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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x, 220 leaves : ill. ; 29 cm.
Weatherspoon, Dave D
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Food and Resource Economics thesis Ph. D
Dissertations, Academic -- Food and Resource Economics -- UF
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Thesis (Ph. D.)--University of Florida, 1993.
Includes bibliographical references (leaves 211-219).
Statement of Responsibility:
by Dave D. Weatherspoon.
General Note:
General Note:

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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oclc - 31303705
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Full Text








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


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.





. . . vi



* viii

. ix





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

. 1


. 11
. 15
. 24
. 27


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 .. ...


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



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


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 ...


5.1 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. .


6.1 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 . .


. 63
* 65

. 70

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

. 96

. 96

. 96
. 97













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






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



REFERENCES . . .. .. .. 211




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 . .



S 35

S 47

S 49

S 50

S. .. 51

S. .. 60

S 64

. .103

. .108

. .112

S .117

S .120

. .123

. .140











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



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 .


. 133

S. .. 133

S. .. 134

. 134

. 135

. 135

. 136

. 136


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



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.


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


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



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.

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,


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

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


The format of this dissertation is as follows. Chapter

2 includes a literature review on convergence while Chapters

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


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.


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.


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


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


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.


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


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


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


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.


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


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


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


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


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


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


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.


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


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


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


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.


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

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.

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.

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.


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

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


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


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.


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.


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.

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

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.

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

most of the studies in this section based their analysis will

be discussed.


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


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


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

United States


W. Germany
United Kingdom

Countries added in Phase II

S. Korea

Countries added in Phase III

Sri Lanka



Countries added in Phase IV

Costa Rica
Dominican Rep.
El Salvador


Countries deleted in Phase IV


Sore Tfel tal 98,p.2



Ivory Coast

Hong Kong




Source: Theil

et al. 1989, p. 2.


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


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.


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


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.


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

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.


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) 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


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.

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:

(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

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


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

category, then the vector for the dependent variable using the

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


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.


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

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


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



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.

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


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

E' (E;; w *** *** 7tj
Pa =

E V.,

or, equivalently,

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

while 7, is defined as

Z E,,
7r =_____


or, equivalently, as

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

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

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


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.


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.

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


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


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


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
United Kingdom
Sri Lanka


. 37-.7,


p. 12.

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

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


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.



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

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

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


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


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


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


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


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.


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


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).

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

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

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

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


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

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

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,

(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

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

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, =

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.


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


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-


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


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.


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


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


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)

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


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


k, rAVk r-ikk,

EX= k21 l
,= rtick r k, rk3k


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


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

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


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


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).


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


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


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