








10

investment. He cautions that these countries are all wealthy

and that the regression may have captured "luck" instead of

the intended relationship. The results may have been

different if more countries were included.

In addition, De Long examined the effects that political

stability and investment in education had on growth. All of

the countries sampled had been stable politically and had

invested heavily in education. He also argued that just the

presence of high tech machinery may have provided a higher

level of education. In testing these relationships, he found

little evidence supporting the education or political

stability influence on growth. De Long (1992) concluded that

when a broader group of countries is considered, there is

little evidence of convergence in the short-run, and in the

long-run, the regressions may not be accurate. Alam (1992),

however, cautions that De Long needed to use other variables

to indicate productivity.

Hanson (1988) examined the convergence of LDCs before

World War I. This study is interesting for two reasons.

First, historical studies of this type conducted on LDCs are

rare. Second, the long period of analysis from 1913 to 1980

is impressive. Hanson corrected the historical data by

extrapolating Summers and Heston's (1984) data backwards and

combining other data sets. He also compared other data sets

to that of Summers and Heston. Unfortunately, his results

were inconclusive.








11

To summarize, there appears to be a long-run relationship

between investment in machinery and growth. The only

countries that appear to be converging are a few

industrialized countries. The LDCs appear to be caught in a

circle of poverty (Alam and Naseer, 1992). It is clear that

human capital is considered an important variable with respect

to growth, and that the relationship may be that higher

equipment investment drives faster growth (Adams, 1990; De

Long and Summers, 1991).


2.3 Kuznets-Type Studies

As mentioned before, Kuznets hypothesized (divergence-

convergence theory) that income inequality increases in the

early stages of economic development, stabilizes at some peak

level, then declines as the latter stages of development

occur. A few of the many studies that have tested this

hypothesis in the international context using various methods

are discussed next. It will become clear that there are no

definite answers as to whether Kuznets' hypothesis is indeed

correct.

Wright (1978) analyzed whether the institutionalist or

Kuznets' hypothesis was correct. The institutionalist

hypothesis states that institutional structures and

governmental policies are the chief determinants of income

inequality. Wright conducted his analysis using a Gini

coefficient inequality measure. He calculated the income

inequality of the GDP per capital for 56 countries. He








12

concluded that the data did not support Kuznets' hypothesis.

Instead, he found that the level of inequality was higher in

the LDCs than the developed countries. Wright concluded that

his results supported the institutionalist hypothesis. Hence,

the reduction of income inequality among countries is

dependent on modifications of institutions and policies.

Ram (1989a) extends Kuznets' hypothesis to the world

system. He hypothesizes that intercountry (world) inequality

across sovereign nation states would first increase with

secular economic growth, then start to decline at some point.

He tested this hypothesis using 115 market economies for the

years 1960 to 1980 from the Summers and Heston 1984 data set.

Average (per capital) world GDP was used as a proxy for the

level of development and Theil's income inequality (J) measure

was used to analyze the inequality (see Section 5.1.2 for

Theil's inequality). In addition, Ram used a Kuznets type

quadratic regression to determine the relationship between the

level of income and development, which represents development

and inequality. The equation is


(2.1) J, = Bo + B, LRY, + B2 (LRY,)2 + u,


where J is the measure of the world inequality and LRY is the

natural logarithm of the average real GDP per capital. The

last term is the disturbance term with the standard properties

(zero mean and a constant variance). He found that world

income inequality has increased since 1960. However, the rate








13

of increase has slowed. The regression results supported the

hypothesis that world inequality may first increase and then

decline with world economic growth. Hence, Ram's study

supports the idea of divergence then convergence of real GDP

worldwide.

A partial contrast of the above results is provided by

Ram in 1988. In this paper, Ram (1988) tests Kuznets'

hypothesis for 32 counties, 8 developed countries and 24 LDCs.

The estimated equation in this paper is the same as the one

used in his 1989a paper. Ram (1988) finds support for

Kuznets' hypothesis when all of the countries are present.

However, when only the LDCs are present, the results do not

support Kuznets' hypothesis.

Branco and Williamson (1988) also tested Kuznets'

hypothesis by analyzing development and income distribution.

This study was unique in that it developed an absolute per

capital income measure for the poorest 40% of the population in

68 countries. Their measure was the percent of income of the

poorest 40% of the nation's population in 1970 divided by 40%

of the 1970 population, then multiplied by the real GDP per

capital of a nation in 1970 (Summers and Heston, 1984 data

set). Bronco and Williamson (1988) felt that this dependent

variable portrayed the situation of the poorest 40% in

different countries. The independent variable was the energy

consumption per capital in 1970 (measured in kilograms of coal

equivalents). This variable is supposedly a better indicator








14

of industrial development across nations than GNP per capital.

They estimated linear, quadratic, logarithmic, and log

quadratic models to determine the best fit and also to prove

or disprove Kuznets' hypothesis. Their results supported

Kuznets hypothesis. Therefore, the countries are expected to

diverge, then converge in terms of income as development

occurs.

Bornschier (1983) reinterpreted Kuznets' theory by

combining two paradigms of world economy and the level of

development. Briefly, the world development paradigm is the

core-periphery division of labor, which has come about due to

multinational corporations. The core specializes in control

over capital, technology, innovation processes, and the

production of the most advanced products, which embodies the

most human capital. -The periphery is engaged-in standardized

and routine industrial production for domestic or maybe world

markets. In a sense the multinational corporations have

created a world division of labor. The core countries are

basically the industrial countries, and the periphery are the

countries with the raw materials.3 The level of development

paradigm is basically Kuznets' hypothesis. Both of these

paradigms have different ideas on how development takes place.

Bornschier (1983) combined the two approaches with the

following deviations from the original hypotheses: the



3For a more detailed explanation of this theory see Amin,
1974, pp. 559-587.








15

countries on the periphery, which were still considered

agrarian based, had the most income inequality; the countries

that assumed less importance for agrarian production had lower

inequality; and the core countries within the world economy

had the lowest income inequality. He showed that developing

countries did not automatically decrease their income

inequality with increased development. In addition, the

reduction of inequality was found to be dependent on the type

of production (services, agriculture, and industry) in which

they were involved.

Several of the studies supported the divergence-

convergence theory (Kuznets' hypothesis) and others did not.

The studies that included the LDCs were also contradictory.

In the study by Bornschier (1983), the author implied that the

type of development countries pursued affectedthe reduction

in income inequality. He indicated that if a country has less

emphasis on agrarian development, then that country is

expected to converge faster than a country that promotes

agricultural development. This may or may not be the actual

case, but it introduces the idea of what has happened within

the LDCs.


2.4 LDC Growth and Poverty

Morawetz (1977) addressed the issue of growth in chapter

2 of his book entitled "Twenty-Five Years of Economic

Development 1950 to 1975." The questions he posed were: "How

rapidly were GNP per capital and population expected to grow in








16

1950, and how has their actual growth compared with these

expectations." He commenced by stating that the status of

development in Africa, Asia, and Latin America was not

considered before 1950. The reason for this was that the

industrialized countries were just getting over the war, and

were still concerned with reconstruction in Europe. The few

researchers who thought about the economic development of the

LDCs had no hope for their short and medium term future. The

industrialized countries only attained 2% growth (per capital)

on average during that period. Therefore, the developing

countries were not expected to perform as well as the

industrialized countries. In addition, it was perceived that

the population growth in the developing countries was high

while their GNP growth was low.

Morawetz stated that no statistical work had been done on

the LDCs. Hence, he conducted a statistical analysis on the

LDCs to determine their economic growth status. His results

indicated that the disparity between the rich and poor

developing countries had increased significantly between 1950

to 1975. However, at the aggregate level, it was not true

that the richest of the developing countries were getting

richer and the poor were getting poorer. When the developing

countries regional averages of income per capital in 1950 were

examined, the richest regions (Latin America and the Middle

East) had grown five to six times faster than the poorest

region (South Asia). By 1975 this gap had increased to 13








17

times for the Middle East and seven times faster for Latin

America than South Asia. When the LDCs were compared to the

developed countries, it was shown that China, East Asia and

the Middle East narrowed the gap, while the gap was widened

for South Asia, Africa, and Latin America. However, the

ranking of 80 individual developing countries remained stable

from 1950 to 1975.

Morawetz (1977) regressed 16 indexes of basic needs on

GNP per capital growth to get a better understanding of how the

change in relative GNP per capital affected poverty. Morawetz

used 16 different regression equations to analyze the problem.

The factors that were found to be significantly related to GNP

per capital growth were three nutrition indicators, infant

mortality, and the percentage of dwellings with access to

electricity. Some of the other variables-that were included

in the analysis but were not significantly related to the

growth in GNP per capital were four indicators for education:

adult literacy rate, primary school enrollment ratio,

secondary school enrollment ratio, and vocational school

enrollments as a percent of secondary school enrollments.

Another study on the LDCs was conducted by Zind (1991).

He tried to determine if the LDCs were converging in terms of

income, and assess the key variables that influenced

convergence such as government policies, population growth,

and investment levels. The Summers and Heston 1984 (1960-80)

data set was used for the comparison of 89 LDCs. His test was








18

a simple regression of real income per capital annual growth

rate against per capital income in 1960. In his model a

negative coefficient indicated convergence. When all of the

countries were included, there was no evidence of convergence.

Reducing the number of countries to 30, results indicated

convergence at the 10% level; reducing the countries further

to 19 yielded convergence at the 5% level. These 19 countries

were the most developed countries in the LDC sample. In

addition, he found that the other variables (the relative size

of government, population growth and investment level),

contributed to convergence in the most developed countries.

Dollar (1992) basically answered the question of how the

slowest growing countries in the LDC category could increase

their growth. Asian (16 countries) LDCs grew at an average

rate of 3.4%, while this occurred at 0.4% in Africa '(43

countries), and only 0.3% in Latin America (24 countries)

(Dollar, 1992). Using the data of Summers and Heston (1984),

he showed that outward oriented countries had lower prices

than inward oriented countries.4 He believes that the price

level was a reflection of the protectionist policies in the

different countries. The Asian countries had the lowest price

levels, followed by Latin America and Africa. He also

considered the variation in exchange rates where the Asian

countries had the lowest variation. He created an index of


4Inward oriented countries are countries that have
protectionist trade policies. Outward oriented countries are
countries that have relatively open trade policies.








19

outward orientation based on the variation of the exchange

rate. This index was found to be highly correlated with per

capital GDP growth. He concluded that Africa and Latin America

could increase their growth through trade liberalization,

devaluation of their real exchange rates, and by maintaining

a stable exchange rate.

Berry et al. (1991) conducted an extensive analysis on

world income inequality. They analyzed over 100 countries

from the time period of 1950 to 1977. The data came from

World Bank Tables, World Bank Atlas, World Development Report,

and the Summers and Heston data set. Their objective was to

determine what had happened to income inequality in the world.

They applied Theil's entropy, Atkinson's inequality, and the

Gini coefficient measure (see Chapter 5 for definitions of

these inequality indices). The uniqueness of this study was

that they applied these inequality measures to gross national

product (GNP) and consumption measured as a percentage of GNP

to determine changes in welfare.

The idea behind using the inequality of consumption was

that the distribution of consumption was less unequal than

that for income for two reasons. First, the savings rate was

below average in many of the poorer countries. Second, the

intracountry distribution of consumption was generally less

unequal than the income distribution. Berry et al. (1991)

attributed this to the fact that the marginal propensities to

consume fall with income and that high income families do most








20
of the saving. The fact that the savings rate was lower than

average in the poorer countries contributes more to worldwide

inequality than the second reason, regardless of whether

income or consumption was used.

They conducted the analysis with and without the non-

market economies for which the data were considered to be

inaccurate (Berry et al., 1991; Summers and Heston, 1991).

The results of their study showed that the 1950s and early

1960s were stable around the world in terms of income.

Between 1964 and 1972 there was a large increase in world

inequality, which gradually continued to increase until 1986.5

The consumption ratio also indicated a worsening of inequality

from 1950 to 1986.

The other unique aspect of this paper was that they broke

the world's inequality into deciles. Using this method they

were able to show that the bottom half of the world's

population income shares remained unchanged, while the top

decile gained at the expense of the sixth, seventh, and eighth

decile. In addition, the middle deciles gained in the 1950s

and 1960s, only to lose it in the 1970s and 1980s. During

this time period, the richest two deciles increased their

share of world consumption from 68.5% to 71.6% at the expense

of the seven lowest deciles.


5They initially stated that this study was from 1950 -
1977. That is the case for their analysis which includes the
communist countries. After 1977, they were not able to get
adequate data for the communist countries; hence, they left
them out of the analysis from 1950 86.








21
The change in inequality in the 1980s was due to slow

growth particularly among the low income countries which had

zero growth during the period of 1980 to 1985. Most of these

countries were in sub-Saharan Africa. Some of the

contributing reasons were the agriculture and debt crisis, and

the rapid population growth.6 The middle-income countries

were not as progressive in terms of economic growth with the

industrialized countries, while the average income of the less

developed countries (LDCs) increased. The South Asian

countries (India, Pakistan, Bangladesh, Sri Lanka, and Nepal)

on the other hand grew faster between 1980 and 1985 than

between 1965 and 1980. The fastest growth occurred in the

newly industrialized countries and the OPEC countries.

However, their presence did not reduce inequality much because

of the relatively small population. In general, the

population has grown faster in the poor and middle-income

countries than in the rich ones. Berry et al. (1991) suggest

that the slow economic growth and the population boom in the

poorest countries had increased the absolute number of poor

around the world (income below $200 U.S. 1970 dollars).

However, to give a full picture, the share of the total

population that was considered poor had decreased.

The results of Berry et al. about the poverty line can be

disputed. Atkinson (1987) examined the issue of measuring


6Theil's entropy measure is sensitive to population
changes. An increase in population increases the inequality
measure if income is held constant.








22
poverty. Specifically, he researched the poverty line,

indexes on poverty, and the relationship between poverty and

inequality. The choice of the poverty level could influence

the results on whether countries were becoming closer in terms

of the absolute number of people in poverty. However, the

choice of the poverty line would have no effect on the income

inequality measures.

Ahluwalia et al. (1979) made some predictions concerning

the future. Their approach to studying growth and poverty in

the LDCs was threefold. First, they estimated the absolute

poverty in the developing countries and the relationship

between income distribution and the rising levels of output.

Second, an analysis of the past trends in growth and poverty

for certain countries was conducted, the results of which were

projected into the future based on the policies at that time.

Lastly, the changes in poverty were considered when income

growth was accelerated, the distribution of income was

improved, and the reduction of fertility was implemented.

This analysis was based on 36 countries, all of which were LDC

market economies. These countries GDPs per capital were

adjusted for purchasing power parity using what was referred

to as the Kravis adjustment factor.7

Ahlualia et al. (1979) used Theil's inequality index to

analyze the trends in inequality and poverty from 1960 to 1975


7The Kravis adjustment factor was an attempt by Ahlualia
et al. to adjust the data for purchasing power parity
estimates by Kravis et al. 1975 and 1978a.








23

among the LDCs. The results indicated that the inequality

among the LDCs increased during this period. In addition,

they projected the inequality level to the year 2000. They

expect the income inequality to increase from .67 in 1975 to

.77 in the year 2000. The reason for the divergence will

increasingly be due to the wider distribution of income among

the countries (from 37% to 50% respectively).s They predict

that India and Bangladesh will have higher growth than the

other LDCs. Therefore, a large percent of the increase in

inequality in the LDCs will be due to the economic events in

India and Bangladesh.

The worsening of the internal distribution of income is

what Ahlualia et al. (1979) attributed to the lack of growth

in the poorest of the LDCs. The middle group of LDCs are not

expected by these authors to reduce their inequality. A

listing of the poorest LDCs and middle LDCs is presented in

Ahluwalia et al. (1979). They expect the relative level of

poverty to decrease and the absolute level of poverty in the

year 2000 to be 600 million.

The studies in this section clearly state that the LDCs

are diverging instead of converging. There were several

reasons given for their slow growth: debt crisis, population



8Income inequality increases if the income of the
different countries continue to grow further apart. That is
the case with India and Bangladesh. They are increasing the
inequality because they continue to grow faster than the other
DCs. Hence, creating a greater dispersion (increasing
inequality).








24
growth, agricultural based economies, and restrictive trade.

Two variables that have been related to convergence in the

other two sections were also found to influence convergence in

the LDCs: government expenditure and investment.


2.5 Human Capital

The effect of human capital on economic growth is

uncertain. Human capital in this text is considered to be a

set of specialized skills that agents can acquire by devoting

time to schooling or special training (Grossman and Helpman,

1991). The more training an individual receives the more

human capital that individual acquires. Human capital has

become more important in the literature recently. The

endogenous growth models show that increasing returns are

possible with a constant return to scale model if human

capital is included (Romer, 1990). In contrast, the older

exogenous growth models assumed that growth is attributed to

exogenous technological change (Solow, 1956).

The key to endogenous growth models is the idea of

learning by doing. Romer (1990) showed that the rate of

growth and technology was a function of total human capital in

an economy. The initial human capital level affects the rate

of growth in the different countries. Romer's approach led to

the suggestion that countries will diverge. Unlike Romer,

Lucas (1988) mathematically showed that human capital has

spillover effects which drive growth (unbounded growth).

However, his conclusion was that there will be no convergence








25

or divergence, but that countries will grow uniformly.

Grossman and Helpman (1991) agree with Lucas; however, they

assume that a finite population can only accumulate a bounded

quantity of human capital.

Glomm and Ravikumar (1992) examined the implications of

public investment in human capital on growth and the evolution

of income inequality. Using an overlapping generations model,

they showed that public education reduced income inequality

faster than private education. However, private education

yielded higher per capital incomes except when the initial

income inequality was sufficiently large.

The main objective in the study reported by Ram (1989b)

was to explain the role of schooling in reducing income

inequality and poverty in LDCs. The first part of Ram's paper

reviewed past literature on this subject. The review of

literature as cited by Ram (1989b) showed the following:

Chiswick (1971, 1974) found that income inequality was reduced

as educational inequality was reduced (based on nine

countries); Chiswick and Mincer (1972) found that in the U.S.,

inequality in schooling did influence income inequality, even

though it had a minimal affect; Adelman and Morris (1973),

Chenery and Syrquim (1975), and Ahluwalia (1976) showed that

for 43 developing countries, 55 LDCs and 60 various countries,

respectively, education reduced income inequality.

Contradictory later findings were also cited. These were the







26

work of Fields (1980), Psacharopoulos and Woodhall (1985), and

Morrison (1987).

The above literature was puzzling to Ram. Hence, he used

the data from Psacharopoulos and Arriagada (1986) and Summers

and Heston (1984) for his analysis. His income inequality

variable was a Gini coefficient, and the independent variable

was mean education level of the labor force. He found little

evidence that the education level affected income inequality,

even for the LDCs. Ram concluded that based on both empirical

evidence and theory, the effects of education on income

inequality were ambiguous. Problems with the data (e.g.

inconsistency or missing information) may have affected the

ability to effectively test the relationship between

educational inequality and income inequality.

Barro (1991) and Baradaran-Shoraka (1992) did empirical

studies on the effect of human capital on growth. Barro used

several proxies for human capital: secondary school

enrollment in the year of 1960 and 1985, primary school

enrollment in the year of 1960 and 1985, and adult literacy in

the year of 1960. The data were pooled for this analysis.

Therefore, there were no time-series implications from the

model. The only significant relationship he found was the

positive relationship between the average growth rate and the

1960 school enrollment.

Baradaran-Shoraka (1992) using the same variable as Barro

found the same result which supported Romer's argument.







27

Baradaran-Shoraka (1992) went one step further to create an

education data set that had four data points, which supposedly

included mean years of schooling of the total population aged

25 years and older, and years of schooling for young workers

for the period of 1969 to 1985. His results indicated that

the variable for human capital was positively and

significantly related to growth, which again supported Romer's

argument. It must be noted, however, that Baradaran-Shoraka

was only able to conduct this analysis for 50 countries due to

data limitations.

The theoretical arguments put forth about the

relationship between convergence and education are

inconclusive. In addition, the empirical studies are also

inconclusive. The small data sample appears to be the major

limiting factor.


2.6 Contemporary Evidence

The first contemporary study reviewed here was done by

Theil. Theil (1989) conducted a study from 1960 to 1985 using

the Summers and Heston 1988 data set. Theil's entropy index

was used to measure the inequality among the North, South, and

the Tropical Middle (Tropical America, Asia, and Africa).9

This analysis was based solely on non-Communist countries.

Theil noted that the population has decreased in the North and

the South while it has increased dramatically in the tropical


9See Theil (1989) for details of the breakdown of the
country categories.








28

middle countries. The ranking of real GDP places the regions

in descending order as stated above. The results showed that

world income inequality has increased over the 25 years.

Using the decomposability of his index, he showed that 80% of

the world inequality was due to inter-regional inequality.10

It has also been shown that the inequality within the North

started with the most inequality and decreased dramatically by

1985. The South's within inequality fluctuated, but stayed

relatively low while Tropical America's was relatively low and

continued to decrease. Tropical Asia started out high and

increased its inequality while Tropical Africa started out the

second lowest in inequality and ended with the highest

inequality. Tropical Africa's inequality increased

approximately three times while the North almost halved its

inequal-ity; These results showed that the world is not

converging. However, there are some regions of the world

which are converging, the North and Tropical America.

Grier and Tullock (1989) investigated postwar economic

growth for 113 countries from 1950 to 1981. The 1984 data set

of Summers and Heston was used in this study. They averaged

the data for every five years and pooled the data into OECD

countries and the rest of the world (ROW). This decision was

made after tests confirmed that the OECD countries and ROW

should not be pooled. They regressed their five year average



'OFor a discussion on the decomposability of Theil's index
see Chapter 5.








29
growth in real GDP against the following variables: initial

real GDP, government as a percent of real GDP, population

growth, standard deviation of real GDP as a percent,

inflation, and the standard deviation for inflation.

Convergence was supported only in the OECD sample. There was

no evidence to support the idea that Africa, Asia, and the

Americas are converging. The variable that was significantly

related to the average five year growth was government. This

relationship was negative for all regions except Asia.

Barro (1991) used a simple multiple regression technique

to analyze the convergence of 98 countries from 1960 to 1985,

and the factors that influenced it. He regressed the average

growth rate from 1960 to 1985 on several independent

variables: real GDP in 1960, and 1970; square root of real GDP

in 1960; secondary school enrollment in 1950, and 1960;

primary school enrollment in 1950, and 1960; average

government expenditure between 1970 and 1985 as a percent of

real GDP; number of revolutions and coups per year; number of

assignations per million population per year; and the

magnitude of the deviation of 1960 purchasing power parity

value for the investment deflator. He also ran regressions

using fertility as a dependent variable on some of the

independent variables. The last regression was run with

investment as the dependent variable.

The results from this set of regressions, 29 in all,

indicated that a few variables were significantly related to








30
growth. The starting point of human capital was shown to be

positively related to growth. This suggested that poor

countries with high human capital per person would eventually

converge with rich countries in terms of real GDP. The second

relationship was a negative one with government. This was

interpreted by Barro (1991) as the distortions governmental

policies (high taxes) introduce and offset private investment

growth. Lastly, the political instability was negatively

related to growth and investment. The more unstable a country

is politically, the less investment and growth are likely to

occur. In support of Barro's findings, Baradaran-Shoraka

(1992) conducted a similar study with a few of the variables

measured differently and found the same results as Barro.

Barro and Sala-i-Martin (1992) also conducted a similar

study to Barro's 1991 study. In this study they used a

neoclassical growth model to analyze the convergence of 98

market economies from 1960 to 1985 (data set of Summers and

Heston, 1988). They were trying to test B convergence which

is a term that Barro defined as countries converging in terms

of income over time." In this model, the log change in GDP

per capital (growth rate) was used as its dependent variable.

A description of the rest of the equation was detailed,

intricate and well illustrated in Barro and Sala-i-Martin

(1992). The independent variables were a constant and the log


"The other type of convergence Barro defines is a
convergence. This type of convergence refers to the
dispersion in income across countries reducing over time.








31
of 1960 per capital GDP. Analysis showed that there was little

to no relationship between the growth rate and the log of 1960

per capital GDP. This finding indicated that the initially

rich countries grew at a faster rate than the poor countries

(divergence). However, the first part of their analysis was

conducted on just the U.S. states, where they found

convergence taking place.

Barro and Sala-i-Martin (1992) extended their analysis to

include primary and secondary school enrollment rates in 1960,

the average ratio of government consumption expenditure to

GDP, proxies for political stability, and a measure of market

distortions based on purchasing power parity ratios for

investment goods. When this was done, the model indicated

convergence conditionally. This meant that to get

convergence, the following variables had to held constant:

initial school enrollment and the ratio of government

consumption to GDP.

In this section, the income inequality studies indicated

that world divergence was taking place, but some regions were

converging (the North and Tropical America). The growth

studies also showed divergence in the world. However, the

OECD countries were found to be converging. In addition,

several other variables were found to be significantly related

to growth: government expenditure, human capital (education),

and political instability. In the next two chapters the

development of the Summers and Heston data series on which








32
most of the studies in this section based their analysis will

be discussed.














CHAPTER 3
THE INTERNATIONAL COMPARISON PROJECT
AND IT'S USEFULNESS IN EXAMINING CONVERGENCE


3.1 Overview of the Construction of the ICP

The objective of the International Comparison Project

(ICP) was to establish a system of comparisons of real product

and purchasing power for a large number of countries. The

reason for this is that it was realized that the use of

exchange rates to conduct international comparisons introduced

errors into the analysis. For example, a 1954 study by

Gilbert and Kravis found that $1000 in US currency, when

converted to sterling at the official exchange rate, bought a

basket of U.K. goods 64% larger than the $1000 could have

purchased in the United States.

This problem was recognized by the Statistical Commission

of the United Nations. The issue was discussed in 1965, at

the United Nations' thirteenth session, and it was concluded

that using exchange rates for currency conversion was

inadequate for many uses of international data (U.N.

Statistical Commission, 1965). The United Nations and the

University of Pennsylvania started the "International

Comparisons Project" in 1968. Initial funding came from the

World Bank, Ford Foundation, some of the countries involved in








34

the first set of data collection, U.S. Agency for

International Development, and the U.S. Social Science

Research Council.

Kravis et al. (1975) published the first results of these

efforts which is referred to as Phase I. In this seminal

attempt, the methodology developed is presented, and actual

comparisons are made for several countries. Since Phase I,

several other successive Phases have been published. Each

successive Phase increased the number of countries and refined

the methodology for calculating gross domestic product for

each country. The countries involved in the first four Phases

are discussed in the next section.


3.2 The Geographic Expansion of the ICP: Phases I to IV

Phase I of the international comparison project (ICP)

began with a pilot study in 1967 (which included data

collection for six countries) and included data collection for

10 countries for 1970. The project was initiated by Irving

Kravis, Zoltan Kenessey, Alan Heston, and Robert Summers, all

at the University of Pennsylvania, and their results in 1975.

The countries included in 1970 are shown at the top of Table

3.1.

These authors later published two successive volumes,

1978a and 1982, referred to as Phases II and III,

respectively. Phase II added six new countries to the ICP.

These are listed in Table 3.1 under countries added in Phase

II. Phase II provides data for 1970 and 1973, but much of the













Table 3.1



Countries Represented in the International Comparisons Project




Africa America Asia Europe


Countries represented in Phase I


Columbia
United States


India
Japan


France
W. Germany
Hungary
Italy
United Kingdom


Countries added in Phase II

Iran
S. Korea
Malaysia
Philippines


Countries added in Phase III


Pakistan
Sri Lanka
Syria
Thailand


Belgium
Netherlands


Austria
Denmark
Ireland
Luxembourg
Poland
Romania
Spain
SYugoslavia


Countries added in Phase IV


Argentina
Bolivia
Canada
Chile
Costa Rica
Dominican Rep.
Ecuador
El Salvador
Guatemala
Honduras
Panama
Paraguay
Peru
Venezuela


Jamaica
Mexico


Countries deleted in Phase IV

Iran
Malaysia
Syria
Thailand


Sore Tfel tal 98,p.2


Malawi
Zambia


Brazil
Jamaica
Mexico
Uruguay


Botswana
Cameroon
Ethiopia
Ivory Coast
Madagascar
Mali
Morocco
Nigeria
Senegal
Tanzania
Tunisia
Zimbabwe


Hong Kong
Indonesia
Israel


Finland
Greece
Norway
Portugal


Romania


Kenya


Source: Theil


et al. 1989, p. 2.








36

1973 data were based on extrapolations; hence 1970 will be the

main focus. Phase II also made corrections on Phase I data;

hence Phase II has the most accurate data for 1970. Phase III

added 18 countries which are reported in Table 3.1 under

countries added in Phase III. The data are for 1975.

Phase IV results were published in two different volumes

(United Nations, 1985 and 1987). Phase IV is different from

the previous three phases in two ways. First, the study was

completed by the Statistical Office of the United Nations

Secretariat, and 33 countries were added in this Phase (see

Table 3.1, countries added in Phase IV). Second, there are

seven countries that participated in Phase III that withdrew

in Phase IV. These countries are also reported in Table 3.1

under Countries deleted in Phase IV. This makes the total

number of-participating countries in Phase IV equal to 60.

In Phases I, II, III, and IV, we have 10, 16, 34, and 60

participating countries, respectively. In Phase IV (including

the seven deleted countries), there are 15 countries in

Africa, 20 in the America's, 13 in Asia, and 19 in Europe. In

all of these countries detailed data were collected. The type

of data and the method in which they were collected follows.


3.3 The Data

There are two main steps to obtaining the type of data

the ICP needed. First, a classification system was developed

for gross domestic product (GDP) so that each countries GDP

could be divided into detailed categories. After the detailed








37

categories were defined, GDP data were collected at the

detailed category level, prices for each item within the

detailed categories, and quantity data for the items which

price data could not be obtained.

The classification system follows the scheme proposed by

the system of national accounts (SNA). Some improvements were

made to this classification system to enhance the

international comparability of the data (Kravis et al. 1975,

p. 26). The format the ICP settled on for phases I and II was

a total of 153 detailed categories, 110 for consumption, 38

for capital formation, and five for government. Phases III

and IV have 151 detailed categories, 108 for consumption, 38

for capital formation, and five for government.1 Once the

classification system was determined the next issue was the

collection of the data.

There were three categories of data used; GDP or

expenditure data for the detailed categories, price data for

each item for which a price could be identified, and quantity

data for those items for which price data could not be

collected. The collection of the expenditure data was simple:

the data were taken from the U.N. national accounts data.

Therefore, expenditure data are not discussed in detail here

but the price and quantity data collection are.



'In Phase IV, the European countries had more detailed
categories than the 151 categories and the African countries
had less. However, the systems were similar making it
possible to use the 151 detailed category system.








38

Accurate price data were very difficult to obtain for

each item, within every category, in each country. The

difficulty was that some items are not found in every country,

and if found in all of the countries, matching the qualities

of the item was complex. To ensure that the items specified

were the same, the U.N. sent price specialists to the

different countries to directly compare the qualities of the

items in question. An example of the specifications used by

the ICP was: fresh chicken eggs, size large (weighing at

least 680.4 grams per dozen), white or brown shell, not of the

best quality, but close to it. The less than best quality's

white is less thick and higher than the best quality. The

best qualities yolk must be firm, high, and not easily broken

(Kravis et al. 1982, p. 38). In this example of the egg

specifications, it can- -be. assumed- that if-- these

specifications were met in any country, the quality is the

same for those countries. For most of the food groups, the

specifications were met.

As mentioned before the U.N. sends price experts to

resolve questions about matching qualities. For example, the

visits helped clear up misunderstandings from the use of

different terminology. In Japan, "cashmere" refers to a weave

rather than yarn, as in the U.S. and Europe. In England, "ox

liver" is used rather than "beef liver," the American

terminology (Kravis et al. 1982, p. 38). These types of goods








39

were referred to as narrowly defined goods. They could be

classified by their characteristics and uses.

Non-narrowly defined goods are the items for which prices

cannot be collected in a systematic way in all of the

countries. For these items quantity data were collected.

These items were called comparison-resistant goods.

Comparison-resistant goods are goods and services that cannot

be put into a category based on their characteristics. Some

examples of comparison-resistant goods are services rendered

by teachers, physicians, and the government.

Dissimilar to most commodities, services constitute a

heterogeneous collection of final products, and the production

of each is necessarily simultaneous with its consumption;

consequently, no service can be stocked. For example, to

compare teachers and physicians around the world is difficult.

The problem is how can the quality and productivity of a

teacher or physicians be measured. However, indicators of

quality and productivity can be obtained. For example, these

indicators for teaching services would include the level of

education, average income, number of students in a classroom,

or the amount of educational inputs available to and used by

the teacher. For doctor's services, the number of patients

seen or the number of operations in a day may be indicators of

their quality and productivity. Government services are also

hard to measure. The amount of capital available to the

worker may help indicate their productivity.








40

Once the base data were collected, there were several

steps and alternatives to calculating purchasing power

parities (PPPs) for each country. The first step was to

calculate the PPPs for each country with respect to a base

country. Then, the real GDP was calculated using those PPPs.

The calculation of the PPPs for comparison-resistant goods is

discussed in Section 3.6 while that for the narrowly defined

goods is discussed next.

3.3.1 The Methodology of Calculating Purchasing Power
Parities

Purchasing power parity (PPP) is the number of currency

units required to buy goods equivalent to what can be bought

with one unit of the currency of the base country (Kravis et

al. 1982, p. 383). From the base data that are collected

purchasing power parities can be calculated. There are

several ways to calculate PPPs, but the methods most commonly

used by the ICP are the country-product-dummy (CPD) and

Elteto-Koves-Szulc (EKS) methods.

The CPD and EKS methods are exactly the same if all of

the prices for every item in each country are present. In

that case, the resulting PPP's from the CPD and EKS are just

geometric means of all of the prices in detailed category a

for country c (Kravis et al. 1975, p. 60). The equation for

the geometric mean of all the prices in country c is:



(3.1) GM- = [ Pic ]v i = l,...,m










where P,, is the price of the ith item in country c.

3.3.2 Country-Product-Dummy Method

The derivation of the CPD method from this representation

is simple. The CPD method is derived by making the following

assumptions: the natural logarithm of the price for the ith

item in country c is composed of an item effect and a country

effect; the PPP's are estimated by least squares; and the

relationship is stochastic. Then the CPD equation becomes:


(3.2) 1/m [ln(Pi,,)] = A, + B, + ei,,.


The symbol e,c represents a normally distributed variable with

mean zero and variance a2. A, is the coefficient which

represents the item effect on the price of item i in country

c. B, is the coefficient that represents the country effect

on the price. In most cases this method is' normalized by a

base country, usually the U.S.

In summary, the CPD method describes the natural

logarithm of the price of item i in country c with respect to

a base country d as the sum of an item effect A,, and a country

effect B,. The coefficient Be is the mean over all items of

the log of the price of item i in country c and is interpreted

as the logarithm of the PPP for that country's currency

relative to the base country (U.S.). Also, Ai is equal to the

mean over c of the log-price of i in c, but that coefficient

is not used in this study (Theil et al. 1989, p. 8).










3.3.3 Elteto-Koves-Szulc Method

To derive the EKS method it takes four steps2. The steps

are: calculate "Laspeyres" and "Paasche" type price ratios;

calculate Fisher binary price ratios; fill in the Fisher

matrix if needed; and then build an EKS matrix of transitive

parities. Only the equations will be shown here, an actual

example will be given in the next section.

Before the derivation of the EKS method the concept of

characteristic items must be introduced. A characteristic

item is an item that is considered to be purchased frequently

within that country. Each country is asked to nominate at

least one product within every detailed category which it

regards as a characteristic item. The characteristic item

chosen must also be priced in at least one other country.

This is done so that the most consistent price-data is used in

the EKS calculations. It will become clear that all

calculations in the EKS method are based on the prices of the

characteristic items.

The first step of the EKS method is to calculate the

Laspeyres and Paasche type price ratios. These ratios are not

true Laspeyres and Paasche ratios and are often referred to as

mini-Laspeyres and mini-Paasche price ratios due to their

similarity to the Laspeyres and Paasche time-series

measurement. The difference is that these are unweighted


2We would like to thank Ms. Harary at the OECD, Economic
Statistics and National Accounts Division for providing
unpublished material on the EKS method.








43

price ratios whereas Laspeyres and Paasche are weighted

indexes (Ward, 1985, pp. 42-43). The mini-Laspeyres formula

is a price ratio of the characteristic item between two

countries, if the base country has only one characteristic

item. If there are more than one characteristic items in the

base country, a geometric mean is taken of all of the price

ratios3. The general representation of the equation for the

mini-Laspeyres equation is:


ic
(3.3) L",d = i /
= Pid


where i = 1,...,m characteristic items in detailed category a.

The mini-Paasche formula is the reciprocal of the transposed

mini-Laspeyres price ratios. The equation for the mini-

Paasche price ratios is:



1= I Pi,d
(3.4) Pdc =[ i / / L ,d



This method does not pick one base country; therefore, a

matrix of mini-Laspeyres is created between countries with a

diagonal of ones, the same is true for the mini-Paasche

ratios.




3To calculate the geometric mean the base country's
characteristic item or items determine the relative parity
ratios. The comparison country's price does not have to be a
characteristic item in order to calculate the geometric mean.








44
Once the mini-Laspeyres and mini-Paasche ratios are

computed, the Fisher binary type price ratios are constructed.

Just as before these are not true Fisher binaries because they

are based on unweighted price ratios. Therefore, these Fisher

type price ratios will be referred to as mini-Fisher binary

price ratios. The mini-Fisher ratios are unweighted geometric

means of the mini-Laspeyres and mini-Paasche price ratios.

The equation for the mini-Fisher price ratios is:


(3.5) Fc,d = (La,d ,d)12


where F,d is the mini-Fisher price ratio for detailed category

a between countries c and d. Note that F,d F, = 1. However,

the matrix of mini-Fisher ratios are not transitive.

Transitivity means that F,/Fc, : F~,d Hence, to make the mini-

Fisher ratios transitive, the EKS method is applied.

Given that all of the price ratios are present, all of

the mini-Fisher ratios can be calculated. Hence, there would

exist a full matrix of mini-Fisher ratios. The EKS method is

then applied to the mini-Fisher ratios. The equation for the

EKS method is:


F"
(3.6) EKS,d = ,d2 1/n where e f cd.
:=l F d,

EKS",d is the PPP for the detailed category a between countries

c and d. This procedure uses direct mini-Fisher price ratios

F,d and indirect ratios F, and F*, which use country e as the








45
bridge country between countries c and d. This method

replaces each direct ratio by the geometric mean of itself and

all corresponding indirect ratios that can be obtained using

as many of the other countries as possible for bridges. The

EKS gives the direct ratio twice the weight of each indirect

ratio since Fd/F, Fc/F,c is the same as Fc,d. The resulting

transformed ratios are all transitive. The overall transitive

parity between any individual pair of countries is therefore

significantly dependent on the indirect ratios involving

prices in all other countries (Ward, 1985, pp. 44-45).

The last step of the EKS method is to choose one country

as a base country so that it can be compared with the CPD

results. A base country can be chosen be observing the values

in any of the country columns of the EKS matrix. To make the

EKS equivalent to a geometric- mean is -simple. The EKS

formula itself is a geometric mean. If all of the prices of

the items are all present and all characteristic items, then

the EKS method is the same as equation (3.1) if Pi, is replaced

with a price ratio. The reason is that the indirect mini-

Fishers and the direct mini-Fisher ratios are equal, that is

F ,e/Fd,e = F,d.

This section shows how the CPD and EKS method calculate

PPP's for a detailed category when all of the prices are

present. Also, it is proven that the CPD equals EKS which

equals the geometric mean when all of the prices are present

and all of them are characteristic items. The next section








46

illustrates the situation where there are missing prices,

which is the case for most detailed categories.


3.4 Estimating Purchasing Power Parities

In many detailed categories, there are several missing

prices. Without the basic prices, the CPD method does not

equal a geometric mean and neither does the EKS method. In

fact with the EKS method the mini-Paasche, Laspeyre, and

Fisher ratios cannot be calculated when there are missing

prices. In this case it should be clear that the CPD method

does not equal the EKS method, although they should deviate

minimally from one another. This section addresses the

procedures the ICP used to estimate the PPP's via the CPD and

EKS methods when there were missing price data

Estimating PPP's with the CPD method is the same as in

section 3.3. Equation 3.3 normalized by the U.S. price is the

equation used to estimate the B,'s. To illustrate this

procedure part of the data from the fresh vegetables detailed

category for 1970 is used (Kravis et al. 1975, p. 59). The

data for four countries and four goods are shown in Table 3.2.

The full matrix for fresh vegetables for 10 countries and 20

countries in 1970 is shown in Appendix A4.

If the prices of vegetables in their respective national

currencies in Table 3.2 are considered to be a detailed



4The PPP's and Al's estimated by Kravis et al. 1975 are
also included in Appendix A.










Table 3.2


Fresh Vegetables for 4 Countries and Items in 1970



United United
Japan Kenya Kingdom States
(Yen) (Shilling) (Pound) (Dollar)


Lettuce 218.1* 0.62 0.5*
Mushrooms 0.54* 1.9
Onions, yellow 98.6* 0.77 0.13 0.35*
Tomatoes 160.9 1.19* 0.31* 0.92*


Source: Kravis et al. 1975, p. 59.
*The starred items are the characteristic items for each
country5.


category, then the vector for the dependent variable using the

U.S. as a base country is equal to:

ln(218.1/.5)
ln(98.6/.35)
ln(160.9/.92)
ln(.62/.5)
ln(.77/.35)
ln(1.19/.92)
ln(.54/1.9)
ln(.13/.35)
ln(.31/.92).

Kravis et al. 1975, 1978a, and 1982 weighted each price ratio

with the reciprocal of the number of prices in the numerator

country by the base country (4/3), and by the supercountry

expenditure (see Appendix B). The independent variables

(dummy variables) for this equation, constructing the country

dummy then the item dummy, are:



5These items are not the actual characteristic items they
are chosen for illustration purposes only.










1 0 0 1 0 0 0
1 0 0 0 0 1 0
1 0 0 0 0 0 1
0 1 0 1 0 0 0
0 1 0 0 0 1 0
0 1 0 0 0 0 1
0 0 1 0 1 0 0
0 0 1 0 0 1 0
0 0 1 0 0 0 1.

This system cannot be estimated because each row for each

independent variable sums to 1. That means there is an adding

up problem. To solve this problem one of the items has to be

dropped. No information is lost when this is done, redundant

information is eliminated from the system. Once one of the

columns from the item dummy is eliminated the regression can

be estimated.

The results from this setup having dropped item 2 and

weighted the price ratio by (4/3)6 are

Bp.U.s = 5.62

BKn.Us = 0.41

BUK.,U.S = -0.99.

These results are the natural logarithm of the PPP between

country c and the U.S. To get the PPP, the exponential of BC

is taken. The PPP's are 275.89, 1.51, and 0.37, respectively.

There are n-1 PPP's because the U.S. is used as the base

country. The explanation of these numbers are given after the

EKS results are calculated and compared with the CPD results.


6The supercountry weighted is not used in this example.








49

The first step of the EKS method is to create the mini-

Laspeyres price ratios. For simplicity, Ld will now be

expressed as LCId and the same for the mini-Paasche price

ratios. The mini-Laspeyres matrix is shown in Table 3.3. All

calculations for the EKS example are shown in Appendix C. In

this.matrix the base country is given by the columns, the rows

are the numerator countries. Since the mini-Paasche matrix is

just the inverse of the numbers in Table 3.3, that is Pu,. =

1/L,, the mini-Paasche matrix will not be shown.


Table 3.3


Mini-Laspeyres Price Ratio Matrix



Japan Kenya U.K. U.S.

Japan 1_0 135.21 519.03 278.02

Kenya 0.0047 1.0 2.48 1.52

U.K. 0.0013 0.26 1.0 0.35

U.S. 0.0029 0.77 3.23 1.0



After the mini-Laspeyres and mini-Paasche price ratios

are calculated, the mini-Fishers are estimated. Table 3.4

shows the results of the mini-Fisher calculations. There are

no missing mini-Fisher ratios in this example. If there were,

a bridge country method would have been implemented to fill in

the missing values. For example, if the mini-Fisher price

ratio between countries c and d (F d) is missing, but the








50
ratios between countries c and e, and d and e exist, then the

mini-Fisher price ratio for countries c and d can be

calculated by dividing F", by F,,. Country e is the bridge

country that links countries c and d. If more than one bridge

country is available, then a simple geometric mean is taken of

all of the indirect estimates. If there are still missing

mini-Fisher ratios then the above procedure is applied until

the matrix has no missing data.


Table 3.4


Mini-Fisher Ratios


Japan Kenya U.K. U.S.

Japan 1.0 169.61 631.87 309.63

Kenya 0.0059 1.0 3.09 1.41

U.K. 0.0016 0.32 1.0 0.33

U.S. 0.0032 0.71 3.04 1.0



The final step in calculating the PPP's is to implement

the EKS method. The EKS method uses the direct and indirect

mini-Fisher ratios to make these parities transitive. The

matrix of transitive PPP's are shown in Table 3.5. The EKS

results are implicitly weighted because only the

characteristic items are used for base countries in the

calculations.










Table 3.5


Transitive PPP's from the EKS method


Japan Kenya U.K. U.S.

Japan 1.0 189.58 667.53 262.67

Kenya 0.0053 1.0 3.50 1.39

U.K. 0.0015 0.28 1.0 0.40

U.S. 0.0038 0.72 3.53 1.0



To compare the EKS results with those from the CPD, the

U.S. column is used because the CPD used the U.S. as its base

country. The values from the CPD compared with the EKS for

fresh vegetables in 1970 for 4 countries and items are as

follows:

CPD EKS

Japan/U.S. 275.89 262.67

Kenya/U.S. 1.51 1.39

U.K./U.S. 0.37 0.40.

The differences between these numbers are negligible. Most of

the variance could be due to weights and rounding error. The

interpretation of the PPP's estimated by both methods is that

one dollar's worth of fresh vegetables in the U.S. equals

between 262.67 275.89 yen worth of fresh vegetables in

Japan, 1.39 1.51 shillings worth of fresh vegetables in

Kenya, and 0.37 0.40 pounds worth of fresh vegetables in the

United Kingdom.









52
The CPD method was used in Phases I, II, and III. The

CPD and EKS methods were used in Phase IV. The reasons for

using the different methods in the different Phases will be

discussed in Chapter 4. Once the PPPs were estimated, they

were used in the Geary-Khamis method. The second stage of the

estimation process is discussed next.


3.5 The Geary-Khamis Method

The objective of the Geary-Khamis method is to provide

multilateral base-invariant price and volume comparisons at

the various levels of aggregation for all countries, where the

volumes are expressed in "international dollars". These

volumes are additive across expenditure categories, while

prices can be obtained by dividing expenditures in national

currency by those in international dollars.

The method was first introduced by Geary who suggested

that a system of homogeneous linear equations be used. These

equations are used to calculate the international prices and

the PPPs simultaneously. Subsequently, Khamis shows that the

system yields non-negative international prices and PPPs.

Thus, Geary and Khamis are responsible for this model.

The derivation of the Geary-Khamis method follows. The

CPD or EKS method can be used to produce the detailed category

PPP's for the Geary-Khamis method. These PPP's are transitive

and relative to the U.S. dollar. Detailed categories are

indicated by the subscript a = 1, ..., A. Let Ec be the per









53

capital expenditure (in national currency) on detailed category

a in country c. The equation for the volume of detailed

category a in country c is


(3.7) V., = E.,/PPP,,.


V., is expressed in U.S. dollars.

Although (3.7) achieves the goal of expressing all

expenditures in the same currency ( U.S. dollars), the V.,'s

have the problem that they are not additive over detailed

categories. To achieve such additivity, the Geary-Khamis

method introduces the international price P. of each detailed

category and the overall purchasing power parity ir of each

country c. The definition of P. is


N
E' (E;; w *** *** 7tj
c=1
Pa =

N
E V.,
c=1


or, equivalently,


N N
(3.8) PaVa = Z (Ec/7c) where V, = E Vc
c=l c=l


while 7, is defined as










A
Z E,,
a=l
7r =_____

A
E PVa
a=I


or, equivalently, as


A
(3.9) GDP(1/ir) = E P.V.,
a=1


where GDPc (the gross domestic product of country c in

national currency) is equal to the sum over a = 1, ..., A of

E.. It is readily verified that (3.8) and (3.9) constitute

a linear system in the A + N -1 unknown P, and 1/w, ( c = 1 for

c = U.S.) (Theil et al. 1989, Appendix A).

The product PV., is interpreted as real expenditure per

capital in international dollars on detailed category a in

country c. This product is additive over detailed categories.

Let S be any grouping of such categories; then the sum over

a E S of PV., is real expenditure per capital or real gross

domestic product (RGDP) per capital in international dollars on

S in c. If S consists of all detailed categories, this sum is

GDP per capital in c.

The exposition given on the CPD, EKS, and Geary-Khamis

methods is a general overview on how PPP's for the detailed

categories and overall, international prices, and RGDP are








55
calculated. The next section deals with calculating PPP's for

the comparison resistant goods.


3.6 Calculating PPP's for Comparison Resistant Goods

In the previous sections the procedure for calculating

PPP's for narrowly defined goods was discussed. In this

section, the calculations for PPP's of comparison resistant

goods are discussed. The procedure for calculating these

PPP's to use in the Geary-Khamis formula is straight forward.

For the comparison-resistant goods and services (i.e.,

services of teachers, physicians, dentists, hospitals, nurses,

and government employees), neither the CPD or EKS method was

used. Quantity comparisons for these categories were based on

a method called "direct quantity" comparisons. For example,

for teachers of first, second, and third level students, the

quantity comparisons were based on the number of standardized

persons engaged in providing the services. For physicians,

dentists, technicians, midwives, and the like, the ICP

quantity comparisons were based on the number of physicians,

dentists, and nurses, respectively.

For Phases I and II, it was assumed that all equally

qualified personnel in these comparison-resistant categories

have the same productivity. In Phases III and later, this

assumption was abandoned, and adjustments were made. In

educational services, the modifications improve the estimates

of teacher inputs by introducing education level and the

number of students as a further dimension of productivity. In








56

medical care and government services, adjustments are made for

the differences in the productivity of inputs for broad groups

of countries and by making adjustments for capital per worker.

After the adjusted final quantity ratios are derived, the

PPPs used for the Geary-Khamis method are considered to be

indirect PPP's. These PPPs are found by dividing the

expenditure ratios by the adjusted quantity ratios. From

there, the Geary-Khamis method is applied as before. The

reader who is interested in these and similar issues should

consult the original source: the work of national and U.N.

price experts (Kravis et al. 1982, p. 38); prices of

construction and consumer durables (Kravis et al. 1982, pp.

50-56); and the treatment of services (Kravis et al. 1982,

Chapter 5).


3.7 Regionalism

Regionalism is a new issue beginning in Phase III. The

previous Phases I and II were limited to a small number of

heterogenous countries. Thus, there is little point in

considering whether comparisons could be improved by

identifying relative homogeneous subsets of countries. The

Geary-Khamis method was applied to the entire set of countries

without any effort to distinguish such subsets or to take them

into account in the index number calculations. This

symmetrical treatment of all countries is called the

"universal" approach.








57

As the number of countries increased significantly in

Phase III, it became necessary to consider whether applying

the CPD or the Geary-Khamis methods in successive stages would

improve the comparisons. The first step would be to look at

the level of sets of relatively homogeneous countries and,

thereafter, at the regional level. Thus, countries in

different regions are compared through regional linkages.

The most obvious basis for identifying homogeneous sets

of countries is geographic closeness. This basis for grouping

countries assumes that these countries have close political

and cultural ties as well as similar customs. Although ad-

hoc, there are some good reasons for using this approach.

Europe and Latin America, for example, are similar in the way

they classify daily business and the way they deal with the

changes in -the political, social, and economic arenas., In

addition, there are usually regional organizations with the

sole responsibility of economic development for that region.

For the actual calculations for Phase III, the ICP opted

to use what is called a modified "universal" approach. This

approach has some regionalism aspects which are introduced via

the organization of the price inputs for the Geary-Khamis

calculations. The objective is to retain base country

invariance or to at least allow all countries within each

region to influence the world comparisons while retaining the

intraregional PPPs and quantity relationships for the detailed

categories and for GDP as a whole.








58
The modified universal approach has 3 steps. First, the

CPD method is applied at the regional level to fill in the

missing prices. Second, the CPD method is applied again, this

time on all countries in the study. Lastly, the PPPs from the

second stage CPD are used as direct inputs to the Geary-Khamis

method.

The first stage CPD takes advantage of the regional

similarities in price structures to cope with a major problem

in deriving the set of PPPs. The problem is primarily

incomplete, overlapping sets of price comparisons among the

participating countries. The first CPD estimation operates at

the regional level to fill in for each country's missing

entries in the vector of item prices. All items for which at

least two countries in the region provided prices are

included. Therefore, this tableau contains-for each region,

a full vector of prices, for each country, for all items

priced by two or more countries in the region. Note that if

the CPD is run on the augmented price tableau for a given

region, it would yield the same PPPs as those produced by the

original incomplete tableau of prices. Thus, the tableau

retains the characteristics of the original tableau.

After each country's price vector has been completed to

match the other country's in the same region, a second CPD is

run. This CPD is calculated for all 34 countries (Phase III),

where these PPPs are used as the direct price inputs for the

Geary-Khamis calculation covering all the countries. This








59

approach embodies a regional element in deriving the category

PPPs, but the aggregation of the PPPs across categories is of

the universal mode.

The results of this new approach relative to the approach

used in Phases I and II, which is based on direct price inputs

of all countries regardless of the region, are improved. The

augmented-price-tableau enhances the influence of

intraregional price relationships. The missing prices are

explicitly filled in on the basis of intraregional price

relationships versus being estimated on the basis of price

relationships in all countries like the universal approach

does.

The last step is to put the PPPs derived from the two-

stage CPD method into the Geary-Khamis equations.

Calculations for all 34 countries (Phase III) were completed

using this method. The results from this approach are

discussed next.


3.8 Phase III Results Compared with Exchange Rates

Using the two stage CPD method to obtain the PPPs for the

detailed categories and then implementing the Geary-Khamis

method, the international prices and GDPs per capitas are

calculated. Table 3.6 provides the results of these efforts

for gross domestic product for the year 1975 (Phase III). The

34 countries are listed in the order of declining GDP per

capital in international dollars.











Table 3.6


GDP Per Capita for 34 Countries in 1975



International Same, Exchange rate
Country dollars U.S.=100b converted
(1) (2) (3) (4)


United States
Germany
Denmark
Luxembourg
France
Belgium
Netherlands
Austria
Japan
United Kingdom
Spain
Italy
Poland
Hungary
Ireland
Uruguay
Iran
Yugoslavia
Mexico
Romania
Brazil
Syria
Jamaica
Colombia
Malaysia
Korea
Philippines
Thailand
Zambia
Sri Lanka
Pakistan
Kenya
India
Malawi


7176.0
5952.7
5910.9
5883.4
5876.9
5574.1
5397.2
4994.8
4906.7
4587.9
4010.2
3861.1
3597.9
3558.9
3048.8
2844.3
2704.6
2591.4
2487.3
2386.8
1811.2
1794.2
1722.6
1608.7
1540.6
1484.1
946.3
936.1
737.8
667.7
590.3
470.5
470.5
351.7


100.0
83.0
82.4
92.0
81.9
77.7
75.2
69.6
68.4
63.9
55.9
53.8
50.1
49.6
42.5
39.6
. 37-.7,
36.1
34.7
33.3
25.2
25.0
24.0
22.4
21.5
20.7
13.2
13.0
10.3
9.3
8.2
6.6
6.6
4.9


100.0
94.7
104.5
90.2
89.6
87.8
84.5
69.8
62.3
57.6
41.0
47.9
36.0
29.6
37.2
18.2
22.1
23.2
20.4
24.3
16.0
10.0
19.6
7.9
10.9
8.1
5.2
5.0
6.9
2.6
2.6
3.4
2.0
1.9


p. 12.


aSummed over all 151 detailed categories.
bSource: Kravis, Heston, and Summers 1982,








61
The differences between the exchange-rate converted

figures and those which Kravis et al. (1978a) obtained using

the Geary-Khamis method are substantial. These differences

increase as real GDP per capital decreases. This is readily

seen in columns 3 and 4 of Table 3.6 where the PPP based

estimates of GDP per capital are compared with the exchange

rate based estimates (both are a percentage of U.S. value).

The use of exchange rates tend to overstate the poverty of

poor nations considerably. For example, when we use exchange

rates, the ratio of the U.S. GDP per capital to its Indian

counterpart is 100/2.0 = 50, but it is only 100/6.6 or about

15 when we use the Kravis approach.

One reason for this dispersion is that services tend to

be cheaper relative to commodities in poorer countries, and

services -make up a small- portion of international trade.

Hence, exchange rates understate the value of services in low

income countries.

Services, which are nontraded goods, are cheap in low-
income countries; hence exchange-rate conversions greatly
underestimate the true quantities of services in low-
income countries relative to those in high-income
countries. (Kravis et al. 1982, p. 23)

In addition, exchange rates have been variable since the

switch-over to floating exchange rates in 1973. However,

there is no reason why the consumption expenditures in

national currencies should reflect this variability exactly.

Converting these expenditures by such wildly fluctuating

exchange rates would yield highly spurious results.










3.9 Phase IV Further Considered

After Phase III regionalism plays a bigger role in the

ICP. Regionalism complicated things in many ways. Therefore,

Phase IV is discussed explicitly.

Phase IV as mentioned before is different from the other

Phases. The information on Phase IV is presented in "World

Comparisons of Purchasing Powers and Real Product for 1980:

Phase IV of the International Comparison Project." This

manuscript has two parts: "Part I: Summary Results for 60

Countries"; and "Part II: Detailed Results for 60 Countries."

These papers are published by the Statistical Office of the

United Nations Secretariat (UNSOS), Statistical Office of the

European Communities (EUROSTAT), and the Organization for

Economic Co-operative and Development (OECD). This work is

discussed here to -address several problems (i.e.,

decentralization, regionalism, and fixity) and the additional

problems they create. The other reason for Phase IV's

importance is that it increased the number of benchmark

countries to 60. Phase IV is similar in many ways to the

previous Phases, so only the deviations from those Phases will

be discussed below.

After Phase III, the ICP was decentralized, which meant

that various regional and country groups assumed major

responsibilities while the Statistical Office of the United

Nations Secretariat was responsible for linking the work of

the various regions. There were seven organization that








63

carried out the work for the country groups: Statistical

Office of the European Communities (EUROSTAT), Economic

Commission for Europe (ECE), OECD, Economic Commission for

Africa (ECA), Economic Commission for Latin America and the

Caribbean (ECLAC), Economic and Social Commission for Asia and

the Pacific (ESCAP), and UNSOS. With the decentralization,

each group carried out its own estimations within its region;

this is referred to as regionalism. This definition

supersedes the definition in section 3.7 for Phase IV and

later. Table 3.7 shows the countries involved in each group

as well as the organization that did the calculations. After

the comparisons within each region are accomplished, then the

regions are compared at the world level.

3.9.1 Other Methods Used in Phase IV

With the decentralization 'and- regionalism of Phase IV,

one problem is that each region can choose any method they

preferred to calculate the PPPs. Europe Group 2 and ECIEL

decided not to use the CPD or EKS method. The European group

implemented a method called the "STAR" system. It is not

clear what the ECIEL group did to calculate their PPPs.

The star system used by Europe group 2 has Austria as the

base country for that group. They carried out four separate

binary comparisons with the four countries representing the

outer points of the star. The detailed category PPPs for each

country are only estimated with respect to Austria. The PPPs

for any two countries are derived from the two sets of binary












Table 3.7


The Organizations that Performed the Calculations and the
Countries Involved in Each Group for Phase IV.



EUROSTAT ECE ECA/EUROSTAT ESCAP/UNSOS ECIEL/ECLAC OECD

-----------Europe--------

Group 1 Group 2 Africa Asia Latin America OECD


Belgium Austria Botswana Hong Kong Argentina Canada
Denmark Finland Cameroon India Bolivia Japan
France Hungary Ethiopia Indonesia Brazil Norway
Germany Poland Ivory Coast Pakistan Chile U.S.
Greece Yugoslavia Kenya Philippines Colombia
Italy Madagascar Korea Costa Rica
Ireland Malawi Sri Lanka Dom. Rep.
Luxembourg Mali Ecuador
Netherlands Morocco El Salvador

United Kingdom Nigeria Guatemala

Portugal Senegal .. Honduras
Spain U.R. of Tunisia Mexico
Israel Tanzania Panama

Zambia Paraguay
Zimbabwe Peru

Uruguay
Venezuela
Source: United Nations, 1985 and 1987.


PPPs (i.e. country C and D's binary PPPS with country B and

D's binary PPPs). Using this method, transitivity is not a

problem since no direct comparisons are made between the


points of the star.


Thus, the EKS system is not necessary.


The Geary-Khamis method is used to aggregate the categories

and calculate GDP as a whole. The weights (expenditure and









65
prices (PPPs) of the countries covered) of the five countries

are taken into account (The Statistical Office of the United

Nations Secretariat 1987, p. 5).

There is less information on what the ECIEL region did.

However, it is clear that neither the CPD nor the EKS method

was implemented. It has been ECIEL's practice that each

country provides prices for every item in the detailed

categories. PPPs are then derived that are transitive across

all countries by obtaining the geometric mean of the price

ratios of each country to any one of the countries chosen as

the numeraire. All that can be said about this method is

that, if all countries provide prices for all of the

commodities, then all of the other methods reduce to a

geometric mean, when estimating PPPs for the detailed

categories (The Statistical Office of the United Nations

Secretariat 1987, p. 11).

3.9.2 Linking the Regions of Phase IV

After the PPPs for the detailed categories were

estimated, the problem was to link all of the country groups

together. The main problem was that each region had a

different base country. In addition, the Europeans (both

groups) have approximately 320 detailed categories while the

other groups typically have approximately 150; the African and

Latin American countries have a more condensed system.

Fortunately, the European, African, and Latin American groups








66

were able to make their respective detailed categories

compatible with those of the world comparisons.

Linking the various country groups requires that the

prices of the overlapping items between countries across the

different country groups be compared. In order for this to

work, there must be at least one country in each group which

has prices for each detailed category so that the PPPs can be

estimated to link the countries. When comparing Europe Groups

1 and 2, for example, only Austria has sufficient prices to

link Group 2 to 1. However, this was sufficient to link the

Europe Group 2 countries with the world comparisons.

There are 20 countries that serve as liaisons like

Austria. These countries act only as a set of countries whose

item prices for comparable goods and services serve as the

basis for linking the country groups. These countries are

called "core" countries. The core countries are: France,

Spain, Israel, and the United Kingdom (Europe Group 1) ;

Austria (Europe Group 2); United States, Canada, and Japan

(OECD); Brazil, Colombia, Uruguay, Dominican Republic, and

Guatemala (ECLAC); Hong Kong, Indonesia, Korea, Pakistan, and

Sri Lanka (ESCAP); and Kenya and Senegal (ECA).

The CPD method was used for the core countries where the

item prices for the 20 core countries were used as inputs.

The expenditure weights used by some of the country groups

were also incorporated into the CPD estimation procedure.

When the CPDs were estimated for each of the detailed








67

categories, PPPs between each core country and the United

States, which was the numeraire country, were provided. The

next problem was how to link these PPPs with the other

countries in these regions.

The method used to link the PPPs to the other countries

is a type of chain-link-procedure. Using the African

countries as an example, the detailed category PPPs exist and

for the core countries of Kenya and Senegal, both with respect

to the African numeraire and with respect to the United

States. The ratio of the geometric means of the core country

to the African PPPs provided a factor which, when multiplied

times the detailed category PPPs within Africa for all of the

African countries, aligned these parities with respect to the

United States dollar. This procedure preserves the

relationship between the basic PPPs for all countries as

originally obtained in the African comparisons, including

Kenya and Senegal. This is the fixity principle (see Appendix

D).

The chain-link-procedure was applied to Latin America,

Europe Group 2, and the OECD countries. In the case of the

ESCAP countries, there was no reason to do the chain link

method since the base country for that group was the U.S. For

India and the Philippines, a slightly different procedure was

used since the price information for these countries became

available too late to include in the core country CPDs. The

item prices were directly compared to the item price estimates








68

that were a part of the CPD output for each detailed category.

The geometric means of these item price ratios, which were

based in national currency units per dollar for each detailed

category, were used as the PPPs.

All methods in which the expenditure and PPPs at the

detailed categories were obtained have been discussed. These

calculations were the basic inputs to the aggregation

procedure. The Geary-Khamis method was used just as in the

previous Phases for the aggregation of the data. The use of

supercountry weighting was also retained. It was important

that the results for countries participating in several phases

of the ICP not be influenced by the addition of new countries.

Hence, the world comparisons utilized a system of supercountry

weights where the dollar GDP of non-participating countries

was assigned to participating countries on- the basis fof

geographical proximity and the level of per capital income.

The problem with the Phase IV data are that the fixity

principle is imposed (see Appendix D). Fixity adversely

affects the data if one is interested in world comparisons.

That is why there are two data sets for Phase IV. The first

set is for researchers who are interested in world comparisons

and the other, which preserves fixity, is for intraregional

comparisons. The first set is made available by the U.N.

Statistical Office upon request by the researcher. The other

data set which has fixity imposed is in the Phase IV








69

publication. The calculations in this thesis were all based

on the data that do not impose the fixity principle.

To calculate RGDP per capital for each country with

respect to the U.S. without fixity, the calculations must be

done like the Phases previous to Phase IV. That is, estimate

the PPPs with the CPD or EKS method using the U.S. as a base

country, then apply the Geary-Khamis method.














CHAPTER 4
EXTRAPOLATIONS


4.1 The Beginning of Extrapolations with ICP Data

There are five publications of the extrapolations on the

different phases of the ICP. The first publication is by

Kravis et al. (1978b). All of the rest are by Summers et al.

(1980 also known as Mark 1,1 1984 Mark 3, 1988 Mark 4, and

1991 MARK 5). These publications sought a way to approximate

real gross domestic product (RGDP) per capital for virtually

all the countries in the world and for every year from 1950 to

1988. This method is referred to as the "short cut" method.

During the years following the first publication in 1978, the

methodology and the quality of the data from the Mark's have

improved.

The purpose of the first paper, "Real GDP Per Capita for

More than One Hundred Countries," by Kravis et al. (1978b) was

to close a gap that the world statistical system had been

unable to fill. At that time, there were no comparative data

on "real" GDP per capital (gross domestic product per capital

adjusted for differences in the purchasing power of

currencies) for a large number of countries. In this paper,



'Mark 2 was not published but it was used in Kravis,
Heston, and Summers (1982).









71
Kravis et al. (1978b) develop a method to calculate these real

GDP per capital (RGDPC) by using the detailed comparisons of

the 16 countries in Phase II. The structural information from

this method allows the RGDPCs to be calculated for non-ICP

countries. Lastly, an extrapolation is made to get RGDPC for

later years.

The short-cut method that Kravis et al. (1978b) developed

concentrates on the relationship found in the 16 countries

between RGDPC and certain independent variables. These

structural relationships were used to estimate other years and

non-benchmark countries. However, the authors caution that

the non-ICP RGDPC's were approximations, and that it would be

some time before more exact comparisons would be available for

a large number of countries. Nonetheless, their numbers are

superior to exchange rate converted GDPs per capital which-were

used prior to PPP conversions.

The model Kravis et al. (1978a) used to find the

structural relationships was

PI,
(4.1) In rj = a+ + a2 In nj + 3 (In nj)2 + a4 In
PIus

OP.
+ a5 In ___ = 1,..., 16
OPus

where j represents countries, rj = Rj/Rus, nj = Nj/Ns, R is real

GDP per capital (adjusted for purchasing power), and N is

nominal or exchange-rate-converted GDP per capital. The








72

variables OP (openness) and PI (price isolation) come from

international trade theory and will be covered in more detail

later (Kravis et al. 1978b, p. 219).

The relationship between r and n has been discussed in

Chapter 3 so it should not be a surprise that a2 is expected

to be between 0 and 1. The value of al is expected to be 0

because r should equal 1 when n, OP, and the PI ratios equal

1, which is the case for the base country. The a3 coefficient

is expected to be negative since its corresponding variable is

the square of a. That is the square of a negative number is

positive, and ln(n) is negative while ln(n)2 is positive;

hence, r and ln(n)2 are negatively related. The expected

signs of OP and PI as well as the variables themselves are

discussed next.

The reason why OP and PI are included-in-the model is

because Kravis et al. (1978b) were influenced by the

productivity differential model. This model is most clearly

stated by Harrod and Balassa cited by Kravis et al. (1978b).

It states: international trade tends to equalize the prices

of traded goods; given equal prices, wages will be high in

high productivity countries; internal factor mobility will

lead to high wages also in non-traded goods industries in high

productivity countries; because international differences in

productivity are smaller in non-traded goods industries

(largely personal services) than in traded goods industries

(largely commodities), the non-traded goods will be higher in









73
high productivity (high incomes) countries; and lastly, the

high prices of non-traded goods have little if any impact on

the exchange rate and thus make possible a difference between

the overall purchasing power of the currency and the exchange

rate. The influence of this model led the authors to attempt

to account for the differences in countries openness to trade.

The degree to which each country's price level is

influenced by foreign prices is measured by the variable

"openness" (OP). This variable basically measures the

exposure to world markets. OP is calculated by the average

ratio of exports plus imports to GDP for the years 1965 to

1973. The period for which the data are used is completely

arbitrary and taken directly from the World Bank Tables, 1976

(Washington D.C.: International Bank for Reconstruction and

Development, 1976).

The expected sign for a5 is ambiguous. The relationship

between OP and r is negative if the following is correct: the

more open an economy, the higher its prices are for non-traded

goods, making the difference between n and r smaller. The

relationship is not clear if the lack of openness is due to

protective commercial policies which could lead to higher

prices for non-traded goods (Kravis et al. 1978b, p. 223).

PI stands for price isolation. The assumption is that

the influence of external factors on a country's price level

at a particular moment in time can be inferred from how

closely its time to time movements over some preceding period









74
are correlated with time to time movements of "world" prices.

The world price index (implicit deflator) is created by

placing countries whose currencies the International Monetary

Fund (IMF) have defined the value of a unit of Special Drawing

Rights (SDRs) on a common base. These are converted to

dollars by division by an appropriate index of exchange rates.

The world index is then constructed by aggregating the SDR

country indices using weights which reflect the importance

assigned to each currency by the IMF in its initial

calculation of the value of an SDR unit in mid 1974. The

implicit deflator is then adjusted for each individual country

to a common base period and correct exchange rate changes.

The final step is to calculate the price isolation index using

the formula,


1970
(4.2) PI = t= (WDt CD)2/8



where WD is the world price index and CD the country price

index, both based on the average over the period 1963 to 1970.

Eight of the ICP countries are included in the set of

countries that the IMF uses in its SDR calculations. Thus PI

can be summarized as the mean squared difference for the years

1963 to 1970 between the country's GDP implicit deflator and

a "world" average GDP implicit deflator.

The sign for a4 is ambiguous like a,, and for similar

reasons. PI and r could be positively related if the








75
following line of reasoning is consistent with what has

actually happened. The reasoning is, the greater the price

isolation, the less a country's non-traded goods prices will

be pulled up to the price levels of the high-income countries;

thus a larger real income (r) is associated with a given

nominal income (n). However, these affects can be negated by

combining different micro and macro economic policies which is

why the sign is ambiguous (Kravis et al. 1978b, p. 223). The

question is empirical and one can only estimate the equation

and see what signs and magnitudes the parameters have.

All of the values for the variables are known for the 16

ICP countries, but r is not known for the other countries.

Hence, the model was run for those 16 countries to obtain the

structural relationships between RGDPC and the other

variables. The resulting signs for this model are a2

positive, a3 negative, a4 positive, and a5 is negative. The

parameter estimates and their respective standard errors can

be found in Kravis et al. (1978b, p. 226). After calculating

r for the non-benchmark countries for 1973, extrapolations

have to be made to other years.

The method of extrapolation is setup to incorporate the

impact on real income through the changes in the terms of

trade. This is done by treating the net foreign balance

component of GDP separately from "domestic absorption." For

domestic absorption (DA), the per capital quantity change

between the benchmark year and the year of extrapolation for








76
each country is estimated by deflating consumption, capital

formation, and government by the implicit deflator for these

sectors. This results in the value of DA in the extrapolation

year being expressed in international dollars of the benchmark

year. The net foreign balance was then valued in benchmark

year international dollars and added to the figure for DA to

obtain GDP per capital in international dollars. Finally, this

sum was compared to the corresponding U.S. total to form the

extrapolation year index for real per capital GDP (Kravis et

al. 1978b, p. 229). The results of this task were estimates

for 1973 and 1974.


4.2 Mark 1

The second paper by Summers et al. (1980) is entitled,

"International Comparisons of Real Product and its

Composition: 1950 to 1977." This study includes 119

countries of which 16 are from the ICP Phase I data set. The

same equation (4.1) is used to calculate r for the ICP

countries and the structural relationships found from those

calculations, are used to calculate r for the non-ICP

countries as before. What is new in this paper is that the

extrapolations for the ICP and non-ICP countries are done

forward and backward through time.

To calculate RGDPj, before and after 1970 is relatively

easy since all of the results are in 1970 dollars (benchmark

year). R is calculated the same as previously (r, =








77
RGDPj,/RGDPus,70) for the year 1970 only. The RGDPJ, for the

other years is obtained using the jth country's constant price

series (in domestic currency units) for GDP as indicated in

the equation below,



GDPj,t /POPjt
(4.3) RGDPj, = (RGDPj7o)

GDPj70 /POPj,70


where GDP is a constant-price value of GDP,, in national

currency and POPj, refers to the population. By using the

constant-price valuation, changes in terms of trade facing the

jth country between the tth year and 1970 are neglected. RGDP

is calculated for all 119 countries from 1950 to 1977 using

these methods.


4.3 Mark 3

The third paper, "Improved International Comparisons of

Real Product and its Composition: 1950 1980" written in

1984 by Summers and Heston, is referred to as Mark 3. Mark 2

was not published but it was used by Kravis, Heston, and

Summers (1982). Mark 3 was different from Mark 1 and Kravis

et al. (1978b) because it utilized the data from Phase III.

This data set included 34 countries for the year 1975. This

difference and the fact that there were two benchmark years of

data (i.e., 1970 and 1975) resulted in the authors using a

different method for calculating the RGDPs in Mark 3.








78

The first change from the earlier papers was that a

slightly different functional form for the regression was

used. However, before that is addressed, the data need to be

considered. There are two benchmark years of data to utilize.

The approach used by Summers and Heston in this paper is a

modification of the approach used in Phase III (Extensions

beyond the ICP countries, pp. 332-340). The cross-section

regressions for the two years were run in terms of per capital

DA instead of per capital GDP as done previously. The slightly

different functional form for the regressions was that the

openness variable in the equation used to summarize the 1970

and 1975 data was introduced additively compared to an

interaction term. Furthermore, the constant terms in both

years were suppressed since they were not significantly

different from -zero,. .-..These -modifications simplify the

equation and make the actual and estimated values for the

numeraire country the same (U.S.). Lastly, the results

obtained from the two benchmark years were combined to get a

single 1975 estimate. Weights were also devised to take into

account the relative precision of the two cross sections.

The regression equation used to summarize the 1970 and

1975 cross-section relationships is


(4.4) In r, = a, (ln n) + a2 (In n)2 + a3 (In OPj) + u


where










r = (DAj/PPPA)/DAus and n = (DA,/XR,)/DAus.


pppDA is the purchasing power parity over domestic absorption,

and XRj the exchange rate. Each is expressed in national

currency units of the jth country per U.S. dollars. OP, is the

measure of relative openness of the jth economy which was

defined as


((Exportsj + Imports))/GDP) / ((Exportss

+ Importsus)/GDPus),

an average of the ratio for five years before the cross-

section year. Before further definitions are given it should

be stated that the a's have the same expected signs as they

did in Kravis et al. (1978b).

The XR, 7 variable was defined by a weighted geometric

mean of the 1975 exchange rate and the real exchange rates of

1974 and 1976. This was done due to the volatility of the

exchange rates for several countries. The equation for XRj,

is then


(4.5) XR,7s = (Pj,75n4XR ,74) (XRj7s) '' (Pj,75n6XRj76)


where Pj,. measures the change in the relative price levels of

domestic absorption of the jth country and the U.S. between t

and t'. X is a weight for the 1974 to 1976 exchange rates.

No averaging implies X = 0 and equal weighting implies X =

2/3. The weighting question is resolved by running a non-








80

linear least squares regression on the data. For 1975, the

results indicate that X is not significantly different from

zero so XRj.7 only depended on XR,7s. The year 1970 was

different in that X was large. Hence, its value was set at

2/3. Thus, XR,,7 is just a simple geometric mean of XRP70 and

the price-level adjusted values of XR,. and XR,7,.

In Summers and Heston (1980), RGDP,, is based on constant-

prices whereas in Mark 3, international trade was incorporated

into RGDP. The net foreign balance was converted by the

exchange rate on the grounds that, at the margin, this is the

conversion factor for an increment to the net foreign balance.

This is equivalent to setting the international price of a

dollar's worth of net balance to 1. Thus, RGDPj7 = r75 (DAus,75

+ NFBj,7/XR,7s) where NFBi,7 is the net foreign balance in 1975

for the jth country. Rj,7 is defined as the geometric mean of

ri from equation 4.4 for the years 1970 and 1975 for all 85

countries.

The extrapolations in Mark 3 were also treated

differently and were calculated at a more disaggregated level.

The tapes of the U.N. constant-price series for consumption,

gross domestic investment, government, and the net foreign

balance were used to get real individual components expressed

in 1975 international dollars for each of the years between

1950 and 1980. Thus, RGDP, was obtained by summing the

components, where the net foreign balance exports and imports

in 1975 were converted to dollars at current exchange rates.








81

The new disaggregate procedure insures that the price weights

used for consumption, investment, and government in each year

in each country reflected 1975 international prices rather

than the individual country's relative prices.

The imprecision of the RGDP estimates varied considerably

from country to country and from year to year. Therefore, the

authors classified a countries' estimates into four quality

classes: A (best), B (better), C (good), and D (fair). The

classifications stemmed from the main source of the

imprecisions in the estimation process. First, imprecisions

were inherent in the ICP benchmark estimates as qualified in

Phase III (Table 3.6). Second, the estimation of the cross-

section regression introduced some error. Third, the authors

did not know what weights to use in averaging the 1970-derived

and 1975 cross-section estimates of r'.

The authors find several general relationships with

respect to the imprecision of their estimates. The ICP

imprecision was inversely correlated with real income; so was

the error term in the cross-section regression. Also Ceteris

paribus, benchmark countries were rated higher than non-

benchmark countries; higher income countries were rated higher

than lower income countries; and African countries were rated

lower than non-African countries. All of these things should

be taken into account when observing the RGDPs. Later, the

quality grading of the data will become crucial.










4.4 Mark 4
The fourth paper by Summers and Heston (1988) was

basically an update to Mark 3. The new issue in this paper

was consistency. Consistency means that the estimates must

obey the national income identity that total product equals

total income generated by the production of the product. The

reason this becomes an issue in Mark 4 was that the

discrepancies between Mark 3 and Phase IV were large for the

1980 RGDP per capital estimates. In addition, the ICP closely

followed a system called the System of Real National Accounts

(SRNA). The basic rule of SRNA was that entries should obey

all temporal identities. The identity that is being violated

when Phase IV and Mark 3 estimates of RGDP for 1980 do not

match is that the value at time period two (t2) equals the

value at time period one (t,) times the growth rate between

the two time periods. To illustrate this point, consider two

countries, A and the U.S. Suppose the 1980 Phase IV RGDP

estimate of Country A is 66% of the U.S.'s 1980 RGDP. How

could this be resolved if the Phase III 1975 relative RGDP

value was 65%, and country A had a 4% growth rate while the

U.S. had a 1% growth rate? This is why consistency has to be

applied.2





2Stone, Champernowne, and Meade (1942) developed a
similar method to make their estimates conform to the national
income accounting identity.









83

The implementation of consistency is done via an errors-

in-variables model. The objective of this model is to adjust

both the benchmark and national accounts data to make them

consistent. To continue with the two country example, this

model would make the Phase IV estimate equal to the Phase III

estimate multiplied by the 1975-1980 growth rate. The

likelihood function for this model is


(4.6) In L(X,,X2,X3G,G,G2/x1,x2,x3,g1,g2;S)= K 1/2 In C

3 3
-1/2 E Xij, (In xi In X,) (In x In X)
I5


5 5
+ E E X (n gi.3 In G3) (In g.3 In G,3)
4 4


where the X's are true values of a country's output at a

particular level of aggregation (e.g., consumption) expressed

in per capital terms and relative to corresponding values for

the U.S. for the three time points, t,, t2, and t3. The G's

are the true values of the country's growth rates for the same

aggregate as the X's, expressed in the same per capital units

relative to the U.S. for the (tM, t2) and (t2, t3) periods,

respectively. Therefore, the temporal identity requires that

X, = X, (G,) and X3 = X2 (G2). The lower-case symbols x,, x2, x3,

g,, and g2 stand for estimated values equivalent to their

corresponding upper-case letters and are obtained from








84

benchmark studies or the national accounts. The errors-in-

variables specification is then


x = Xi (vi) i = 1, 2, 3


9g = G, (v4) and g2 = G2 (vS).


The five v's are joint random variables with a multivariate

lognormal distribution n(0,E ).

The a priori information about the relative accuracies of

the data sources were introduced through the specification of

the entries in E which is the variance-covariance matrix of

the v's. The information is parameterized in the form of a

five element vector (ki, k2, k3, r,, r2) and an assumed pattern

of independence among the v's. The variances among the v's

associated with the g's (growth rate v's) were all assumed to

be the same and equal to 1. The v's associated with the x's

(benchmark v's) were expressed relative to the variances of

the growth rate v's and are called k's. The correlation

between v, and v2 and also between v, and v3 was given by r,;

the correlation between v, and v3, because of the longer time

interval, was assumed to equal r2; the correlation between the

two growth rate v's was given by r2; and the benchmark and

growth rate v's were assumed to be independent. All of these

assumptions imply that E has the form


x o











where


k, rAVk r-ikk,

EX= k21 l
,= rtick r k, rk3k



and


1 r2

r2 1


The Xis in equation 4.6 are just the elements in '-.

This maximum likelihood procedure corrects the data

sources so that they are consistent. The only problem is that

the maximum likelihood asymptotic properties cannot be claimed

for this estimation. The reason is that additional parameters

are added as more time points were introduced, an estimation

problem called the incidental parameter problem (Judge et al.

1980, pp. 543-546). However, it is claimed that the maximum

likelihood estimates are of the same variance-minimizing

estimates obtained from averaging all possible unbiased point

estimates.

The data from Phases II, III, and IV and the U.N.

constant-price series are made consistent by following the

errors-in-variable approach. The non-benchmark countries do

not need this. They are just aligned appropriately with the

benchmark country estimates. With the consistent data, the









86
1980 RGDP for the benchmark and non-benchmark countries are

computed similar to the way they are computed for the base

year (1975) in Mark 3.

There are a few differences from Mark 3 other than

consistency in the manner in which the RGDP's were calculated.

Mark 4 drops the openness variable. The exchange rates were

too volatile throughout the late 1970's, and the openness

variable was no longer significantly related to RGDP by 1980

so it was not used in Mark 4. Dummy variables for Africa were

also introduced to allow for divergence. The last adjustment

came with the replacement in the equation of exchange rates

with a combination of price indexes called the international

post-allowance price index. The two indexes that compose the

post-allowance index were the International Civil Service

Commission index and the Employment Conditions Abroad index.

The International Civil Service Commission index is published

in the Monthly Bulletin of Statistics of the United Nations

Statistical Office and uses New York city as a base. The

Employment Conditions Abroad index is an organization based in

London with members including multinational firms,

governments, and non-profit international agencies. This

organization produces a number of binary indexes.

The extrapolations forward and backward were accomplished

by following the procedures used in Mark 3 precisely. The

preciseness of the estimates were also graded A to D using the

same standards developed in Mark 3. This was done for 130








87

countries for the years 1950 to 1985. The estimates for RGDP

still suffer from large errors for low income countries and

African countries.


4.5 Mark 5

The most current paper written updating these data is by

Summers and Heston (1991). Their data for RGDP per capital was

used in this thesis for analysis. Mark 5 covered 139

countries and RGDP per capital was obtained by extrapolating

these cross-section comparisons interspacially to non-

benchmark countries and then intertemporally to other years.

Mark 5 is arguably the best of the Marks and utilizes ICP

data from 4 benchmark years: 1970, 1975, 1980, and 1985.

Eighty-one countries participated in these benchmark studies

and 47 participated in more than one benchmark study. Thus,

the need for relying on non-benchmark estimating methods was

reduced. The national accounts data have also improved by

using the World Bank's archive data. Most of all, the

methodology for obtaining RGDP per capital for a large number

of countries has improved. Hence, all of these factors make

Mark 5 the most accurate and most recently published

international comparisons data of this type.

The four ICP benchmark studies, Phases II V, used in

this study were all compiled in different ways and have

different countries participating in different years. This is

why the data have to be made consistent. Consistency, as

discussed in the previous review of Mark 4, is calculated the








88

same way in Mark 5 (using equation 4.6). What needs to be

addressed is the benchmark data itself. The biggest problem

with the benchmark data was that Phase V had not been

published by the time Mark 5 was published.3 Summers and

Heston calculated the RGDPs on their own, using only the raw

data provided by the U.N. and World Bank. The method used by

Summers and Heston to calculate the values in Mark 5 are

discussed next.

There are three main changes to the Phase IV results for

this paper. First, Phase IV introduces the issue of fixity.

It should be clear that the 1980 values mentioned here do not

use the fixity principle. Instead, the Geary-Khamis method is

used for all 60 countries. However, there is an allowance

made for supercountry weighting. Second, the 1980 estimates

that underlay the Mark 4 estimates were recalculated using

national accounts data of May, 1990 which are the latest

current national accounts data for the countries. The U.N. in

some cases used national accounts data that are available for

1982 or 1983. Third, there was a slightly different treatment

of two categories, change in stocks and compensation of

government employees. They also used a slightly different

normalization procedure which only affects the valuation of

the net foreign balance.




3Actually Phase V was never published, instead the U.N.
decided to publish regional data (i.e. OECD, EUROSTAT, ECA,
ESCAP, and ECIEL) (see Table 3.7).








89

The countries that participate in the 1985 benchmark

comparisons fall into five groups: 22 OECD countries, 11

Asian countries including Japan, 22 African countries, 5

European Group II countries including Finland and Austria, and

a group of Caribbean countries. The Caribbean countries'

comparisons were not complete at that time. The Geary-Khamis

method was implemented for the OECD and Asian countries. The

African countries, Hungary, Poland, and Yugoslavia all have

data that allow the authors to link them to the OECD and Asian

countries. The total number of countries from Phase V used in

this study is 57. Once again fixity was not imposed on these

results.

A different method was used for those countries that did

not participate in the 1985 benchmark study, but did

participate in a previous benchmark study. The procedure was

to value their 1975 or 1980 benchmark estimates of C, I, and

G at 1985 international prices. The growth rates for their

components from the national accounts data and their change in

international prices of the components between 1975 and 1985

or 1980 and 1985 were used. The changes in international

prices were estimated from the benchmark estimates and the

deflator for the numeraire country, the U.S.

The 1975 and 1970 data were also re-analyzed. The May

1990 national accounts data were used to revise those years.

The Geary-Khamis method was then implemented to aggregate the

data.








90
After the benchmark data were aggregated, re-estimated,

and made consistent, the non-benchmark countries RGDP per

capitas were estimated. The same equation used in Mark 4 was

also used in Mark 5 with some minor changes. The left hand

side variable was r* which was per capital domestic currency DA

converted to international dollars expressed relative to the

U. S. Mark 4 used a post adjustment index to estimate the

real domestic absorption of each country. This estimate was

obtained by dividing the national currency DA by the PPP

implicit in the post adjustment index.

The post allowance index was made up of two indexes for

Mark 4 and three for Mark 5. The International Civil Service

Commission index (variable ruj) and the Employment Conditions

Abroad index (variable rcAj) was used as post adjustment

indexes in Mark 4. Mark 5 used both of those indexes and

another index produced by the U.S. State Department. The U.S.

State Department provides housing or a separate housing

allowance indexes (variable rusj). This was an area in which

the data were less reliable (including the ICP data). Hence,

the added information from this index was used. All of the

post allowance indexes were designed to supplement salaries in

a way that equalize real incomes of high-ranking civil

servants and business executives assigned to different foreign

countries. Each of these indexes have shortcomings. The most

notable was that all of the countries were not included in any

of these indexes. A structural relationship, however, was




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FILES


CROSS COUNTRY CONVERGENCE OF GROSS DOMESTIC
PRODUCTS AND ASSOCIATED FACTORS:
A COINTEGRATION APPROACH
By
DAVE D. WEATHERSPOON
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1993

ACKNOWLEDGEMENTS
First, I would like to thank my wife for her support and
encouragement throughout this process. She provided me with
the incentives and assistance necessary to complete this
degree. I appreciate the standards of excellence expected and
portrayed by my parents. The supportive discussions with them
as well as my in-laws and siblings made this process somewhat
easier. I will always be indebted to my forefathers who stood
up for their rights so that people like myself can enter and
finish at any higher educational institution in the United
States.
The many hours of individual attention Dr. James Seale,
Jr., provided me during my course of study are much
appreciated. I would also like to acknowledge the extra
efforts of Dr. Charles Moss in helping me complete this
degree. The additional suggestions during the preparation of
this dissertation by Dr. Jong-Ying Lee, Dr. Gary Fairchild,
Dr. Douglas Waldo, Dr. M. Langham, and Dr. Henri Theil are
much appreciated.
The financial support as a McKnight Doctoral Fellow from
the Florida Endowment Fund for Higher Education made this all
possible. The additional financial support by Dr. James
Seale, Jr., and Dr. Henri Theil is much appreciated.
ii

TABLE OF CONTENTS
page
ACKNOWLEDGEMENTS ii
LIST OF TABLES vi
LIST OF FIGURES viii
ABSTRACT ix
CHAPTERS
1 INTRODUCTION 1
2 CONVERGENCE 6
2.1 Overview of Convergence 6
2.2 Historical Evidence 8
2.3 Kuznets-Type Studies 11
2.4 LDC Growth and Poverty 15
2.5 Human Capital 24
2.6 Contemporary Evidence ..... 27
3 THE INTERNATIONAL COMPARISON PROJECT AND ITS'
USEFULNESS IN EXAMINING CONVERGENCE 33
3.1 Overview of the Construction of the ICP .... 33
3.2 The Geographic Expansion of the ICP:
Phases I to IV 34
3.3 The Data 3 6
3.3.1 The Methodology of Calculating
Purchasing Power Parity 40
3.3.2 Country-Product-Dummy Method 41
3.3.3 Elteto-Koves-Szulc Method 42
3.4 Estimating Purchasing Power Parity 46
3.5 The Geary-Khamis Method 52
3.6 Calculating PPP's for Comparison
Resistant Goods 55
3.7 Regionalism 56
3.8 Phase III Results Compared with
Exchange Rates 59
3.9 Phase IV Further Considered 62

3.9.1 Other Methods Used in Phase IV 63
3.9.2 Linking the Regions of Phase IV 65
4 EXTRAPOLATIONS 70
4.1 The Beginning of Extrapolations with
ICP Data 70
4.2 Mark 1 76
4.3 Mark 3 77
4.4 Mark 4 82
4.5 Mark 5 87
4.6 The Centrally Planned Economies 93
5 INEQUALITY IN THE G-7 AND OECD 96
5.1 Inequality Measures 96
5.1.1 Graphical Inequality 96
5.1.2 Inequality Indices 97
5.1.3 Properties of an Inequality Index . . . .100
5.2 Income Inequality in the G-7 102
5.3 Variables of Interest 106
5.3.1 Inequality in Government Expenditure. . .107
5.3.2 Inequality in Investment Expenditure. . .111
5.3.3 Inequality in Industrial Employment . . .113
5.4 Inequality in Selected OECD Countries 114
5.4.1 Income Inequality in the
OECD Countries 115
5.4.2 Inequality of Government Expenditure
in the OECD 119
5.4.3 Investment Inequality in the OECD . . . .122
5.4.4 OECD Inequality in Industrial
Employment 124
5.5 Summary of the Inequality Results 125
6 COINTEGRATION 127
6.1 An Overview of Cointegration 127
6.2 Unit Root Tests 131
6.2.1 Augmented Dickey-Fuller (ADF) Test. . . .132
6.2.2 Phillips Test 137
6.2.3 Unit Root Results 139
6.3 Pairwise Cointegration 141
6.3.1Durban Watson 141
IV

6.3.2 Augmented Dickey-Fuller
Cointegration Test 142
6.3.3 Pairwise Cointegration Results 143
6.4 Johansen's Multiple Cointegration Test 146
6.4.1 1(1) Procedure 14 6
6.4.2 1(2) Procedure 154
6.4.3 G-7 Multiple Cointegration Results. . . .161
6.4.4 OECD Multiple Cointegration Results . . .170
6.4.5 Other 7 Multiple Cointegration
Results 178
6.5 Summary and Interpretation 182
7 SUMMARY AND CONCLUSION 190
APPENDICES
A PRICES PER KILOGRAM OF FRESH VEGETABLES AND
ESTIMATED PPP'S IN 10 COUNTRIES FOR 1970 197
B SUPERCOUNTRY WEIGHTING 199
C EKS CALCULATIONS 2 02
D FIXITY 205
E DATA AVAILABILITY 2 07
F EXTRAPOLATIONS OF INDUSTRIAL DATA 209
REFERENCES 211
BIOGRAPHICAL SKETCH 220
v

LIST OF TABLES
Table page
3.1 Countries Represented in the International
Comparison Project 35
3.2 Fresh Vegetables for 4 Countries and Items
in 1970 47
3.3 Mini-Laspeyres Price Ratio Matrix 49
3.4 Mini-Fisher Ratios 50
3.5 Transitive PPP's from the EKS Method 51
3.6 GDP Per Capita for 34 Countries in 1975 60
3.7 The Organizations that Performed the
Calculations and the Countries Involved
in Each Group for Phase IV 64
5.1 Income Per Capita and Income Inequality
(G-7 Countries) 103
5.2 Government, Investment, and the Number of
People Employed in Industry Inequalities
(G-7 Countries) 108
5.3 Investment Expenditure per Capita, and
the Rate of Investment Expenditures
for the G-7 112
5.4 Income Per Capita and Income Inequality
(OECD Countries) 117
5.5 Government, Investment, and the Number of
People Employed in Industry Inequalities
(OECD Countries) 120
5.6 Investment Expenditure per Capita, and the
Rate of Investment Expenditure for the
OECD 123
6.1 Unit Root Tests 140
vi

6.2 Pairwise Tests for Cointegration 144
6.3 Johansen's Multiple Cointegration Test 162
6.4 Cointegrating Vectors and Adjustment
Coefficients from the G-7 165
6.5 Estimates of Gamma from the G-7 169
6.6 Johansen's Multiple Cointegration Test (OECD) . . . .172
6.7 Cointegrating Vectors and Adjustment
Coefficients from the OECD 174
6.8 Estimates of Gamma from the OECD 177
6.9 Johansen's Multiple Cointegration Test (Other 7). . .179
6.10 Summary of Integration and Cointegration
Analysis 183
vii

LIST OF FIGURES
Figure page
6.1 Total Income Inequality for the G-7 133
6.2 Total Government Inequality for the G-7 13 3
6.3 Total Investment Inequality for the G-7 134
6.4 Total Industrial Employment Inequality
for the G-7 134
6.5 Total Income Inequality for the G-7
Second Differenced 135
6.6 Total Government Inequality for the G-7
Second Differenced 135
6.7 Total Investment Inequality for the G-7
Second Differenced 136
6.8 Total Industrial Employment Inequality
for the G-7 Second Differenced 136
viii

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
CROSS COUNTRY CONVERGENCE OF GROSS DOMESTIC
PRODUCTS AND ASSOCIATED FACTORS:
A COINTEGRATION APPROACH
By
Dave D. Weatherspoon
December 1993
Chairman: James L. Seale, Jr.,
Major Department: Food and Resource Economics
The convergence of income in the G-7 and selected OECD
countries was tested using Theil's inequality (entropy) index
between the years of 1950 to 1988. Theil's inequality index
was also applied to three potential factors of influence on
economic growth. These factors were government expenditure,
investment expenditure, and the number of people employed in
industry. The financial indicator variables were adjusted for
purchasing power parity based on Summers and Heston's 1991
data series. The derivation of this data set is also
discussed in this dissertation.
The results of the convergence test confirmed that all
four inequality indices were declining. This suggested that
income, government expenditure, investment expenditure, and
industrial employment are converging within the G-7 and within
the selected OECD countries. The inequality indices were then
tested to determine if they move together over time.

Pairwise and multiple cointegration tests were conducted
on the inequality indices that were found to be 1(2). In
general, there was support for pairwise cointegration of all
the variables for the G-7 and the selected OECD countries.
Johansen's 1(2) method was used to test multiple
cointegration. Multiple cointegration was supported for three
of the four variables for the G-7 sample, suggesting that
there exists a long-run equilibrium among the inequality in
income, investment expenditure, and the number of people
employed in industry. The OECD selected sample supported
multiple cointegration of all four variables. It was also
determined that industrial employment was the primary factor
in the sample that adjusts to return the four inequality
indices to their long-run equilibrium when innovations occur.
The G-7 equilibrium was stable without government
expenditure while the OECD sample was stable with government
expenditure. This may suggest that the OECD countries
excluding the G-7 rely on government expenditures for economic
growth and stabilization of their economies.
x

CHAPTER 1
INTRODUCTION
Cross-country economic convergence means that a group of
countries are becoming closer in terms of income. This
definition is usually operationalized as the faster rate of
productivity growth by less productive countries (Barro and
Sala-i-Martin, 1992). The result of which is the faster rate
of income growth of relatively poor countries than relatively
rich countries. Worldwide income growth and the factors that
influence this growth have been of interest for quite some
time. The interest in the economic welfare of current and
future trading partners is one reason why the U.S. in
particular is concerned with the area of economic growth and
convergence.
The literature has supported the idea that the high
income countries are converging (Grier and Tullock, 1989 and
Goa et al., 1992). However, none of the studies can
definitively state the factors in these economies that are
causing convergence. Therefore, the objective of this study
is to determine a method of measuring convergence, test the
method on a group of countries, and determine the factors that
influence convergence over time.
There are two hypotheses being tested in this
dissertation. First, it is hypothesized that the G-7 and the
1

2
selected OECD countries are converging in terms of income.1
Theil's inequality measure is used to test this hypothesis.
The second hypothesis is that the inequality of income has a
long-run relationship with the inequality of other factors in
the economy. The factors considered to influence the
convergence of income across countries are the inequalities in
government expenditure, investment expenditure, and the number
of people employed in industry. This hypothesis is tested by
using pairwise cointegration analysis and Johansen's multiple
cointegration technique.
The G-7 and OECD countries were chosen for this study for
several reasons. The most important factor is the
availability and the superior quality of their data. The fact
that the G-7 and OECD countries are some of the most powerful
countries economically in the world also influenced this
decision. The growth rate of per capita income for the G-7
and OECD has been sustained at a positive rate for a long time
period. In fact, per capita income in both groups increased
almost threefold during the 38-year period from 1950 to 1988.
These positive growth rates are not considered to be a random
process but are believed to be systematically related to other
factors in the economy (Grossman and Helpman, 1991).
‘The G-7 countries are Canada, W. Germany, Italy, Japan, the
U.K., the U.S., and France. The selected 14 OECD countries are
Austria, Belgium, Denmark, the Netherlands, Norway, Ireland, Spain,
and the G-7 countries.

3
This analysis is not the first attempt to associate
economic growth and convergence to specific factors in an
economy. One of the models that influenced the way economists
approached the idea of convergence was put forth by Solow
(1956). Solow (1956) and the generalized neoclassical growth
model by Brock and Mirman (1972) implied that economies with
identical technology and preferences will converge regardless
of initial conditions. The driving force in both models was
technology. Several empirical studies have shown that the
world is not converging in terms of income and only recently
have the theoretical models begun to challenge the cross¬
country implications of Solow's model (Romer, 1986; and Lucas,
1989).
Another approach was put forth by Kuznets (1955). He
approached convergence in an indirect manner by relating
personal income to economic development. Specifically,
Kuznets' (1955) hypothesis was that income inequality within
a country first increased then decreased as development
proceeded (divergence-convergence theory). This theory has
since been expanded to cross-country analysis where the
hypothesis is that countries first diverge then converge in
terms of income inequality as development occurs (Wright 1978,
Branco and Williamson 1988, and Ram 1988 and 1989a). The
cross-country interpretation of Kuznets hypothesis is not
directly tested in this dissertation. However, if the G-7 and
the OECD countries are found to be converging, then the

4
results may support Kuznets cross-country hypothesis since the
G—7 and OECD countries are developed countries. The
literature concerning the convergence or divergence of the
countries around the world is discussed in Chapter 2.
There are two main reasons why the topic of convergence
and economic growth are important. First, the factors that
cause convergence or economic growth have not been exclusively
identified. Second, the quality of international data have
been improved recently.
The problem in the past with output and income data from
different countries was that international comparisons require
the data to be converted to a common currency by using
official exchange rates. Official exchange rates do not
reflect the relative purchasing powers of different
currencies. For example, the official exchange rate does not
reflect domestic services since they are not traded
internationally (i.e. haircuts, house cleaning, etc.) (Kravis
et al. 1975, 1978a, and 1982). Hence, errors are introduced
into international comparisons when exchange rates are used.
This problem has been addressed and much improved by
Summers and Heston (1988 and 1991). They developed a data
series that is based bn purchasing power parity. This data
set along with others are used to test the hypotheses stated
above.
The format of this dissertation is as follows. Chapter
2 includes a literature review on convergence while Chapters

5
3 and 4 include a discussion on the methodology used to
calculate gross domestic product without using exchange rates.
Specifically, the international comparison project (ICP)
methodology is addressed in Chapter 3. Then the data series
by Summers and Heston, which is based on the ICP, is
addressed.
The convergence of income, government expenditure,
investment expenditure, and the number of people employed in
industry is tested using Theil's inequality index in Chapter
5. Theil's decomposable index allows one to determine which
countries are driving the convergence. Then, these four
inequality indices are tested for cointegration using pairwise
cointegration and Johansen's 1(2) multiple cointegration test
in Chapter 6. This method determines if there exists a long-
run equilibrium among the four indices. If the series are
cointegrated, then the four inequality indices cannot drift
apart in the long-run given that there are no structural
changes. Chapter 7 presents the summary and conclusion of
this dissertation.

CHAPTER 2
CONVERGENCE
2.1 Overview of Convergence
The meaning of cross-country convergence in its simplest
form is that the income level of countries are becoming
closer. To get this result the less productive countries must
increase their productivity growth rate at a faster rate than
the more productive countries (Barro and Sala-i-Martin, 1992) .
The result is that income grows at a faster rate in relatively
poor countries than in relatively rich countries. There has
been an interest in reducing the income gap (convergence)
between the developed countries (DCs) and the lesser developed
countries (LDCs) for some time (Berry et al., 1991). The
Pearson Commission (1969) was set up to address the income gap
problem. Specifically, the commission was to identify ways to
reduce the income gap between the developed and the developing
countries (Berry et al., 1991).
Kuznets (1955) influenced many researchers to explore
convergence through his hypothesis. Kuznets' hypothesis (also
known as the divergence-convergence theory) basically states
that income inequality within a country increases in the early
stages of economic development, stabilizes at some peak level,
then declines as the latter stages of development occur.
6

7
Kuznets was writing about a single country; however, this
hypothesis was quickly expanded to address international
development. Many studies attempt to directly and indirectly
prove or disprove Kuznets' hypothesis with income inequality
measures (Wright, 1978; Branco and Williamson, 1988; Ram,
1988, 1989a) or with regression analysis (Grier and Tullock,
1989; Barro, 1991; Barro and Sali-i-Martin, 1992; and
Baradaran-Shoraka, 1992). However, the results of all of
these studies have been inconclusive.
Three observations about economic growth in the world
economy frame the phenomenon examined in this study. First,
the growth of per capita income has been sustained at a
positive rate for many countries for a long time period.
Second, the performance of countries has varied across
countries and time. These two observations lead to the
conjecture that growth in income is not a random process.
They are believed to be systematically related to other
factors in the economy (Grossman and Helpman, 1991).
The third observation deals with the ability to study the
growth patterns around the world. Convergence of the world
cannot be thoroughly studied over long periods of time due to
data constraints. However, there are data available for many
countries starting in the 1950s. These data are largely due
to the efforts of Summers and Heston (1991) who developed a
time-series for several economic indicators for most of the

8
world for the years 1950 through 1988.1 In the studies
mentioned above, the data of Summers and Heston as well as
other sources are used to analyze convergence from a
historical point of view. The international comparison
studies conducted prior to this data set were misspecified due
to the use of exchange rates (Kravis et al. 1975, 1978a, and
1982).
There have been two main approaches to studying
convergence, inequality measures and regression analysis.2
The review of the studies that follow represent both
approaches. The first section covers studies that analyze
what happened in the past.
2.2 Historical Evidence
Machinery investment and productivity growth have been
strongly associated over the past century in countries where
adequate data exist (Canada, Germany, Italy, Japan, the United
Kingdom, and the United States). In the recent past, the same
association holds for more countries (De Long, 1992) . The
real question is whether high machinery investment causes
rapid growth?
Baumol (1986) showed that industrialized market economies
supported convergence using data from 1870 to 1979 (the data
‘The development of the Summers and Heston data series is
discussed in the next two chapters.
2A summary of the inequality measures is given in
Chapter 5.

9
are not time-series) . Baumol analyzed the G-7 countries along
with Australia for this time period. To extend his analysis
to a larger number of countries, he used the Summers and
Heston data from 1950 to 80. In this data set, the variable
used was output per capita. The results showed that
convergence is not supported when LDCs are included in the
analysis. The results of a similar study conducted by Dollar
and Wolff (1988) supported Baumol's 1986 results of
convergence.
In a follow up article criticizing Baumol's (1986)
findings, De Long (1988) showed that Baumol's study was
flawed. He commented that Baumol only used successful
countries (selection bias). In response to De Long's article,
Baumol and Wolff (1988) admitted to data mining in previous
studies. When they re-examined the results, it appeared that
a small group of countries began to converge in 1860. Since
then, more countries have joined the group according to
Baumol.
De Long (1992) reviewed the issue of productivity growth
and machinery investment similar to that done by Baumol. De
Long studied six countries (Canada, Germany, Italy, Japan, the
United Kingdom, and the United States) from 1870 to 1980, and
then a large number of countries on all six continents from
1950 to 1980. He divided up his study into 15 year periods to
offset any cycles and the effects of wars. This study showed
a strong positive relationship between growth and machinery

10
investment. He cautions that these countries are all wealthy
and that the regression may have captured "luck" instead of
the intended relationship. The results may have been
different if more countries were included.
In addition, De Long examined the effects that political
stability and investment in education had on growth. All of
the countries sampled had been stable politically and had
invested heavily in education. He also argued that just the
presence of high tech machinery may have provided a higher
level of education. In testing these relationships, he found
little evidence supporting the education or political
stability influence on growth. De Long (1992) concluded that
when a broader group of countries is considered, there is
little evidence of convergence in the short-run, and in the
long-run, the regressions may not be accurate. Alam (1992),
however, cautions that De Long needed to use other variables
to indicate productivity.
Hanson (1988) examined the convergence of LDCs before
World War I. This study is interesting for two reasons.
First, historical studies of this type conducted on LDCs are
rare. Second, the long period of analysis from 1913 to 1980
is impressive. Hanson corrected the historical data by
extrapolating Summers and Heston's (1984) data backwards and
combining other data sets. He also compared other data sets
to that of Summers and Heston. Unfortunately, his results
were inconclusive.

11
To summarize, there appears to be a long-run relationship
between investment in machinery and growth. The only
countries that appear to be converging are a few
industrialized countries. The LDCs appear to be caught in a
circle of poverty (Alam and Naseer, 1992). It is clear that
human capital is considered an important variable with respect
to growth, and that the relationship may be that higher
equipment investment drives faster growth (Adams, 1990; De
Long and Summers, 1991).
2.3 Kuznets-Type Studies
As mentioned before, Kuznets hypothesized (divergence-
convergence theory) that income inequality increases in the
early stages of economic development, stabilizes at some peak
level, then declines as the latter stages of development
occur. A few of the many studies that have tested this
hypothesis in the international context using various methods
are discussed next. It will become clear that there are no
definite answers as to whether Kuznets' hypothesis is indeed
correct.
Wright (1978) analyzed whether the institutionalist or
Kuznets' hypothesis was correct. The institutionalist
hypothesis states that institutional structures and
governmental policies are the chief determinants of income
inequality. Wright conducted his analysis using a Gini
coefficient inequality measure. He calculated the income
inequality of the GDP per capita for 56 countries. He

12
concluded that the data did not support Kuznets' hypothesis.
Instead, he found that the level of inequality was higher in
the LDCs than the developed countries. Wright concluded that
his results supported the institutionalist hypothesis. Hence,
the reduction of income inequality among countries is
dependent on modifications of institutions and policies.
Ram (1989a) extends Kuznets' hypothesis to the world
system. He hypothesizes that intercountry (world) inequality
across sovereign nation states would first increase with
secular economic growth, then start to decline at some point.
He tested this hypothesis using 115 market economies for the
years 1960 to 1980 from the Summers and Heston 1984 data set.
Average (per capita) world GDP was used as a proxy for the
level of development and Theil's income inequality (J) measure
was used to analyze the inequality (see Section 5.1.2 for
Theil's inequality). In addition, Ram used a Kuznets type
quadratic regression to determine the relationship between the
level of income and development, which represents development
and inequality. The equation is
(2.1) J, = B0 + B, LRYt + B2 (LRYt)2 + ut
where J is the measure of the world inequality and LRY is the
natural logarithm of the average real GDP per capita. The
last term is the disturbance term with the standard properties
(zero mean and a constant variance) . He found that world
income inequality has increased since 1960. However, the rate

13
of increase has slowed. The regression results supported the
hypothesis that world inequality may first increase and then
decline with world economic growth. Hence, Ram's study
supports the idea of divergence then convergence of real GDP
worldwide.
A partial contrast of the above results is provided by
Ram in 1988. In this paper, Ram (1988) tests Kuznets'
hypothesis for 32 counties, 8 developed countries and 24 LDCs.
The estimated equation in this paper is the same as the one
used in his 1989a paper. Ram (1988) finds support for
Kuznets' hypothesis when all of the countries are present.
However, when only the LDCs are present, the results do not
support Kuznets' hypothesis.
Branco and Williamson (1988) also tested Kuznets'
hypothesis by analyzing development and income distribution.
This study was unique in that it developed an absolute per
capita income measure for the poorest 40% of the population in
68 countries. Their measure was the percent of income of the
poorest 40% of the nation's population in 1970 divided by 40%
of the 1970 population, then multiplied by the real GDP per
capita of a nation in 1970 (Summers and Heston, 1984 data
set). Bronco and Williamson (1988) felt that this dependent
variable portrayed the situation of the poorest 40% in
different countries. The independent variable was the energy
consumption per capita in 1970 (measured in kilograms of coal
equivalents). This variable is supposedly a better indicator

14
of industrial development across nations than GNP per capita.
They estimated linear, quadratic, logarithmic, and log
quadratic models to determine the best fit and also to prove
or disprove Kuznets' hypothesis. Their results supported
Kuznets hypothesis. Therefore, the countries are expected to
diverge, then converge in terms of income as development
occurs.
Bornschier (1983) reinterpreted Kuznets' theory by
combining two paradigms of world economy and the level of
development. Briefly, the world development paradigm is the
core-periphery division of labor, which has come about due to
multinational corporations. The core specializes in control
over capital, technology, innovation processes, and the
production of the most advanced products, which embodies the
most human capital. The periphery is engaged in standardized
and routine industrial production for domestic or maybe world
markets. In a sense the multinational corporations have
created a world division of labor. The core countries are
basically the industrial countries, and the periphery are the
countries with the raw materials.3 The level of development
paradigm is basically Kuznets' hypothesis. Both of these
paradigms have different ideas on how development takes place.
Bornschier (1983) combined the two approaches with the
following deviations from the original hypotheses: the
3For a more detailed explanation of this theory see Amin,
1974, pp. 559-587.

15
countries on the periphery, which were still considered
agrarian based, had the most income inequality; the countries
that assumed less importance for agrarian production had lower
inequality; and the core countries within the world economy
had the lowest income inequality. He showed that developing
countries did not automatically decrease their income
inequality with increased development. In addition, the
reduction of inequality was found to be dependent on the type
of production (services, agriculture, and industry) in which
they were involved.
Several of the studies supported the divergence-
convergence theory (Kuznets' hypothesis) and others did not.
The studies that included the LDCs were also contradictory.
In the study by Bornschier (1983), the author implied that the
type of development countries pursued affected the reduction
in income inequality. He indicated that if a country has less
emphasis on agrarian development, then that country is
expected to converge faster than a country that promotes
agricultural development. This may or may not be the actual
case, but it introduces the idea of what has happened within
the LDCs.
2.4 LDC Growth and Poverty
Morawetz (1977) addressed the issue of growth in chapter
2 of his book entitled "Twenty-Five Years of Economic
Development 1950 to 1975." The questions he posed were: "How
rapidly were GNP per capita and population expected to grow in

16
1950, and how has their actual growth compared with these
expectations." He commenced by stating that the status of
development in Africa, Asia, and Latin America was not
considered before 1950. The reason for this was that the
industrialized countries were just getting over the war, and
were still concerned with reconstruction in Europe. The few
researchers who thought about the economic development of the
LDCs had no hope for their short and medium term future. The
industrialized countries only attained 2% growth (per capita)
on average during that period. Therefore, the developing
countries were not expected to perform as well as the
industrialized countries. In addition, it was perceived that
the population growth in the developing countries was high
while their GNP growth was low.
Morawetz stated that no statistical work had been done on
the LDCs. Hence, he conducted a statistical analysis on the
LDCs to determine their economic growth status. His results
indicated that the disparity between the rich and poor
developing countries had increased significantly between 1950
to 1975. However, at the aggregate level, it was not true
that the richest of the developing countries were getting
richer and the poor were getting poorer. When the developing
countries regional averages of income per capita in 1950 were
examined, the richest regions (Latin America and the Middle
East) had grown five to six times faster than the poorest
region (South Asia) . By 1975 this gap had increased to 13

17
times for the Middle East and seven times faster for Latin
America than South Asia. When the LDCs were compared to the
developed countries, it was shown that China, East Asia and
the Middle East narrowed the gap, while the gap was widened
for South Asia, Africa, and Latin America. However, the
ranking of 80 individual developing countries remained stable
from 1950 to 1975.
Morawetz (1977) regressed 16 indexes of basic needs on
GNP per capita growth to get a better understanding of how the
change in relative GNP per capita affected poverty. Morawetz
used 16 different regression equations to analyze the problem.
The factors that were found to be significantly related to GNP
per capita growth were three nutrition indicators, infant
mortality, and the percentage of dwellings with access to
electricity. Some of the other variables that were included
in the analysis but were not significantly related to the
growth in GNP per capita were four indicators for education:
adult literacy rate, primary school enrollment ratio,
secondary school enrollment ratio, and vocational school
enrollments as a percent of secondary school enrollments.
Another study on the LDCs was conducted by Zind (1991).
He tried to determine if the LDCs were converging in terms of
income, and assess the key variables that influenced
convergence such as government policies, population growth,
and investment levels. The Summers and Heston 1984 (1960-80)
data set was used for the comparison of 89 LDCs. His test was

18
a simple regression of real income per capita annual growth
rate against per capita income in 1960. In his model a
negative coefficient indicated convergence. When all of the
countries were included, there was no evidence of convergence.
Reducing the number of countries to 30, results indicated
convergence at the 10% level; reducing the countries further
to 19 yielded convergence at the 5% level. These 19 countries
were the most developed countries in the LDC sample. In
addition, he found that the other variables (the relative size
of government, population growth and investment level),
contributed to convergence in the most developed countries.
Dollar (1992) basically answered the question of how the
slowest growing countries in the LDC category could increase
their growth. Asian (16 countries) LDCs grew at an average
rate of 3.4%, while this occurred at 0.4% in Africa (43
countries), and only 0.3% in Latin America (24 countries)
(Dollar, 1992). Using the data of Summers and Heston (1984),
he showed that outward oriented countries had lower prices
than inward oriented countries.4 He believes that the price
level was a reflection of the protectionist policies in the
different countries. The Asian countries had the lowest price
levels, followed by Latin America and Africa. He also
considered the variation in exchange rates where the Asian
countries had the lowest variation. He created an index of
4Inward oriented countries are countries that have
protectionist trade policies. Outward oriented countries are
countries that have relatively open trade policies.

19
outward orientation based on the variation of the exchange
rate. This index was found to be highly correlated with per
capita GDP growth. He concluded that Africa and Latin America
could increase their growth through trade liberalization,
devaluation of their real exchange rates, and by maintaining
a stable exchange rate.
Berry et al. (1991) conducted an extensive analysis on
world income inequality. They analyzed over 100 countries
from the time period of 1950 to 1977. The data came from
World Bank Tables, World Bank Atlas, World Development Report,
and the Summers and Heston data set. Their objective was to
determine what had happened to income inequality in the world.
They applied Theil's entropy, Atkinson's inequality, and the
Gini coefficient measure (see Chapter 5 for definitions of
these inequality indices). The uniqueness of this study was
that they applied these inequality measures to gross national
product (GNP) and consumption measured as a percentage of GNP
to determine changes in welfare.
The idea behind using the inequality of consumption was
that the distribution of consumption was less unequal than
that for income for two reasons. First, the savings rate was
below average in many of the poorer countries. Second, the
intracountry distribution of consumption was generally less
unequal than the income distribution. Berry et al. (1991)
attributed this to the fact that the marginal propensities to
consume fall with income and that high income families do most

20
of the saving. The fact that the savings rate was lower than
average in the poorer countries contributes more to worldwide
inequality than the second reason, regardless of whether
income or consumption was used.
They conducted the analysis with and without the non-
market economies for which the data were considered to be
inaccurate (Berry et al.f 1991; Summers and Heston, 1991).
The results of their study showed that the 1950s and early
1960s were stable around the world in terms of income.
Between 1964 and 1972 there was a large increase in world
inequality, which gradually continued to increase until 1986.5
The consumption ratio also indicated a worsening of inequality
from 1950 to 1986.
The other unique aspect of this paper was that they broke
the world's inequality into deciles. Using this method they
were able to show that the bottom half of the world's
population income shares remained unchanged, while the top
decile gained at the expense of the sixth, seventh, and eighth
decile. In addition, the middle deciles gained in the 1950s
and 1960s, only to lose it in the 1970s and 1980s. During
this time period, the richest two deciles increased their
share of world consumption from 68.5% to 71.6% at the expense
of the seven lowest deciles.
5They initially stated that this study was from 1950 -
1977. That is the case for their analysis which includes the
communist countries. After 1977, they were not able to get
adequate data for the communist countries; hence, they left
them out of the analysis from 1950 - 86.

21
The change in inequality in the 1980s was due to slow
growth particularly among the low income countries which had
zero growth during the period of 1980 to 1985. Most of these
countries were in sub-Saharan Africa. Some of the
contributing reasons were the agriculture and debt crisis, and
the rapid population growth.6 The middle-income countries
were not as progressive in terms of economic growth with the
industrialized countries, while the average income of the less
developed countries (LDCs) increased. The South Asian
countries (India, Pakistan, Bangladesh, Sri Lanka, and Nepal)
on the other hand grew faster between 1980 and 1985 than
between 1965 and 1980. The fastest growth occurred in the
newly industrialized countries and the OPEC countries.
However, their presence did not reduce inequality much because
of the relatively small population. In general, the
population has grown faster in the poor and middle-income
countries than in the rich ones. Berry et al. (1991) suggest
that the slow economic growth and the population boom in the
poorest countries had increased the absolute number of poor
around the world (income below $200 U.S. 1970 dollars).
However, to give a full picture, the share of the total
population that was considered poor had decreased.
The results of Berry et al. about the poverty line can be
disputed. Atkinson (1987) examined the issue of measuring
6Theil's entropy measure is sensitive to population
changes. An increase in population increases the inequality
measure if income is held constant.

22
poverty. Specifically, he researched the poverty line,
indexes on poverty, and the relationship between poverty and
inequality. The choice of the poverty level could influence
the results on whether countries were becoming closer in terms
of the absolute number of people in poverty. However, the
choice of the poverty line would have no effect on the income
inequality measures.
Ahluwalia et al. (1979) made some predictions concerning
the future. Their approach to studying growth and poverty in
the LDCs was threefold. First, they estimated the absolute
poverty in the developing countries and the relationship
between income distribution and the rising levels of output.
Second, an analysis of the past trends in growth and poverty
for certain countries was conducted, the results of which were
projected into the future based on the policies at that time.
Lastly, the changes in poverty were considered when income
growth was accelerated, the distribution of income was
improved, and the reduction of fertility was implemented.
This analysis was based on 36 countries, all of which were LDC
market economies. These countries GDPs per capita were
adjusted for purchasing power parity using what was referred
to as the Kravis adjustment factor.7
Ahlualia et al. (1979) used Theil's inequality index to
analyze the trends in inequality and poverty from 1960 to 1975
7The Kravis adjustment factor was an attempt by Ahlualia
et al. to adjust the data for purchasing power parity
estimates by Kravis et al. 1975 and 1978a.

23
among the LDCs. The results indicated that the inequality
among the LDCs increased during this period. In addition,
they projected the inequality level to the year 2000. They
expect the income inequality to increase from .67 in 1975 to
.77 in the year 2000. The reason for the divergence will
increasingly be due to the wider distribution of income among
the countries (from 37% to 50% respectively).8 They predict
that India and Bangladesh will have higher growth than the
other LDCs. Therefore, a large percent of the increase in
inequality in the LDCs will be due to the economic events in
India and Bangladesh.
The worsening of the internal distribution of income is
what Ahlualia et al. (1979) attributed to the lack of growth
in the poorest of the LDCs. The middle group of LDCs are not
expected by these authors to reduce their inequality. A
listing of the poorest LDCs and middle LDCs is presented in
Ahluwalia et al. (1979). They expect the relative level of
poverty to decrease and the absolute level of poverty in the
year 2000 to be 600 million.
The studies in this section clearly state that the LDCs
are diverging instead of converging. There were several
reasons given for their slow growth: debt crisis, population
“income inequality increases if the income of the
different countries continue to grow further apart. That is
the case with India and Bangladesh. They are increasing the
inequality because they continue to grow faster than the other
DCs. Hence, creating a greater dispersion (increasing
inequality).

24
growth, agricultural based economies, and restrictive trade.
Two variables that have been related to convergence in the
other two sections were also found to influence convergence in
the LDCs: government expenditure and investment.
2.5 Human Capital
The effect of human capital on economic growth is
uncertain. Human capital in this text is considered to be a
set of specialized skills that agents can acquire by devoting
time to schooling or special training (Grossman and Helpman,
1991). The more training an individual receives the more
human capital that individual acquires. Human capital has
become more important in the literature recently. The
endogenous growth models show that increasing returns are
possible with a constant return to scale model if human
capital is included (Romer, 1990). In contrast, the older
exogenous growth models assumed that growth is attributed to
exogenous technological change (Solow, 1956).
The key to endogenous growth models is the idea of
learning by doing. Romer (1990) showed that the rate of
growth and technology was a function of total human capital in
an economy. The initial human capital level affects the rate
of growth in the different countries. Romer's approach led to
the suggestion that countries will diverge. Unlike Romer,
Lucas (1988) mathematically showed that human capital has
spillover effects which drive growth (unbounded growth).
However, his conclusion was that there will be no convergence

25
or divergence, but that countries will grow uniformly.
Grossman and Helpman (1991) agree with Lucas; however, they
assume that a finite population can only accumulate a bounded
quantity of human capital.
Glomm and Ravikumar (1992) examined the implications of
public investment in human capital on growth and the evolution
of income inequality. Using an overlapping generations model,
they showed that public education reduced income inequality
faster than private education. However, private education
yielded higher per capita incomes except when the initial
income inequality was sufficiently large.
The main objective in the study reported by Ram (1989b)
was to explain the role of schooling in reducing income
inequality and poverty in LDCs. The first part of Ram's paper
reviewed past literature on this subject. The review of
literature as cited by Ram (1989b) showed the following:
Chiswick (1971, 1974) found that income inequality was reduced
as educational inequality was reduced (based on nine
countries); Chiswick and Mincer (1972) found that in the U.S.,
inequality in schooling did influence income inequality, even
though it had a minimal affect; Adelman and Morris (1973),
Chenery and Syrquim (1975), and Ahluwalia (1976) showed that
for 43 developing countries, 55 LDCs and 60 various countries,
respectively, education reduced income inequality.
Contradictory later findings were also cited. These were the

26
work of Fields (1980) , Psacharopoulos and Woodhall (1985) , and
Morrison (1987).
The above literature was puzzling to Ram. Hence, he used
the data from Psacharopoulos and Arriagada (1986) and Summers
and Heston (1984) for his analysis. His income inequality
variable was a Gini coefficient, and the independent variable
was mean education level of the labor force. He found little
evidence that the education level affected income inequality,
even for the LDCs. Ram concluded that based on both empirical
evidence and theory, the effects of education on income
inequality were ambiguous. Problems with the data (e.g.
inconsistency or missing information) may have affected the
ability to effectively test the relationship between
educational inequality and income inequality.
Barro (1991) and Baradaran-Shoraka (1992) did empirical
studies on the effect of human capital on growth. Barro used
several proxies for human capital: secondary school
enrollment in the year of 1960 and 1985, primary school
enrollment in the year of 1960 and 1985, and adult literacy in
the year of 1960. The data were pooled for this analysis.
Therefore, there were no time-series implications from the
model. The only significant relationship he found was the
positive relationship between the average growth rate and the
I960 school enrollment.
Baradaran-Shoraka (1992) using the same variable as Barro
found the same result which supported Romer's argument.

27
Baradaran-Shoraka (1992) went one step further to create an
education data set that had four data points, which supposedly
included mean years of schooling of the total population aged
25 years and older, and years of schooling for young workers
for the period of 1969 to 1985. His results indicated that
the variable for human capital was positively and
significantly related to growth, which again supported Romer's
argument. It must be noted, however, that Baradaran-Shoraka
was only able to conduct this analysis for 50 countries due to
data limitations.
The theoretical arguments put forth about the
relationship between convergence and education are
inconclusive. In addition, the empirical studies are also
inconclusive. The small data sample appears to be the major
limiting factor.
2.6 Contemporary Evidence
The first contemporary study reviewed here was done by
Theil. Theil (1989) conducted a study from 1960 to 1985 using
the Summers and Heston 1988 data set. Theil's entropy index
was used to measure the inequality among the North, South, and
the Tropical Middle (Tropical America, Asia, and Africa).9
This analysis was based solely on non-Communist countries.
Theil noted that the population has decreased in the North and
the South while it has increased dramatically in the tropical
9See Theil (1989) for details of the breakdown of the
country categories.

28
middle countries. The ranking of real GDP places the regions
in descending order as stated above. The results showed that
world income inequality has increased over the 25 years.
Using the decomposability of his index, he showed that 80% of
the world inequality was due to inter-regional inequality.10
It has also been shown that the inequality within the North
started with the most inequality and decreased dramatically by
1985. The South's within inequality fluctuated, but stayed
relatively low while Tropical America's was relatively low and
continued to decrease. Tropical Asia started out high and
increased its inequality while Tropical Africa started out the
second lowest in inequality and ended with the highest
inequality. Tropical Africa's inequality increased
approximately three times while the North almost halved its
inequality; These results showed- that the world is not
converging. However, there are some regions of the world
which are converging, the North and Tropical America.
Grier and Tullock (1989) investigated postwar economic
growth for 113 countries from 1950 to 1981. The 1984 data set
of Summers and Heston was used in this study. They averaged
the data for every five years and pooled the data into OECD
countries and the rest of the world (ROW). This decision was
made after tests confirmed that the OECD countries and ROW
should not be pooled. They regressed their five year average
10For a discussion on the decomposability of Theil's index
see Chapter 5.

29
growth in real GDP against the following variables: initial
real GDP, government as a percent of real GDP, population
growth, standard deviation of real GDP as a percent,
inflation, and the standard deviation for inflation.
Convergence was supported only in the OECD sample. There was
no evidence to support the idea that Africa, Asia, and the
Americas are converging. The variable that was significantly
related to the average five year growth was government. This
relationship was negative for all regions except Asia.
Barro (1991) used a simple multiple regression technique
to analyze the convergence of 98 countries from 1960 to 1985,
and the factors that influenced it. He regressed the average
growth rate from 1960 to 1985 on several independent
variables: real GDP in 1960, and 1970; square root of real GDP
in 1960; secondary school enrollment in 1950, and 1960;
primary school enrollment in 1950, and 1960; average
government expenditure between 1970 and 1985 as a percent of
real GDP; number of revolutions and coups per year; number of
assignations per million population per year; and the
magnitude of the deviation of 1960 purchasing power parity
value for the investment deflator. He also ran regressions
using fertility as a dependent variable on some of the
independent variables. The last regression was run with
investment as the dependent variable.
The results from this set of regressions, 29 in all,
indicated that a few variables were significantly related to

30
growth. The starting point of human capital was shown to be
positively related to growth. This suggested that poor
countries with high human capital per person would eventually
converge with rich countries in terms of real GDP. The second
relationship was a negative one with government. This was
interpreted by Barro (1991) as the distortions governmental
policies (high taxes) introduce and offset private investment
growth. Lastly, the political instability was negatively
related to growth and investment. The more unstable a country
is politically, the less investment and growth are likely to
occur. In support of Barro's findings, Baradaran-Shoraka
(1992) conducted a similar study with a few of the variables
measured differently and found the same results as Barro.
Barro and Sala-i-Martin (1992) also conducted a similar
study to Barro's 1991 study. In this study they used a
neoclassical growth model to analyze the convergence of 98
market economies from 1960 to 1985 (data set of Summers and
Heston, 1988). They were trying to test B convergence which
is a term that Barro defined as countries converging in terms
of income over time.11 In this model, the log change in GDP
per capita (growth rate) was used as its dependent variable.
A description of the rest of the eguation was detailed,
intricate and well illustrated in Barro and Sala-i-Martin
(1992) . The independent variables were a constant and the log
“The other type of convergence Barro defines is a
convergence. This type of convergence refers to the
dispersion in income across countries reducing over time.

31
of 1960 per capita GDP. Analysis showed that there was little
to no relationship between the growth rate and the log of 1960
per capita GDP. This finding indicated that the initially
rich countries grew at a faster rate than the poor countries
(divergence). However, the first part of their analysis was
conducted on just the U.S. states, where they found
convergence taking place.
Barro and Sala-i-Martin (1992) extended their analysis to
include primary and secondary school enrollment rates in 1960,
the average ratio of government consumption expenditure to
GDP, proxies for political stability, and a measure of market
distortions based on purchasing power parity ratios for
investment goods. When this was done, the model indicated
convergence conditionally. This meant that to get
convergence, the following variables had to held constant:
initial school enrollment and the ratio of government
consumption to GDP.
In this section, the income inequality studies indicated
that world divergence was taking place, but some regions were
converging (the North and Tropical America). The growth
studies also showed divergence in the world. However, the
OECD countries were found to be converging. In addition,
several other variables were found to be significantly related
to growth: government expenditure, human capital (education),
and political instability. In the next two chapters the
development of the Summers and Heston data series on which

32
most of the studies in this section based their analysis will
be discussed.

CHAPTER 3
THE INTERNATIONAL COMPARISON PROJECT
AND IT'S USEFULNESS IN EXAMINING CONVERGENCE
3.1 Overview of the Construction of the ICP
The objective of the International Comparison Project
(ICP) was to establish a system of comparisons of real product
and purchasing power for a large number of countries. The
reason for this is that it was realized that the use of
exchange rates to conduct international comparisons introduced
errors into the analysis. For example, a 1954 study by
Gilbert and Kravis found that $1000 in US currency, when
converted to sterling at the official exchange rate, bought a
basket of U.K. goods 64% larger than the $1000 could have
purchased in the United States.
This problem was recognized by the Statistical Commission
of the United Nations. The issue was discussed in 1965, at
the United Nations' thirteenth session, and it was concluded
that using exchange rates for currency conversion was
inadequate for many uses of international data (U.N.
Statistical Commission, 1965). The United Nations and the
University of Pennsylvania started the "International
Comparisons Project" in 1968. Initial funding came from the
World Bank, Ford Foundation, some of the countries involved in
33

34
the first set of data collection, U.S. Agency for
International Development, and the U.S. Social Science
Research Council.
Kravis et al. (1975) published the first results of these
efforts which is referred to as Phase I. In this seminal
attempt, the methodology developed is presented, and actual
comparisons are made for several countries. Since Phase I,
several other successive Phases have been published. Each
successive Phase increased the number of countries and refined
the methodology for calculating gross domestic product for
each country. The countries involved in the first four Phases
are discussed in the next section.
3.2 The Geographic Expansion of the ICP: Phases I to IV
Phase I of the international comparison project (ICP)
began with a pilot study in 1967 (which included data
collection for six countries) and included data collection for
10 countries for 1970. The project was initiated by Irving
Kravis, Zoltán Kenessey, Alan Heston, and Robert Summers, all
at the University of Pennsylvania, and their results in 1975.
The countries included in 1970 are shown at the top of Table
3.1.
These authors later published two successive volumes,
1978a and 1982, referred to as Phases II and III,
respectively. Phase II added six new countries to the ICP.
These are listed in Table 3.1 under countries added in Phase
II. Phase II provides data for 1970 and 1973, but much of the

35
Table 3.1
Countries Represented in the International Comparisons Project
Africa
America
Asia
Europe
Countries represented
in Phase I
Kenya
Columbia
India
France
United States
Japan
U. Germany
Hungary
Italy
United Kingdom
Comtries added in
Phase II
I ran
Belgium
S. Korea
Netherlands
Malaysia
Philippines
Comtries added in 1
Phase III
Malawi
Brazil
Pakistan
Austria
Zambia
Jamaica
Sri Lanka
Denmark
Mexico
Syria
Ireland
Uruguay
Thai land
Luxembourg
Poland
Romania
Spain
" ' »r! . * *. • ' . ' • * • *: - ‘r *
^ Yugoslavia
Comtries added in
Phase IV
Botswana
Argentina
Hong Kong
Finland
Cameroon
Bolivia
Indones i a
Greece
Ethiopia
Canada
Israel
Norway
Ivory Coast
Chi le
Portugal
Madagascar
Costa Rica
Mali
Dominican Rep.
Morocco
Ecuador
Nigeria
El Salvador
Senegal
Guatemala
Tanzania
Honduras
Tunisia
Panama
Zimbabwe
Paraguay
Peru
Venezuela
Comtries deleted in Phase IV
Jamaica
I ran
Romania
Mexico
Malaysia
Syria
Thai land
Source: Theil et al. 1989, p~. 27

36
1973 data were based on extrapolations; hence 1970 will be the
main focus. Phase II also made corrections on Phase I data;
hence Phase II has the most accurate data for 1970. Phase III
added 18 countries which are reported in Table 3.1 under
countries added in Phase III. The data are for 1975.
Phase IV results were published in two different volumes
(United Nations, 1985 and 1987). Phase IV is different from
the previous three phases in two ways. First, the study was
completed by the Statistical Office of the United Nations
Secretariat, and 33 countries were added in this Phase (see
Table 3.1, countries added in Phase IV). Second, there are
seven countries that participated in Phase III that withdrew
in Phase IV. These countries are also reported in Table 3.1
under Countries deleted in Phase IV. This makes the total
number of participating countries in Phase IV equal to 60.
In Phases I, II, III, and IV, we have 10, 16, 34, and 60
participating countries, respectively. In Phase IV (including
the seven deleted countries), there are 15 countries in
Africa, 20 in the America's, 13 in Asia, and 19 in Europe. In
all of these countries detailed data were collected. The type
of data and the method in which they were collected follows.
3.3 The Data
There are two main steps to obtaining the type of data
the ICP needed. First, a classification system was developed
for gross domestic product (GDP) so that each countries GDP
could be divided into detailed categories. After the detailed

37
categories were defined, GDP data were collected at the
detailed category level, prices for each item within the
detailed categories, and guantity data for the items which
price data could not be obtained.
The classification system follows the scheme proposed by
the system of national accounts (SNA). Some improvements were
made to this classification system to enhance the
international comparability of the data (Kravis et al. 1975,
p. 26). The format the ICP settled on for phases I and II was
a total of 153 detailed categories, 110 for consumption, 38
for capital formation, and five for government. Phases III
and IV have 151 detailed categories, 108 for consumption, 38
for capital formation, and five for government.1 Once the
classification system was determined the next issue was the
collection of the data.
There were three categories of data used; GDP or
expenditure data for the detailed categories, price data for
each item for which a price could be identified, and quantity
data for those items for which price data could not be
collected. The collection of the expenditure data was simple:
the data were taken from the U.N. national accounts data.
Therefore, expenditure data are not discussed in detail here
but the price and quantity data collection are.
'in Phase IV, the European countries had more detailed
categories than the 151 categories and the African countries
had less. However, the systems were similar making it
possible to use the 151 detailed category system.

38
Accurate price data were very difficult to obtain for
each item, within every category, in each country. The
difficulty was that some items are not found in every country,
and if found in all of the countries, matching the qualities
of the item was complex. To ensure that the items specified
were the same, the U.N. sent price specialists to the
different countries to directly compare the qualities of the
items in question. An example of the specifications used by
the ICP was: fresh chicken eggs, size large (weighing at
least 680.4 grams per dozen), white or brown shell, not of the
best quality, but close to it. The less than best quality's
white is less thick and higher than the best quality. The
best qualities yolk must be firm, high, and not easily broken
(Kravis et al. 1982, p. 38). In this example of the egg
specifications, . it -can - -be >•assumed- that, if - these
specifications were met in any country, the quality is the
same for those countries. For most of the food groups, the
specifications were met.
As mentioned before the U.N. sends price experts to
resolve questions about matching qualities. For example, the
visits helped clear up misunderstandings from the use of
different terminology. In Japan, "cashmere" refers to a weave
rather than yarn, as in the U.S. and Europe. In England, "ox
liver" is used rather than "beef liver," the American
terminology (Kravis et al. 1982, p. 38). These types of goods

39
were referred to as narrowly defined goods. They could be
classified by their characteristics and uses.
Non-narrowly defined goods are the items for which prices
cannot be collected in a systematic way in all of the
countries. For these items quantity data were collected.
These items were called comparison-resistant goods.
Comparison-resistant goods are goods and services that cannot
be put into a category based on their characteristics. Some
examples of comparison-resistant goods are services rendered
by teachers, physicians, and the government.
Dissimilar to most commodities, services constitute a
heterogeneous collection of final products, and the production
of each is necessarily simultaneous with its consumption;
consequently, no service can be stocked. For example, to
compare teachers and physicians around the world is difficult.
The problem is how can the quality and productivity of a
teacher or physicians be measured. However, indicators of
quality and productivity can be obtained. For example, these
indicators for teaching services would include the level of
education, average income, number of students in a classroom,
or the amount of educational inputs available to and used by
the teacher. For doctor's services, the number of patients
seen or the number of operations in a day may be indicators of
their quality and productivity. Government services are also
hard to measure. The amount of capital available to the
worker may help indicate their productivity.

40
Once the base data were collected, there were several
steps and alternatives to calculating purchasing power
parities (PPPs) for each country. The first step was to
calculate the PPPs for each country with respect to a base
country. Then, the real GDP was calculated using those PPPs.
The calculation of the PPPs for comparison-resistant goods is
discussed in Section 3.6 while that for the narrowly defined
goods is discussed next.
3.3.1 The Methodology of Calculating Purchasing Power
Parities
Purchasing power parity (PPP) is the number of currency
units required to buy goods equivalent to what can be bought
with one unit of the currency of the base country (Kravis et
al. 1982, p. 383). From the base data that are collected
purchasing power parities can be calculated. There are
several ways to calculate PPPs, but the methods most commonly
used by the ICP are the country-product-dummy (CPD) and
Elteto-Koves-Szulc (EKS) methods.
The CPD and EKS methods are exactly the same if all of
the prices for every item in each country are present. In
that case, the resulting PPP's from the CPD and EKS are just
geometric means of all of the prices in detailed category a
for country c (Kravis et al. 1975, p. 60). The equation for
the geometric mean of all the prices in country c is:
(3.1) GM“ = [ f| Pi>c ]1/m i = 1, . . . ,m

41
where Pic is the price of the ith item in country c.
3.3.2 Countrv-Product-Dummv Method
The derivation of the CPD method from this representation
is simple. The CPD method is derived by making the following
assumptions: the natural logarithm of the price for the ith
item in country c is composed of an item effect and a country
effect; the PPP's are estimated by least squares; and the
relationship is stochastic. Then the CPD equation becomes:
(3.2) l/m [In(Pjc) ] = A( + Bc + eic.
The symbol eic represents a normally distributed variable with
mean zero and variance a2. A¡ is the coefficient which
represents the item effect on the price of item i in country
c. Bc is the coefficient that represents the country effect
on the price. In most cases this method is normalized by a
base country, usually the U.S.
In summary, the CPD method describes the natural
logarithm of the price of item i in country c with respect to
a base country d as the sum of an item effect A¡, and a country
effect Bc. The coefficient Bc is the mean over all items of
the log of the price of item i in country c and is interpreted
as the logarithm of the PPP for that country's currency
relative to the base country (U.S.). Also, A¡ is equal to the
mean over c of the log-price of i in c, but that coefficient
is not used in this study (Theil et al. 1989, p. 8).

42
3.3.3 Elteto-Koves-Szulc Method
To derive the EKS method it takes four steps2. The steps
are: calculate "Laspeyres" and "Paasche" type price ratios;
calculate Fisher binary price ratios; fill in the Fisher
matrix if needed; and then build an EKS matrix of transitive
parities. Only the equations will be shown here, an actual
example will be given in the next section.
Before the derivation of the EKS method the concept of
characteristic items must be introduced. A characteristic
item is an item that is considered to be purchased frequently
within that country. Each country is asked to nominate at
least one product within every detailed category which it
regards as a characteristic item. The characteristic item
chosen must also be priced in at least one other country.
This is done so that the most consistent price data is used in
the EKS calculations. It will become clear that all
calculations in the EKS method are based on the prices of the
characteristic items.
The first step of the EKS method is to calculate the
Laspeyres and Paasche type price ratios. These ratios are not
true Laspeyres and Paasche ratios and are often referred to as
mini-Laspeyres and mini-Paasche price ratios due to their
similarity to the Laspeyres and Paasche time-series
measurement. The difference is that these are unweighted
2We would like to thank Ms. Harary at the OECD, Economic
Statistics and National Accounts Division for providing
unpublished material on the EKS method.

43
price ratios whereas Laspeyres and Paasche are weighted
indexes (Ward, 1985, pp. 42-43). The mini-Laspeyres formula
is a price ratio of the characteristic item between two
countries, if the base country has only one characteristic
item. If there are more than one characteristic items in the
base country, a geometric mean is taken of all of the price
ratios3. The general representation of the equation for the
mini-Laspeyres equation is:
(3.3)
0,
1/m
where i = 1,...,m characteristic items in detailed category a.
The mini-Paasche formula is the reciprocal of the transposed
mini-Laspeyres price ratios. The equation for the mini-
Paasche price ratios is:
(3.4)
pa
* d,c
0,
i,d
l,C
1/m
= l/L
c,d '
This method does not pick one base country; therefore, a
matrix of mini-Laspeyres is created between countries with a
diagonal of ones, the same is true for the mini-Paasche
ratios.
3To calculate the geometric mean the base country's
characteristic item or items determine the relative parity
ratios. The comparison country's price does not have to be a
characteristic item in order to calculate the geometric mean.

44
Once the mini-Laspeyres and mini-Paasche ratios are
computed, the Fisher binary type price ratios are constructed.
Just as before these are not true Fisher binaries because they
are based on unweighted price ratios. Therefore, these Fisher
type price ratios will be referred to as mini-Fisher binary
price ratios. The mini-Fisher ratios are unweighted geometric
means of the mini-Laspeyres and mini-Paasche price ratios.
The equation for the mini-Fisher price ratios is:
(3.5) F“d = (L“d * P“d),/2
where F“d is the mini-Fisher price ratio for detailed category
a between countries c and d. Note that F“d * Fdc = 1. However,
the matrix of mini-Fisher ratios are not transitive.
Transitivity means that F“e/Fde f F“d. Hence, to make the mini-
Fisher ratios transitive, the EKS method is applied.
Given that all of the price ratios are present, all of
the mini-Fisher ratios can be calculated. Hence, there would
exist a full matrix of mini-Fisher ratios. The EKS method is
then applied to the mini-Fisher ratios. The equation for the
EKS method is:
(3.6)
EKS
c,d
Fct 2
c,d
1/n
where e f cd.
EKS“d is the PPP for the detailed category a between countries
c and d. This procedure uses direct mini-Fisher price ratios
F“d and indirect ratios F“e and Fdc which use country e as the

45
bridge country between countries c and d. This method
replaces each direct ratio by the geometric mean of itself and
all corresponding indirect ratios that can be obtained using
as many of the other countries as possible for bridges. The
EKS gives the direct ratio twice the weight of each indirect
ratio since F“d/F£d * F“c/Fdc is the same as F"d2. The resulting
transformed ratios are all transitive. The overall transitive
parity between any individual pair of countries is therefore
significantly dependent on the indirect ratios involving
prices in all other countries (Ward, 1985, pp. 44-45).
The last step of the EKS method is to choose one country
as a base country so that it can be compared with the CPD
results. A base country can be chosen be observing the values
in any of the country columns of the EKS matrix. To make the
EKS equivalent to a geometric mean is simple. The EKS
formula itself is a geometric mean. If all of the prices of
the items are all present and all characteristic items, then
the EKS method is the same as equation (3.1) if Pic is replaced
with a price ratio. The reason is that the indirect mini-
Fishers and the direct mini-Fisher ratios are equal, that is
rc,e/rd,e rc,d*
This section shows how the CPD and EKS method calculate
PPP's for a detailed category when all of the prices are
present. Also, it is proven that the CPD equals EKS which
equals the geometric mean when all of the prices are present
and all of them are characteristic items. The next section

46
illustrates the situation where there are missing prices,
which is the case for most detailed categories.
3.4 Estimating Purchasing Power Parities
In many detailed categories, there are several missing
prices. Without the basic prices, the CPD method does not
equal a geometric mean and neither does the EKS method. In
fact with the EKS method the mini-Paasche, Laspeyre, and
Fisher ratios cannot be calculated when there are missing
prices. In this case it should be clear that the CPD method
does not equal the EKS method, although they should deviate
minimally from one another. This section addresses the
procedures the ICP used to estimate the PPP's via the CPD and
EKS methods when there were missing price data
Estimating PPP's with the CPD method is the same as in
- - r - r . . •
section 3.3. Equation 3.3 normalized by the U.S. price is the
equation used to estimate the Bc's. To illustrate this
procedure part of the data from the fresh vegetables detailed
category for 1970 is used (Kravis et al. 1975, p. 59). The
data for four countries and four goods are shown in Table 3.2.
The full matrix for fresh vegetables for 10 countries and 20
countries in 1970 is shown in Appendix A4.
If the prices of vegetables in their respective national
currencies in Table 3.2 are considered to be a detailed
4The PPP's and A¡'s estimated by Kravis et al. 1975 are
also included in Appendix A.

47
Table 3.2
Fresh Vegetables for 4 Countries and Items in 1970
Japan
(Yen)
Kenya
(Shilling)
United
Kingdom
(Pound)
United
States
(Dollar)
Lettuce
218.1*
0.62
0.5*
Mushrooms
-
-
0.54*
1.9
Onions, yellow
98.6*
0.77
0.13
0.35*
Tomatoes
160.9
1.19*
0.31*
0.92*
Source: Kravis et al. 1975, p. 59.
*The starred items are the characteristic items for each
country5.
category, then the vector for the dependent variable using the
U.S. as a base country is equal to:
In (218.1/ . 5)
In(98.6/.35)
In(160.9/.92)
In(.62/.5)
In(.77/.35)
In(1.19/.92)
In(.54/1.9)
In(.13/.35)
ln(.31/.92).
Kravis et al. 1975, 1978a, and 1982 weighted each price ratio
with the reciprocal of the number of prices in the numerator
country by the base country (4/3), and by the supercountry
expenditure (see Appendix B) . The independent variables
(dummy variables) for this equation, constructing the country
dummy then the item dummy, are:
5These items are not the actual characteristic items they
are chosen for illustration purposes only.

48
1 0 0 1 0 0 0
1 0 0 0 0 1 0
1 0 0 0 0 0 1
0 10 10 0 0
0 1 0 0 0 1 0
0 1 0 0 0 0 1
0 0 1 0 10 0
0 0 1 0 0 1 0
0 0 1 0 0 0 1.
This system cannot be estimated because each row for each
independent variable sums to 1. That means there is an adding
up problem. To solve this problem one of the items has to be
dropped. No information is lost when this is done, redundant
information is eliminated from the system. Once one of the
columns from the item dummy is eliminated the regression can
be estimated.
The results from this setup having dropped item 2 and
weighted the price ratio by (4/3)6 are
Bj»p,u.s. = 5.62
®Ken,U.S. = 0.41
®u.k.,u.s. = “ 0.99.
These results are the natural logarithm of the PPP between
country c and the U.S. To get the PPP, the exponential of Bc
is taken. The PPP's are 275.89, 1.51, and 0.37, respectively.
There are n-1 PPP's because the U.S. is used as the base
country. The explanation of these numbers are given after the
EKS results are calculated and compared with the CPD results.
6The supercountry weighted is not used in this example.

49
The first step of the EKS method is to create the mini-
Laspeyres price ratios. For simplicity, L“d will now be
expressed as Lc/d and the same for the mini-Paasche price
ratios. The mini-Laspeyres matrix is shown in Table 3.3. All
calculations for the EKS example are shown in Appendix C. In
this matrix the base country is given by the columns, the rows
are the numerator countries. Since the mini-Paasche matrix is
just the inverse of the numbers in Table 3.3, that is Pjap/Us =
1 /Lus/jap, the mini-Paasche matrix will not be shown.
Table 3.3
Mini-Laspeyres Price Ratio Matrix
Japan
Kenya
U.K.
U.S.
Japan
1.0
135.21
519.03
278.02
Kenya
0.0047
1.0
2.48
1.52
U.K.
0.0013
0.26
1.0
0.35
U.S.
0.0029
0.77
3.23
1.0
After the mini-Laspeyres and mini-Paasche price ratios
are calculated, the mini-Fishers are estimated. Table 3.4
shows the results of the mini-Fisher calculations. There are
no missing mini-Fisher ratios in this example. If there were,
a bridge country method would have been implemented to fill in
the missing values. For example, if the mini-Fisher price
ratio between countries c and d (F“d) is missing, but the

50
ratios between countries c and e, and d and e exist, then the
mini-Fisher price ratio for countries c and d can be
calculated by dividing F“e by Fjc. Country e is the bridge
country that links countries c and d. If more than one bridge
country is available, then a simple geometric mean is taken of
all of the indirect estimates. If there are still missing
mini-Fisher ratios then the above procedure is applied until
the matrix has no missing data.
Table 3.4
Mini-Fisher Ratios
Japan
Kenya
U.K.
U.S.
Japan
1.0
169.61
631.87
309.63
Kenya
0.0059
1.0
3.09
1.41
U.K.
0.0016
0.32
1.0
0.33
U.S.
0.0032
0.71
3.04
1.0
The final step in calculating the PPP's is to implement
the EKS method. The EKS method uses the direct and indirect
mini-Fisher ratios to make these parities transitive. The
matrix of transitive PPP's are shown in Table 3.5. The EKS
results are implicitly weighted because only the
characteristic items are used for base countries in the
calculations.

51
Table 3.5
Transitive
PPP's from the
EKS method
Japan
Kenya
U.K.
U.S.
Japan
1.0
189.58
667.53
262.67
Kenya
0.0053
1.0
3.50
1.39
U.K.
0.0015
0.28
1.0
0.40
U.S.
0.0038
0.72
3.53
1.0
To compare the EKS results with those from the CPD, the
U.S. column is used because the CPD used the U.S. as its base
country. The values from the CPD compared with the EKS for
fresh vegetables in 1970 for 4 countries and items are as
follows:
CPD EKS
Japan/U.S. 275.89 262.67
Kenya/U.S. 1.51 1.39
U.K./U.S. 0.37 0.40.
The differences between these numbers are negligible. Most of
the variance could be due to weights and rounding error. The
interpretation of the PPP's estimated by both methods is that
one dollar's worth of fresh vegetables in the U.S. equals
between 262.67 - 275.89 yen worth of fresh vegetables in
Japan, 1.39 - 1.51 shillings worth of fresh vegetables in
Kenya, and 0.37 - 0.40 pounds worth of fresh vegetables in the
United Kingdom.

52
The CPD method was used in Phases I, II, and III. The
CPD and EKS methods were used in Phase IV. The reasons for
using the different methods in the different Phases will be
discussed in Chapter 4. Once the PPPs were estimated, they
were used in the Geary-Khamis method. The second stage of the
estimation process is discussed next.
3.5 The Gearv-Khamis Method
The objective of the Geary-Khamis method is to provide
multilateral base-invariant price and volume comparisons at
the various levels of aggregation for all countries, where the
volumes are expressed in "international dollars". These
volumes are additive across expenditure categories, while
prices can be obtained by dividing expenditures in national
currency by those in international dollars.
The method was first introduced by Geary who suggested
that a system of homogeneous linear equations be used. These
equations are used to calculate the international prices and
the PPPs simultaneously. Subsequently, Khamis shows that the
system yields non-negative international prices and PPPs.
Thus, Geary and Khamis are responsible for this model.
The derivation of the Geary-Khamis method follows. The
CPD or EKS method can be used to produce the detailed category
PPP's for the Geary-Khamis method. These PPP's are transitive
and relative to the U.S. dollar. Detailed categories are
indicated by the subscript a = 1, ..., A. Let Eac be the per

53
capita expenditure (in national currency) on detailed category
a in country c. The equation for the volume of detailed
category a in country c is
(3.7) Va,c = Ea c/PPPa c.
Vac is expressed in U.S. dollars.
Although (3.7) achieves the goal of expressing all
expenditures in the same currency ( U.S. dollars), the Vac's
have the problem that they are not additive over detailed
categories. To achieve such additivity, the Geary-Khamis
method introduces the international price Pa of each detailed
category and the overall purchasing power parity 7rc of each
country c. The definition of Pa is
N
r (E;c7Tfcy•
C=1
Pa =
N
2 V«,c
C=1
or, equivalently,
N N
(3.8) PaVa = Z (Eac/7Tc) where Va = E Va>c
c=l c=l
while n„ is defined as

54
A
2 E„,c
a=l
=
A
E P V
« a,c
a=l
or, equivalently, as
A
(3.9) GDPc (1/ttc) = E PaVa c
a=l
where GDPC (the gross domestic product of country c in
national currency) is equal to the sum over a = 1, ..., A of
Eac. It is readily verified that (3.8) and (3.9) constitute
a linear system in the A + N -1 unknown Pa and l/nc (7rc = 1 for
c = U.S.) (Theil et al. 1989, Appendix A).
The product PaVac is interpreted as real expenditure per
capita in international dollars on detailed category a in
country c. This product is additive over detailed categories.
Let S be any grouping of such categories; then the sum over
a e S of PaVac is real expenditure per capita or real gross
domestic product (RGDP) per capita in international dollars on
S in c. If S consists of all detailed categories, this sum is
GDP per capita in c.
The exposition given on the CPD, EKS, and Geary-Khamis
methods is a general overview on how PPP's for the detailed
categories and overall, international prices, and RGDP are

55
calculated. The next section deals with calculating PPP's for
the comparison resistant goods.
3.6 Calculating PPP's for Comparison Resistant Goods
In the previous sections the procedure for calculating
PPP's for narrowly defined goods was discussed. In this
section, the calculations for PPP's of comparison resistant
goods are discussed. The procedure for calculating these
PPP's to use in the Geary-Khamis formula is straight forward.
For the comparison-resistant goods and services (i.e.,
services of teachers, physicians, dentists, hospitals, nurses,
and government employees), neither the CPD or EKS method was
used. Quantity comparisons for these categories were based on
a method called "direct quantity" comparisons. For example,
for teachers of first, second, and third level students, the
¡ o? i<• • or | - -. . ■; i r • • j i - *;' • ¡ •'* »vr y • • •j ; * * : '*'’*
quantity comparisons were based on the number of standardized
persons engaged in providing the services. For physicians,
dentists, technicians, midwives, and the like, the ICP
quantity comparisons were based on the number of physicians,
dentists, and nurses, respectively.
For Phases I and II, it was assumed that all equally
qualified personnel in these comparison-resistant categories
have the same productivity. In Phases III and later, this
assumption was abandoned, and adjustments were made. In
educational services, the modifications improve the estimates
of teacher inputs by introducing education level and the
number of students as a further dimension of productivity. In

56
medical care and government services, adjustments are made for
the differences in the productivity of inputs for broad groups
of countries and by making adjustments for capital per worker.
After the adjusted final quantity ratios are derived, the
PPPs used for the Geary-Khamis method are considered to be
indirect PPP's. These PPPs are found by dividing the
expenditure ratios by the adjusted quantity ratios. From
there, the Geary-Khamis method is applied as before. The
reader who is interested in these and similar issues should
consult the original source: the work of national and U.N.
price experts (Kravis et al. 1982, p. 38); prices of
construction and consumer durables (Kravis et al. 1982, pp.
50-56); and the treatment of services (Kravis et al. 1982,
Chapter 5).
r 1 • • '. • " i?■ • . • • • •<> '• n vi ■ • • -1 • *n
3.7 Regionalism
Regionalism is a new issue beginning in Phase III. The
previous Phases I and II were limited to a small number of
heterogenous countries. Thus, there is little point in
considering whether comparisons could be improved by
identifying relative homogeneous subsets of countries. The
Geary-Khamis method was applied to the entire set of countries
without any effort to distinguish such subsets or to take them
into account in the index number calculations. This
symmetrical treatment of all countries is called the
"universal" approach.

57
As the number of countries increased significantly in
Phase III, it became necessary to consider whether applying
the CPD or the Geary-Khamis methods in successive stages would
improve the comparisons. The first step would be to look at
the level of sets of relatively homogeneous countries and,
thereafter, at the regional level. Thus, countries in
different regions are compared through regional linkages.
The most obvious basis for identifying homogeneous sets
of countries is geographic closeness. This basis for grouping
countries assumes that these countries have close political
and cultural ties as well as similar customs. Although ad-
hoc, there are some good reasons for using this approach.
Europe and Latin America, for example, are similar in the way
they classify daily business and the way they deal with the
changes in the political, social, and economic arenas. - In
addition, there are usually regional organizations with the
sole responsibility of economic development for that region.
For the actual calculations for Phase III, the ICP opted
to use what is called a modified "universal" approach. This
approach has some regionalism aspects which are introduced via
the organization of the price inputs for the Geary-Khamis
calculations. The objective is to retain base country
invariance or to at least allow all countries within each
region to influence the world comparisons while retaining the
intraregional PPPs and quantity relationships for the detailed
categories and for GDP as a whole.

58
The modified universal approach has 3 steps. First, the
CPD method is applied at the regional level to fill in the
missing prices. Second, the CPD method is applied again, this
time on all countries in the study. Lastly, the PPPs from the
second stage CPD are used as direct inputs to the Geary-Khamis
method.
The first stage CPD takes advantage of the regional
similarities in price structures to cope with a major problem
in deriving the set of PPPs. The problem is primarily
incomplete, overlapping sets of price comparisons among the
participating countries. The first CPD estimation operates at
the regional level to fill in for each country's missing
entries in the vector of item prices. All items for which at
least two countries in the region provided prices are
included. Therefore, this tableau contains for each region,
a full vector of prices, for each country, for all items
priced by two or more countries in the region. Note that if
the CPD is run on the augmented price tableau for a given
region, it would yield the same PPPs as those produced by the
original incomplete tableau of prices. Thus, the tableau
retains the characteristics of the original tableau.
After each country's price vector has been completed to
match the other country's in the same region, a second CPD is
run. This CPD is calculated for all 34 countries (Phase III),
where these PPPs are used as the direct price inputs for the
Geary-Khamis calculation covering all the countries. This

59
approach embodies a regional element in deriving the category
PPPs, but the aggregation of the PPPs across categories is of
the universal mode.
The results of this new approach relative to the approach
used in Phases I and II, which is based on direct price inputs
of all countries regardless of the region, are improved. The
augmented-price-tableau enhances the influence of
intraregional price relationships. The missing prices are
explicitly filled in on the basis of intraregional price
relationships versus being estimated on the basis of price
relationships in all countries like the universal approach
does.
The last step is to put the PPPs derived from the two-
stage CPD method into the Geary-Khamis equations.
Calculations for all 34 countries (Phase III> were completed
using this method. The results from this approach are
discussed next.
3.8 Phase III Results Compared with Exchange Rates
Using the two stage CPD method to obtain the PPPs for the
detailed categories and then implementing the Geary-Khamis
method, the international prices and GDPs per capitas are
calculated. Table 3.6 provides the results of these efforts
for gross domestic product for the year 1975 (Phase III) . The
34 countries are listed in the order of declining GDP per
capita in international dollars.

60
Table 3.6
GDP Per Capita for 34 Countries in 1975
Country
(1)
International
dollars*
(2)
Same,
U. S.=100b
(3)
Exchange rate
converted1*
(4)
United States
7176.0
100.0
100.0
Germany
5952.7
83.0
94.7
Denmark
5910.9
82.4
104.5
Luxembourg
5883.4
92.0
90.2
France
5876.9
81.9
89.6
Belgium
5574.1
77.7
87.8
Netherlands
5397.2
75.2
84.5
Austria
4994.8
69.6
69.8
Japan
4906.7
68.4
62.3
United Kingdom
4587.9
63.9
57.6
Spain
4010.2
55.9
41.0
Italy
3861.1
53.8
47.9
Poland
3597.9
50.1
36.0
Hungary
3558.9
49.6
29.6
Ireland
3048.8
42.5
37.2
Uruguay
2844.3
39.6
18.2
Iran
--••'2704.6
37.7-i
22.1
Yugoslavia
2591.4
36.1
23.2
Mexico
2487.3
34.7
20.4
Romania
2386.8
33.3
24.3
Brazil
1811.2
25.2
16.0
Syria
1794.2
25.0
10.0
Jamaica
1722.6
24.0
19.6
Colombia
1608.7
22.4
7.9
Malaysia
1540.6
21.5
10.9
Korea
1484.1
20.7
8.1
Philippines
946.3
13.2
5.2
Thailand
936.1
13.0
5.0
Zambia
737.8
10.3
6.9
Sri Lanka
667.7
9.3
2.6
Pakistan
590.3
8.2
2.6
Kenya
470.5
6.6
3.4
India
470.5
6.6
2.0
Malawi
351.7
4.9
1.9
“Summed over all 151 detailed categories.
bSource: Kravis, Heston, and Summers 1982, p. 12

61
The differences between the exchange-rate converted
figures and those which Kravis et al. (1978a) obtained using
the Geary-Khamis method are substantial. These differences
increase as real GDP per capita decreases. This is readily
seen in columns 3 and 4 of Table 3.6 where the PPP based
estimates of GDP per capita are compared with the exchange
rate based estimates (both are a percentage of U.S. value).
The use of exchange rates tend to overstate the poverty of
poor nations considerably. For example, when we use exchange
rates, the ratio of the U.S. GDP per capita to its Indian
counterpart is 100/2.0 = 50, but it is only 100/6.6 or about
15 when we use the Kravis approach.
One reason for this dispersion is that services tend to
be cheaper relative to commodities in poorer countries, and
services make up a small portion of international trade.
Hence, exchange rates understate the value of services in low
income countries.
Services, which are nontraded goods, are cheap in low-
income countries; hence exchange-rate conversions greatly
underestimate the true quantities of services in low-
income countries relative to those in high-income
countries. (Kravis et al. 1982, p. 23)
In addition, exchange rates have been variable since the
switch-over to floating exchange rates in 1973. However,
there is no reason why the consumption expenditures in
national currencies should reflect this variability exactly.
Converting these expenditures by such wildly fluctuating
exchange rates would yield highly spurious results.

62
3.9 Phase IV Further Considered
After Phase III regionalism plays a bigger role in the
ICP. Regionalism complicated things in many ways. Therefore,
Phase IV is discussed explicitly.
Phase IV as mentioned before is different from the other
Phases. The information on Phase IV is presented in "World
Comparisons of Purchasing Powers and Real Product for 1980:
Phase IV of the International Comparison Project." This
manuscript has two parts: "Part I: Summary Results for 60
Countries"; and "Part II: Detailed Results for 60 Countries."
These papers are published by the Statistical Office of the
United Nations Secretariat (UNSOS), Statistical Office of the
European Communities (EUROSTAT), and the Organization for
Economic Co-operative and Development (OECD). This work is
discussed here to address several problems- (i.e.,
decentralization, regionalism, and fixity) and the additional
problems they create. The other reason for Phase IV's
importance is that it increased the number of benchmark
countries to 60. Phase IV is similar in many ways to the
previous Phases, so only the deviations from those Phases will
be discussed below.
After Phase III, the ICP was decentralized, which meant
that various regional and country groups assumed major
responsibilities while the Statistical Office of the United
Nations Secretariat was responsible for linking the work of
the various regions. There were seven organization that

63
carried out the work for the country groups: Statistical
Office of the European Communities (EUROSTAT), Economic
Commission for Europe (ECE), OECD, Economic Commission for
Africa (ECA), Economic Commission for Latin America and the
Caribbean (ECLAC), Economic and Social Commission for Asia and
the Pacific (ESCAP), and UNSOS. With the decentralization,
each group carried out its own estimations within its region;
this is referred to as regionalism. This definition
supersedes the definition in section 3.7 for Phase IV and
later. Table 3.7 shows the countries involved in each group
as well as the organization that did the calculations. After
the comparisons within each region are accomplished, then the
regions are compared at the world level.
3.9.1 Other Methods Used in Phase IV
With the decentralization and regionalism of Phase IV,
one problem is that each region can choose any method they
preferred to calculate the PPPs. Europe Group 2 and ECIEL
decided not to use the CPD or EKS method. The European group
implemented a method called the "STAR" system. It is not
clear what the ECIEL group did to calculate their PPPs.
The star system used by Europe group 2 has Austria as the
base country for that group. They carried out four separate
binary comparisons with the four countries representing the
outer points of the star. The detailed category PPPs for each
country are only estimated with respect to Austria. The PPPs
for any two countries are derived from the two sets of binary

64
Table 3.7
The Organizations that Performed the Calculations and the
Countries Involved in Each Group for Phase IV.
EUROSTAT
ECE
ECA/EUROSTAT
ESCAP/UNSOS
ECIEL/ECLAC
OECD
Europe-
Group 1
Group 2
Africa
Asia
Latin America
OECD
Belgium
Austria
Botswana
Hong Kong
Argentina
Canada
Denmark
Finland
Cameroon
India
Bolivia
Japan
France
Hungary
Ethiopia
Indonesia
Brazil
Norway
Germany
Poland
Ivory Coast
Pakistan
Chile
U.S.
Greece
Yugoslavia
Kenya
Philippines
Colombia
Italy
Madagascar
Korea
Costa Rica
Ireland
Malawi
Sri Lanka
Dorn. Rep.
Luxembourg
Mal i
Ecuador
Netherlands
Morocco
El Salvador
United Kingdom
Nigeria
Guatemala
Portugal
Senegal - ■ • ~ • •
-Honduras
• - S TV
Spain
U.R. of Tunisia
Mexico
Israel
Tanzania
Panama
Zambia
Paraguay
Zimbabwe
Peru
Uruguay
Venezuela
Source: United Nations, 1985 and
1987.
PPPs (i.e.
country
C and D's binary PPPS
with country
B and
D's binary PPPs). Using this method, transitivity is not a
problem since no direct comparisons are made between the
points of the star. Thus, the EKS system is not necessary.
The Geary-Khamis method is used to aggregate the categories
and calculate GDP as a whole. The weights (expenditure and

65
prices (PPPs) of the countries covered) of the five countries
are taken into account (The Statistical Office of the United
Nations Secretariat 1987, p. 5).
There is less information on what the ECIEL region did.
However, it is clear that neither the CPD nor the EKS method
was implemented. It has been ECIEL's practice that each
country provides prices for every item in the detailed
categories. PPPs are then derived that are transitive across
all countries by obtaining the geometric mean of the price
ratios of each country to any one of the countries chosen as
the numeraire. All that can be said about this method is
that, if all countries provide prices for all of the
commodities, then all of the other methods reduce to a
geometric mean, when estimating PPPs for the detailed
categories (The Statistical Office of the United Nations
Secretariat 1987, p. 11).
3.9.2 Linking the Regions of Phase IV
After the PPPs for the detailed categories were
estimated, the problem was to link all of the country groups
together. The main problem was that each region had a
different base country. In addition, the Europeans (both
groups) have approximately 320 detailed categories while the
other groups typically have approximately 150; the African and
Latin American countries have a more condensed system.
Fortunately, the European, African, and Latin American groups

66
were able to make their respective detailed categories
compatible with those of the world comparisons.
Linking the various country groups requires that the
prices of the overlapping items between countries across the
different country groups be compared. In order for this to
work, there must be at least one country in each group which
has prices for each detailed category so that the PPPs can be
estimated to link the countries. When comparing Europe Groups
1 and 2, for example, only Austria has sufficient prices to
link Group 2 to 1. However, this was sufficient to link the
Europe Group 2 countries with the world comparisons.
There are 20 countries that serve as liaisons like
Austria. These countries act only as a set of countries whose
item prices for comparable goods and services serve as the
basis for linking the country groups. These countries are
called "core" countries. The core countries are: France,
Spain, Israel, and the United Kingdom (Europe Group 1) ;
Austria (Europe Group 2) ; United States, Canada, and Japan
(OECD); Brazil, Colombia, Uruguay, Dominican Republic, and
Guatemala (ECLAC); Hong Kong, Indonesia, Korea, Pakistan, and
Sri Lanka (ESCAP); and Kenya and Senegal (ECA).
The CPD method was used for the core countries where the
item prices for the 20 core countries were used as inputs.
The expenditure weights used by some of the country groups
were also incorporated into the CPD estimation procedure.
When the CPDs were estimated for each of the detailed

67
categories, PPPs between each core country and the United
States, which was the numeraire country, were provided. The
next problem was how to link these PPPs with the other
countries in these regions.
The method used to link the PPPs to the other countries
is a type of chain-link-procedure. Using the African
countries as an example, the detailed category PPPs exist and
for the core countries of Kenya and Senegal, both with respect
to the African numeraire and with respect to the United
States. The ratio of the geometric means of the core country
to the African PPPs provided a factor which, when multiplied
times the detailed category PPPs within Africa for all of the
African countries, aligned these parities with respect to the
United States dollar. This procedure preserves the
relationship between the basic PPPs for all countries as
originally obtained in the African comparisons, including
Kenya and Senegal. This is the fixity principle (see Appendix
D) .
The chain-link-procedure was applied to Latin America,
Europe Group 2, and the OECD countries. In the case of the
ESCAP countries, there was no reason to do the chain link
method since the base country for that group was the U.S. For
India and the Philippines, a slightly different procedure was
used since the price information for these countries became
available too late to include in the core country CPDs. The
item prices were directly compared to the item price estimates

68
that were a part of the CPD output for each detailed category.
The geometric means of these item price ratios, which were
based in national currency units per dollar for each detailed
category, were used as the PPPs.
All methods in which the expenditure and PPPs at the
detailed categories were obtained have been discussed. These
calculations were the basic inputs to the aggregation
procedure. The Geary-Khamis method was used just as in the
previous Phases for the aggregation of the data. The use of
supercountry weighting was also retained. It was important
that the results for countries participating in several phases
of the ICP not be influenced by the addition of new countries.
Hence, the world comparisons utilized a system of supercountry
weights where the dollar GDP of non-participating countries
was assigned to participating countries on the basis of
geographical proximity and the level of per capita income.
The problem with the Phase IV data are that the fixity
principle is imposed (see Appendix D) . Fixity adversely
affects the data if one is interested in world comparisons.
That is why there are two data sets for Phase IV. The first
set is for researchers who are interested in world comparisons
and the other, which preserves fixity, is for intraregional
comparisons. The first set is made available by the U.N.
Statistical Office upon request by the researcher. The other
data set which has fixity imposed is in the Phase IV

69
publication. The calculations in this thesis were all based
on the data that do not impose the fixity principle.
To calculate RGDP per capita for each country with
respect to the U.S. without fixity, the calculations must be
done like the Phases previous to Phase IV. That is, estimate
the PPPs with the CPD or EKS method using the U.S. as a base
country, then apply the Geary-Khamis method.

CHAPTER 4
EXTRAPOLATIONS
4.1 The Beginning of Extrapolations with ICP Data
There are five publications of the extrapolations on the
different phases of the ICP. The first publication is by
Kravis et al. (1978b). All of the rest are by Summers et al.
(1980 also known as Mark l,1 1984 Mark 3, 1988 Mark 4, and
1991 MARK 5). These publications sought a way to approximate
real gross domestic product (RGDP) per capita for virtually
all the countries in the world and for every year from 1950 to
1988. This method is referred to as the "short cut" method.
During the years following the first publication in 1978, the
methodology and the guality of the data from the Mark's have
improved.
The purpose of the first paper, "Real GDP Per Capita for
More than One Hundred Countries," by Kravis et al. (1978b) was
to close a gap that the world statistical system had been
unable to fill. At that time, there were no comparative data
on "real" GDP per capita (gross domestic product per capita
adjusted for differences in the purchasing power of
currencies) for a large number of countries. In this paper,
‘Mark 2 was not published but it was used in Kravis,
Heston, and Summers (1982).
70

71
Kravis et al. (1978b) develop a method to calculate these real
GDP per capita (RGDPC) by using the detailed comparisons of
the 16 countries in Phase II. The structural information from
this method allows the RGDPCs to be calculated for non-ICP
countries. Lastly, an extrapolation is made to get RGDPC for
later years.
The short-cut method that Kravis et al. (1978b) developed
concentrates on the relationship found in the 16 countries
between RGDPC and certain independent variables. These
structural relationships were used to estimate other years and
non-benchmark countries. However, the authors caution that
the non-ICP RGDPC's were approximations, and that it would be
some time before more exact comparisons would be available for
a large number of countries. Nonetheless, their numbers are
superior to exchange rate converted GDPs per capita which were
used prior to PPP conversions.
The model Kravis et al. (1978a) used to find the
structural relationships was
PIi
(4.1) In rj = a, + a2 In n; + a3 (In nj)2 + a4 In
Plus
0Pj
+ a5 In j = 1,..., 16
where j represents countries, ri = Rj/Rus, nj = Nj/Nus, R is real
GDP per capita (adjusted for purchasing power) , and N is
nominal or exchange-rate-converted GDP per capita. The

72
variables OP (openness) and PI (price isolation) come from
international trade theory and will be covered in more detail
later (Kravis et al. 1978b, p. 219).
The relationship between r and n has been discussed in
Chapter 3 so it should not be a surprise that a2 is expected
to be between 0 and 1. The value of a, is expected to be 0
because r should equal 1 when n, OP, and the PI ratios equal
1, which is the case for the base country. The a3 coefficient
is expected to be negative since its corresponding variable is
the square of a2 That is the square of a negative number is
positive, and ln(n) is negative while ln(n)2 is positive;
hence, r and ln(n)2 are negatively related. The expected
signs of OP and PI as well as the variables themselves are
discussed next.
The reason why OP and PI are included "in“the model is
because Kravis et al. (1978b) were influenced by the
productivity differential model. This model is most clearly
stated by Harrod and Balassa cited by Kravis et al. (1978b).
It states: international trade tends to equalize the prices
of traded goods; given equal prices, wages will be high in
high productivity countries; internal factor mobility will
lead to high wages also in non-traded goods industries in high
productivity countries; because international differences in
productivity are smaller in non-traded goods industries
(largely personal services) than in traded goods industries
(largely commodities), the non-traded goods will be higher in

73
high productivity (high incomes) countries; and lastly, the
high prices of non-traded goods have little if any impact on
the exchange rate and thus make possible a difference between
the overall purchasing power of the currency and the exchange
rate. The influence of this model led the authors to attempt
to account for the differences in countries openness to trade.
The degree to which each country's price level is
influenced by foreign prices is measured by the variable
"openness" (OP). This variable basically measures the
exposure to world markets. OP is calculated by the average
ratio of exports plus imports to GDP for the years 1965 to
1973. The period for which the data are used is completely
arbitrary and taken directly from the World Bank Tables, 1976
(Washington D.C.: International Bank for Reconstruction and
Development, 1976).
The expected sign for a5 is ambiguous. The relationship
between OP and r is negative if the following is correct: the
more open an economy, the higher its prices are for non-traded
goods, making the difference between n and r smaller. The
relationship is not clear if the lack of openness is due to
protective commercial policies which could lead to higher
prices for non-traded goods (Kravis et al. 1978b, p. 223).
PI stands for price isolation. The assumption is that
the influence of external factors on a country's price level
at a particular moment in time can be inferred from how
closely its time to time movements over some preceding period

74
are correlated with time to time movements of "world" prices.
The world price index (implicit deflator) is created by
placing countries whose currencies the International Monetary
Fund (IMF) have defined the value of a unit of Special Drawing
Rights (SDRs) on a common base. These are converted to
dollars by division by an appropriate index of exchange rates.
The world index is then constructed by aggregating the SDR
country indices using weights which reflect the importance
assigned to each currency by the IMF in its initial
calculation of the value of an SDR unit in mid 1974. The
implicit deflator is then adjusted for each individual country
to a common base period and correct exchange rate changes.
The final step is to calculate the price isolation index using
the formula,
1970
(4.2) PI = y (WD, - CD,)2/8,
t= 1963
where WD is the world price index and CD the country price
index, both based on the average over the period 1963 to 1970.
Eight of the ICP countries are included in the set of
countries that the IMF uses in its SDR calculations. Thus PI
can be summarized as the mean squared difference for the years
1963 to 1970 between the country's GDP implicit deflator and
a "world" average GDP implicit deflator.
The sign for a4 is ambiguous like a5, and for similar
reasons. PI and r could be positively related if the

75
following line of reasoning is consistent with what has
actually happened. The reasoning is, the greater the price
isolation, the less a country's non-traded goods prices will
be pulled up to the price levels of the high-income countries;
thus a larger real income (r) is associated with a given
nominal income (n). However, these affects can be negated by
combining different micro and macro economic policies which is
why the sign is ambiguous (Kravis et al. 1978b, p. 223). The
question is empirical and one can only estimate the equation
and see what signs and magnitudes the parameters have.
All of the values for the variables are known for the 16
ICP countries, but r is not known for the other countries.
Hence, the model was run for those 16 countries to obtain the
structural relationships between RGDPC and the other
variables. The resulting signs for this model are a2
positive, a3 negative, a4 positive, and a5 is negative. The
parameter estimates and their respective standard errors can
be found in Kravis et al. (1978b, p. 226). After calculating
r for the non-benchmark countries for 1973, extrapolations
have to be made to other years.
The method of extrapolation is setup to incorporate the
impact on real income through the changes in the terms of
trade. This is done by treating the net foreign balance
component of GDP separately from "domestic absorption." For
domestic absorption (DA), the per capita quantity change
between the benchmark year and the year of extrapolation for

76
each country is estimated by deflating consumption, capital
formation, and government by the implicit deflator for these
sectors. This results in the value of DA in the extrapolation
year being expressed in international dollars of the benchmark
year. The net foreign balance was then valued in benchmark
year international dollars and added to the figure for DA to
obtain GDP per capita in international dollars. Finally, this
sum was compared to the corresponding U.S. total to form the
extrapolation year index for real per capita GDP (Kravis et
al. 1978b, p. 229). The results of this task were estimates
for 1973 and 1974.
4.2 Mark 1
The second paper by Summers et al. (1980) is entitled,
"International Comparisons of Real Product and its
Composition: 1950 to 1977." This study includes 119
countries of which 16 are from the ICP Phase I data set. The
same equation (4.1) is used to calculate r for the ICP
countries and the structural relationships found from those
calculations, are used to calculate r for the non-ICP
countries as before. What is new in this paper is that the
extrapolations for the ICP and non-ICP countries are done
forward and backward through time.
To calculate RGDPJt before and after 1970 is relatively
easy since all of the results are in 1970 dollars (benchmark
year) . R is calculated the same as previously (rjt =

77
RGDPj,/RGDPUS70) for the year 197 0 only. The RGDPj, for the
other years is obtained using the jth country's constant price
series (in domestic currency units) for GDP as indicated in
the equation below,
GDPj t /POPj t
(4.3) RGDPj, = (RGDPj 70) ,
GDPjjo /POPjjo
where GDP is a constant-price value of GDPjt in national
currency and POPjt refers to the population. By using the
constant-price valuation, changes in terms of trade facing the
jth country between the tth year and 1970 are neglected. RGDP
is calculated for all 119 countries from 1950 to 1977 using
these methods.
4.3 Mark 3
The third paper, "Improved International Comparisons of
Real Product and its Composition: 1950 - 1980" written in
1984 by Summers and Heston, is referred to as Mark 3. Mark 2
was not published but it was used by Kravis, Heston, and
Summers (1982). Mark 3 was different from Mark 1 and Kravis
et al. (1978b) because it utilized the data from Phase III.
This data set included 34 countries for the year 1975. This
difference and the fact that there were two benchmark years of
data (i.e., 1970 and 1975) resulted in the authors using a
different method for calculating the RGDPs in Mark 3.

78
The first change from the earlier papers was that a
slightly different functional form for the regression was
used. However, before that is addressed, the data need to be
considered. There are two benchmark years of data to utilize.
The approach used by Summers and Heston in this paper is a
modification of the approach used in Phase III (Extensions
beyond the ICP countries, pp. 332-340). The cross-section
regressions for the two years were run in terms of per capita
DA instead of per capita GDP as done previously. The slightly
different functional form for the regressions was that the
openness variable in the eguation used to summarize the 1970
and 197 5 data was introduced additively compared to an
interaction term. Furthermore, the constant terms in both
years were suppressed since they were not significantly
different from zero. - These modifications simplify the
eguation and make the actual and estimated values for the
numeraire country the same (U.S.). Lastly, the results
obtained from the two benchmark years were combined to get a
single 1975 estimate. Weights were also devised to take into
account the relative precision of the two cross sections.
The regression eguation used to summarize the 1970 and
1975 cross-section relationships is
(4.4) In rj = a, (In nj) + a2 (In n-)2 + a3 (In OPj) + Uj
where

79
rj = (DAj/PPPj*A) /DAUS and nj = (DtyXRj) /DAUS.
pppDA tj^e pUrchasing power parity over domestic absorption,
and XRj the exchange rate. Each is expressed in national
currency units of the jth country per U.S. dollars. OPj is the
measure of relative openness of the jth economy which was
defined as
((ExportSj + ImportSj)/GDPj) / ( (Exportsus
+ Importsus) /GDPUS) ,
an average of the ratio for five years before the cross-
section year. Before further definitions are given it should
be stated that the a's have the same expected signs as they
did in Kravis et al. (1978b).
The XR-75 variable was defined by a weighted geometric
mean of the 1975 exchange rate and the real exchange rates of
1974 and 1976. This was done due to the volatility of the
exchange rates for several countries. The equation for XRj75
is then
(4.5) XR:.75 = (Pj>75/74XRj 74) m (XRj 75) 1_X (Pj,75/76^Rj.76) ^
where PJt/t. measures the change in the relative price levels of
domestic absorption of the jth country and the U.S. between t
and t' . X is a weight for the 1974 to 1976 exchange rates.
No averaging implies X = 0 and equal weighting implies X =
2/3. The weighting question is resolved by running a non-

80
linear least squares regression on the data. For 1975, the
results indicate that X is not significantly different from
zero so XRj75 only depended on XRj75. The year 197 0 was
different in that X was large. Hence, its value was set at
2/3. Thus, XRj70 is just a simple geometric mean of XRj70 and
the price-level adjusted values of XRj69 and XRj_7,.
In Summers and Heston (1980), RGDPJt is based on constant-
prices whereas in Mark 3, international trade was incorporated
into RGDP. The net foreign balance was converted by the
exchange rate on the grounds that, at the margin, this is the
conversion factor for an increment to the net foreign balance.
This is equivalent to setting the international price of a
dollar's worth of net balance to 1. Thus, RGDPj75 = r”75 (DAUS75
+ NFBj75/XRj75) where NFBj75 is the net foreign balance in 1975
for the jth country. R-’75 is defined as t:he geometric mean of
rj from equation 4.4 for the years 1970 and 1975 for all 85
countries.
The extrapolations in Mark 3 were also treated
differently and were calculated at a more disaggregated level.
The tapes of the U.N. constant-price series for consumption,
gross domestic investment, government, and the net foreign
balance were used to get real individual components expressed
in 1975 international dollars for each of the years between
1950 and 1980. Thus, RGDPj was obtained by summing the
components, where the net foreign balance exports and imports
in 1975 were converted to dollars at current exchange rates.

81
The new disaggregate procedure insures that the price weights
used for consumption, investment, and government in each year
in each country reflected 1975 international prices rather
than the individual country's relative prices.
The imprecision of the RGDP estimates varied considerably
from country to country and from year to year. Therefore, the
authors classified a countries' estimates into four quality
classes: A (best), B (better), C (good), and D (fair). The
classifications stemmed from the main source of the
imprecisions in the estimation process. First, imprecisions
were inherent in the ICP benchmark estimates as qualified in
Phase III (Table 3.6). Second, the estimation of the cross-
section regression introduced some error. Third, the authors
did not know what weights to use in averaging the 1970-derived
and 1975 cross-section estimates of r'.
The authors find several general relationships with
respect to the imprecision of their estimates. The ICP
imprecision was inversely correlated with real income; so was
the error term in the cross-section regression. Also Ceteris
paribus, benchmark countries were rated higher than non¬
benchmark countries; higher income countries were rated higher
than lower income countries; and African countries were rated
lower than non-African countries. All of these things should
be taken into account when observing the RGDPs. Later, the
quality grading of the data will become crucial.

82
4.4 Mark 4
The fourth paper by Summers and Heston (1988) was
basically an update to Mark 3. The new issue in this paper
was consistency. Consistency means that the estimates must
obey the national income identity that total product equals
total income generated by the production of the product. The
reason this becomes an issue in Mark 4 was that the
discrepancies between Mark 3 and Phase IV were large for the
1980 RGDP per capita estimates. In addition, the ICP closely
followed a system called the System of Real National Accounts
(SRNA). The basic rule of SRNA was that entries should obey
all temporal identities. The identity that is being violated
when Phase IV and Mark 3 estimates of RGDP for 1980 do not
match is that the value at time period two (t2) equals the
value at time period one (t,) times the growth rate between
the two time periods. To illustrate this point, consider two
countries, A and the U.S. Suppose the 1980 Phase IV RGDP
estimate of Country A is 66% of the U.S.'s 1980 RGDP. How
could this be resolved if the Phase III 1975 relative RGDP
value was 65%, and country A had a 4% growth rate while the
U.S. had a 1% growth rate? This is why consistency has to be
applied.2
2Stone, Champernowne, and Meade (1942) developed a
similar method to make their estimates conform to the national
income accounting identity.

83
The implementation of consistency is done via an errors-
in-variables model. The objective of this model is to adjust
both the benchmark and national accounts data to make them
consistent. To continue with the two country example, this
model would make the Phase IV estimate equal to the Phase III
estimate multiplied by the 1975-1980 growth rate. The
likelihood function for this model is
(4.6) In L(X1,X2,X3,G1,G2/x1,x2,x3,g1,g2; £ ) = K - 1/2 In £
-1/2
3 3
E E X::, (In X: - In X¡) (In Xj - In X¡)
i i j i j
5 5
+ E E X1J (In g¡.3 - In G¡.3) (In g^ - In G^)
4 4
where the X's are true values of a country's output at a
particular level of aggregation (e.g., consumption) expressed
in per capita terms and relative to corresponding values for
the U.S. for the three time points, t,, t2, and t3. The G's
are the true values of the country's growth rates for the same
aggregate as the X's, expressed in the same per capita units
relative to the U.S. for the (t,, t2) and (t2, t3) periods,
respectively. Therefore, the temporal identity requires that
X2 = X, (G,) and X3 = X2 (G2) . The lower-case symbols x,, x2, x3,
g,, and g2 stand for estimated values equivalent to their
corresponding upper-case letters and are obtained from

84
benchmark studies or the national accounts. The errors-in-
variables specification is then
Xj = X¡ (v¡) i = 1, 2, 3
g, = G, (v4) and g2 = G2 (v5) .
The five v's are joint random variables with a multivariate
lognormal distribution n(0,£).
The a priori information about the relative accuracies of
the data sources were introduced through the specification of
the entries in E which is the variance-covariance matrix of
the v's. The information is parameterized in the form of a
five element vector (kw k2, k3, r,, r2) and an assumed pattern
of independence among the v's. The variances among the v's
associated with the g's (growth rate v's) were all assumed to
be the same and equal to 1. The v's associated with the x's
(benchmark v's) were expressed relative to the variances of
the growth rate v's and are called k's. The correlation
between v, and v2 and also between v2 and v3 was given by r,;
the correlation between v, and v3, because of the longer time
interval, was assumed to equal r\', the correlation between the
two growth rate v's was given by r2; and the benchmark and
growth rate v's were assumed to be independent. All of these
assumptions imply that E has the form
E - [ E' ° 1
L o eJ

85
where
*1
r,Vk, k2
r fvOc, k 3
ryk¡ k2
k2
r¿\/k2k3
r^/k, k3
rjVkjkj
k3
and
The X¡jS in equation 4.6 are just the elements in £'*.
This maximum likelihood procedure corrects the data
sources so that they are consistent. The only problem is that
the maximum likelihood asymptotic properties cannot be claimed
for this estimation. The reason is that additional parameters
■ ■ t I i : • • - ■ • • ■
are added as more time points were introduced, an estimation
problem called the incidental parameter problem (Judge et al.
1980, pp. 543-546). However, it is claimed that the maximum
likelihood estimates are of the same variance-minimizing
estimates obtained from averaging all possible unbiased point
estimates.
The data from Phases II, III, and IV and the U.N.
constant-price series are made consistent by following the
errors-in-variable approach. The non-benchmark countries do
not need this. They are just aligned appropriately with the
benchmark country estimates. With the consistent data, the

86
1980 RGDP for the benchmark and non-benchmark countries are
computed similar to the way they are computed for the base
year (1975) in Mark 3.
There are a few differences from Mark 3 other than
consistency in the manner in which the RGDP's were calculated.
Mark 4 drops the openness variable. The exchange rates were
too volatile throughout the late 1970's, and the openness
variable was no longer significantly related to RGDP by 1980
so it was not used in Mark 4. Dummy variables for Africa were
also introduced to allow for divergence. The last adjustment
came with the replacement in the equation of exchange rates
with a combination of price indexes called the international
post-allowance price index. The two indexes that compose the
post-allowance index were the International Civil Service
Commission index and the Employment Conditions Abroad index.
The International Civil Service Commission index is published
in the Monthly Bulletin of Statistics of the United Nations
Statistical Office and uses New York city as a base. The
Employment Conditions Abroad index is an organization based in
London with members including multinational firms,
governments, and non-profit international agencies. This
organization produces a number of binary indexes.
The extrapolations forward and backward were accomplished
by following the procedures used in Mark 3 precisely. The
preciseness of the estimates were also graded A to D using the
same standards developed in Mark 3. This was done for 130

87
countries for the years 1950 to 1985. The estimates for RGDP
still suffer from large errors for low income countries and
African countries.
4.5 Mark 5
The most current paper written updating these data is by
Summers and Heston (1991). Their data for RGDP per capita was
used in this thesis for analysis. Mark 5 covered 139
countries and RGDP per capita was obtained by extrapolating
these cross-section comparisons interspacially to non¬
benchmark countries and then intertemporally to other years.
Mark 5 is arguably the best of the Marks and utilizes ICP
data from 4 benchmark years: 1970, 1975, 1980, and 1985.
Eighty-one countries participated in these benchmark studies
and 47 participated in more than one benchmark study. Thus,
the need for relying on non-benchmark estimating methods was
reduced. The national accounts data have also improved by
using the World Bank's archive data. Most of all, the
methodology for obtaining RGDP per capita for a large number
of countries has improved. Hence, all of these factors make
Mark 5 the most accurate and most recently published
international comparisons data of this type.
The four ICP benchmark studies, Phases II - V, used in
this study were all compiled in different ways and have
different countries participating in different years. This is
why the data have to be made consistent. Consistency, as
discussed in the previous review of Mark 4, is calculated the

88
same way in Mark 5 (using equation 4.6). What needs to be
addressed is the benchmark data itself. The biggest problem
with the benchmark data was that Phase V had not been
published by the time Mark 5 was published.3 Summers and
Heston calculated the RGDPs on their own, using only the raw
data provided by the U.N. and World Bank. The method used by
Summers and Heston to calculate the values in Mark 5 are
discussed next.
There are three main changes to the Phase IV results for
this paper. First, Phase IV introduces the issue of fixity.
It should be clear that the 1980 values mentioned here do not
use the fixity principle. Instead, the Geary-Khamis method is
used for all 60 countries. However, there is an allowance
made for supercountry weighting. Second, the 1980 estimates
that underlay the Mark 4 estimates were recalculated using
national accounts data of May, 1990 which are the latest
current national accounts data for the countries. The U.N. in
some cases used national accounts data that are available for
1982 or 1983. Third, there was a slightly different treatment
of two categories, change in stocks and compensation of
government employees. They also used a slightly different
normalization procedure which only affects the valuation of
the net foreign balance.
Actually Phase V was never published, instead the U.N.
decided to publish regional data (i.e. OECD, EUROSTAT, ECA,
ESCAP, and ECIEL) (see Table 3.7).

89
The countries that participate in the 1985 benchmark
comparisons fall into five groups: 22 OECD countries, 11
Asian countries including Japan, 22 African countries, 5
European Group II countries including Finland and Austria, and
a group of Caribbean countries. The Caribbean countries'
comparisons were not complete at that time. The Geary-Khamis
method was implemented for the OECD and Asian countries. The
African countries, Hungary, Poland, and Yugoslavia all have
data that allow the authors to link them to the OECD and Asian
countries. The total number of countries from Phase V used in
this study is 57. Once again fixity was not imposed on these
results.
A different method was used for those countries that did
not participate in the 1985 benchmark study, but did
participate in a previous benchmark study. The procedure was
to value their 1975 or 1980 benchmark estimates of C, I, and
G at 1985 international prices. The growth rates for their
components from the national accounts data and their change in
international prices of the components between 1975 and 1985
or 1980 and 1985 were used. The changes in international
prices were estimated from the benchmark estimates and the
deflator for the numeraire country, the U.S.
The 1975 and 1970 data were also re-analyzed. The May
1990 national accounts data were used to revise those years.
The Geary-Khamis method was then implemented to aggregate the
data.

90
After the benchmark data were aggregated, re-estimated,
and made consistent, the non-benchmark countries RGDP per
capitas were estimated. The same equation used in Mark 4 was
also used in Mark 5 with some minor changes. The left hand
side variable was r* which was per capita domestic currency DA
converted to international dollars expressed relative to the
U. S. Mark 4 used a post adjustment index to estimate the
real domestic absorption of each country. This estimate was
obtained by dividing the national currency DA by the PPP
implicit in the post adjustment index.
The post allowance index was made up of two indexes for
Mark 4 and three for Mark 5. The International Civil Service
Commission index (variable r^j and the Employment Conditions
Abroad index (variable rECAJ) was used as post adjustment
indexes in Mark 4. Mark 5 used both of those indexes and
another index produced by the U.S. State Department. The U.S.
State Department provides housing or a separate housing
allowance indexes (variable russj) . This was an area in which
the data were less reliable (including the ICP data). Hence,
the added information from this index was used. All of the
post allowance indexes were designed to supplement salaries in
a way that equalize real incomes of high-ranking civil
servants and business executives assigned to different foreign
countries. Each of these indexes have shortcomings. The most
notable was that all of the countries were not included in any
of these indexes. A structural relationship, however, was

91
found in the benchmark countries between PPP and its post
allowance PPP. This structural relationship was exploited to
estimate the non-benchmark countries missing PPPs from their
post allowance PPPs.
There were 81 benchmark countries and 57 non-benchmark
countries that have to be estimated. The authors estimate 12
different regressions for the non-benchmark countries. The
expected sign of the parameters are given in the equation.
The equations are
(4.7)
In
•
=
-
“i
+
“2
In r^
(4.8)
In
•
rj
=
-
“i
+
0-2
In rECAJ
(4.9)
In
•
rj
=
“i
+
a2
In
rUSSj
(4.10)
In
•
=
-
+
°2
In r^
+
a3 rECAj
(4.11)
In
•
rj
=
a.
+
a2
In
rUNj
+
“3
russj
(4.12)
In
•
=
a,
+
a2
In
russ,j
+
a-3
rECA j
(4.13)
In
•
=
a,
+
a2
In
rUN,j
+
“3
AD
(4.14)
In
•
rj
=
a.
+
a2
In
r ECA j
+
“3
AD
(4.15)
In
*
rj
=
a.
+
a2
In
rUSSj
+
a3
AD
(4.16)
In
•
rj
=
ai
+
a2
In
r UN j
+
a3
rECA,j “
a4
AD
(4.17)
In
•
rj
=
ai
+
tt2
In
rUN j
+
“3
russj
“4
AD
(4.18)
In
•
rJ
=
a.
+
a2
In
russ,j
+
a3
rECAj
«4
AD.
The AD variable represents a dummy variable for Africa. If
the non-benchmark country have all of the post adjustment
indexes, equation (4.12) and (4.18) were used. If only two
indexes were available for the countries, one of the equations

92
from (4.10) - (4.12) or (4.16) - (4.18) was used, and if only
one index was available, equations (4.7) - (4.9) or (4.13) -
(4.15) were used. Thus, there were two alternative estimates
of DA for non-benchmark countries for 1985, and the results
have to be merged.
The first equations to be estimated from equations (4.12)
- (4.18) were those that showed a significant relationship
between their squared residuals (SR) and the level of per
capita domestic absorption relative to the U.S. (rj) . That
is, the squared residuals from equations (4.12) - (4.18) were
estimated first if they were found to be related to the
dependent variable in equations (4.12) - (4.18). The
calibrated equations used to estimate the SR value for each
non-benchmark country are
(4.19) SR85j = .076 (.012) - .108 rj (.033): n = 77
(4.20) SR80j = .036 (.008) - .029 rj (.019): n = 66.
The reciprocal of each SR estimate was used to weight the two
estimated rj for the non-benchmark countries. The resulting
average domestic absorption relative to the U.S. was then the
base for all 1985 estimates.
The final step was to merge the non-benchmark with the
benchmark data. A Geary-Khamis aggregation was performed,
producing consistent national absorption for all of the
countries. This procedure was different to that used in Marks
3 and 4. The benchmark values were not necessarily preserved
for the benchmark countries in the base year for Mark 5.

93
Grades were also given in Mark 5; this will be covered in
Section 5.1. It is still apparent that estimates of RGDP for
poor and African countries were less accurate than estimates
for rich countries.
4.6 The Centrally Planned Economies
Some background information is needed on the centrally
planned economies before the reasons why they were dropped
from this thesis were given. Hungary is the first centrally
planned economy (CPE) to participate in the ICP benchmark
studies (1970). No CPEs were added to the 1975 benchmark
study. The three that were added in 1980 are Poland, Romania,
and Yugoslavia. None were added in 1985, but one was deleted,
Romania. Romania is deleted because its results could not be
extrapolated due to the lack of necessary national time-series
* I - . • . ' . ' ' . I ‘ '.! • • . • _
data.
CPE's were not included in the Marks until Mark 3. In
that paper nine CPE's were added: Hungary, Poland, Romania,
Yugoslavia, China, Soviet Union, Bulgaria, Czechoslovakia, and
the Democratic Republic of Germany. The estimates of the
first four were based on the ICP. The rest were based on
various data sources. The same nine CPEs were estimated in
Mark 4.
Mark 5 is different. Only four of the CPEs have full
representation: China, Hungary, Poland, and Yugoslavia. Each
of these countries have data over time. The estimates for
these four countries were carried out the same way as the

94
market economies. The other 5 countries included in Marks 3
and 4 were dropped from Mark 5 for two main reasons. They did
not have data over time, and there was a consensus among CPE
specialists that both the levels and growth rates in those
economies were overstated.
China also has a problem, which necessitated treating it
different from the other CPEs included in Mark 5. The
published growth rates for China are high (the World Bank
accepts a per capita figure of 5.4% from 1965 to 1988 (World
Development Report 1990, p. 187) implying a doubling every 13
years. This was what Summers and Heston 1991 (Appendix B, p.
20) have to say about China's growth rate.
When Kravis initially published an estimate of China as
12.3% of the U.S. in 1975 (India was 6.6%), it was
criticized as too high but the critics did not offer
reasons to change it. However, that figure coupled with
- China's growth rate would have put China well over 20% of
the U.S. in 1988, which most observers do believe is too
high.
Our conjecture is that Chinese growth rates are too
high because they are heavily based on growth in physical
output figures rather than deflated expenditure series.
...we have extrapolated the Kravis PPPs forward to 1985
and used that as the basis for making China's estimates
for that year because we feel this more closely
approximates a correct deflation procedure...This
procedure puts China at about 13% of the U.S. in 1988,
and almost 3 times the level of India. This differential
with India may be high because the benchmark estimate for
India in 1985 was unusually low (its consumption per
capita was less than Bangladesh!) compared to earlier
benchmarks, so that our best guess is that China would be
somewhat over twice India rather than three times India.
Again, the user is warned...
Given the aforementioned problems with China, it was dropped
from this thesis. The opinion that the remaining three CPEs,
Hungary, Poland, and Yugoslavia, may have similar problems

95
resulted in them being dropped from this thesis. The RGDP
data for the CPEs calculated by Summers and Heston (1991) were
not used in this thesis.

CHAPTER 5
INEQUALITY IN THE G-7 AND OECD
5.1 Inequality Measures
There are basically two types of inequality indices;
graphical (histogram, Pen's Parade, and the Lorenz Curve), and
measures (variance, coefficient of variation, gini
coefficient, and Theil's entropy index). These measures
analyze the dispersion between individuals or groups. From
these measures, researchers can determine if the two groups
are becoming closer (convergence) or further apart
(divergence). These measures are typically used to determine
the inequality in income, as several studies in the
Convergence chapter reviewed. However, the initial use of
these measures was on domestic issues. The graphical
inequalities and inequality measures are discussed followed by
the necessary properties of an inequality index. Then the
inequality index that was chosen for this study is discussed.
5.1.1 Graphical Inequality
A common graphical inequality index is the histogram. A
histogram shows the number of people with income in a
particular range (Osberg, 1991). The first step with this
technique is to determine the number of intervals in the
96

97
range, then create a frequency table showing how many people
fall into each range (class frequency). After the intervals
have been decided two more steps are needed to construct a
frequency histogram. Next a graph with the class intervals on
the X axis and the frequencies on the Y axis is produced.
Lastly, a rectangle over each class interval with a height
equal to the number of measurements falling in a given
subinterval is drawn (Ott, 1984). There are several
variations of the histogram (relative, log, and Pen's Parade),
but they are all based on the same steps outlined above.
The other graphical index is the Lorenz Curve (LC). The
Lorenz Curve basically plots the cumulative population share
on the X axis against the cumulative income share on the Y
axis (Osberg, 1991). If one person had all of the income then
the -curve would actually be represented by the axis. If
everyone had the same income, then the curve would be a
diagonal line (the X and Y axis range is from 0 to 1). This
graphical representation of inequality can be transformed to
be a measure. The measures are discussed next.
5.1.2 Inequality Indices
There are several inequality measures. The most commonly
used in statistics of dispersion within a distribution is
variance (V). The equation for variance is
n
V = (1/n) £ (Yi - y.)2
i=l
(5.1)

98
where y¡ is a vector of n income values with a mean n. The
square root of V is the standard deviation which is also used
as an inequality measure. Another variant of V is to divide
the standard deviation by /¿. This is referred to as the
coefficient of variation (Osberg, 1991).
A commonly used inequality statistic is the Gini
coefficient (G) which is based on the Lorenz Curve. The
formula for G is
n n
(5.2) G = [l/(2n2M) ] 2 Z | y¡ - Yj |
i=l i=j
where | . | represents the absolute value of the difference
between all pairs of income (Osberg, 1991). In graphical
terms, this inequality statistic measures the ratio of the
area between the diagonal and the Lorenz Curve to the total
area below the diagonal.
The last index discussed here is Theil's entropy index
(T) also referred to as Theil's inequality index.1 Theil's
index is based on an information measure developed by Shannon
(1949). Shannon cited by Moss and Mulkey (1993), wanted to
determine how much information content exists in a given
signal. Theil further developed this idea to measure the
change in the posterior distribution associated with a given
‘There are several derivatives of Theil's inequality
index. These indices are referred to as the entropy family of
indices and have similar properties to Theil's index. Another
family of indices with similar properties to Theil's is the
Atkinson's family of indices (Osberg, 1991).

99
signal (Theil, 1967). In terms of income inequality, the
approach is to determine whether the information regarding a
country can be used to predict the level of income.
Theil's income inequality measures inequality by taking
the logarithm of the ratio of the arithmetic mean income to
geometric mean income (Theil 1989b, and 1979).2 When this
measure is applied to n countries, it can be written as
n
(5.3) J = E p¡ log(Pi/yj) ,
i=l
where Pi is the population share of country i and y¡ is its
income share (the shares of i is the total n population and in
total n income, respectively).
The advantage of using J is its convenient additive
decomposition. For example, let R,,...,Rg represent regions so
that each country is in only one region. Let Pg and Yg be the
population and income shares of region R^P^E^ and Yg=Eiyi,
where the summations are over iGRg (g=l,...,G). Then the
extension of equation (5.3) to regions is
G
(5.4) JR = E Pg log (Pg/Yg) ,
g=l
which measures the inequality between the two regions, while
2A11 logarithms in this paper are natural logarithms.

100
(5.5) Jg = Síér. (Pi/Pg) l°g[ (Pi/Pg) / (Yi/^g) ]
measures the inequality among the countries of region . It
is then easily verified that
n
(5.6) J = JR+ J’ where J* = S PgJgf
g=i
which is an additive decomposition expressing total inequality
J among the n countries as the sum of regional inequality JR
and the average within-region inequality J*. This average is
a weighted average with weights proportional to the
populations.
5.1.3 Properties of an Inequality Index
The determination of which inequality index to use is
dependent on the objective of the study as well as the
properties of the index. The objective of this study is to
calculate a consistent statistic for inequality over time.
Given the objective, the graphical representations are
eliminated. The statistical measures need to meet certain
criteria to be considered consistent estimators.
There are four properties an inequality measure should
satisfy. These properties are: symmetry, mean independence,
population homogeneity, and the Pigou-Dalton condition.
Symmetry is also referred to as anonymity which means that the
social aspects of the country are irrelevant in calculating
the inequality measure. Both mean independence and income-

101
homogeneous of degree zero state that if all incomes are
multiplied by the same scalar the ineguality measure should be
invariant. Population homogeneity requires that the
inequality measure be invariant to replications of the sample
distribution. More precisely, given two identical populations
X, and X2 with identical income distributions, the inequality
measure would be the same for X, and X2 as well as when the X's
are merged. An inequality measure satisfies the Pigou-Dalton
condition, also known as the principle of transfer condition,
if the level of inequality decreases when income is
transferred from a rich country to a poor country
(Bourguignon, 1979; Osberg, 1991).
The inequality index that is used to analyze convergence
in this dissertation is Theil's income inequality index.
There aire three main reasons for this choice. First, Theil's
index meets all four criteria for an inequality index
(symmetry, mean-independence, population homogeneity, and the
Pigou-Dalton condition). Second, this index yields a
statistic (not a graphical representation). Thirdly, this
index, or some derivative thereof, is the only additively
decomposable inequality index (equation (5.6))(Osberg, 1991).
Bourguignon (1979) defines additive decomposability as a
measure that the total inequality of a population, can be
broken down into a weighted average of the inequality existing
within subgroups of the population, and the inequality
existing between them.

102
Theil's Inequality index is the optimal inequality index
for this study. This index meets all four properties and
produces a consistent statistic. The decomposability of the
index was used to determine the drivinq forces behind the
changes in inequality.
5.2 Income Inequality in the G-7
In this section Theil's inequality index is applied to
the Summers and Heston 1991 data. Summers and Heston data
were used for an analysis of income changes in the G-7
countries (USA, Canada, Japan, UK, W. Germany, France and
Italy) (Gao et al. 1992). Theil (1989b) did a similar
analysis of inequality on a much larger group of countries,
based on earlier data from Summers and Heston. This
dissertation focuses on the G-7 because of their increased
importance in recent years and the fact that the data for
these countries are relatively accurate. For simplicity the
word "income" is substituted for real gross domestic product
per capita. Hence, when income inequality is referred to, it
represents the inequality of real gross domestic product per
capita.
Column 2 of Table 5.1 shows per capita income of the
combined G-7 from 1950-1988. Income per capita is obtained by
weighting the per capita incomes of the seven countries in
each year proportionally to their populations. Note that the
G-7 per capita income increased almost threefold during the
38-year period.

103
Table 5.1
Income per Capita and Income Inequality (G-7 Countries)
Per Capita
Income
Income Inequality
Year
(1)
North
All G-7 America
(2) (3)
Other
Five
(4)
All G-7
(5)
Regional
(6)
Average
Within
Region
(7)
(6) as a
percentage
of (5)
(8)
North
America
(9)
Other
Five
(10)
1950
5019
8520
2889
0.2182
0.1432
0.0750
0.6562
0.0018
0.1195
1951
5258
8820
3069
0.2023
0.1366
0.0658
0.6752
0.0023
0.1048
1952
5400
8964
3188
0.1888
0.1310
0.0578
0.6938
0.0018
0.0925
1953
5586
9164
3346
0.1811
0.1246
0.0565
0.6880
0.0020
0.0906
1954
5617
8976
3496
0.1660
0.1092
0.0567
0.6578
0.0024
0.0911
1955
5972
9497
3725
0.1628
0.1076
0.0552
0.6609
0.0025
0.0887
1956
6105
9573
3873
0.1520
0.1007
0.0513
0.6625
0.0017
0.0831
1957
6201
9552
4025
0.1396
0.0919
0.0477
0.6583
0.0018
0.0775
1958
6165
9297
4113
0.1260
0.0819
0.0441
0.6500
0.0016
0.0719
1959
6468
9694
4337
0.1209
0.0797
0.0412
0.6592
0.0022
0.0670
1960
6706
9782
4656
0.1036
0.0679
0.0356
0.6554
0.0024
0.0577
1961
6898
9826
4932
0.0867
0.0586
0.0281
0.6758
0.0026
0.0452
1962
7167
10210
5114
0.0840
0.0590
0.0250
0.7023
0.0024
0.0403
1963
7429
10491
5353
0.0767
0.0559
0.0209
0.7288
0.0022
0.0335
1964
7802
10923
5673
0.0705
0.0530
0.0176
0.7517
0.0021
0.0281
1965
8116
11447
5836
0.0735
0.0560
0.0174
0.7619
0.0021
0.0279
1966
8481
11954
6094
0.0695
0.0561
0.0134
0.8071
0.0021
0.0212
1967
8726
12143
6366
0.0608
0.0515
0.0093
0.8470
0.0021
0.0143
1968
9156
12557
6792
0.0534
0.0467
0.0068
0.8745
0.0021
0.0100
1969
9510
12816
7215
0.0461
0.0408
0.0053
0.8850
0.0017
0.0078
1970
9705
12710
7611
0.0367 •
0.0324
0.0043
0.8828
0.0015
0.0062-
1971
9914
12974
7777
0.0364
0.0323
0.0040
0.8873
0.0011
0.0061
1972
10290
13393
8118
0.0348
0.0309
0.0038
0.8879
0.0019
0.0052
1973
10820
13943
8627
0.0315
0.0284
0.0030
0.9015
0.0017
0.0039
1974
10720
13698
8627
0.0296
0.0264
0.0032
0.8918
0.0016
0.0044
1975
10540
13385
8532
0.0276
0.0250
0.0026
0.9057
0.0006
0.0040
1976
11047
14009
8941
0.0275
0.0249
0.0026
0.9054
0.0007
0.0039
1977
11461
14572
9236
0.0278
0.0257
0.0021
0.9244
0.0003
0.0034
1978
11900
15131
9573
0.0280
0.0259
0.0021
0.9250
0.0007
0.0031
1979
12231
15357
9964
0.0249
0.0231
0.0017
0.9277
0.0007
0.0025
1980
12277
15162
10171
0.0211
0.0197
0.0013
0.9336
0.0005
0.0020
1981
12434
15382
10267
0.0214
0.0202
0.0012
0.9439
0.0003
0.0018
1982
12262
14829
10362
0.0169
0.0159
0.0010
0.9408
0.0004
0.0014
1983
12584
15346
10526
0.0183
0.0176
0.0007
0.9617
0.0002
0.0010
1984
13164
16303
10811
0.0216
0.0209
0.0007
0.9675
0.0005
0.0008
1985
13399
16609
10976
0.0219
0.0213
0.0006
0.9726
0.0005
0.0006
1986
13833
17118
11339
0.0215
0.0211
0.0004
0.9813
0.0003
0.0005
1987
14232
17587
11670
0.0212
0.0209
0.0003
0.9858
0.0003
0.0002
1988
14759
18140
12161
0.0203
0.0199
0.0004
0.9802
0.0006
0.0002

104
This increase is in sharp contrast to the behavior of the
inequality of the seven per capita incomes. The inequality
measure has a lower bound of 0 but no upper bound. Zero
represents the case where there exists no inequality. In
column 5, inequality is measured using equation (5.3). The
results in column 5 indicate that inequality declined
drastically: from almost 0.22 in 1950 to about 0.02 in 1988,
or more than 90 percent. Thus the G-7 countries became much
more affluent on the average, and also much more "equal." How
did this happen? First of all, Canada and the U.S. had the
highest per capita incomes among the G-7 in each year. The
second reason is illustrated by grouping the seven countries
into two regions, R, is North America (USA and Canada), and R2
is the Other 5. Columns 3 and 4 contain their per capita
incomes. In 1950, R2 was approximately one-third of R¡;
However, by 1988 R2 rose to be almost two-thirds of R,. Thus,
the Other 5 succeeded in substantially narrowing the gap
between themselves and North America.
The last five columns of Table (5.1) provide an analogous
extension of the inequality analysis. Columns 6 and 7 show
that both the regional inequality JR and the average within-
region inequality j’ declined drastically. Initially, in
1950, total inequality J was almost 0.22 and about two-thirds
of this was regional (see column 8) . Ten years later, in
1960, total inequality was reduced by more than 50 percent and
the regional share of this was still about two-thirds.

105
Another 10 years later, in 1970, total inequality was reduced
even more (by almost two-thirds), and the regional component
increased to almost 90 percent. Then, in 1980, total
inequality declined further to about 0.02, after which it
ceased to decline, but the regional component increased
further until about 98 percent in the late 1980's.
Columns 9 and 10 contain the within-region inequalities
Jg for North America (g=l) and the Other 5 (g=2). The North
American figures are small and slightly irregular, implying
that the U. S.-Canadian differences in per capita income are
small and uninteresting. The decline of the inequality among
the Other 5 was from 0.12 in 1950 to 0.0002 in 1988. This
reflects the increase of Japan's affluence toward Western
European levels.
The results for the G-7 countries clearly indicate that
these countries were converging over the time period of 1950
to 1988. Japan's rapid growth in income was one of the
biggest influences in the decrease in inequality between the
G-7 nations. Germany and Italy also grew at a faster rate
than the other countries. Thus, they helped influence the
convergence of the G-7 also. The next section analysis some
of the factors that are expected to have influenced the
convergence of the G-7 countries.

106
5.3 Variables of Interest
The prior section determined that the G-7 countries have
converged over the period between 1950 to 1988. This section
uses the same inequality index (Theil's) to determine if the
inequality in some other variables have also converged. Three
of the variables that have been associated with the inequality
of income, or growth are examined (see Chapter 2). The
criterion for choosing these time-series, in addition to the
hypothesized relationships, was that the data series needed to
extend back to 1950. These two restrictions narrowed the
variables down to: total government expenditure (G) , total
investment (I), and the number of people employed in industry
(E) (see Appendix E concerning other variables that would
enhance this study).
The data used in this dissertation are from two sources.
The financial indicators came from the Summers and Heston
(1991) data set (income, G, and I). The total population in
each country also came from Summers and Heston (1991) data
set. Summers and Heston defined government expenditure as
public consumption and investment expenditure as private and
public expenditure. The number of people employed in industry
came from the OECD (1963, 1969, 1989, 1991a, and 1991b).
The government and investment data in Summers and Heston
data series were measured in terms of a ratio. Their
variables were transformed from real government expenditure as
a percent of income and real investment expenditure as a

107
percent of real income to total government expenditure and
total investment expenditure. These variables were analyzed
here with Theil's inequality index.
In the case of the number of people employed in industry,
several countries did not have a complete data series. When
considering the G-7 countries, only Japan and Italy had
incomplete series. The method of extrapolation to fill in the
missing observations is presented in Appendix F.
The results from applying Theil's inequality index on
government and investment expenditure, and the number of
people employed in industry are shown in Table (5.2). This
table is arranged such that the total, regional, and within
inequalities are presented for each variable. The average
within inequality is not shown here; however, J - JR is equal
to the- average within inequality as illustrated in equation
(5.6).
5.3.1 Inequality in Government Expenditure
The total inequalities of G, I, and E in Table 5.2
(columns 1, 5, and 9) appear to decline over time, similar to
income inequality. Specifically the inequality in government
expenditure decreased from .14 in 1950 to .05 in 1988, which
is a 65% decrease. The 1950 value is much lower than the
other values in the 1950's. In fact, the inequality in
government expenditure only attains the 1950 value of 0.1374
in 1963, 13 years later. Therefore, consider the 1951 value,
the inequality then declines by 78% compared to 65%.
Either

Table 5.2
Government, Investment, and the Number of People Employed in
Industry Inequalities (G-7 Countries)
Government Inequality Investment Inequality Industrial Employment Inequality
Year
J
(1)
Jr
(2)
N. Am.
J0
(3)
Other 5
(4)
J
(5)
Jr
(6)
N. Am.
Ju
(7)
Other 5
(8)
J
(9)
Jr
(10)
N. Am.
J,
(11)
Other 5
J.
(12)
1950
0.1374
0.0633
0.0100
0.1130
0.2579
0.1602
0.0001
0.1571
0.0246
0.0002
0.0000
0.0392
1951
0.2152
0.1261
0.0142
0.1351
0.1675
0.1140
0.0000
0.0865
0.0297
0.0009
0.0002
0.0464
1952
0.2254
0.1412
0.0149
0.1272
0.1690
0.0981
0.0008
0.1144
0.0270
0.0012
0.0004
0.0415
1953
0.2333
0.1463
0.0166
0.1311
0.1736
0.0941
0.0011
0.1287
0.0281
0.0011
0.0005
0.0436
1954
0.2009
0.1200
0.0151
0.1225
0.1452
0.0640
0.0000
0.1324
0.0318
0.0042
0.0004
0.0447
1955
0.1893
0.1121
0.0135
0.1177
0.1561
0.0678
0.0000
0.1446
0.0329
0.0045
0.0004
0.0463
1956
0.1849
0.1062
0.0134
0.1207
0.1298
0.0545
0.0022
0.1223
0.0285
0.0053
0.0002
0.0380
1957
0.1900
0.1105
0.0163
0.1205
0.0918
0.0334
0.0027
0.0946
0.0276
0.0080
0.0001
0.0322
1958
0.1799
0.1081
0.0159
0.1084
0.0919
0.0246
0.0016
0.1104
0.0305
0.0132
0.0000
0.0286
1959
0.1685
0.0981
0.0173
0.1054
0.0875
0.0274
0.0004
0.0994
0.0278
0.0116
0.0002
0.0268
1960
0.1568
0.0888
0.0169
0.1021
0.0553
0.0096
0.0002
0.0760
0.0301
0.0145
0.0004
0.0257
1961
0.1527
0.0890
0.0142
0.0969
0.0291
0.0029
0.0000
0.0438
0.0332
0.0198
0.0003
0.0222
1962
0.1474
0.0873
0.0147
0.0908
0.0387
O.0O62
0.0000
0.0544
0.0308
0.0197
0.0002
0.0186
1963
0.1352
0.0810
0.0140
0.0816
0.0302
0.0062
0.0000
0.0403
0.0302
0.0202
0.0002
0.0166
1964
0.1297
0.0790
0.0143
0.0755
0.0200
0.0036
0.0001
0.0276
0.0215
0.0127
0.0004
0.0145
1965
0.1240
0.0761
0.0137
0.0713
0.0301
0.0101
0.0001
0.0336
0.0204
0.0109
0.0004
0.0158
1966
0.1328
0.0873
0.0144
0.0668
0.0247
0.0105
0.0003
0.0237
0.0177
0.0087
0.0004
0.0150
1967
0.1386
0.0929
0.0150
0.0668
0.0093
0.0045
0.0000
0.0080
0.0145
0.0082
0.0007
0.0102
1968
0.1342
0.0929
0.0136
0.0605
0.0060
0.0015
0.0000
0.0077
0.0147
0.0087
0.0008
0.0095
1969
0.1274
0.0882
0.0127
0.0576
0.0075
0.0002
0.0002
0.0123
0.0144
0.0084
0.0008
0.0095
1970
0.1149
0.0791
0.0085
0.0548
0.0115
0.0026
0.0001
0.0150
0.0164
0.0109
0.0008
0.0087
1971
0.1026
0.0682
0.0066
0.0538
0.0096
0.0003
0.0001
0.0158
0.0184
0.0136
0.0004
0.0079
1972
0.0952
0.0610
0.0060
0.0540
0.0116
0.0000
0.0000
0.0198
0.0159
0.0113
0.0004
0.0076
1973
0.0854
0.0520
0.0042
0.0538
0.0077
0.0000
0.0000
0.0131
0.0142
0.0093
0.0003
0.0081
1974
0.0833
0.0493
0.0034
0.0554
0.0092
0.0000
0.0010
0.0149
0.0132
0.0093
0.0001
0.0066
1975
0.0783
0.0438
0.0024
0.0571
0.0131
0.0007
0.0063
0.0168
0.0150
0.0121
0.0000
0.0051
1976
0.0697
0.0373
0.0019
0.0540
0.0080
0.0000
0.0029
0.0117
0.0110
0.0082
0.0000
0.0048
1977
0.0643
0.0350
0.0013
0.0493
0.0087
0.0012
0.0009
0.0123
0.0095
0.0068
0.0002
0.0045
1978
0.0597
0.0312
0.0012
0.0481
0.0107
0.0030
0.0001
0.0132
0.0075
0.0044
0.0004
0.0049
1979
0.0540
0.0267
0.0012
0.0462
0.0102
0.0012
0.0013
0.0146
0.0066
0.0033
0.0003
0.0054
1980
0.0507
0.0243
0.0010
0.0451
0.0159
0.0000
0.0035
0.0248
0.0074
0.0044
0.0001
0.0051
1981
0.0463
0.0222
0.0008
0.0412
0.0215
0.0017
0.0045
0.0311
0.0073
0.0042
0.0000
0.0055
1982
0.0456
0.0223
0.0006
0.0400
0.0152
0.0009
0.0030
0.0228
0.0103
0.0070
0.0002
0.0056
1983
0.0432
0.0211
0.0005
0.0381
0.0091
0.0002
0.0021
0.0139
0.0107
0.0066
0.0003
0.0070
1984
0.0441
0.0230
0.0008
0.0364
0.0141
0.0076
0.0001
0.0113
0.0091
0.0037
0.0005
0.0091
1985
0.0500
0.0292
0.0013
0.0356
0.0122
0.0051
0.0010
0.0118
0.0100
0.0036
0.0004
0.0120
1986
0.0483
0.0297
0.0016
0.0316
0.0117
0.0037
0.0019
0.0126
0.0101
0.0031
0.0003
0.0122
1987
0.0508
0.0305
0.0019
0.0344
0.0113
0.0032
0.0025
0.0122
0.0099
0.0027
0.0002
0.0126
1988
0.0480
0.0282
0.0015
0.0338
0.0105
0.0016
0.0037
0.0128
0.0114
0.0031
0.0001
0.0146
108

109
way, it is clear that the inequality in the level of
government expenditure has declined over time. This suggests
that the G-7 countries have been converging in their
expenditure on public consumption. The question is, "why?"
The decomposability of Theil's index gives some insights
on why the G-7 are converging in terms of government
expenditure. Column 2 shows the government regional
inequality declines 56% from 1950 and 78% from 1951 to 1980
which is similar to the movements in total government
inequality (i.e. the percentage decline). The inequality
between the two regions has decreased significantly. The
question is, How much of the regional inequality decline
accounts for the reduction in total inequality? This question
can be answered by dividing column 2 by column 1 (not shown).
The result of this is that regional government inequality
accounts for an average of 50% to 55% of the total government
inequality. The amount of total inequality accounted for by
regional inequality is fairly constant over time.
Given those results, the within inequality values are
analyzed to find the driving force behind the decline in
government inequality. Column 3 contains the North American
within inequality and column 4 contains the Other 5. The
inequality between Canada and the U.S. has decreased 86% since
1950. The reason for this large decrease is due to Canada's
increase in government expenditure per capita. In the 1950's
and 60's, Canada's expenditure was only half of the U.S.'s.

110
The 1980's showed an increase to about 82% of the U.S.'s
government expenditure per capita. Stated another way,
between 1950 and 1988, Canada increased its expenditures three
times while the U.S.'s only increased 1.5 times.
The Other 5 countries only reduced their within
inequality by 30% from 1950 to 1988. The U.K. had the largest
initial level of expenditure in this group: 3.6 times larger
than Japan, 2.6 times larger than Italy, 2.1 times larger than
W. Germany, and 1.4 times larger than France. Over time this
situation changed considerably with W. Germany and France
having approximately the same per capita expenditure as the
U.K.; Japan and Italy still lagged behind but closed the gap
some. In 1988, Japan spent 1.9 times less, and Italy spent
1.2 less than the U.K. in terms of government expenditure per
capita. However, the rate of increase for Japan (3.3 times
their initial value) was similar to W. Germany (3.4), France
(2.3), and Italy (3.6). In contrast, the U.K.'s rate of
increase was only 1.7 times its initial value for 1950.3
Therefore, the convergence in terms of government expenditure
appears to be due to the slow rate of increase in the U.S. and
the U.K. and the fast rate of increase in government
expenditure in the other countries.
3The growth rates for the U.S. and Canada during this
time period were 1.9 and 2.8, respectively.

Ill
5.3.2 Inequality in Investment Expenditure
The decrease in the total inequality in investment is
similar to the situation with income inequality. Column 5 of
Table 5.2 shows that total investment inequality decreased by
96% from 1950 to 1988. Once again if the 1951 value is used,
the reduction is still extremely high, 94%. Column 6 shows
that regional inequality also decreased dramatically, 99%.
The interesting fact about the drastic decrease in both
the total and regional inequalities is that the majority of
the reduction in total inequality is due to the average within
inequality. The average within inequality accounts for the
following percentage of the decrease in total investment
inequality by decade: 64% in the 1950's, 76% in the 1960's,
91% in the 1970's, and 78% in the 1980's. The relatively
dramatic rate of r convergence ^ is " largely due ’ to - within
inequality.
The North American within inequality, however, is close
to being nonexistent (Table 5.2, Column 7). Therefore, the
reduction in inequality must be due to the within inequality
in the Other 5 (Table 5.2, column 8). The Other 5 within
inequality reduced 92% from 1950 to 1988, and 85% from 1951 to
1988. To determine which countries are responsible for this
decrease, consider Table 5.3. This table illustrates each
countries initial (1950) and final (1988) per capita
investment expenditure and the rate of increase in investment,

112
the latter is defined as dividing the final expenditure by the
initial expenditure.
Table 5.3.
Investment Expenditure per Capita, and the Rate of
Investment Expenditure for the G-7
G-7 Countries
Year
Canada
U.S.
Japan
U.K.
W. Germany
France
Italy
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
1950
1562
1640
185
516
845
752
569
1988
4661
3513
3878
2465
3094
3050
2921
Rate of Investment
Expenditure
3 2 21 4.8 4 3.7 5
The initial value for Japan is clearly significantly low
in comparison to the other G-7 countries. However, their
increase in the rate of expenditure on investment per capita
(21 times initial value) has boosted them to being one of the
top countries in terms of investment expenditure per capita.
Hence, Japan's increase in investment expenditure is part of
the reason for the large decrease in the total inequality of
investment expenditure. The relatively fast rate of increase
in investment expenditure in Italy and the U.K. is partly
responsible for the reduction in the Other 5. In terms of the
G-7, the relatively slow rate of increase of investment in the

113
U.S. and Canada allowed the other countries, all of which
increased their expenditure at a faster rate, to catch up.
5.3.3 Inequality in Industrial Employment
The total inequality in industrial employment is
different than the other three inequalities. The total
inequality in industrial employment has always been below 0.04
for the sample period which is small in comparison to the
other three inequalities.4 The total inequality in industrial
employment shown in column 9 of Table 5.2 decreased 54% from
1950 to 1988. If the 1951 value is taken, the decline in
inequality is larger, 62%.
Regional inequality for industrial employment in column
10 is also different from the other three inequality results.
The regional inequality actually increases 94% from 1950 to
1988 and 71% for 1951 to 1988. The total industrial
employment inequality is decreasing while the regional
industrial employment inequality is increasing. To figure out
what is occurring, consider the percent of total inequality
due to regional inequality. In the 1950's regional inequality
accounted for 18% of total inequality, 57% in the 1960's, 68%
in the 1970's, and 46% in the 1980's. Hence, regional
inequality became more important until the 1970's, then having
an effect equal to that of the average within inequality by
the 1980's.
4The industrial employment data for countries that have
incomplete data for the number of people employed in industry
were extrapolated as explained in Appendix E.

114
The within inequalities are straight forward. The North
American (column 11) within inequality is basically non¬
existent. The Other 5 inequality is small, but its inequality
is the largest out of all of the inequalities for industry.
The inequality for the Other 5 decreased by 63% from 1950-88
and 68% from 1951-88. It is apparent that the regional
inequality and the average within inequality are going in
opposite directions. Given that the two (regional and average
within) have basically an equal effect on total inequality,
total inequality declines largely because of the reduction in
the average within region inequality. In addition, after 1975
regional inequality starts to decline.
In summary, the convergence in the number of people
employed in industry is due to the reduction in inequality in
the Other 5. The rate of increase in'industrial employment
from 1950 to 1988 (final value divided by initial value) for
each country was: Canada, 1.7; U.S., 1.5; Japan, 2.5; U.K.,
.77; W. Germany, 1.2; France, 1.1; and Italy, 1.3. Once again
Japan's was largely responsible for the decrease in
inequality.
5.4 Inequality in Selected OECD Countries
In this section Theil's inequality index is applied to 14
of the Organization for Economic Co-operation and Development
(OECD) countries (the U.S., Canada, Japan, the U.K., W.
Germany, France, Italy, Austria, Belgium, Denmark, the

115
Netherlands, Norway, Ireland, and Spain).5 The reason for
selecting 14 out of the 24 OECD for this analysis was solely
based on the availability of data. The data for income from
1950 is available for most of these countries but the data is
too sparse for the other three variables for the countries not
included in this analysis. As in the G-7 case, the data for
the 14 OECD countries, which will now be referred to as the
OECD, were taken from the Summers and Heston 1991 data set,
and the OECD statistics.
The main reason for expanding this study to the OECD is
to compare the results with those of the G-7. The comparison
of the results from the G-7 and OECD is a way to check the
performance of the instruments used in this study. In fact,
it would be helpful if a larger group of countries could be
included. > However, it was mention prior that the data
limitations will not allow such a comparison. In the next
section Theil's ineguality measure is applied to the 14 OECD
countries data.
5.4.1 Income Inequality in the OECD Countries
Column 2 of Table 5.4 shows per capita income of the
combined OECD countries from 1950 to 1988. Income per capita
5The Signatories of the Convention on the OECD were
Austria, Belgium, Canada, Denmark, France, the Federal
Republic of Germany, Greece, Iceland, Ireland, Italy,
Luxembourg, the Netherlands, Norway, Portugal, Spain, Sweden,
Switzerland, Turkey, the United Kingdom, and the United
States. The list of countries that subsequently joined this
Convention are given along with the date of accession: Japan
(April, 1964) , Finland (January, 1969) , Australia (June,
1971), and New Zealand (May, 1973) (Ward, 1985).

116
is obtained by weighting the per capita incomes of the 14
countries in each year proportionally to their populations.
Note that the OECD per capita income increased almost
threefold during the 38-year period. As mentioned in section
5.2, the G-7 increased its income approximately threefold
during the same time period. The Other 7 has increased its
income by 3.3 times.
Once again equation (5.3) is used to determine the
movement of inequality in income over time. The results in
column 5 indicate that inequality declined from 0.21 in 1950
to 0.03 in 1988, or 86 percent. Thus the OECD countries
became much more affluent on the average, and also much more
"equal." This is not surprising considering the G-7 accounts
for most of the income and population.
As in the G-7 analysis, the OECD countries were grouped
into two regions. The first region was the G-7 and the second
region was the Other 7 countries. Column 6 shows that
regional inequality only reduced by 40% from 1950 to 1988.
Column 8 confirms that regional inequality only accounted for
a minimal part of the reduction in total income inequality in
the 1950's. The percent of regional income inequality
accounting for total income inequality grew every year to
reach a maximum of 30% in 1988. However, average within-
region inequality is responsible for the decrease in income
inequality. The average within-region inequality (column 7)

117
Table 5.4
Income per Capita and Income Inequality (OECD Countries)
Per Capita
Income
Income Inequality
Year
ALL
OECD
G-7
Other
7
ALL
OECD
Regional
Average
Within
Region
(6) as a
percentage
of (5)
Ui thin
G-7
Within
Other
7
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
1950
4749
5019
2897
0.2143
0.0146
0.1996
0.0683
0.2182
0.0725
1951
4976
5258
3038
0.1975
0.0145
0.1830
0.0735
0.2023
0.0498
1952
5109
5400
3096
0.1856
0.0148
0.1708
0.0800
0.1888
0.0460
1953
5282
5586
3164
0.1812
0.0154
0.1657
0.0851
0.1811
0.0589
1954
5340
5617
3404
0.1633
0.0121
0.1512
0.0742
0.1660
0.0479
1955
5672
5972
3566
0.1610
0.0127
0.1482
0.0791
0.1628
0.0457
1956
5808
6105
3714
0.1502
0.0118
0.1383
0.0789
0.1520
0.0418
1957
5907
6201
3816
0.1387
0.0113
0.1274
0.0814
0.1396
0.0407
1958
5878
6165
3834
0.1254
0.0108
0.1146
0.0861
0.1260
0.0330
1959
6153
6468
3893
0.1237
0.0122
0.1115
0.0986
0.1209
0.0437
1960
6383
6706
4067
0.1095
0.0118
0.0977
0.1080
0.1036
0.0553
1961
6588
6898
4348
0.0914
0.0101
0.0813
0.1109
0.0867
0.0427
1962
6855
7167
4589
0.0876
0.0095
0.0781
0.1081
0.0840
0.0353
1963
7111
7429
4801
0.0799
0.0091
0.0708
0.1138
0.0767
0.0280
1964
7475
7802
5101
0.0745
0.0086
0.0658
0.1158
0.0705
0.0317
1965
7783
8116
5360
0.0761
0.0082
0.0679
0.1081
0.0735
0.0273
1966
8132
8481
5586
0.0722
0.0083
0.0638
0.1155
0.0695
0.0228
1967
8367
8726
5754
0.0647
0.0083
0.0564
0.1282
0.0608
0.0242
1968
8772
9156
5988
0.0585
0.0086
0.0499
0.1472
0.0534
0.0241
1969
9129
9510
6350
0.0511
0.0078
0.0433
0.1531
0.0461
0.0229
1970
9331
9705
6604
0.0424
0.0071
0.0352
0.1683
0.0367
0.0245
1971- '
9539
- - 9914 •
6803
•• 8.0418
0.0068
â–  - 0.0350
-r -0.1634
0.0364
• ’-0.0248
1972
9911
10290
7137
0.0395
0.0065
0.0330
0.1636
0.0348
0.0201
1973
10425
10820
7534
0.0362
0.0063
0.0299
0.1748
0.0315
0.0180
1974
10373
10720
7831
0.0330
0.0048
0.0282
0.1459
0.0296
0.0178
1975
10203
10540
7736
0.0310
0.0047
0.0264
0.1505
0.0276
0.0173
1976
10681
11047
8012
0.0317
0.0050
0.0266
0.1589
0.0275
0.0206
1977
11061
11461
8145
0.0327
0.0057
0.0270
0.1736
0.0278
0.0209
1978
11460
11900
8248
0.0340
0.0065
0.0275
0.1911
0.0280
0.0233
1979
11765
12231
8362
0.0321
0.0070
0.0252
0.2165
0.0249
0.0274
1980
11822
12277
8495
0.0286
0.0065
0.0221
0.2282
0.0211
0.0297
1981
11953
12434
8429
0.0298
0.0072
0.0225
0.2431
0.0214
0.0308
1982
11800
12262
8406
0.0254
0.0068
0.0186
0.2688
0.0169
0.0309
1983
12091
12584
8463
0.0275
0.0075
0.0200
0.2722
0.0183
0.0331
1984
12621
13164
8616
0.0319
0.0085
0.0234
0.2660
0.0216
0.0369
1985
12841
13399
8719
0.0326
0.0087
0.0239
0.2662
0.0219
0.0392
1986
13256
13833
8979
0.0322
0.0088
0.0234
0.2722
0.0215
0.0379
1987
13639
14232
9237
0.0313
0.0088
0.0226
0.2791
0.0212
0.0331
1988
14143
14759
9554
0.0304
0.0088
0.0216
0.2908
0.0203
0.0314

118
has declined by 89%. Which region is responsible for this
change?
The G-7 movements in inequality for income were discussed
in section 5.2. It was determined that Japan was the driving
force behind the decline in income inequality for the G-7.
Column 9 in Table 5.4 is the same as column 5 in Table 5.1.
It was determined that the G-7 inequality declined 90%.
Comparing this result with the Other 7's within-region
inequality (column 10) which only decreased 57% indicates that
the G-7 dominated the OECD results.
Income inequality of the 14 selected OECD countries
declined mainly due to the G-7 countries and their heavy
weighting in the index. Although the Other 7 countries were
converging, they were converging within themselves at a slower
rate than the G-7.> The two regions, -G-7 and the Other 7 were
also converging. It was determined in section 5.2 that the
convergence of the G-7 was largely due to Japan's rapid income
growth. Germany and Italy were also fast growers which helped
in the convergence.
The Other 7 on average grew faster than the G-7, but
there were no extremely fast growers like Japan. Austria and
Spain had the fastest growth rates in the Other 7 followed by
Norway. The other countries grew at slower rates than the
OECD average. Therefore, the countries largely responsible
for convergence in the Other 7 were Austria, Spain, and
Norway. Overall convergence is due to the fast income growth

119
of Japan, Germany, Italy, Austria, Spain, and Norway. The
slow growth of the U.S. and Canada also helped the convergence
of the OECD countries. In fact the U.S. had the slowest
growth rates followed by Canada and the U.K.
5.4.2 Inequality of Government Expenditure in the OECD
The total inequalities of G, I, and E in Table 5.5
(columns 1, 5, and 9) appear to decline over time, similar to
income inequality. Specifically the inequality in government
expenditure decreased from .17 in 1950 to .055 in 1988, which
is approximately a 67% decrease. The inequality among the
OECD countries started out higher than the inequality in the
G-7. However, by 1988, the inequality in the OECD had
decreased more than the inequality in the G-7 indicating that
the Other 7 countries increased their expenditure at a faster
rate. When the population weighted averages are considered
these results are confirmed. The G-7 have increased their
government expenditures 2.3 times over the 39 year period
while the Other 7 have increased theirs by 3.4 times.
The regional inequality, however, only accounted for a
small percentage of the total inequality, 10 - 15% during the
39 year period. In addition, the regional inequality (Table
5.5, column 2) was fairly small when the within-region
inequalities were considered. As mentioned in the G-7
discussion, total government inequality of the G-7 decreased
65% which was mainly due to the small increases in government
expenditure in the U.S. and the U.K over time.

Table 5.5
Government, Investment, and the Number of People Employed in
Industry Inequalities (OECD Countries)
Government Inequality Investment Inequality Industrial Employment Inequality
G-7
Other 7
G-7
Other 7
G-7
Other 7
J
Jr
J,
J.
J
Jr
Jo
J,
J
Jr
J,
J,
Year
LLL
iUL
(3)
(¿0
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
1950
0.1699
0.0264
0.1374
0.1848
0.2489
0.0072
0.2579
0.1302
0.0266
0.0003
0.0246
0.0381
1951
0.2446
0.0370
0.2152
0.1555
0.1647
0.0081
0.1675
0.0813
0.0348
0.0015
0.0297
0.0576
1952
0.2612
0.0435
0.2254
0.1645
0.1669
0.0087
0.1690
0.0829
0.0308
0.0015
0.0269
0.0457
1953
0.2700
0.0416
0.2333
0.1945
0.1715
0.0070
0.1736
0.1015
0.0306
0.0013
0.0281
0.0382
1954
0.2300
0.0322
0.2009
0.1765
0.1394
0.0026
0.1451
0.0787
0.0325
0.0006
0.0318
0.0329
1955
0.2170
0.0294
0.1893
0.1757
0.1497
0.0055
0.1561
0.0606
0.0325
0.0004
0.0329
0.0266
1956
0.2107
0.0280
0.1849
0.1670
0.1258
0.0042
0.1298
0.0635
0.0280
0.0004
0.0285
0.0210
1957
0.2142
0.0282
0.1900
0.1573
0.0915
0.0028
0.0918
0.0662
0.0271
0.0004
0.0276
0.0208
1958
0.2062
0.0288
0.1799
0.1596
0.0887
0.0031
0.0919
0.0407
0.0290
0.0002
0.0305
0.0168
1959
0.1954
0.0286
0.1685
0.1551
0.0923
0.0058
0.0874
0.0798
0.0267
0.0002
0.0278
0.0171
1960
0.1848
0.0271
0.1568
0.1643
0.0646
0.0040
0.0553
0.0984
0.0292
0.0003
0.0301
0.0203
1961
0.1809
0.0278
0.1527
0.1566
0.0349
0.0022
0.0291
0.0593
0.0316
0.0002
0.0332
0.0186
1962
0.1752
0.0271
0.1474
0.1529
0.0404
0.0017
0.0387
0.0388
0.0292
0.0001
0.0308
0.0164
1963
0.1609
0.0243
0.1352
0.1466
0.0318
0.0022
0.0302
0.0256
0.0284
0.0001
0.0302
0.0148
1964
0.1562
0.0240
0.1297
0.1509
0.0233
0.0010
0.0200
0.0389
0.0210
0.0004
0.0215
0.0143
1965
0.1496
0.0235
0.1240
0.1414
0.0301
0.0006
0.0301
0.0251
0.0199
0.0004
0.0204
0.0126
1966
0.1595
0.0256
0.1328
0.1425
0.0246
0.0004
0.0246
0.0206
0.0174
0.0005
0.0177
0.0114
1967
0.1651
0.C265
0.1386
0.1385
0.0124
0.0006
0.0093
0.0301
0.0145
0.0006
0.0145
0.0102
1968
0.1609
0.0263
0.1342
0.1373
0.0099
0.0012
0.0060
0.0283
0.0147
0.0007
0.0147
0.0091
1969
0.1524
0.0239
0.1274
0.1367
0.0104
0.0011
0.0075
0.0225
0.0143
0.0007
0.0143
0.0083
1970
0.1376
0.0209
0.1149
0.1292
0.0144
0.0007
0.0115
0.0303
0.0160
0.0006
0.0164
0.0081
1971
0.1247
0.0191
0.1026
0.1281
0.0139
0.0011
0.0096
0.0364
0.0176
0.0004
0.0183
0.0084
1972
0.1165
0.0178
0.0952
0.1240
0.0141
0.0014
0.0116
0.0210
0.0153
0.0005
0.0159
0.0073
1973
0.1055
0.0166
0.0854
0.1149
0.0106
0.0017
0.0077
0.0179
0.0140
0.0006
0.0142
0.0071
1974
0.1007
0.0151
0.0833
0.1028
0.0102
0.0004
0.0092
0.0140
0.0130
0.0006
0.0132
0.0068
1975
0.0949
0.0142
0.0783
0.0986
0.0135
0.0000
0.0131
0.0159
0.0143
0.0003
0.0150
0.0065
1976
0.0847
0.0121
0.0697
0.0932
0.0104
0.0005
0.0080
0.0235
0.0113
0.0006
0.0110
0.0084
1977
0.0784
0.0110
0.0643
0.0904
0.0122
0.0014
0.0087
0.0257
0.0101
0.0007
0.0095
0.0086
1978
0.0728
0.0095
0.0597
0.0896
0.0159
0.0034
0.0107
0.0255
0.0087
0.0012
0.0074
0.0083
1979
0.0664
0.0082
0.0540
0.0885
0.0173
0.0045
0.0102
0.0325
0.0085
0.0016
0.0066
0.0096
1980
0.0623
0.0072
0.0507
0.0867
0.0213
0.0030
0.0159
0.0363
0.0097
0.0019
0.0074
0.0106
1981
0.0583
0.0067
0.0463
0.0902
0.0300
0.0066
0.0215
0.0375
0.0105
0.0026
0.0073
0.0119
1982
0.0566
0.0063
0.0456
0.0849
0.0216
0.0039
0.0152
0.0359
0.0132
0.0026
0.0103
0.0130
1983
0.0537
0.0060
0.0432
0.0809
0.0191
0.0062
0.0091
0.0411
0.0140
0.0029
0.0107
0.0138
1984
0.0544
0.0065
0.0441
0.0760
0.0297
0.0093
0.0141
0.0665
0.0139
0.0038
0.0091
0.0164
1985
0.0596
0.0070
0.0500
0.0717
0.0276
0.0089
0.0122
0.0667
0.0152
0.0040
0.0100
0.0202
1986
0.0574
0.0071
0.0483
0.0657
0.0246
0.0067
0.0117
0.0641
0.0149
0.0037
0.0101
0.0198
1987
0.0580
0.0063
0.0508
0.0586
0.0220
0.0069
0.0113
0.0433
0.0135
0.0029
0.0099
0.0157
1988
0.0547
0.0061
0.0480
0.0536
0.0203
0.0067
0.0105
0.0369
0.0141
0.0024
0.0114
0.0143
120

121
The reduction in the within-region inequality of the
Other 7 is a different story. The within-region inequality of
the Other 7 decreased 71% from 1950 to 1988. The rate of
increase in government expenditure for the G-7 countries was
discussed in section 5.3.1; hence, this section will focus on
the Other 7's. Government expenditure for the Other 7
increased from 1950 to 1988 by the following values: Spain,
5.8; Denmark, 4.8; Norway, 4.6; Belgium, 3.3; Ireland,2.8;
Austria, 2.7; and the Netherlands, 2, respectively. Lastly,
the 1950 government expenditure per capita for each country
was: Netherlands $808; Denmark, $596; Austria, $555; Norway,
$468; Belgium, $452; Ireland, $342; and Spain, $171,
respectively.
Considering the initial value and the rate of increased
expenditureconvergence in the Other 7 wars due ta Spain and
Norway's increased expenditure on public goods. The
Netherlands slow rate of government expenditure also helped
the countries to converge by allowing the other countries to
catch up. Ireland appeared to be growing slow as well as
having a small initial value. Therefore, Ireland may be
slowing the convergence of the Other 7 countries. Denmark had
a high rate of increased expenditure and had a relatively high
expenditure in 1950, thus, this country is diverging instead
of converging. Denmark may have slowed the rate of
convergence in the Other 7 sample. Although there are

122
converging and diverging forces in the sample, the overall
effect is that the Other 7 and OECD countries are converging.
5.4.3 Investment Inequality in the OECD
Column 5 of Table 5.5 shows the dramatic decline in
investment inequality. Investment inequality decreased by 92%
from 1950 to 1988. Actually investment inequality reached its
lowest level in 1968, from .25 in 1950 to .01 in 1968, a 96%
decline in 19 years. The inequality increased slightly after
1968 to reach .02 in 1988. Hence, investment inequality
increased by 51% from 1968 to 1988. Little of the total
inequality was due to regional inequality until the late
1970's. The average regional inequality between the 1950 and
the late 1970's is around 6%. After the late 1970's, total
inequality due to regional inequality jumped to an average of
30%. .-St±il,~regional inequality has remained low between the
two regions during the whole time period.
Within-region inequality appears to be the major reason
for the reduction in total investment inequality. The G-7
section determines that the 96% decrease in inequality in the
G-7 was mainly due to the rapid increase in investment by
Japan. The within-region inequality for the Other 7 decreased
by 72%. To extend Table 5.3, Table 5.6 is added to the text.
Table 5.6 shows the initial, final, and the rate of investment
expenditure per capita for the Other 7 countries.
The initial values for the Other 7 were lower than the G-
7 on average. The average population weighted value for the

123
G-7 is $941 compared to the Other 7 value of $644 per capita.
However, if Japan's initial value is removed, the G-7 level
would be a little higher. Denmark, Norway, and the
Netherlands have high initial values compared to the rest of
the OECD with the exception of the U.S. and Canada. Just like
the U.S. and Canada, Denmark and the Netherlands increased
their expenditure on investment at a slower rate allowing
other countries to catch up. Norway, however, increased its
expenditure rate at a fairly fast rate (3.2) to end up as the
second highest value for 1988. The average population
weighted rate of investment expenditure for all 14 countries
is 3.6. Using that value as a guide, the countries that have
influenced convergence in the Other 7 can be determined.
Table 5.6
Investment Expenditure per Capita, and the Rate of
Investment Expenditure for the Other 7
Other 7
Countries
Year
(1)
Austria
(2)
Belgium
(3)
Denmark
(4)
Nethrlds
(5)
Norway
(6)
Ireland
(7)
Spain
(8)
1950
544
812
1120
1013
1394
488
341
1988
3534
2598
2473
2275
4404
1287
1921
Rate of Investment
Expenditure
6.5
3.2
2.2
2.3
3.2
2.6
5.6

124
Austria and Spain had the fastest rates in investment
expenditure for the Other 7 countries. Thus, their fast rate
of increase in investment expenditure and the slow rate of
Denmark and the Netherlands have influenced convergence in the
Other 7. Convergence in terms of investment per capita in the
OECD countries was supported by the fast rate of investment
expenditure in Japan, Austria, Spain, Italy, and the U.K. The
slow rate of investment expenditure in the U.S. and Canada
(they had the slowest rate) helped the other countries to
catch up, therefore, converge.
5.4.4 OECD Inequality in Industrial Employment
The inequality in the number of people employed in
industrial is shown in column 9 of Table 5.5.6 Total
inequality has decreased 47% from 1950 to 1988. The lowest
level of inequalityâ– occurred in 1979 among the 14 countries.
As in the G-7 case, regional inequality has increased even
though total inequality has decreased. The regional
inequality has increased 88% (column 10), which means the two
regions have grown further apart over time. However, regional
inequality only accounts for less than 5% on average until the
late 1970's. Then regional inequality jumps to almost 22% of
total inequality.
Once again within-region inequality is responsible for
the reduction in total inequality. As noted in the G-7
6The countries that have incomplete data for the number
of people employed in industry were extrapolated as explained
in Appendix E.

125
section, inequality among the G-7 decreased 54% (reproduced in
Table 5.5, column 11). The driving force behind the reduction
in the G-7 is the rate of increase in the number of people
employed in industry in Japan. The within-region inequality
for the Other 7 decreased 62% from 1950 to 1988 (column 12).
In summary, the convergence in the number of people
employed in industry was due to the reduction in the within-
region inequality. The rate of increase in industrial
employment (final value divided by initial value) for each
group was: G-7 (Canada, 1.7; U.S., 1.5; Japan, 2.5; U.K., .77;
W. Germany, 1.2; France, 1.1; and Italy, 1.3), and the Other
7 (Austria, 1.2432; Belgium, 0.7; Denmark, 1.3; Netherlands,
1.0; Norway, 1.1; Ireland, 1.9; and Spain, 1.5). Once again
Japan's was largely responsible for the decrease in the
inequality of the G-7. The relatively fast rate of increase
in industrial employment by Ireland and Spain have influenced
the convergence of the Other 7.
5.5 Summary of the Inequality Results
The overall summary of the findings is that convergence
is supported for all four variables (income, government,
investment, and the number of people employed in industry
inequalities) for the G-7 and for the OECD countries. In
general, convergence occurred at a faster rate in the income
and investment variables. However, there was a relatively low
level of inequality among the countries in terms of the number
of people employed in industry. The next section analyzes

126
these results further by determining if there exists any long
term relationships among these variables and the movement
within them.

CHAPTER 6
COINTEGRATION
6.1 An Overview of Cointecrration
Cointegration is used in this analysis to determine the
long-run relationships among the four inequality indices for
the G-7 and selected OECD countries. Several studies in the
Convergence section combined inequality measures with multiple
regression techniques (Braun, 1988; Ram, 1989b; Ram, 1992;
McGillivray, 1991; and Amos, 1991). This study, however
attempts to establish the co-movement of these inequality
indices over time. This objective is important because the
long-run equilibrium has not previously been explained. The
co-movements over time will explain the long-run equilibrium
instead of the static equilibrium which regression analysis
addresses. The most appropriate statistical method to
establish the co-movements over time is cointegration
analysis. Cointegration analysis will explain if there is or
is not a long-run equilibrium, and which variables are
included in that equilibrium.
There are three basic differences between standard
regression analysis and cointegration analysis. First,
regression analysis establishes a linear or nonlinear
127

128
combination of the dependent variable and independent
variables that must be equal to white noise.1 Cointegration
analysis only requires that slow or trending movements in the
dependent variable equal linear combinations of similar
movements in the independent variable. The cointegrating
relationship does not have to be purely random. It can be a
stationary process.
The second difference is that there is no need to
designate a variable as exogenous. If the two series are
found to be cointegrated, then the relationship is symmetric.
That is, if y and x are cointegrated, then x and y are
cointegrated (Engle and Yoo, 1991). In addition, regression
analysis only describes the positive or negative influence of
the dependent variable on the independent variable.
The last reason cointegration analysis is used is to
determine the long-run trends in the data series. Regular
regression analysis produces spurious results if it is used on
variables that have trends in them (Maddala, 1992) . In order
to resolve this problem, the data need to be differenced or
transformed until stationary, then regressed. However, when
this is done all of the long-run information in the series is
lost. Cointegration analysis on the contrary incorporates
non-stationary levels data along with the differenced
‘White noise in time series is a sequence of uncorrelated
random variables with zero mean and identical finite variances
(Judge et al., 1980).

129
stationary data.2 Therefore, the long-run information is not
lost, and the regression is not spurious.
Testing for cointegration begins with analyzing the
residuals from a cointegrating regression for stationarity.
Stationarity refers to a time-series having a constant mean
and a bounded variance over time. If the residuals from a
cointegrating equation are stationary, then the variables are
cointegrated. If the residuals are not stationary, then any
deviation between the series causes them to diverge infinitely
as time approaches infinity, versus being stable when the
residuals are stationary (Maddala 1992, Moss 1992). Stated
another way, if two vectors are cointegrated, then any
deviation between the two series dissipates quickly. However,
if the two series are not cointegrated then a deviation
persists.3
Three of the four variables (income, investment
expenditure, and government expenditure) of interest in this
dissertation have been tested for cointegration in other
studies. The variables in those studies are defined
2The error correction model incorporates levels data with
stationary data to describe the long-run relationships. The
error correction model is explicitly or implicitly used in
most multiple cointegration models.
3Cointegrated series have short memories meaning that any
innovation in the model does not last long. Non-cointegrated
series have long memories, that is innovations last a long
time. For example, if the series are cointegrated, then old
shocks in the series have no effect on the current values.

130
differently than in this dissertation, but there results will
be helpful in interpreting the results from this dissertation.
Kugler (1991) tested the multivariate cointegration of
income, consumption, investment, and exports from 1970 to 1987
for seven countries: the U.S., Japan, Switzerland, W.
Germany, the U.K., and France. Income was defined as GDP for
all of the countries except the U.S. where GNP was used.
Investment was defined as the gross fixed business investment
for all of the countries except Switzerland where investment
only covers equipment. The data came from the Quarterly
National Accounts for each respective country. In general,
Kugler found the time-series data to be 1(1). The
multivariate cointegration results supported the relationships
among income, consumption, and investment, but not exports.
The U.K. had no statistically significant cointegrating
relationships.
Government expenditure has been tested for cointegration
with income by MacDonald et al. (1989) . They conducted a
study on the cointegration between the log of government
expenditure and income for four countries: U.K., Canada,
Germany, and the U.S. from 1965 to 1986. Income was defined
as GDP less government expenditure. Both variables were
deflated by their respective consumer price indexes. The data
for the study came from the International Financial Statistics
(quarterly data) . In general, they found that the log of
government expenditure and income to be 1(1). Cointegration

131
was found between these two variables in three countries:
Germany, the U.K., and the U.S. Canada's sample did not
support cointegration between the log of government
expenditure and income.
Before the inequality indices can be tested for
cointegration and compared with Kugler (1991) and MacDonald et
al. 1989 certain requirements must be met. The next section
covers those requirements and is followed by the derivation of
the cointegration method. Then the results are presented and
interpreted.
6.2 Unit Root Tests
A necessary prerequisite of cointegration analysis is
that the variables under consideration be integrated of the
same order. This means that the variables being compared
require the same number of differences to attain stationarity.
A time-series variable is integrated of order d if the dth
difference of x, is stationary, denoted 1(d). An 1(0) series
means that the series is stationary without any differencing.
In this case, the error term is white noise and there is no
correlation between the error terms for all time t (Maddala,
1992) .
Maddala (1992) suggests examining graph's of the time-
series over time as well as using unit root tests to determine
if a time-series is stationary. A stationary time-series is
expected to have regular crossings of the mean. The graphs

132
for the inequality of income, government, investment, and the
number of people employed in industry for the G-7 countries
are shown in Figures 6.1 to 6.4. All four variables have a
trend indicating that they are non-stationary. The problem is
not that the data are non-stationary, but if a regression is
run with one time-series being stationary and another being
non-stationary, then the results would be spurious (Maddala
1992) .
One way to correct the non-stationarity is to first
difference or detrend the non-stationary variable. The data
series were first differenced, but they still appeared to be
non-stationary. Therefore the series was second differenced
and are shown in Figures 6.5 to 6.8. It appears that all four
data series are stationary after second differencing which
means the series are integrated of order 2.
6.2.1 Augmented Dickev-Fuller ÍADF) Test
The other way to determine the order of integration of a
series is to use a unit root test. Two unit root tests will
be applied to the data. The first test is the Augmented
Dickey-Fuller (ADF) test. The model is
k
(6.1) y, = 7 + it + ay,., + £ ©jAy,., + u,
j=l
where y, is the time-series, t is time, and u, is a covariance
stationary process with zero mean. The Ay,., terms (lags) are

Government Inequality Income Inequality
133
0.26
0.2
0.16
0.1
0.06
0
1060 I960 1970 1980 1988
Years
FIGURE 6.1
Total Income Inequality for the G-7
FIGURE 6.2
Total Government Inequality for the G-7

Industry Inequality Investment Inequality
134
Years
FIGURE 6.3
Total Investment Inequality for the G-7
FIGURE 6.4
Total Industrial Employment Inequality for the G-7

Government Inequality Income Inequality
135
FIGURE 6.5
Total Income Inequality for the G-7
Second Differenced
0.04
0.02
o
«0.02)
«0.04)
«0.061
«0.081
1962 1960 1970 1980 1988
Years
FIGURE 6.6
Total Government Inequality for the G-7
Second Differenced

Industry Inequality Investment Inequality
136
FIGURE 6.7
Total Investment Inequality for the G-7
Second Differenced
1962 1900 1970 1900 1988
Years
FIGURE 6.8
Total Industrial Employment Inequality for the G-7
Second Differenced

137
added to whiten the residuals (i.e. remove the autoregressive-
moving-average (ARMA)). The number of lags is determined by
comparing the significance levels as more lags are added.
This method was chosen because the power of the unit root
tests decrease when small samples are used and as more lags
are added, degrees of freedom are also lost. The first step
in the procedure is to estimate (6.1) with the hypothesis
being that there is a unit root which means a = 1. A t-test
is used as the criteria in determining if a = 1. This t-test
does not have a limiting normal distribution (Engle and
Granger, 1991). The distribution is skewed to the left and is
referred to as a Dickey-Fuller distribution. The t-test is
(6.2) t(l) = (a - l)/SE(a)
where a is the ordinary least squares (OLS) estimate of (6.1),
SE(¿) is the standard error of a, and the 1 represents the
hypothesis that a is equal to 1. The critical values for this
test are in Fuller (1976), where 6 is assumed to be zero.
6.2.2 Phillips Test
The second unit root test is by Phillips (1987). The
model is similar to the ADF model with less parameters. The
model is
(6.3) y, = ay,., + u,
where all the symbols have the same meaning as equation (6.1),
and the null hypothesis is the same as (6.1). The difference

138
from ADF is that this is a non-par ame trie procedure that uses
the residuals from the first order model to correct the t-
statistic. Phillips' new tests for unit roots are Z„ and Zt.
The Z(( statistic is a transformation of the standard estimator
T(a - 1), and Z, is a transformation of the regression t-
statistic. The equation for Za is
T
(6.4) Za = T (a - 1) - (1/ 2) (SjL - S*) / (T2 S y*,)
t=l
where
T
Sj = T-1 Z u?
t=l
and
T L T
S^L = T'1 Z u] + 2T"1 Z WtL Z utu,.T
t=l T=1 t=T+l
given that
WtL = 1 - t/(L + 1) .
The symbol T represents the sample size, L is referred to as
the lag truncation number by Phillips (1987) . The lag
truncation number represents the number of autocorrelations
and is determined empirically. Since the sample
autocorrelations of first differenced economic time-series
decay quickly, the value of L will be small (Phillips, 1987).

139
SyL is a consistent estimator of a2 if the autocovariance
increases as T approaches positive infinity, but the rate of
increase is controlled so that L = 0(T1/4). is a consistent
estimator of a2 when á = 1.
The other statistic which is a transformation of the t-
statistic is
T
(6.5) Z, = (S yi,)1/2(¿ ~ 1) /STL - (1/2) (S^ - S2)
t=l
T
[ sTL (T"2 s yt-i)1/2 ]'* •
t=i
All of the definitions are the same as in the Za statistic.
To test the unit root hypothesis, the Za and Zt statistics are
computed and compared with the critical values in Evans and
Savin (1981) and Fuller (1976).
6.2.3 Unit Root Results
The results of the G-7 in Table 6.1 for the ADF and
Phillips unit root tests confirm the interpretation of the
graphs. The unit root tests indicate that the inequality in
income, investment, industry, and government are all 1(2).
Both tests supported these results at the 1% level. In
addition, increasing the number of lags (autocovariance terms
for Phillips tests) in the model had no effect on the
significance level for the 1(2) series.

140
Table 6.1.
Unit Root Tests
Tests
Income
G-7 Results
Government
Investment
Industry
ADF*,b
9.40
4.65
10.01
10.23
Phillips"
9.67
10.16
10.30
10.54
OECD Results
Tests
Income
Government
Investment
Industry
ADFab
10.38
8.30
11.21
10.08
Phillips"
10.68
8.54
11.53
10.37
Note: Only the second differenced results are reported.
“The reported values are for 0 lagged difference terms.
bThe critical values for the Augmented Dickey-Fuller test and
Phillips test are 3.56, and 2.94 for the 0.01, and 0.05
confidence levels respectively.
cThe reported values are for 1 autocorrelation term.

141
The same tests were applied to the OECD data. The
results are reported in Table 6.1. As expected these data
were also found to be 1(2) for all of the variables. Given
that all of the variables appear to be integrated of the same
order, the long-run relationships can be estimated. Pairwise
cointegration analysis will be conducted first, followed by
multiple cointegration tests.
6.3 Pairwise Cointeqration for the G-7
Engle and Granger (1987) state that two 1(d) variables,
x, and y,, are cointegrated of order (d,b) , if there exist a
constant B f 0 such that ut = y, - a - Bx, is integrated of
order (d - b), b > 0. If these restrictions are satisfied,
then x, and y, are cointegrated which is written as CI(d,b).
In this example, a is a constant and u, is the residual vector.
The two tests that are used to determine pairwise
cointegration are the Durbin Watson test and the Dickey-Fuller
test. These test will be used on the following inequality
measures: income - government expenditures, income
investment expenditure, and income - the number of people
employed in industry.
6.3.1 Durbin Watson
The Durbin Watson pairwise cointegration vector is tested
as
(6.6)
y, = Bxt + a + u,

142
where all of the variable and coefficients are defined in the
prior section. After estimating (6.6), the Durbin Watson
statistic is used to determine if the residuals are
stationary. The Durbin Watson statistic is
(6.7) DW = E (Ú, - ú,.,)2/ E u2.
The DW statistic approaches zero if the residuals contain a
unit root. An autoregressive unit root in the residual is
represented by ut = pu,_j + et, where p = 1. That is why DW
approaches zero because DW a 2(1 - p). Therefore, the null
hypothesis of non-cointegration means that DW = 0.
Cointegration is supported if DW is significantly different
than zero.
6.3.2 Augmented Dickey-Fuller Cointegration Test
To explain the Augmented Dickey-Fuller cointegration
(ADFC) test, the Dickey-Fuller (DFC) test for cointegration is
first discussed. The DFC test uses the same regression as the
Durbin Watson test. That is after (6.6) is estimated, the
residuals are regressed on the lags of themselves using the
following equation:
(6.8) AÚ, = $ut., + et.
Now the test for cointegration is a t-statistic for the $
coefficient. To extend this to the Augmented Dickey-Fuller
test for cointegration, some terms are added so that the
residuals are uncorrelated. The ADFC equation is

143
P .
(6.9) Au, = $u,_, + Z ut.¡ + et
i=l
where p is selected to make e, white noise (see footnote 1 in
this Chapter for a definition of white noise). Once again the
ADFC is a t-statistic for the 4 coefficient. The null
hypothesis is that 4=1, or non-cointegration.
6.3.3 Pairwise Cointegration Results
The results from the two pairwise tests for the G-7 are
somewhat inconsistent. Table 6.2 shows that the Durbin Watson
statistic is significantly different from 0 at the 1% level
for income inequality and investment expenditure inequality.
Government inequality and the inequality of income are only
significant at the 10% confidence level. The inequality of
the number of people employed in industry and income
inequality pair is not significantly different from zero for
the Durbin Watson statistic. The Durbin Watson tests indicate
that non-cointegration is rejected for investment and possibly
government, but, cannot be rejected for the number of people
employed in industry.
The CADF tests reject non-cointegration for all three
pairs. The government regression rejects non-cointegration at
the 1% level, while the number of people employed in industry
rejects non-cointegration at the 5% level. The investment
regression rejects non-cointegration at the 10% level.

144
Table 6.2
Pairwise Tests for Cointegration
G-7 Results
Tests
Government Investment Industry
Durbin-Watson
Regression3 0.374 0.524 0.263
Augmented
Dickey-Fuller
Regressionb,c 7.25 3.14 3.76
OECD Results
Tests
Government Investment Industry
Durbin-Watson
Regression3 0.296 0.429 0.471
Augmented
Dickey-Fuller
Regressionbc 6.07 2.76 4.27
“The critical values for the Durbin-Watson regression are
.511, .386, .322 for the 0.01, 0.05, and 0.10 confidence
levels respectively (Engle and Granger, 1987) .
bThe critical values for the Augmented Dickey-Fuller
regression are 4.02, 3.4, and 3.09 for the 0.01, 0.05,
and 0.10 confidence levels respectively.
cThe reported values are for 0 lags.

145
The results for the OECD countries are similar to the
outcome of the G-7 analysis. Table 6.2 shows that the Durbin
Watson statistic is significantly different from 0 at the 5%
level for the following pairs: income inequality and
investment expenditure inequality, and income inequality and
the inequality in the number of people employed in industry.
The Durbin Watson statistic is not significantly different
from zero for government inequality and the inequality of
income. The Durbin Watson tests indicate that non-pairwise
cointegration is rejected for investment and the number of
people in industry, but cannot be rejected for the government.
The CADF tests tells a different story from that of the
Durbin Watson test results. The government and the number of
people employed in industry regressions reject non¬
cointegration at the 1% level. The investment regression does
not reject non-cointegration.
It is fairly common in time-series studies to get two
tests indicating two different results. In this case the
small sample size may have a lot to do with these results. In
general, the test results indicate that income inequality is
cointegrated with the inequalities of the other three
variables. This suggests that there exists a long-run
equilibrium among income inequality and the inequality in
government expenditure, inequality in investment expenditure,
and inequality in the number of people employed in industry
for the G-7 and OECD countries. The results from this

146
section do not prove the hypothesis of this thesis. The
hypothesis of all four variables being cointegrated is what
needs to be proved. These results only illustrate that two
variables are cointegrated not all four. As a final step,
this study analyzes whether multiple cointegration exists
among the four variables. The methodology of the test to
prove or disprove this hypothesis is discussed next.
6.4 Johansen's Multiple Cointeqration Test
Johansen's cointegration test is a test for cointegration
for a general vector autoregressive (VAR) model with p
variables and k lags. The time-series are collected in a
vector such as X( = [xlt, x2t, . . . , xpt] . It is assumed that the
X('s are integrated of the same order. The test for 1(1)
variables is discussed first followed by the case where the
variables are 1(2). The 1(2) case is covered simply because
all of the variables tested here seem to be 1(2).
6.4.1 Ifl) Procedure
Johansen (1988) and Johansen and Juselius (1990) begin by
defining a general polynomial distributed lag model for X, as
k
(6.10) X, = n + E 7TiXt.1 + e, t=l, . . . , T
i=l
where ¿i is a constant and et is an independently identically

147
distributed p dimensional vector with zero mean and variance
matrix A.4 Given this framework, the cointegrating matrix is
(6.11) I —77,—7T2 . . . -7rk = n.
The n matrix is therefore a p x p matrix. The number of
cointegrating relationships among the variables in X is r,
where r is the rank of w. If all of the variables are 1(1)
then the most r can be is p-1. If n is expressed as
(6.12) tt = aB'
where a and B are p x r matrices, then the rows of B form r
distinct cointegrating vectors.
In order to implement this idea, Johansen (1988) put
forth the following theorem. The maximum likelihood estimate
of space spanned by B is the space spanned by the r canonical
variates. These variates correspond to the r largest squared
canonical correlations between the residuals of X,.k and AXt,
which are corrected for the effect of the lagged differences
of the X process. The likelihood ratio test statistic for the
hypothesis that there are at most r cointegrating vectors is
P
(6.13) -21n(Qr) = -T X ln(l - X¡)
i=r+l
4In Johansen's 1988 paper /n is assumed to equal zero.
The same assumption is made here.

148
where Ar+1,...,Ap are the p-r smallest canonical correlations.
Johansen then shows that the likelihood ratio test has an
asymptotic distribution for which a set of critical values can
be tabulated which are correct for all models.
The implementation of this theorem requires the
reparameterization of (6.10) into a first differenced model
(error correction model)
k-1
(6.14) AX, = n + X TjAX,., + rkX,.k + e,
i=l
where rk = . . +7Tk. The equilibrium matrix 7r=aB' is
equal to -rk. Therefore, B is the p x r matrix of
cointegrating vectors, and a is a corresponding coefficient
matrix.
The loglikelihood representation of this model is
T k-1
(6.15) In L(r¡,rk,A) = -T/2 ln|A| -1/2 X (AX, - X AX,.^
t=l i=l
k-1
- X,.krk) 'A-1 (AX, - z Ax^r, - xt.krk).
i=l
The parameters r,, . . . , rk., can be eliminated by partially
maximizing (6.15) with respect to r¡. The result of taking the
partial maximization with respect to r¡ is

149
(6.16)
T k-l k-l
ainL/dr, = 1/2 Z (E AX,_¡) 'A'1 (AX, - E AXt.iri - X,.krk)
t=l i=l i=l
T k-l k-l
+ 1/2 Z (AX, - Z AX,.^ - X,.krk) 'A1 (E AX,.¡) = 0.
t=l i=l i=l
This can be further reduced by multiplying (6.16) by 2, and
A yields
(6.17)
T k-l k-l
dlnL/dr, = Z (Z AX,.¡) ' (AX, - z Ax,.¡r, - x,.krk)
t=l i+1 i+1
T k-l k-l
+ Z (AX, - Z AXj.jFi - X,_krk) ' (Z AX,.j) = 0.
t=l i=l i=l
If the matrices in (6.17) are multiplied out, the similar
terms added, and then divide everything by two the result is
T k-1
(6.18) E Z [ (AX^AX, - AX^AX^Tj - AX^rj ] = 0.
t=l i=l
Solving (6.18) for T, yields
(6.19)
T k-l
r, = z z [ (Axi^x^Ax^Ax,,) -1 - (Ax,.iAx,.i) •1Ax;.ixt.krk) ]
t=l i=l
Substituting aB' in for -rk makes (6.19) the same as
regressing AX, + aB'X,.k on the lagged differences. Johansen
(1988) suggests doing this procedure in two steps using OLS.
First AX, is regressed on the lagged differences yielding

150
residuals R^, and then Xt.k is regressed on the lagged
differences yielding residuals Rkt.
After that is done the concentrated maximum likelihood
function in terms of a, B, A is
T
(6.20)L (a, B, A) = | A | T/2exp [-1/2 Z (R^ + aB'Rkt) 'A'1
t=l
(Rot + aB'Rkt) ] .
If the log of (6.20) is taken, it yields
T
(6.21)In L(a,B,A) = -T/2 In|A| -1/2 Z (Rw + aB'RJ'A1
t=l
(Rot + aB,Ria) •
The objective is to maximize (6.21) with respect to a and A.
The maximization with respect to a yields
T
(6.22)dlnL/da = -1/2 Z (B'Rkt) 'A'1 (R* + aB'Rkt)
t=l
T
-1/2 Z (R^ + aB'Rkl) 'A'1 (B'Rkt) = 0.
t=l
Multiply (6.22) by -2, and A yields
dlnL/da = Z (B'Rkt) ' (R^ + aB'Rkl)
t=l
(6.23)

151
T
+ 2 (R* + ctB'RJ ' (B' Rkl) = 0.
t=l
Now define the product moment matrices of the residuals as
(6.24) S¡j = T-1 Z RjtRj,
and multiply the matrices in (6.23) to get
(6.25) dlnL/da = T’S^B + T'crB'S^B + T-'S^B + T-'aB'S^B = 0
or equivalently
23^6 + 2aB,SkkB = 0.
Solving for a yields
(6.26) a (B) = -S^B (B' S^B).
Now the consistent estimator for A must be derived. This
is done by first rewriting (6.21) with equivalent trace (tr)
notation. The result is
T
(6.27) In L(a,B,A) = -T/2 ln|A| -1/2 Z triR^ + aB'R^) '
t=l
(Rq< + aB,Rkt) A-1.
T
Let Z = Z tr (R^ + aB^,) ' (RM + aB'Rkl)
t=l
and maximize with respect to A to get

152
(6.28) dlnL/dA = -T/2 tr A1 dA - 1/2 tr Z dA'1 = 0.
Multiply (6.28) by 2 and manipulate the last term on the
right hand side (Magnus, 1988) to get
(6.29) dlnL/dA = -T tr A'1 dA + tr Z A1 (dA) A"1 = 0.
This can be rewritten as
(6.30) tr dA (TA_1 - A'1 Z A'1) = 0.
where A'1 - A'1 Z A-1 is symmetric. The necessary condition
for a maximum (Magnus, 1988) is
(6.31) TA’1 - A1 Z A1 = 0.
That is
T
(6.32) A = 1/T Z = 1/T S trfR* + aB' RJ ' (RM + aB'Rkt)
t=l
and if the matrices in (6.32) are multiplied using the
definition in (6.24), the result is
(6.33) A = + 2aB' Sko + aB'S^Ba' = 0.
Rearrange and substitute in for a (equation 6.26) to get
(6.34) A = S, - 2SokB(B'SkkB)-1B'Sko +
[ S^B (B' S^B) -1 ]B'S^B[S^B(B'S^B)1]'
which reduces to

153
(6.35) A = - S^B (B' S^B) _1B' Sko.
Solving (6.35) for B requires maximizing the following
likelihood function
(6.36) L-2T(B) = | A (B) | = | Sgg - SokB(B,SkkB)'1B'Sko| .
To proceed in estimating B the following identity is
applied (Johansen, 1988 and 1991c; Tso, 1981)
(6.37) | - S^BiB'S^Br'B'Sj =
ISoollB'S^B - B' Sko (SM) 'S^B | / IB'S^BI =
I Soo I I B' (Skk - Sko ( Sqq) ’’S^) B I / | B' S^B | .
Maximizing the likelihood function in (6.36) is now reduced to
minimizing the last term in (6.37) with respect to B. This
minimization can be determined by solving the following
eigenvalue problem
(6.38) | - Sk0(S00) ‘S0k) | = 0.
Equation (6.38) yield the eigenvalues X¡, . . . ,\p and
eigenvectors V = (v,,...,vp) normalized such that V'S^V = I.
The maximum likelihood estimator of B is now given by the
first r rows of V, that is the first r eigenvectors of
Sko (Soo) 'Sok with respect to S^. The eigenvectors are the
canonical variates, and the corresponding eigenvalues are the

154
squared canonical correlations of R* with respect to R0. These
eigenvalues are used to test how many cointegrating vectors
exist. The likelihood ratio test that there are at most r
cointegrating vectors is given in equation (6.13). The
estimates of the other parameters are found by inserting the
estimate of B into the respective equations.
6.4.2 1(2) Procedure
The discussion in section 6.4.1 is correct for the
situation where all of the variables are 1(1). However, all
of the variables in this dissertation have been confirmed to
be 1(2). Therefore, a few extensions have to be made to
account for the I(2)-ness.5 Fortunately, the discussion in
section 6.4.1 is basically correct for the 1(2) process with
a few exceptions.
The error correction model that anticipates 1(2)
variables is
k-2
(6.39) A2X, = Z + TAX,., + IIA2^., + et.
i=l
This model's error correction equation is similar to (6.14)
but more complicated. The parameter restrictions for the 1(2)
model are
5This section is based on Johansen's computer program and
the following preprint articles: October, 1990; June, 1991;
September, 1991; and October, 1992; and the published article
by Johansen, 1992a.

155
(6.40) II = otB'
(6.41) a}'TB} = 0r]'
where a and B are p x r matrices of rank r and 0 and 77 are (p-
r) x s matrices. Here s = 0,1,...,p-r, and a± and B± are
orthogonal to a and B. This insures that the 1(1) processes
is orthogonal to the 1(2) processes (i.e. no relationships
exist between the 1(1) process and the 1(2) process). The
general definition of 1 as a superscript is that a1' = (a'aj 'a,
a'a1 = I, and a'ai = 0.
The derivation of this model is similar to the derivation
of the 1(1) model in the prior section. The first step is to
arrange (6.39) into a loglikelihood function:
T k-2
(6.42) In L(II,r,A) = -T/2 ln|A| -1/2 E [ (A2Xt - E AX^Tj
t=l i=l
k-2
-AX,.,r - Xl2II) 'A-1 (A2X, - E AX^Tj
i=l
- AXt.,r - X,2II) ] .
The parameters rlf...,rk., can be eliminated by partially
maximizing (6.42) with respect to T,. When that is done the
result is
T k-2
(6.43) ainL/ar, = 1/2 E E [ (A2Xt.¡) 'A‘(A2Xt - AX^T, - AX^T
t=l i=l

156
- Xt.2II) + 1/2 (A2X, - AXt.¡Tj - AXt.,r
- X,.2II) 'A1 (AX,,) = 0.
To solve (6.43) for r¡ multiply by - and A, then multiply the
matrices out and add the like terms. When this is done the
result is
T k-2
(6.44) T, = Z Z[( A2x;,A2Xt) (A2x;„iA2X,.1)
t=l i=l
- (AXiAXj 'fAX^x^r)
- (A2x;.iA2xt,)-,(A2x;,xt.2n) ].
Substituting aB' in for II makes (6.44) the same as regressing
A2Xt, AX,.,r, and aB'Xt.2 on A2X„, . . . , A2X,_k+2. This yields the
residuals Rq,, Rlt, and R2t, and the residual product moment
matrices which is the same as (6.24).
The concentrated maximum loglikelihood function for the
1(2) model is then
T
(6.45) In L(a,B,A) = -T/2 ln|A| -1/2 Z [ (Re + TRlt
t=l
+ aB'R2t)'A-‘ (Rw + rRu + aB'R2t) ] .
However, instead of dealing with (6.45) Johansen (1992b)
suggests manipulating the following regression equation
Re = rRlt + aB'R2t + e,.
(6.46)

157
From (6.46) the 1(1) and 1(2) analysis can be performed. The
1(1) model is given by eliminating the unrestricted parameter
T and carrying out the analysis as in the previous section.
The first step in calculating the 1(2) model is to get
the values for r, a, and B from the 1(1) model with r
unrestricted (6.46). To solve the 1(1) portion of the model,
follow the steps outlined from equations (6.22) to (6.38) with
the exception of the additional parameter F (Johansen, 1992b).
Once the parameters and value of r are found, assume that they
are fixed and multiply (6.46) by a1' and a}'. The results of
multiplying (6.46) by a1' and a}' yields
(6.47) a1' = a1' TR,, + B'R2t + a‘'et, and
(6.48) oí i 'Rot = o-i'rR,, + aj'e,.
‘ '•' ' > * • i ■ ! : ■. i* i . .i . ■. _ :)ni.r¡ j • • i i •: í ry. c t *
The 1(2) model eigenvalue problem is based on solving
(6.48) . That is because by multiplying by a}' makes sure that
the 1(1) and 1(2) processes have no relationship. Define I =
B'B' + BjBj/ and substitute this definition into (6.48) to get
(6.49) = a*'r(B‘B' + B{Bx ') R„ + a}'et.
This equation can be rewritten as
(6.50) ai'R« = ai'TB^B'R,,) + The objective is to eliminate aj'TB1 similarly to the way a
was eliminated in the 1(1) model (equations (6.22) - (6.25)).

158
This is done by arranging (6.50) in maximum loglikelihood
format and maximizing the eguation with respect to ai'TB1.
The result of this expression is
(6.51) ai'TB1 = -ax ' S10B (B' SnB) '* - 07, • (B^ S„B) (B' S„B) '.
The actual eigenvalue problem is determined by solving
for A. This is accomplished the same way as before. Maximize
the likelihood representation of (6.50) in the trace format
like eguations (6.27) to (6.31) where Z = [aj'R,* + a} 'TB1 (B'Rlt)
+ 07,' (B.'RJ ] ' [0^'Rq, + a} 'TB1 (B'Rn) + 07,' (Bx 'Rlt) ] . Solving
this setup and substituting in (6.51) where needed the
eigenvalue problem is
(6.51) A = |pBx (S„ - SnB(B'S11B)1B'S11)Bi
- [B;;(Sio - S,,B (B'SnB) 'B^Sjo) a* ]
[aj' (So, - S10B(B'S11B)1B'SI0)al]
[B;(Sio - SnB(B'S11B)1B'SI0)a-l] | = 0.
The solution to (6.51) gives eigenvalues p, > ... > Pp_r > 0 and
eigenvectors W = (w,, . . . ,Wp_r) normalized by W'[BX(S„
S,,B (B' SUB) ‘B' S,,) Bx ] W = I. Note, B and Bx transform the
differences which are 1(1) variables. The aj coefficient
transforms the second differences which are stationary by
assumption. The likelihood ratio test to determine the number
of eigenvalues that are significantly different than zero is

159
p-r
(6.52) -2 In (Qr,) = -T 2 ln(l - p,)
i=s+l
where s = (0,1,...,p-r-1). The maximum likelihood estimators
(for fixed values r, a, and B) are r¡ = (w,,...,w(), and 0 =
[B1(S10 - S,,B (B' S,,B) '*B'S10) a} ]77. The variance matrix A is equal
to (6.51) without the absolute value symbols and p.
In summary, the steps that need to be taken to determine
the number of 1(2) cointegrating equations using Johansen's
method are:
1. Compute using OLS on the regression AXt on AX,^, ..., AXj.
k+1/ and Rjrt from the regression X,_k on AXt.¡, . . . , AXt.k+1.
2. Compute the moment matrices S^, S^, and Sk0.
3. Solve the equation | Xs^ - S^ScJ-'S*) |=0, yielding p
eigenvalues \ and determine the corresponding
H- V-, .•» y ( t I • 1 ,• - -j . , .
eigenvector matrix V. Normalize V such that V 'S^V = I.
4. Determine the number of cointegrating vectors using the
likelihood ratio test statistic for the hypothesis test
that there are at most r cointegrating vectors:
P
-2ln(Qr ) = -T I In (1 - X.)
i=r+l
where Xr+1,...,Xp are the p-r smallest canonical
correlations (eigenvalues).
5. Plug the in the value for a and B from the 1(1) model
into the 1(2) model. Compute a new set of residuals by

160
regressing A2Xt, AXt.,r, and aB'X,.2 on A2Xn, . . . , A2Xt.k+2. This
yields the residuals R^, R„, and R2t respectively.
6. Compute the moment matrices S10 and S„.
7. Solve the following eigenvalue problem
A= |pB^ (Sn - S11B(B'S11B)'1B,S11)Bi
- [Bi(S10 - S,,B (B' SnB) '*B' S,0) a} ]
[aj' (Soo - S10B (B' S,,B) "‘B' S10) a j ]
[B; (S10 - S,,B (B/SI1B)'1B'S10) a| ] I = 0.
where the eigenvalues are p, > ... > Pp_r > 0 and
eigenvectors W = (w,,...,w ) are normalized by W'[B^(Sn -
SuBÍB'SpBr'B'SuJBJW = I.
8. Determine the number of cointegrating vectors using the
. . ' ... . r • - • .N i- L - » , . . 4. . , •
likelihood ratio test statistic for the hypothesis test
that there are at most p-r cointegrating vectors:
p-r
-21n(Qrs) = -T E ln(l - Pi)
i=s+l
where s = (0,1,...,p-r-1).
9. Given those results there are p-r-s 1(2) trends.
The next section applies the 1(2) method on the inequalities
calculated in Chapter 5.

161
6.4.3 G-7 Multiple Cointeqration Results
This section tests the hypothesis that all four total
inequalities (income, government expenditure, investment
expenditure, and industrial employment) for the G-7 countries
are cointegrated. It was determined in Chapter 5 that all
four of these inequalities are converging for the G-7 and has
since been hypothesized that these variables have a long-run
equilibrium. That is the four inequality indices may drift
apart in the short-run, but will return to the long-run
equilibrium.
The results from Johansen's test are shown in Table 6.3.
First, the results of the eigenvalue problem (eq. 6.38) and
the associated eigenvectors are presented. The value of r or
the number of significant eigenvalues are determined by
reading the Qr column from top to bottom and comparing the
observed value with the 95% critical value (C,,.,) for p-r
degrees of freedom. Once the value of r has been determined,
then the value of s is chosen by reading the row associated
with the selected r value in the Qrs rows. The observed values
are compared with the critical values at the bottom of the
table (Cp.r.s) . The value of s determines the number of 1(1)
trends in the model. For example, if s is equal to one, then
there is one 1(1) trend in the model.
The trace statistic clearly rejects r = 0, since the test
statistic is 80.87 and the 95% calculated critical value is
only 49.09. The hypothesis H, of r < 1 is also clearly

162
Table 6.3
Johansen's” Multiple Cointegration Test (G-7)
Eigenvalue (o) :
0.638
0.536
0.280
0.123
Eigenvectors
55.047
(B) :
-251.057
107.747
224.610
-6.439
32.678
-12.882
-133.018
-32.331
177.140
-40.991
-106.753
125.960
283.937
-323.738
-17.699
Test Statistics
p-r r
Qr,s
Qr Cp_r(95%)
4 0
103.411
s=0
48.233
S=1
16.545
s=2
3.056
s=3
80.870
49.097
3 1
71.819
s=0
27.182
S=1
1.756
s=2
44.241
31.618
2 2
36.999
s=0
2.303
S=1
16.567
17.652
1 3
29.536
s=0
4.742
8.106
p-r-s
4
3
2
1
Cp-r-s
(95%)
49.097
31.618
17.652
8.106

163
rejected with the statistic being 44.24 and the critical value
being 31.62. Therefore, r does not equal 0 or 1. The
hypothesis H2 of r < 2 is a borderline case since the
statistic 16.57 corresponds roughly to the 95% critical value
17.65 in the asymptotic distribution. The hypothesis that r
= 2 cannot be rejected, determining that r = 2 means that
there are two linear combinations of x, that are stationary.
More will be stated about this after the value of s is
determined.
To determine the value of s, the row equal to r = 2 is
read. The hypothesis H20 (i.e. r = 2 and s = 0) is rejected
given the test statistic 37.00 and the critical value of
17.65. Therefore, s does not equal 0. The next test for s <
1 cannot be rejected. This is determined by comparing Q2, =
2.3 with the critical value of 8.11. Therefore, the number of
common 1(2) trends in the data series is p-r-s = 1 and the
number of common 1(1) trends is s = 1.
Having decided that r = 2, the estimate of the two
cointegrating vectors (B) are given by the first two columns
of eigenvectors in Table 6.3. The complication is that since
all of the variables are 1(2), the cointegrating vectors are
1(1).6 The vectors B'X, in this case are two linear
combinations, and they are 1(1) (not stationary). However,
this representation can be made stationary (1(0)) by including
6If all of the variables were 1(1) then the two
cointegrating vectors would be stationary at the 1(0) level.

164
the differences, that is B'X, + /cB^'AX, (Johansen, 1991a and
b). The k coefficient is equal to (a'a) ‘a'TBj(B7'B7) 1 =
a{'TB7 (Bj'B7)'1, a} = a(a'a)'1, and B7 = Bj^. The two
normalized stationary relationships become
(6.53) INC - .12 GOV, -.59 INV, + 2.29 IND, + 144.93 AINC
+ 78.33 AGOV, + 202.67 AINV, - 7.31 AIND,
and
(6.54) INC - .13 GOV, -.71 INV, - 1.13 IND, - 70.17 AINC
- 37.93 AGOV, - 98.13 AINV, + 3.54 AIND,.
The B vectors used in (6.53) and (6.54) are in Table 6.4,
and are equal to the first two columns of the eigenvector in
Table 6.3, with the exception of being normalized" by the
income coefficient. These two equations represent the long-
run equilibrium among the four inequality indices for the G-7.
Given that there are two stationary relationships, the
equilibrium can be thought of as a plane instead of a line in
hyperspace.7
The next step is to use all the information from this
estimation to determine which variable or variables are
determining this equilibrium. The two normalized
7Hyperspace in this case refers to a four dimensional
space with two stationary relationships forming an equilibrium
within this space. Since there are two relationships, the
equilibrium is a plane.

165
Table 6.4
Cointegrating Vectors and Adjustment Coefficients
from the G-7
The estimates
of the cointegrating
vectors B, and
the
supplementary
vectors Bj1' = (BiBi)
'B^rj, and B^ =
B*
Bj1'
B l
1.0
1.0
5.509
10.533
-0.12
-0.13
-61.812
5.693
-0.59
-0.71
19.934
14.729
2.29
-1.13
-0.451
-0.531
The estimates
the supplementary
a
of the cointegrating
vectors a}1' = (a’a1)
a}1'
vectors a, and
‘a, and a2± = a1 al
-.002
.001
0.009
-0.011
. 001
-.001
0.008
0.006
-.007
-.002
-0.002
-0.001
-.001
. 000
0.002
0.034
'These B's are normalized by Income.

166
cointegrating vectors (Table 6.4) roughly have the following
relationships (1,*,-1,*) and (1,*,-1,-1). The interpretation
of the first vector is that income inequality and the
inequality in investment are stationary and the other two
variables do not affect this equilibrium. If either income or
investment were removed from the equation, the result would be
a non-stationary relationship. The other two inequalities do
not contribute to this stationary equilibrium. The
interpretation of the second vector is that the inequality in
income, investment, and industrial employment form a
stationary long-run equilibrium. In this case government
expenditure inequality has no effect on this equilibrium.
Determining the number of significant s's identifies how
many common 1(1) processes there are in the model. It was
found that there is one common 1(1) process. In addition,
there is only one common 1(2) trend that drives all of the
variables. To determine the common 1(1) trend is difficult.
Therefore, the determination of the common 1(2) trend is
addressed.
The coefficient in Table 6.4 shows which variables are
actually 1(2).8 The variable that has a coefficient closest
to one or negative one is the common 1(2) trend. The B¿
vector indicates that the inequality in the number of people
8To clarify the B's further, the px(r+s) matrix (B,B|)
represents all possible cointegrating relationships. That is,
(B,B})'Xt is either 1(1) or 1(0), whereas B^'Xt is an 1(2)
process that does not cointegrate.

167
employed in industry is the 1(2) variable. That means that
when an innovation occurs and the inequalities are out of
equilibrium, the inequality in the number of people employed
in industry adjusts to restore the equilibrium. The
inequality in government expenditure is in equilibrium with
the rest of the variables, but government does not contribute
to this equilibrium.
To develop this further, the interpretation of a is
addressed. The coefficient a in Table 6.4 is interpreted as
the weights with which the inequalities enter the system. The
economic interpretation is that a represents the average speed
of adjustment towards the estimated equilibrium. The small
coefficients indicate a slow adjustment and a large
coefficient represents a fast adjustment. The adjustment
coefficients for a in Table 6.4 are small indicating that the
inequalities of the variables adjust minimally to the
deviations among the inequality in income, investment, and
industry. This interpretation of a would be important if the
variables were 1(1), however, they are 1(2).
The important a in Table 6.4 is a\. a\ is interpreted
as the linear combination that describes the common 1(2)
trend. The heaviest weights are given to industrial
employment and income. Industrial employment has the heaviest
weight, hence, the I(2)-ness of the model is ascribed to the
inequality of the number of people in industry. Thus, the
number of people in industry is the variable that reacts the

168
most to innovations. In simpler terms, when a shock to one of
the inequalities occurs which forces the inequalities out of
equilibrium, the main force to restore the equilibrium comes
from the inequality in industrial employment.
The importance of the discussion on the a's and B's is
that they help explain the equilibrium. It was determined
that the common 1(2) trend in the model is the inequality in
industrial employment. In addition, the inequality in
industrial employment reacts first and the strongest to any
innovation in the model.
To complete the analysis the meaning of B}1' and a}1' is
discussed. There exist other combinations in the model that
reduce the 1(2) variables to an 1(1) relationship. That is
what the B}1' vector represents. The 1(1) combination appears
to be income, government, and investment. The a}1' vector
indicates that the main force behind this relationship is the
inequality of government and income. However, this
combination does not cointegrate with the first differences of
the variables by design of the model (Johansen, 1991) . These
coefficients are not used in this thesis.
The final table, Table 6.5, is provided to give the
estimates of r. r is the coefficient of the lagged first
difference term in the error correction model (eq. 6.39).
These estimates allow the error correction model to be
estimated, but are not utilized in this dissertation. The
values of T are similar because there is only one parameter

169
restriction. This is due to the fact that the reduced rank
hypothesis aj'rB1 = matrix to have rank s = 1. The estimates of r in the 1(1)
model are shown in Table 6.5 under the unrestricted results.
The estimates for the 1(2) model are under the restricted
heading.
Table 6.5
Estimates of Gamma from the G-7
T Estimated from the 1(1) model (unrestricted)
INC
-1.043
-0.200
-0.073
-0.548
GOV
2.498
-1.191
-0.716
0.997
INV
-0.121
-0.598
-1.833
-1.411
IND
-0.735
0.141
0.075
' .'-I ' ' "X —
-1.494
r estimated from
the 1(2)
model (restricted)
INC -0.895
-0.179
-0.070
-0.480
GOV 2.448
-1.198
-0.717
0.974
INV 0.148
-0.560
-1.827
-1.288
IND -0.825
0.128
0.073
-1.536
In summary, the stationary equilibrium is dependent on
two stationary relationships. The first stationary
relationship for the G-7 is described as the inequality in
income and the inequality in investment expenditure. The

170
second relationship is the inequality in income, investment
expenditure, and the number of people employed in industry.
The inequality in industrial employment was determined to be
the common 1(2) trend. That means that whenever an innovation
occurs in one of the inequalities, and there is a deviation
from the long-run equilibrium, industrial employment adjusts
first to return the economy to the long-run equilibrium. This
long-run equilibrium can be described but not represented
graphically. The graphical representation is that of a plane
in four dimensional space. The two stationary relationships
create a plane in the four inequality variable space. This
plane acts as an attractor every time the four inequities
deviate from this equilibrium.
6.4.4 OECD Multiple Cointegration Results
This section tests the hypothesis that all four total
inequalities (income, government expenditure, investment
expenditure, and the employment in industry) for the 14 OECD
countries are cointegrated.9 It was determined in Chapter 5
that all four of these inequalities are converging for the
OECD and was hypothesized that these variables have a long-run
equilibrium. This hypothesis addresses the implications of
adding more countries to the G-7 long-run equilibrium.
9The 14 OECD countries included in this analysis are the
U.S., Canada, Japan, the U.K., W. Germany, France, Italy,
Austria, Belgium, Denmark, the Netherlands, Norway, Ireland,
and Spain.

171
The reason for adding more countries to the G-7 was to
broaden the policy implications from this work. The G-7
countries are highly integrated meaning their economies are
intertwined. Therefore, more countries are added to this
system to determine if the eguilibrium is affected. The Other
7 countries are all fairly rich, and it would enhance the
results of this dissertation if middle income countries could
be included. Unfortunately, due to data constraints only
seven more countries could be added (see APPENDIX E about data
constraints). The additional seven countries that were added
to the G-7 were Austria, Belgium, Denmark, the Netherlands,
Norway, Ireland, and Spain.
The results from the OECD analysis are similar to the G-7
in the sense that there appears to be two cointegrating
vectors. This is not surprising considering that the G-7
dominates the 14 OECD countries. Table 6.6 contains the
output from the Johansen's cointegration analysis. Once
again, r = 2 and s = 1 cannot be rejected at the 95%
significance level. Hence, there are two cointegrating
vectors, one common 1(1) trend and one common 1(2) trend.
Having decided that r = 2, the estimate of the two
cointegrating vectors (B) are given by the first two columns
of eigenvectors in Table 6.6. The two normalized stationary
relationships for the OECD are
(6.55) INC - .61 GOV, - .64 INV, - 5.27 IND, + 128.4 AINC

172
Table 6.6
Johansen's Multiple Cointegration Test (OECD)
Eigenvalue (o):
0.688 0.504
0
.260
0.143
Eigenvectors (B):
-35.
718 -225.140
133
.669
215.392
21.
627 23.452
-33
. 151
-111.575
22 .
905 154.150
-41
.214
-107.683
188.
173 179.047
-358
.899
31.076
Test
Statistics
• r - • . _
p-r
r
Qr,s
O
O
,r(95%)
4
0 99.633 46.278
16.756
2.807
83.555
49.097
s=0 s=l
s=2
s=3
3
1 73.589
27.506
4.782
41.646
31.618
s=0
S=1
s=2
2
2
38.685
3.930
16.398
17.652
S=0
S=1
1
3
27.406
5.557
8.106
s=0
p-r-s 4
3 2 1
Cprs 49.097 31.618 17.652 8.106
(95%)

173
+ 48.83 AGOV, + 184.39 AINV, -3.68 AIND,
and
(6.56) INC - .1 GOVt -.69 INV, - .80 IND, - 135.12 AlNC
- 51.4 AGOV, - 194.1 AINV, + 3.88 AIND,
The B vectors used in (6.55) and (6.56) are in Table 6.7.
These two vectors are equal to the first two columns of the
eigenvectors in Table 6.6, with the exception of being
normalized by the income coefficient.
The cointegrating 1(1) relationships are different than
the G-7. Both eigenvectors appear to have strong
relationships. The first eigenvector may have the following
cointegrating relationship (1,-1,-1,*) and the second
cointegrating relationship may be (1,*,-1,-1). The first
vector indicates that income inequality, the inequality of
government expenditure, and the inequality in investment
expenditure form a stationary equilibrium. The second vector
is the same as the G-7 case where income inequality, the
inequality of investment expenditure, and the number of people
employed in industry form a stationary equilibrium. The
interesting development here is that government expenditure
plays a more important role in the 14 OECD countries than in
the G-7.

174
Table 6.7
Cointegrating Vectors and Adjustment Coefficients
from the OECD
The estimates of the cointegrating vectors B, and
the supplementary vectors B{w = (BXBX) '*B^77, and Bx = Bxi/x
B*
Bj1'
B
2
1
1.0
1.0
6.227
11.397
-0.61
-0.10
-54.325
4.334
-0.64
-0.69
10.174
16.366
-5.27
-0.80
6.187
-.327
The estimates
the supplementary
a
of the cointegrating
vectors aj1' = (axax)
ai1'
vectors a, and
■'ax0, and ax = a1 a±
-.002
.001
0.010
0.006
.000
-.002
0.004
0.010
-.007
-.001
-0.003
-0.006
-.001
. 000
-0.002
0.056
’These B's are normalized by Income.

175
The coefficient Bj in Table 6.7 shows which variables are
actually 1(2).10 The variable that has a coefficient closest
to one or negative one is the common 1(2) trend. The B\
vector indicates that the inequality in the number of people
employed in industry is the 1(2) variable. That means when an
innovation creates disequilibrium, the inequality in the
number of people employed in industry adjusts in such a way
that the four inequality indices return to their long-run
equilibrium. This is the same as the G-7 case.
The result that industrial employment is the main force
is confirmed by in Table 6.7. As in the G-7 case, the
heaviest weight is given to the inequality in industrial
employment. Therefore, the stabilizing force in this model is
the inequality in industrial employment. However, the second
largest value for a2± is the inequality of government
expenditure. Hence, when the economy is out of equilibrium,
the inequality of government expenditure helps to return the
economy to the long-run equilibrium. This result is contrary
to the G-7 results where government expenditure was not
important to the equilibrium process.
To complete the analysis the meaning of B}1' and a}1'
should be discussed. There exist other combinations in the
model that reduce the 1(2) variables to an 1(1) relationship.
10To clarify the B's further, the px(r+s) matrix (B,Bj)
represents all possible cointegrating relationships. That is,
(BjBjj'X, is either 1(1) or 1(0), whereas B^')^ is an 1(2)
process that does not cointegrate.

176
That is what the B}1' vector represents. The 1(1) combination
appears to be income and government. The a}1' vector
indicates that the force behind this relationship is the
inequality of government expenditure and income which is the
same as the G-7 case. As stated before, this combination does
not cointegrate with the differences by design of the model
(Johansen, 1991a). These coefficients are not directly used
in this thesis.
The final table, Table 6.8, is provided to give the
estimates of T. T is the coefficient of the lagged first
difference term in the error correction model (eq. 6.39).
These estimates allow the error correction model to be
estimated. These values are not utilized in this
dissertation. The values of r are similar because there is
only one parameter restriction. This is due to the fact that
the reduced rank hypothesis aj'rB1 = r) =2x2 matrix to have rank s=l. The estimates of r in the
1(1) model is shown in Table 6.8 under the unrestricted
results. The estimates for the 1(2) model are under the
restricted heading.
In summary, there appears to be two stationary
relationships in the OECD sample. The first relationship
includes the inequality in income, government expenditure, and
investment expenditure. The second equilibrium is the same as
the G-7 equilibrium: the inequality of income, investment
expenditure, and the number of people employed in industry.

177
Table 6.8
Estimates of Gamma from the OECD
T Estimated from the 1(1) model (unrestricted)
INC
-1.227
-.217
-.092
-.723
GOV
3 . Ill
-1.250
-.942
1.690
INV
-.793
-.496
-1.701
-1.733
IND
-.448
. 101
. 071
-1.198
r Estimated from the 1(2) model (restricted)
INC
-1.096
-.219
-.096
-.730
GOV
2.927
-1.247
-.937
1.699
INV
-.487
-.501
-1.710
-1.749
IND
-.567
. 103
.075
-1.191
The inequality in industrial employment was determined to be
the common 1(2) variable. In addition, whenever the economy
deviates from the long-run equilibrium, industrial employment
adjusts first to return the economy to the long-run
equilibrium. Lastly, government expenditure is the second
variable to assist in returning the economy to the long-run
equilibrium. Given the fact that government expenditure is
important in the 14 country OECD sample and not the G-7, some
analysis should be done to determine the structure of the
Other 7.

178
6.4.5 Other 7 Multiple Cointeqration Results
The fact that the G-7 and the 14 selected countries of
the OECD yield such different results the cointegration of the
Other 7 is examined.11 This can be done simply due to the
properties of Theil's inequality index. Theil's inequality
index is additively decomposable. Therefore, the within-
region inequalities for the Other 7 which are reported in
Tables 5.4 and 5.5 are the same as the total inequality for
the Other 7.
Chapter 5 established that all four inequality indices
were declining for the Other 7, indicating that these
countries are converging in terms of income, government
expenditure, investment expenditure, and industrial
employment. Johansen's multiple cointegration analysis is
applied to determine if there is a long-run relationship among
the four inequalities for the Other 7.
The results of Johansen's test are shown in Table 6.9.
These results are different than the G-7 and 14 country OECD
sample in that there appears to be only one cointegrating
vector. Comparing the trace statistic of 59.43 with the 95%
significance level of 49.1 assures that r is greater than
zero. The hypothesis H, of r < 1 is a borderline case since
the statistic is 31.5 and the critical value is 31.6. The
test for the hypothesis that r < 2 is clearly rejected.
“The Other 7 countries are defined as Austria, Belgium,
Denmark, the Netherlands, Norway, Ireland, and Spain.

179
Table 6.9
Johansen's Multiple Cointegration Test (Other 7)
Eigenvalue (o):
0.539 0.490
0.170
0.015
Eigenvectors
(B) :
112.726
-614.485
18.477
257.797
-27.867
-4.397
-11.576
-37.536
59.672
261.158
-118.687
-73.889
-455.087
109.353
265.419
0.401
Test
p-r
Statistics
r
Qm
Qr
Cp.r(95%)
4
0 102.093
56.855
21.615
6.947
59.429
49.097
3
s=0
1
S=1
66.834
s=2
31.603
s=3
10.371
31.514
31.618
2
2
s=0
S=1
22.096
s=2
7.561
7.257
17.652
1
3
s=0
S=1
4.611
s=0
0.561
8.106
p-r-s 4
^p-r-s
(95%)
3 2 1
49.097
31.618
17.652
8.106

180
Therefore, it is accepted that r = 1. That is, there exists
one cointegrating vector in the Other 7 sample.
The number of 1(1) and 1(2) trends can be determined
after the value for s is determined. To determine the value
of s, the row equal to r = 1 is read. The hypothesis H, 0 (i.e.
r = 1 and s = 0) is rejected given the test statistic 66.83
and the critical value of 31.62. Therefore, s does not equal
0. The next test for s < 1 is also rejected. This is
determined by comparing Q,, = 31.6 with the critical value of
17.7. The last hypothesis of s < 3 also cannot be rejected.
The critical value for this hypothesis (H13 that is r = 1 and
s = 3) is 8.1 and the statistic is 10.4. That means that r =
1, s = 3, and p-r-s = 0. The interpretation is that there is
one cointegrating vector, three 1(1) trends, and no 1(2)
trends in the model. In other words, this is an 1(1) model
not 1(2) .12
The apparent stationary relationship is given by the
first vector in B. The stationary relationship is formed by
the inequality in investment expenditure and government
expenditure. Normalizing this vector by investment
expenditure the stationary relationship is then
1.88 INC - .467 GOV, + INV, + 7.63 INDt.
12The inequalities of the Other 7 data were confirmed to
be 1(1) using the Augmented Dickey-Fuller and Phillips unit
root tests.

181
Since the model is 1(1), this cointegrating relationship is
1(0). It is appropriate to state that the inequality in
income and industrial employment are in equilibrium, but do
not influence this equilibrium. These results are contrary
to the G-7 results. In fact, these results indicate that the
two groups are dissimilar. The G-7 sample clearly has an 1(2)
trend while the Other 7 only has an 1(1) trend. The 14
country OECD sample has an 1(2) trend because when an 1(1) and
1(2) are added together the series becomes 1(2) (Engle and
Granger, 1991).
The differences between the Other 7 and G-7 indicates
that there are underlying structural differences. In the G-7
case income, investment expenditure, and industrial employment
create an equilibrium; where the Other 7's equilibrium is
between investment and"government expenditure. < The OECD
equilibrium may reflect the complexity of combining two
equilibriums from different populations and creating one
equilibrium. The OECD equilibrium has two stationary
relationships; income, investment expenditure, and industrial
employment, and income, government expenditure, and investment
expenditure. The first vector mentioned appears to show the
G-7 influence on the equilibrium and the latter shows the
Other 7 influence on the equilibrium. The fact that the two
groups of countries are structurally different may indicate
that they should not be pooled.

182
There is no way to resolve this problem given the current
techniques and data. Summers and Heston did an excellent job
of creating a large data set that represented many of the
countries in the world. Hopefully, as the World Bank takes
over this task, they will improve the data as well as be able
to extend the length of the data for more countries. This
would allow the complex issue of what happens to the
equilibrium as more countries are added to the system.
6.5 Summary and Interpretation
The analysis began by confirming convergence among the G-
7 and the 14 selected OECD countries in terms of the
inequality in income, government expenditure, investment
expenditure, and in the number of people employed in industry.
The next step was to determine if any of the movements were
-* ' • • •■>*•<* • ' » r • *, # ■ i * » ■* | * r y . * v fr>; ■ • • • • . • >
cointegrated, that is, was there a long-run equilibrium among
the variables of interest. A summary of the integration and
multiple cointegration results are presented in Table 6.10.
The order of integration in Table 6.10 (column 2)
indicates that the country samples are not the same. The G-7
and the 14 OECD countries have an 1(2) structure while the
Other 7 has an 1(1) structure. This indicates that the
inequalities for the Other 7 are less disperse than the G-7
and OECD sample. The implication of the G-7 and Other 7 being
integrated of different levels implies that the two groups
have different structures. This becomes more clear as the
cointegration analyses are summarized.

Table 6.10
Summary of Integration and Cointegration Analysis
Johansen's Multiple Cointegration
Group of
Countries
ÃœJ
Order of
Integration
L2J
I(D
Relationships
UJ
1(2)
Relationships
LD
G-7
1(2)
fa. Income and Investment
Industrial
Employment
b. Income, Investment, &
Industrial Employment
Industrial
Employment
OECD
1(2)
a. Income, Government, &
Investment
Industrial
Employment
b. Income, Investment, &
Industrial Employment
Industrial
Employment
Other 7
KD
Investment & Government
N/A
183

184
The cointegration analysis of the G-7 found that there
appears to be two cointegrating vectors (column 3) . These two
stationary relationships (the inequality in income and
investment expenditure; and the inequality of income,
investment expenditure, and industrial employment) appear to
form a long-run equilibrium. The long-run equilibrium for the
14 selected OECD countries also includes two stationary
relationships (the inequality in income, government
expenditure, and investment expenditure; and the inequality of
income, investment expenditure, and industrial employment).
The Other 7's equilibrium only consists of the inequality in
government expenditure and investment expenditure. All of
these relationships are 1(1). These long-run equilibriums are
stationary as long as no structural changes take place.
The last -column in Table 6.10 shows the -1(2) trend in
each sample. The Other 7 does not have an 1(2) trend that is
why N/A is placed there. The 1(2) trend for the OECD and G-7
is the inequality in industrial employment. The
interpretation of these results and the relationships found in
this study compared with others is discussed next.
Several studies in the Convergence Chapter indicated that
investment is influential to economic growth (Zind, 1991;
Barro, 1991; Baradaran-Shoraka, 1992; and De Long, 1992).
Kugler (1991) found a cointegrating relationship between
income and investment expenditure. Although he used a few
different countries than the G-7 sample, his results support

185
those of the G-7 in this dissertation. In fact, investment
expenditure was shown to be cointegrated in all of the samples
(G-7, OECD, and Other 7).
The difficulty is in interpreting the results concerning
the inequality of government expenditure. The inequality of
government expenditure is in equilibrium with the other
variables in the G-7; however, it does not influence this
equilibrium. Although the inequality in government
expenditure declines over time, its movements or changes over
time do not appear to be similar to the other three inequality
indices. MacDonald et al. (1989) showed that there was a
long-run equilibrium between the log of government expenditure
and income for three of the G-7 countries.
In this dissertation, the G-7 pairwise cointegration
results between the inequality in government expenditure and
the inequality in income was also tested. Once again, the
relationship between government and income is not
overwhelmingly supported (significant at the 10% confidence
level). There may be several reasons why MacDonald et al.
(1989) found a relationship between government expenditure and
income and no relationship was found in this dissertation.
First, the data for the two studies came from different
sources, and the MacDonald et al. data were not adjusted for
purchasing power parity. Second, the variables were defined
differently. In this dissertation, an index was created that
represented all of the countries simultaneously. MacDonald et

186
al. (1989) actually tested the cointegration of income and
government within each country. Therefore, their study did
not deal with international relationships. Rather they just
compared the cointegration results within the U.S. with those
of the other three countries. Lastly, the objectives of the
studies were different. In this dissertation an attempt to
describe the co-movements of the inequalities of major factors
in the G-7 economy was made. The MacDonald et al. study in
contrast established a relationship within an economy of two
major factors in the economy for four countries.
The analysis is more complex when the Other 7 and the
OECD are considered. These two groups supported the idea that
government expenditures influence the equilibrium for the
Other 7 and the 14 OECD countries. The fact that the G-7
equilibrium was stationary without government expenditure and
the OECD had a stationary vector with government expenditure
suggests two things. First, as more countries are added to
the G-7 sample, government expenditure becomes more important.
Second, the inequality in government expenditure changes over
time, similarly to the changes in the other inequality indices
for the 14 country sample.
The Other 7 and OECD results are similar to what Barro
(1991) and Baradaran-Shoraka (1992) found. Both of their
studies found that government expenditure was significantly
related to the growth rate of income for 98 countries. The
Institutionalist idea of governmental policies being the chief

187
determinant of income inequality (Wright, 1978) was also
supported with the Other 7 and OECD sample. Grier and Tullock
(1989) found that OECD countries were converging in terms of
income and that government expenditure was significantly
related to the growth rate of income for the OECD and the rest
of the world.
The evidence that government expenditure is more
important for the Other 7 is clear. Consider the eigenvector
value for government expenditure. It was close to zero for
the G-7. When the Other 7 were added to the G-7 sample, the
coefficient for government expenditure increased to above 0.5.
This suggests that adding seven countries, which on average
are less endowed than the G-7, changed the equilibrium. The
Other 7 countries are smaller in all terms than the G-7
(population, income,- government and investment expenditure,
and the number of people employed in industry). However, they
influenced the stationary equilibrium. This can be
interpreted as the reliance of the Other 7 on government
expenditure as a means of economic growth. If Section 5.4.2
is referred to, it is confirmed that the Other 7 increased
government expenditures at a faster rate than the G-7. In
addition, the multiple cointegration test for the Other 7
indicated that the only stationary equilibrium that existed
was between the inequality in investment and government
expenditure.

188
The way to interpret the government expenditure results
is to look at the level of economic development of the group
of countries in question. The Other 7 countries are less
endowed than the G-7. They can be considered the second
strata. The structures of the first strata (G-7) and the
second strata (Other 7) are different. The second strata
depends on investment and government expenditure for economic
growth while the G-7 depend on investment expenditure and
industrial employment for growth. However, the Other 7 are
converging in terms of income with the G-7. Therefore, their
dependence on investment and government expenditure should not
be considered a suboptimal growth equilibrium. When these
two groups are combined into 14 countries, the influence of
both groups are reflected in the new equilibrium.
The last set of.results to interpret are those concerning
the industrial employment. It was determined that industrial
employment was the 1(2) variable in the G-7 and OECD sample.
In addition, the number of people employed in industry adjusts
the quickest to correct short-run deviations from the long-run
equilibrium. These deviations occur when innovations take
place. This indicates that labor demand in the G-7 and OECD
responds the most to innovations within the economies. These
results are similar to what is discussed in several
introductory macroeconomic text books about the relationship
between income growth and the unemployment level (Baumol and
Blinder, 1985; McConnell and Brue, 1990). That is, during

189
fast economic growth unemployment decreases and during
slowdowns in growth, unemployment increases.
It is clear that there exists a long-run eguilibrium
among the ineguality in income, investment expenditure, and
industrial employment for the G-7 and 14 country OECD sample.
Investment expenditure and specifically industrial employment
were extremely important when considering the convergence of
those groups of countries. It was determined that the
inequality in industrial employment was the major factor that
adjusted when an innovation occurred for the G-7 and OECD.
The Other 7, however, indicated the importance of government
expenditure in their economy but not industrial employment.
The Other 7 are an example of a group of countries that are
converging with the G-7 although they have a different
underlying structure. • i< •- —. i >- •— - —

CHAPTER 7
SUMMARY AND DISCUSSION
Two hypotheses were tested in this dissertation. The
first hypothesis was to determine whether the countries in the
G-7 and 14 selected OECD countries are converging in terms of
income, government expenditure, investment expenditure, and
industrial employment. This hypothesis was tested using
Theil's inequality index. The second hypothesis tested
whether the four inequality transformed variables have a long-
run equilibrium (i.e. do they move together over time). This
test required the use of cointegration analysis.
The results from testing the first hypothesis were no
surprise. It’was determined that the inequality in all four
variables for the G-7, Other 7, and 14 OECD countries has
declined over the period 1950 to 1988 suggesting convergence.
A couple of other studies have shown that the richest
countries in the world are converging in terms of income (Gao
et al. 1992; Grier and Tullock, 1989).
The new information came from the other variables that
were tested for convergence. Government expenditure,
investment expenditure, and industrial employment were all
found to be converging for the G-7, Other 7, and the 14
190

191
countries of the OECD. The fact that the indices all declined
gives support to the idea that they may be cointegrated (move
together over time).
The four inequality indices were then tested for
cointegration. Before cointegration tests could be done, the
level of integration was determined. The augmented Dickey-
Fuller and Phillips tests showed that the four inequality
indices were all 1(2) for the G-7 and the OECD. Given that
the indices were all integrated of the same level,
cointegration tests were conducted.
The inequality transformed variables were tested for
pairwise cointegration (Durbin Watson and Augmented Dickey-
Fuller cointegration tests) where the inequality of income was
regressed against the other three inequalities. In general
the results indicated that all three pairs were cointegrated.
These findings indicated that the inequality in income forms
binary stationary equilibriums with the inequality in
government expenditure, the inequality in investment
expenditure, and the inequality in industrial employment. The
stationary equilibriums were found in the G-7 and the 14
country OECD sample. These results were helpful in describing
the co-movements in the inequalities. However, the hypothesis
was that all four inequality indices were in equilibrium. To
test that hypothesis, multiple cointegration was used.
The samples were tested for multiple cointegration using
Johansen's 1(2) method. The G-7 had two stationary long-run

192
relationships. The first cointegrating vector was between the
inequality in income and investment expenditure. The second
cointegrating vector was among the inequality in income,
investment expenditure, and industrial employment. These
results indicated that there is a long-run equilibrium among
the indices that is stationary as long as no structural
changes take place. The inequality of government expenditure
is in equilibrium with the other variables in the G-7, but it
does not influence this equilibrium. Although the inequality
in government expenditure declines over time, its movements or
changes over time do not appear to be similar to the other
three inequality indices.
It was also determined that industrial employment was the
1(2) variable in the G-7 model. Industrial employment adjusts
the quickest out of the four inequality indices to correct
short-run deviations from the long-run equilibrium. These
deviations would occur when innovations take place. This
suggests that labor demand in the G-7 responds to innovations
within the economies.
The G-7 was then combined with seven more countries from
the OECD which are referred to as the Other 7 (Austria,
Belgium, Denmark, the Netherlands, Norway, Ireland, and
Spain). This 14 country OECD sample was assembled to broaden
the policy implications from the results. The G-7 countries
economies are highly integrated (i.e. intertwined). The
obvious question is, "what happens to the G-7 equilibrium when

193
more countries are added?” The Other 7 countries are all
fairly rich and it would enhance this dissertation if middle
income countries could be included. Unfortunately, due to
data constraints only seven more countries could be added (see
APPENDIX E about data constraints).
Given the argument above, the results from the 14 OECD
countries cointegration test were similar to that of the G-7
in that there were two cointegrating vectors. The two
cointegrating vectors were the inequality of income,
government expenditure, and investment expenditure; and the
inequality of income, investment expenditure, and the number
of people employed in industry. These two stationary
relationships appear to form a long-run equilibrium. The 1(2)
variable in the OECD model was determined to be industrial
employment and is interpreted in the same way as the G-7 case.
The first cointegrating vector which included government
expenditure added considerable information to the analysis.
The fact that the G-7 equilibrium was stationary without
government expenditure and the OECD had a stationary vector
with government expenditure suggests two things. First, as
more countries are added to the G-7 sample, government
expenditure becomes more important. Second, the inequality in
government expenditure changes over time similarly to the
other inequality indices in the 14 country sample.
Given that the results between the G-7 and the 14 OECD
countries were different, cointegration tests were run on the

194
Other 7 sample. It was determined that the Other 7 inequality
indices were all 1(1) indicating that the Other 7 has a
different structure than the G-7. The long-run equilibrium in
the Other 7 sample was between government expenditure and
investment expenditure. This can be interpreted as the
reliance of the Other 7 on government expenditure as a means
of economic growth. When the inequality indices were
consulted, it was confirmed that the Other 7 increased
government expenditures at a faster rate than the G-7. The
reliance of the Other 7 on government expenditure and
investment expenditure is not necessarily a suboptimal long-
run path simply because the Other 7 and G-7 are converging.
This result just reflects the different ways growth can be
accomplished given the economic strata of a country.
It is clear that there exists a long-run equilibrium
among the inequality in income, investment expenditure, and
industrial employment for the G-7 and OECD sample. Investment
expenditure and specifically industrial employment were
extremely important when considering the convergence of
countries. It was determined that the inequality in
industrial employment was the major factor that adjusts when
an innovation occurred. The implication from the government
equilibrium, however, may be that as countries less endowed
than the G-7 are considered, government expenditure may play
a bigger role in the economy and in the influence of the
convergence of countries in terms of income.

195
The implications of these results are potentially
important when considering the economic growth in the middle
income and possibly the lower income countries. The Other 7
results show that a country can converge with the G-7 without
mimicking the structural setup of the G-7. If the low income
countries devote increased expenditures on investment and
government in per capita terms in an appropriate fashion, then
they may begin to converge with the developed countries in
terms of income per capita.
These interesting issues should be pursued as the data
becomes available for more countries. This dissertation would
be enhanced if more countries had data for income adjusted for
purchasing power parity that began in 1950. In addition, the
other data series used (government expenditure, investment
expenditure, and industrial employment) would need to begin in
1950. Another way to enhance this dissertation would be to
include trade indicators and educational indicators over time.
However the data for those variables only date back to the
early 1960's for most countries.
There are two limitations of this study. The first has
already been discussed which is the lack of data. The second
deals with the sample size. There are 39 observations for
each country and all four indices in this study. That means
the parameters are a third of the sample size. Therefore,
some caution should be taken when considering the results of
these tests.

196
In conclusion, both hypotheses were confirmed in this
dissertation. The G-7 and OECD are converging in terms of
income, government expenditure, investment expenditure, and
industrial employment. These four variables are also
cointegrated for the 14 country OECD sample and all but
government expenditure is cointegrated in the G-7 sample. In
addition, Industrial employment is the factor in the economy
that adjusts when the inequalities deviate from their long-run
equilibrium. Lastly, government expenditure may be a factor
that contributes to economic growth for countries less endowed
than the G-7.

APPENDIX A
PRICES PER KILOGRAM OF FRESH VEGETABLES AND ESTIMATED PPP'S
IN 10 COUNTRIES FOR 1970
197

Columbia
(Peso)
France W. Germany Hungary India
(Franc) (0. Mark) (Florint) (Rupee)
1. Artichokes
-
2.75
3.26
-
-
2. Beets
3.90
-
-
-
-
3. Brussels sprouts
-
2.35
1.69
-
-
4. Cabbage
1.41
.98
.55
2.9
.91
5. Cauliflower
5.33
1.90
1.13
-
1.27
6. Carrots
2.10
.93
.86
3.2
.75
7. Celery, pascal
4.49
-
-
*
-
8. Cucumbers
-
-
-
4.7
.87
9. Eggplant
-
-
-
-
.72
10. Escarole
-
1.82
.98
-
-
11. Green peppers
17.40
2.62
2.32
8.7
-
12. Kunde greens
-
-
-
-
.56
13. Lettuce
4.82
3.23
2.27
9.3
-
14. Mushrooms
-
7.90
5.60
-
-
15. Onions, yellow
5.59
1.18
.86
4.8
.67
16. Radishes
-
-
-
-
.55
17. Red cabbage
-
1.27
.56
-
-
18. Spinach
4.71
-
-
-
-
19. Tomatoes
5.79
2.55
1.85
6.7
1.21
20. Yellow squash
2.29
-
-
1.5
-
Coefficient Bc
1.96
.92
.57
2.02
.34
Anti log (PPP's)
7.11
2.52
1.77
7.53
1.41
"This entry represents
a correction
of the
corresponding
figure in
Kravis et
Source: Kravis et al. 1975, p. 59.
Italy
Japan
Kenya
(Lira)
(Yen)
(Shilling)
646
-
-
485
.
_
157
75.4
.47
195
156.6
2.58
172
115.1
2.58
173.3
212
186
195.4
-
-
-
.79
239
218.1
.62
790
-
-
127*
98.6
.77
m
133.8
-
226
160.9
1.19
5.68
5.32
.57
291.9
204.5
1.76
United
Kingdom
(Pound)
Uni ted
States
(Dollar)
Coeffic
A.
_
2.22
.56
.07
.42
-.89
-
1.89
-.23
.08
.32
-1.02
.17
.63
-.18
.07
.39
-.67
-
.44
-.59
-
.61
-.39
-
.59
-.63
-
-
-.41
-
1.16
.14
-
.67
-.78
-
.53
-.21
.54
1.95
1.00
.13
.35
-.66
-
.88
-.68
-
.12
-1.20
-
1.24
-.29
.31
.92
-.10
-
.66
-1.22
-1.56
.00
.21
1.00

APPENDIX B
SUPERCOUNTRY WEIGHTING
A supercountry is a representative country assumed to
have the some price and quantity structure of a group of
countries (Kravis et al. 1975, p. 289). The objective of
supercountry weighting is to assign to each country's price
structure a weight that reflects its GDP as well as other
countries in the world which were not included in the ICP.
Supercountry weighting also insures that countries who
participate in several phases of the ICP will not be
influenced by the addition of new countries in later Phases.
The world comparisons utilized a system of supercountry
weights where the dollar GDP of non-participating countries is
assigned to participating countries on the basis of
geographical proximity and the level of per capita income. It
must be made clear that the supercountry analysis is for
estimating average prices only.
The starting point of this procedure is the cross¬
classification of all the countries of the world by region and
by per capita nominal (exchange rate converted) GDP. Once the
income class is selected, the aggregate population and nominal
GDP of each cell is assigned to one of the 34 Phase III
countries for example. The aggregate GDP is divided evenly
199

200
among the countries in the same cell, with the provision that
no country receives less than its own GDP as a weight.
The supercountry weighting is used with the CPD method.
The prices of each item are weighted by the supercountry
expenditure for that category and by the reciprocal of the
number of items priced by country. Thus, the function of the
supercountry weights is to assign each country's price
structure a weight that reflects the importance of its GDP, as
well as all the other countries in the world not included in
the ICP for which the ICP country's price structure can be
regarded as representative. From the weighted CPD method, the
PPPs are obtained and the Geary-Khamis method applied. The
aggregate GDP of the supercountry is used to weight the prices
of the representative country in the process of deriving
average international prices. Each country's own quantities
(obtained from its expenditures and prices) are then valued at
these supercountry-based average prices (for further
discussion of supercountry weighting see Kravis et al. 1982,
pp. 79-88).
If the GDPs of countries not included in the ICP are
appropriately assigned to ICP countries, the "true" world
average price structure is obtained. Then, if more countries
are subsequently added to the ICP set, the reassignment of
supercountry weights should leave the average prices
essentially unchanged. Thus, the extent to which the
multilateral comparisons of the 10 countries of Phase I

201
remained approximately the same after the six countries were
added in Phase II. This reassures the success of supercountry
weighting.

APPENDIX C
EKS CALCULATIONS
To calculate the mini-Laspeyres price ratios, the
geometric mean of the characteristic items for the base
country is taken. Table 3.2 in the text has the matrix of
characteristic items. To derive the mini-Paasche price
ratios, the inverse of the mini-Laspeyres price ratios are
taken. For simplicity, Japan is country A, Kenya B, U.K. C,
and the U.S. is country D. The mini-Laspeyres index is:
^A/A
=
1
=
1
Lb/a
[ (.62/218.1) *(.77/98.6) ]1/2
=
0.0047
^C/A
=
.13/98.6
=
0.0013
^D/A
=
[(. 5/218.1) *(.35/98.6) ]1/2
=
0.0029
^A/B
=
160.9/1.19
=
135.21
^B/B
=
1
=
1
kc/B
=
.31/1.19
=
0.26
^D/B
—
.92/1.19
=
0.77
^A/C
=
160.9/.31
=
519.03
^B/C
=
.77/.31
=
2.48
Lc/c
=
1
=
1
^D/C
=
[(1.9/.54)*(.92/.31)]m
=
3.23
â– ^A/D
=
[ (218.1/. 5) *(98.6/. 35) *(160.9/. 92) ]1/3
—
278.02
^B/D
=
[ (.62/. 5) *(.77/. 35) *(1.19/. 92) ]1/3
—
1.52
^C/D
=
[(,13/.35)*(.31/.92)]m
=
0.35
^D/D
=
1
=
1
The
mini-Paasche index is:
^A/A
=
1/La/a = 1
^A/B
=
1 / Lb/a = 212.77
^A 1C
=
1 / LC/a = 769.23
^A/D
=
1/Ld/a = 344.83
^B/A
=
1 / La/b = 0.0074
^B/B
=
i / i’B/B = i
^B/C
=
1 / Lc/b =3.85
^B/D
=
1 / LD/B =1.3
Pc/A
=
1 / LA/C = 0.0019
^C/B
=
i / ^b/c = 0.4
202

203
’c/c -
i / ^C/C —
1
C/D =
i / i*D/C =
0.31
D/A =
1/La/d =
0.0036
D/B =
1 / i’B/D ~
0.66
D/C =
1 / i*C/D =
2.86
D/D =
i / i'D/D =
1.
To calculate the mini-Fishers, multiply the mini-Laspeyres
times mini-Paasche and take the square root. For example: FB/A
- (i'B/A
. * Fb/a) 1/2 / thus the
mini-Fishers
^A/A
=
(1 * l)m
=
1
^B/A
=
(.0047 * .0074)1/2
=
0.0059
^C/A
=
(.0013 * .0019)1/2
=
0.0016
^D/A
=
(.0029 * .0036)1/2
=
0.0032
^A/B
=
(135.21 * 212.77)1/2
169.61
^B/B
=
(1 * l)m
=
1
^C/B
=
(.2 6 * .4)1/2
=
0.32
Fd/B
=
(.77 * . 66)1/2
=
0.71
Fa/C
—
(519.03 * 769.23 )1/2
631.87
^B/C
=
(2.48 * 3.85)1/2
=
3.09
FC/c
=
(1 * 1)1/2
=
1
Fd/c
—
(3.23 * 2.86) 1/2
=
3.04
Fa/d
=
(278.02 * 3 4 4.8 3 )1/2
=
309.63
Fb/d
=
(1.52 * 1.3)1/2
=
1.41
Fc/d
=
(.35 * . 31)1/2
=
0.33
Fd/d
=
(1 * l)m
=
1.
Then the calculation of the EKS method is completed by
utilizing all the information available with the direct and
indirect mini-Fisher ratios. The EKS equations are:
eksa/a
=
[(l)2 * i *
1),/4
=
1
EKSa/b
=
[(169.61)2
* 631.87/3.09 * 309.63/1.41]1/4
=
189.58
EKSa/c
=
[(631.87)2
* 169.61/.32 * 309.63/.33]1/4
=
667.53
EKSa/d
=
[(309.63)2
* 169.61/.71 * 631.87/3.04 ]1/4
=
262.67
EKSb/a
=
[(.0059)2 *
3.09/631.87 * 1.41/309.63]1/4
—
0.0053
eksb/b
=
[(l)2 * 1 *
1]1/4
=
1
eksb/c
=
[(3.09)2 *
.0059/.0016 * 1.41 / . 3 3 ]1/4
=
3.5
EKSb/d
=
((1.41)2 *
.0059/.0032 * 3.09 / 3.04 ]1/4
=
1.39
eksc/a
=
[(.0016)2 *
.32/169.61 * . 33/309.63]1/4
=
0.0015
EKSc/b
=
[(•32)2 * .
0016/.0059 * . 3 3 /1.41 ]1/4
=
0.28
EKSC/C
=
[(l)2 * 1 *
1]1/4
=
1

EKSC/D = [ ( . 3 3)2 * .0016/.0032 * .32/.71]I/4
EKSd/a = [ (. 0032 ) 2 * .71/169.61 * 3.04 / 631.87 ]1/4
EKSd/b = [ ( . 71) 2 * .0032/.0059 * 3.04 / 3.09 ]1/4
EKSD/C = [ (3.04)2 * .0032/.0016 * .71/.32]1'4
eksd/d = [ (l)2 * 1 * 1]1/4
204
= 0.4
= 0.0038
= 0.72
= 2.53
= 1.

APPENDIX D
FIXITY
The fixity principle requires that any index calculated
and published for a regional comparison remain unchanged when
it is involved in other comparisons embracing a larger group
of countries. Decentralization requires that all regions
calculate everything as a region, but certain regions also
want their results, when compared to the rest of the world, to
exemplify the fixity principle. For example, if the European
Community (EC) regional comparison results in the per capita
GDP of France being 25.6% higher than Italy's, then all other
comparisons, OECD or world comparison, must yield a
France/Italy per capita GDP index of 1.256.
(.it . * ! • • ' • 1 ' - n ' • . ¡ | -• v._; < - - • '
This idea becomes a problem in Phase IV because there are
several regions, each observing the fixity principle, and some
of the countries belong to more than one country group. There
are no resolutions on what is to be done if a country falls
into more than one region or grouping. Austria and Finland
are members of both the OECD and the Europe 2 group. However,
it is possible to satisfy the requirements of fixity for these
two countries in the world comparison, but not simultaneously
for the two regional comparisons. There is no justifications
for the subordination of one region to another (Kurabayashi
1986).
205

206
The cost of fixity, if strictly adhered to, is that only
total GDP is comparable across regions. For any subdivisions
of GDP such as household or food consumption, or fruit and
vegetables, the quantity comparisons are affected by the fact
that these aggregates are expressed in different regional
(relative) prices. Therefore, one can not compare, for
example, the food consumption volume between two countries in
different regions.

APPENDIX E
DATA AVAILABILITY
There are several other countries and variables that
should be included in this study. However, the data are not
available for the length of time needed for this type of
study. Cointegration analysis requires a fairly long time-
series .
The variables that I would have liked to have included in
this analysis was imports and exports and a variable
representing education. The import-export data is important
because the G-7 and OECD export a considerable amount of their
produce. These exports as well as imports are included in the
income of these countries. Therefore, it would be interesting
to test to see if the inequality in "traded goods" are
cointegrated with the inequality in income. The data from the
OECD National Accounts for imports and exports only starts in
1960 for 13 of the 22 OECD countries.
The second variable is important because several studies
in Chapter 2 associated education with growth and income
inequality. The other variable that would enhance this study
would be a time-series for the education level of the work
force. The inequality of the educational level of the work
force may be cointegrated with the inequality of income. The
207

208
data from the OECD National Accounts has expenditures on
education data starting from 1960. Only eight of the 22 OECD
countries begin their series in that year.
Lastly, it would be beneficial if more countries could be
included in this analysis. Unfortunately, Summers and Heston
(1991) data set includes over 100 countries but many of their
time-series only start in the late 1950's or early 1960's.

APPENDIX F
EXTRAPOLATION OF INDUSTRIAL DATA
Fourteen OECD countries were used in this analysis
(Canada, the U.S, Japan, Austria, Belgium, Denmark, France,
Germany, Ireland, Italy, Netherlands, Norway, Spain, and the
U.K. The following countries did not have a complete data
series for the number of people employed in industry: Japan
(1950-52), Austria (1950-55), Denmark (1950-54), France (1950-
53), Ireland (1950-55), Italy (1950-53), and Spain (1951-55).
The data for the years that were missing is indicated in
parenthesis, next to the countries name.
The method of extrapolation was based on multiple
regression. The 'independent variables were the number of
people employed in industry in the U.S., Canada, Germany, and
the U.K. The independent country was the country with missing
data. The equation was:
Yit = a^Canada, + ai2U.St + ai3Germanyt + ai4U.K.t + ai5t + ai6t2
where Y¡ represents the number of people employed in country
i, and t represents time. This equation was estimated for the
period for which observations exist for country i. After the
equation was estimated, the parameters were used to predict
the missing values. The full equation was used for the
209

210
following countries: Austria, France, and Ireland. The
following countries data was best fit when the time and time
squared trend was removed from the model: Japan, Denmark, and
Italy. Spain was a unique country and were best estimated by
only regressing Germany and the U.K. on it and then adding a
constant. The constant was equal to the difference between
the estimated value for spain in 1950 and its actual
observation.

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BIOGRAPHICAL SKETCH
Dave Deniel Weatherspoon of Vandalia, Michigan, completed his
B.S. degree in crop and soil science at Michigan State
University in 1987. After working for six months as a
consultant in the Caribbean Islands he returned to the U.S. to
pursue a master's degree. Dave received his Master of Science
degree in 1989 from Penn State University in agricultural
economics with a specialty in international development. Dave
was awarded the McKnight Doctoral Fellowship to attend the
University of Florida where he pursued a Ph.D. in food and
resource economics. His areas of specialty are International
Trade and Demand Analysis.

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
nes L. Seale,
Associate Professor of Food
and Resource Economics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
'jfoh ^
Charles B. Moss, Cochair
Associate Professor of Food
and Resource Economics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
a
¿ Adjunct Professor of Food
and Resource Economics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Gary Fi Fairchild,
Professor of Food and
Resource Economics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Douglafs G. Waldo,
Associate Professor of
Economics

This dissertation was submitted to the Graduate Faculty
of the College of Agriculture and to the Graduate School and
was accepted as partial fulfillment of the reguirements for
the degree of Doctor of Philosophy.
December 1993
Dean, College of
Agriculture
Dean, Graduate School

UNIVERSITY OF FLORIDA