CROSS COUNTRY CONVERGENCE OF GROSS DOMESTIC
PRODUCTS AND ASSOCIATED FACTORS:
A COINTEGRATION APPROACH
DAVE D. WEATHERSPOON
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
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
The financial support as a McKnight Doctoral Fellow from
the Florida Endowment Fund for Higher Education made this all
possible. The additional financial support by Dr. James
Seale, Jr., and Dr. Henri Theil is much appreciated.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS . . ... ii
LIST OF TABLES
. . . vi
LIST OF FIGURES . .. .
ABSTRACT . . .
1 INTRODUCTION . . .
2 CONVERGENCE . . .
Overview of Convergence .
Historical Evidence . .
Kuznets-Type Studies . .
LDC Growth and Poverty . .
Human Capital . .
Contemporary Evidence ..
3 THE INTERNATIONAL COMPARISON PROJECT AND ITS'
USEFULNESS IN EXAMINING CONVERGENCE .
3.1 Overview of the Construction of the ICP
3.2 The Geographic Expansion of the ICP:
Phases I to IV . .
3.3 The Data . . .
3.3.1 The Methodology of Calculating
Purchasing Power Parity .
3.3.2 Country-Product-Dummy Method .
3.3.3 Elteto-Koves-Szulc Method .. ...
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. .
3.9.1 Other Methods Used in Phase IV .
3.9.2 Linking the Regions of Phase IV .
4 EXTRAPOLATIONS. . . .
4.1 The Beginning of Extrapolations with
ICP Data . . .
4.2 Mark 1 . . .
4.3 Mark 3 . . .
4.4 Mark 4 . . .
4.5 Mark 5 . . .
4.6 The Centrally Planned Economies ...
5 INEQUALITY IN THE G-7 AND OECD. . .
5.1 Inequality Measures. . .
5.1.1 Graphical Inequality. . .
5.1.2 Inequality Indices. . .
5.1.3 Properties of an Inequality Index .
5.2 Income Inequality in the G-7 . .
5.3 Variables of Interest . .
5.3.1 Inequality in Government Expenditure. .
5.3.2 Inequality in Investment Expenditure. .
5.3.3 Inequality in Industrial Employment .
5.4 Inequality in Selected OECD Countries .
5.4.1 Income Inequality in the
OECD Countries. .
5.4.2 Inequality of Government Expenditure
in the OECD . .
5.4.3 Investment Inequality in the OECD .
5.4.4 OECD Inequality in Industrial
Employment. . .
5.5 Summary of the Inequality Results. .
6 COINTEGRATION . . .
6.1 An Overview of Cointegration . .
6.2 Unit Root Tests . .
6.2.1 Augmented Dickey-Fuller (ADF) Test. .
6.2.2 Phillips Test . .
6.2.3 Unit Root Results . .
6.3 Pairwise Cointegration . .
6.3.1 Durban Watson . .
6.3.2 Augmented Dickey-Fuller
Cointegration Test ..142
6.3.3 Pairwise Cointegration Results. ... ..143
6.4 Johansen's Multiple Cointegration Test ... .146
6.4.1 I(1) Procedure. . .146
6.4.2 1(2) Procedure. . .154
6.4.3 G-7 Multiple Cointegration Results. .161
6.4.4 OECD Multiple Cointegration Results .170
6.4.5 Other 7 Multiple Cointegration
Results . ... .178
6.5 Summary and Interpretation ... .182
7 SUMMARY AND CONCLUSION. . .190
A PRICES PER KILOGRAM OF FRESH VEGETABLES AND
ESTIMATED PPP'S IN 10 COUNTRIES FOR 1970. .197
B SUPERCOUNTRY WEIGHTING. . .199
C EKS CALCULATIONS . .. 202
D FIXITY. . . ... ... .205
E DATA AVAILABILITY . .. ... 207
F EXTRAPOLATIONS OF INDUSTRIAL DATA .... .... .209
REFERENCES . . .. .. .. 211
BIOGRAPHICAL SKETCH. . . .220
LIST OF TABLES
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. .. 51
S. .. 60
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. . . .
LIST OF FIGURES
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 .
S. .. 133
S. .. 134
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
CROSS COUNTRY CONVERGENCE OF GROSS DOMESTIC
PRODUCTS AND ASSOCIATED FACTORS:
A COINTEGRATION APPROACH
Dave D. Weatherspoon
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
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
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
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
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
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
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
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
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
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
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
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
THE INTERNATIONAL COMPARISON PROJECT
AND IT'S USEFULNESS IN EXAMINING CONVERGENCE
3.1 Overview of the Construction of the ICP
The objective of the International Comparison Project
(ICP) was to establish a system of comparisons of real product
and purchasing power for a large number of countries. The
reason for this is that it was realized that the use of
exchange rates to conduct international comparisons introduced
errors into the analysis. For example, a 1954 study by
Gilbert and Kravis found that $1000 in US currency, when
converted to sterling at the official exchange rate, bought a
basket of U.K. goods 64% larger than the $1000 could have
purchased in the United States.
This problem was recognized by the Statistical Commission
of the United Nations. The issue was discussed in 1965, at
the United Nations' thirteenth session, and it was concluded
that using exchange rates for currency conversion was
inadequate for many uses of international data (U.N.
Statistical Commission, 1965). The United Nations and the
University of Pennsylvania started the "International
Comparisons Project" in 1968. Initial funding came from the
World Bank, Ford Foundation, some of the countries involved in
the first set of data collection, U.S. Agency for
International Development, and the U.S. Social Science
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
Countries Represented in the International Comparisons Project
Africa America Asia Europe
Countries represented in Phase I
Countries added in Phase II
Countries added in Phase III
Countries added in Phase IV
Countries deleted in Phase IV
Sore Tfel tal 98,p.2
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
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 /
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.
Fresh Vegetables for 4 Countries and Items in 1970
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
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.
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.
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
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
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
(3.8) PaVa = Z (Ec/7c) where V, = E Vc
while 7, is defined as
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,
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
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
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.
GDP Per Capita for 34 Countries in 1975
International Same, Exchange rate
Country dollars U.S.=100b converted
(1) (2) (3) (4)
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
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
The Organizations that Performed the Calculations and the
Countries Involved in Each Group for Phase IV.
EUROSTAT ECE ECA/EUROSTAT ESCAP/UNSOS ECIEL/ECLAC OECD
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
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
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
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
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
(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,
(4.3) RGDPj, = (RGDPj7o)
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
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
((Exportsj + Imports))/GDP) / ((Exportss
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,
(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
-1/2 E Xij, (In xi In X,) (In x In X)
+ E E X (n gi.3 In G3) (In g.3 In G,3)
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
k, rAVk r-ikk,
EX= k21 l
,= rtick r k, rk3k
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
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
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