FILE COPY A Survey and Critique of World Bank Supported Research on International Comparisons of Real Product Public Disclosure Authorized SWP365

World Bank Staff Working Paper No. 365 P.C.C. 1

December 1979 Public Disclosure Authorized Public Disclosure Authorized

Prepared by: Robin Marris (Consultant) Economic Analysis & Projections Department

Copyright ( 1979 The World Bank 1818 H Street, N.W.

Public Disclosure Authorized Washington, D.C. 20433, U.S.A.

The views and interpretations in this document are those of the author and should not be attributed to the World Bank, to its affiliated organizations, or to any individual acting in their behalf.

Che views and interpretations in this document are those of the author and should not be attributed to the World Bank, to its iffiliated organizations or to any individual acting in their behalf.

WORLD BANK

Staff Working Paper No.365

December 1979

A SURVEY ANID CRITIQUE OF WORLD BANK SUPPORTED RESEARCH'ON INTERNATIONAL COHPARISONS OF REAL PRODUCT

This paper describes the nature and content of the statistical data generated by the project on International Comparisons of Real Product (ICP). It analyzes their theoretical implications, investigates more generally the problems of international comparisons of economic welfare, discusses and criticizes the methods used by the ICP to compare internationally expendi- ture in the services sectors, reconsiders the applied theory of the rela- tionship between price-structure, economic development and purchasing power exchange rates.

Prepared by: Robin Marris (Consultant) Economic Analysis & Projections Department

Copyright® 1979 The World Bank 1818 H Street, N.W. Washington, D.C. 20433 U.S.A.

INTRODUCTION

During the middle of the decade 1970-80, the World Bank, the United Nations, the Ford Foundation and other institutions provided substantial finan- cial and administrative support for a major research project on international comparisons of real product undertaken by Irving Kravis, Alan Heston and Roy Summers at the University of Pennsylvania0 Irving Kravis was, of course, the creator of data on the same subject relating to France, Italy, the U.K. and the U.S., published by the OECD in the 1950's. From time to time, as pro- posals for extending or continuing the earlier work came up, Foundations receiving grant applications in the field became accustomed to consulting Kravis, and in due course, when it had been decided to fund new work in the UN, he was the natural choice for leader. The Bank became intimately involved when it decided to agree to a request that it become a co-sponsor and major financial supporter.

The results of the new project have been in process of publication since the middle of 1975. The first volume appeared in 1975, the second in 1978, and a third is expected in 1980.* In addition to these publications, Kravis, Heston and Summers published an article in 1978* giving the results of an indirect method for estimating the results that could have been expected for GDP per capita for over a hundred countries if all these countries had been intensively studied by the direct method.

This Staff Paper is the result of a consultancy undertaken by the author in 1978-79 to summarize, survey and criticize the methods and results of Phases I and Io. A Summary of its contents follows.

* For references, see footnote, p. below.

SUMMARY

Section I, Nature and Content of ICP Data, summarizes the data published in Phases I and II, namely quantities for 153 commodities in, eventually, 34 countries, for benchmark years 1970 and 1973, and in some countries, 1975, with resulting calculations of overall real GDP per capita and various sub-aggregates according to Laspeyres-type, Paasche-type, Ideal and "multilateral" index numbers.

Section II, A More Formal Account, provides a mathematical summary of the basic data and of the conceptual character of the various international comparisons that may be derived from them. It sets out potential intransitivi- ties and weighting instabilities contained in the system of binary comparisons, together with a more precise definition of the multilateral system.

Section III, Purposes and Uses of the Data. In a First Account of Purposes, this section lists six different types of pragmatic uses of these data, including aid policy, research on economic growth, development planning, studies in income distribution and growth, etc.

In the subsection "Product Comparisons or Welfare Comparisons," the section questions the validity of the traditional distinction between measurements of production and measurements of welfare on the grounds that, in international comparisons, one is effectively treating each country as if it contained only one (representative) individual. It also digresses on some questions in the logic of evaluating world income distribution.

A subsection called "More General Discussions of Purposes" discusses the meaning of international comparisons at a more abstract level and con- cludes that, whether one likes it or not, the fundamental purpose of these data is to support cardinal international comparisons of economic welfare. It goes on to defend this position against conventional "ordinalist" cri- ticism.

Section IV, Theoretical Problems in International Welfare Compari- sons, investigates various kinds of quantity index-numbers in the interna- tional context, with special reference to the problem of taste differences. Some of the theoretical material is original. A new empirical relation between price dispersion and per capita GDP levels is reported. This creates the possibility of non-monotonic bias in the ICP multilateral indices.

Section V, Problems of Quality Differences and the Services Sectors, describes the methods used in the ICP to deal with quality differences in the "hardware" sectors, such as automobiles. The section then continues to a critique of the methods used to deal with the analogous problem of measuring output (or consumption) of the services sectors, especially those concerned with public goods or publicly provided goods. It argues that, for about 15% of the typical country's GDP, the methods used by the ICP do not represent measures of output, but rather of input, and therefore must not be used for productivity comparisons. A statistical investigation is conducted of the - ii

effects, which are showu to be potentially a:,nkfAcant0 Possible alternative solutions to an admittedly extremely difficult problem are discussed. The general argument concerning services is illustrated by detailed comparisons of the structure of the ICP measures for Health Care and Public Administra- tion, as between India, West Germany, the U.K. and the U.S.

Section VI, Price Structure, Econowic Development and Exchange Rates. Sultan Ahmad, Bela Balassa, Christopher Clague, Irving Kravis, Stephen Marris, Vito Tanzi, Paul Samuelson and others have iuvestigated the empirical rela- tionship between national price structures, levels of development and exchange deviations. This section develops an Analysis of Variance of prices and pro- ductivities in the course of economic development, on which some alternative models, or V'scenarios" are based, in the hope of helping to explain the empiri- cal relationship between economic development and price dispersion reported in Section IV. Initially these models abstract from international trade, but are then married with trade models to review the classic contributions of Balassa, et al. It is concluded that the theory behind the association between exchange deviations and GDP levels is quite complex and that, as argued by Clague and Tanzi, though empirically supported, is not inevitable. It is considered possible, though unlikely, that the empirical phenomenon is mainly due to underestimates, in the ICP methodology, of the comparative productivity of services in rich countrieso

Acknowledgements

I wish to acknowledge the benefit of conversations with Prof. Christopher Clague, University of Maryland; Professors Irving Kravis, Alan Heston, and Roy Summers, of the University of Pennsylvania; Dr. Sultan Ahmand, Dr. Helen Hughes and Dr. R. McPheeters of the World Bank. None of these individuals, however, is in any way responsible for errors. -1-

I. NATURE AND CONTENT OF THE ICP DATA

As already indicated, the results of the project have been orgauized in three phases. Phase I, published in 1975, related to ten countries: six developed, three developing, and one "centrally planned" (Hungary). Phase II, published in 19789 added six countries, including four developing countries. Phase III is expected to add 18 more countries of various types. In addi- tion, an important article, referred to below as "KHS," providing indirect estimates of total real per capita GDP for over a hundred countries was also published by Kravis, Heston and Summers, in 1978. 1/

Most data presented in Phase I are also available in the Phase II publication. Some of the methodological discussion found in Phase I is not, however, repeated in Phase II. For the various countries represented in the several Phases, the results as a whole provide, inter alia:

(a) Binary real GDP comparisons for the years 1970 and 1973 of each country with the United States, using own-country price weights, and U.S. price weights (Phase II, page 8, commodity detail, pp. 173-230).

(b) Ideal-index comparisons between all pairs of coun- tries (Phase II, page 12).

1/ The full title of the Phase I publication was A System of International Comparisons of Gross Product and Purchasing Power, by Irving B. Kravis and associates, Johns Hopkins Press, Baltimore, for United Nations and the World Bank, 1975. Phase II is called International Comparisons of Real Product and Purchasing Power, same authors, publishers, etc., 1978. KHS is called "Real GDP Estimates for More than One Hundred Countries," by Irving Kravis, Alan Heston, and Robert Summers, Economic Journal, June 1978. - 2 -

(c) Extrapolations, 1/ based mainly on national data, for the same countries to the years 1965-1975, based on national series adjusted for changes in the terms of trade in such a way that real GGP is treated as an "income" rather than as a "production" concept 2/ (Phase II, p. 133)o

1/ In Phase I, p. 8, an important comparison is made between the main results for the UK, France, Germany and Italy (with US=100) in 1970 and results obtained by extrapolating national data from the benchmarks estimated in the earlier work of Kravis and Milton Gilbert relating to the year 1950. Given the nature of the extrapolatory material including the requirement to splice through changes in weighting systems and statis- tical coverage in most of the national series, the discrepancies thus generated are surprisingly small, and the results thus support confi- dence in the method as a whole. The extrapolation method understates Italy's GDP in 1970 by 17 percent, France's by 9 percent, West Germany's by 8 percent. It is significant that the smallest discrepancy (repre- senting one third of one percent per annum in the implicit estimate of economic growth) is found in the U.K., a country which, during the period in question, is recognized as having had the most thoroughly- compiled national data for constant-price GDP. By contrast; if GDP comparisons in 1970 are made on the basis of official exchange rates, rather than on the ICP data, the Italian figure is understated by 27 percent, the French by 21 percent, the German by 18 percent and the British by 28 percent. Thus, in the case of the British, to have used an extrapolated version of Kravis 1950 (had Kravis 1970 not been car- ried out) as against official exchange rates would have represented a very substantial improvement. In fact, in the British case for 1970 the official exchange rate figure is so far out as to be almost useless.

2/ For the conceptual problems involved, see R. Marris, Economic Arithmetic, London, 1958, pp. 318, et seq. and R.C. Geary in Studies in Social and Financial Accounting, Phyllis Dean (ed.), London, 1961 and ICP Phase II, p. 129. In the "income" concept a country with zero trade balance (nominal) and constant production in both year 0 and year 1 would expe- rience an increase in GDP if its terms had improved and a decrease if they had deteriorated. On the "production" concept, the terms of trade would have left the defined real GDP unchanged as long as, in fact, domestic production were unchanged. In the income concept the foreign sector is regarded as a machine for transforming exports into imports; if the terms of trade improve this machine is seen as having become more efficient, with effects exactly corresponding to an improvement in tech.Acal productivity in some domestic sector. Clearly, for some purposes (e.g. the measure of technical progress in an economy) such changes are extraneous, and the production concept to be preferred. Faced with a choice of concepts, the ICP staff were clearly right to choose the income concept, however, since the terms of trade are among the many factors affecting a country's welfare. In future publications it would be desirable to show annual series of internationally comparable data with figures for both concepts as alternatives. -3-

(d) Per capita quantity ratios, U.S. = 100 f or each of the 153 commodities in each country (Phase II, p. 152-158).

(e) "Multilateral" international comparisons of GDP, in which the quantities entering into the GDP of each country are valued at a standard set of dollar prices, namely a quantity-weighted average of the corresponding prices in the world economy estimated from the prices displayed among the 16 Phase II coun- tries (Phase II, p. 8). In particular, in Appendix Table 4.2 (Phase II, pp. 158-165) the quantities of each of 153 commodities for sixteen countries (i.e. including US) are valued at these prices. This table has the considerable advantage of being internationally commensurable in both columns and rows: any desired subaggregation can therefore be obtained and inter- nationally compared. Aggregate index numbers based on these data are also provided: unlike Paasche, Laspeyres and Fisher, this system of index numbers is free of potential intransitivities. Disaggrega- tions, both in binary and multilateral data, into broad sub-aggregates of Consumption, Investment, Government, etc., plus further disaggregations (the Summary Tables) into categories narrower than these, but broader than the 153 commodity-list are also provided (Phase II, pp. 85-113).

(f) Purchasing-power-parity exchange rates for each of the 153 commodities in each country, i.e., the rate for bread in the U.K. is the exchange rate between pounds and dollars required to make the dollar price of bread the same in both countries (Phase II, 146-158).

(g) Overall purchasing-power-parity exchange rates; for each country, in sub-categories such as Consumption, Investment, etc.; and for total GDP (Phase II, pp. 20-21). - 4 -

(h) Exchange deviations for bench-mark years between each country's overall p.p.p. exchange rate and the average official rate during that year (Phase II, p. 10) . 1/

(i) Percentage shares of each of the 153 items in the GDP of each country based on national currencies (Phase II, pP. 140-146).

(j) A wide variety of miscellaneous data and calcula- tions, including a set of demand equations calcu- lated in international cross section; tests of the hypothesis that luxuries are more expensive in rich countries; studies of systematic differences in rela- tive prices; studies of similarity/dissimilarity in economic structure, and etc.

(k) Detailed discussions of the definitions of the sources and nature of individual items, with special chapters on the problem of quality and of measurement problems for particular items such as rent, health and educa- tion.

These are therefore measures of "over-valuation" (or undervaluation as the case may be) of individual currencies. Relative prices for indi- vidual commodities in particular countries may be defined by dividing the own-commodity p.p.p. rate by the overall p.p.p. rate for the same country. This is an excellent method (made possible by the ICP) for practical purposes, such as use in demand equations, but requires one to know the overall p.p.p. rate before one can define the relative price for any one commodity. It is therefore expositorily inconvenient when needing a concept of relative prices in developing the definitions of index numbers which include, inter alia, the definitions of the over- all p.p.p. rates themselves. In Section II below, therefore, commodity prices are normalized (conceptually) by dividing each's price in national currency by the price in national currency of an arbitrarily selected referency commodity. No conclusions are affected. In practical work, as indicated, it is recommended that relative prices be defined by the method implied, above, in the ICP publications; e.g., for bread in the U.K. look up the p.p.p. exchange rate in the Tables on pp. 146-158 Phase II and divide by the overall rate found in the table on page 20. -5-

II. A MORE FORMAL ACCOUNT

1) Definition of the Data

The data set represents m specified commodities, for which prices and quantities were collected in the benchmark years 1970 and 1973, for n dif- ferent countries. After the completion of Phase III, n - 34; m, in the pub- lished tables = 153. Throughout the remainder of this section all references to quantities and prices refer to some given benchmark year, such as 1970.

Let qi signify the quantity per capita of commodity i in country k and let Pik signtfy the-price of i in k expressed in units of k's currency.

Let a particular commodity, s, the same in all countries, be defined as the reference commodity.

Let, Pik '=pik is (2.1) Then pik is called the relative price of i in k. 1/

Let Q signify a matrix of m rows and n columns whose elements are qik. Thus Q contains the quantity data collected by the ICP.

Let P signify a matrix of m rows and n columns whose elements are P all the elements in the s'th column being unity. Thus P contains all e relative-price data.

Although Q is not published in international units, the basic infor- mation is presented, in (Phase II, Appendix Table 4.4) in relative form, with the U.S. quantity of each commodity = 100. The quantities are also presented valued in constant international dollars in Phase II, Appendix Table 4.5.

The matrix P is also not presented as such but may easily be com- puted from Appendix Table 4.3.

2) The "Kravis Matrix"

In honor of the leader of the ICP, we then define a matrix K, obtained by matrix pre-multiplication of Q by the transpose of P. Thus, K is an n X n (country-by-country) matrix such as,

1/ For an alternative definition of relative prices, see Section I above. -b -

A 1 A 1k Aln

K A kl A kn (2.2) A A A n1 nk nn where an element such as I k represents country h's quantities aggregated at country k's relative prlces. Thus K includes each country's quantities aggregated at each country's relative prices, including, in the leading diagonal, at its own prices. 1/

3) The Binary Matrix

Let Log K represent the matrix K in which every element has been replaced by its natural logarithm. Consider a column vector of Log K, say, k . Since index numbers are essentially proportional concepts, k may be seen as a set of index numbers of per capita GDP for all n countries, each using the relative prices of country j for weighting the quantities.

From k may be derived a triangular matrix, with leading diagonal zero, in which, then countries are again arranged, n X n, all possible dif- ferences between country pairs represented in k. are recorded: since k; is logarithmic, these relationships are proportional. 2/

This matrix B1, may be called a j-weighted "Cardinal Binary Matrix." It has (1/2)n(n-1) non-zero elements.

From B1 may be derived a corresponding j-weighted "Ordinal Binary Matrix" in which only the signs of the elements of B are recorded.

The entire system of binary 1 compari ons permitted by the ICP results may therefore be conceived as a set B ..... B .....B (associated with which there also 0 ..... Qn.....0 ) of which each particular binary matrix is a subset. Let this general binary set be referred to as B or as 0 as the case may be. It has (1/2)n(n -n) non-zero elements. With n = 34 this figure is 19,074. Consequently the published ICP binary comparisons are confined to

1/ I am totally indebted to Graham Pyatt for this neat way of describing the position.

2/ It follows that no relationships of relevance to international compari- sons are affected by the choice of reference commodity, s. - 7 - much smaller number, in which each country is compared only to the U.S. at its own prices and at U.S. prices. In effect, this is as if, before deriving B from K, all elements in K had been suppressed except those in the leading diagonal and those in the U.S. column.

4) The Ideal Matrix

From the set, B, it is possible to derive a single triangular matrix containing the (1/2)n(n-1) "Ideal" or "Fisher" index-number comparisons that could be computed as between any pair among the n countries. In this matrix, which may be signified F, every element, such as fjk' is defined as,

Log fjk = (1/2) (Log A -Log Akj + Log Ajk - Log Akk) (2.3)

As in the case of B, so in the case of F, we may derive a corresponding ordinal system in which only the signs of F are represented. Where a distinction is necessary the one system will be referred to as c-F, the other as o-F. In the Phase II publication, the F matrix is presented (for both 1970 and 1973) in Table 1.3. 1/

5). Properties of the Binary Set

The following properties relate to B, 0, c-F and o-F.

(a) Dimensional Independence

All elements of B, 0 and F are invariant to "non-real" dimensional effects such as: changes in national currency units or official exchange rates; changes in the units in which any commodity is measured; proportional variations in all quantities (a scalar operation on Q); or proportional changesy in all prices. 2/

(b) Intransitivities h (i) A given Ordinal Binary Matrix, such as 0 , is necessarily transitive;

(ii) No o-F matrix (Ordinal Ideal Matrix) is necessarily transitive.

1/ The comparisons are presented not as log differences but as ratios (i.e., as antilog f ). Each ratio appears twice, once as country A divided by country Bj%percent) and once as country B divided by country A (per- cent).

2/ Given the definition of P, this is not a scalar operation on that matrix, rather, this matrix is unchanged. -8-

(c) Instabilities

Vi) Cardinal Instability

Even when n 2 it is generally the case that,

B# B (2.4)

In other words cardinal binary comparisons are generally dependent on the choice.of weighting system.

(ii) Ordinal Instability

If, as is typicai, Bik# Bk jeith r of the following are possible: 0 - 0 or 0 # 0 . (2.5)

6) Implications of Intransitivities and Instabilities

On this subject, the following comments may be made:

(1) Because Ideal indexes have theoretically useful proper- ties, their potential intransitivity in a system of multilateral comparisons represents a serious handicap.

(2) Following the Paretian philosophy, it is customary to regard Ordinal Instability as a more serious problem than Cardinal Instability. However, two considerations may cast doubt on this view: -

(a) Suppose Bj B but O o . Then a small change in the data, of intuikively litt 1 e ecpnomic significance, could leave B 0 B but now 0 0 O . (b) From Bi re may derive a second-order cardinal binary matrix B - a triangular matrix setting out all the binary differences that may be computed from Bj. Cardinal binary matrices of higher order may also be calculated. With this hierarchy of binary cardinal matrices there is assQciated a corresponding hierarchy of ordinal matrices O°J °2O° etc. Now we may surmise that it can be proved if at some order level there is cardinal instability but not ordinal instability, ordinal instabilty must appear (given the same data) at some higher order level. -9-

Consideration (a) seems to question the econo i.c significance of the distinction between the two forms of instability, and consideration (b) reinforces the argument by implying that, wherever there is cardinal instabil- ity in a basic set of (first-order) binary differences, ordinal instability must be lurking in the ordering of the differences of differences, or in the differences of differences of differences, or and so on. Orderings of dif- ferences of differences (and so on) are, however, one of the major intuitive operational applications of international real-product comparisons.

It is possible, of course, that the theoretical possibilities of intransitivities and instabilities are of less importance at the practical level. For example, it might be found, when the full B and F systems had been computed, that the incidence of intransitivities in the ordinal versions, or the quantitative magnitude of instabilities in the cardinal versions, was relatively modest. Testing this requires data from the ICP working sheets that is not available in the published volume. However, even if the results of such computations seemed to reduce the practical significance of the prob- lem, we believe the force of our argument for an easily-computable alternative system, which will be advocated in Section IV below, would not be effectively reduced.

'Multilateral" Comparisons

The presence of potential intransitivities and instabilities in the binary system encourages the use of some system that is free of these handi- caps. Any system that uses only one set of price weights is free of these handicaps but then subject to the apparent handicap that the selection of any one country's prices as a basis for comparing all countries is clearly an arbitrary act. It is therefore attractive to consider weights that repre- sent some kind of average of the relative prices observed in the countries studied, especially when these may perhaps be regarded as a representative sample of world prices. In celebrated contributions, Geary, 1/ and subse- quently Khamis, 2/ suggested what amounts to a vector Pr, where Pir is an average of the relative prices observed in each country weighted by the cor- responding quantity observed in that country. Bearing in mind that, because of our method of normalizing prices, our presentation does not follow exactly the same path as that followed by Geary, Khamis and Kravis, the resulting system may be set out as follows:

1/ R.C. Geary, Journal of the Royal Statistical Society, 1958, pp. 97-99.

2/ S.H. Khamis, Bulletin of the International Statistical Institute, 1967, pp. 213-320. 10

k-a =kn

irT- 1ik hk / qk (2.6)

Let S represent a diagonal matrix whose elements are the reciprocals of the row totals of QO Then the vector pr may be obtained by matrix multiplica- tion (PF - transpose of P)

Pr SQFO (207)

The generation of the Cardinal Multilateral Matrix, Br, is then achieved by computing the binary differences in a vector obtained by pre-multiplying the matrix of Q by the vector pr (in other words the complete matrix operation is SQP'Qo

Manipulations and Disaggregations

When the relative-price systems P and Pr are normalized by a refer2 ence commodity ,, they do not represent convenient units when it is desired , for example, to derive sub-aggregates from the commodity data and to make international comparisons of such sub-aggregates, perhaps in the process re- arranging or otherwise manipulating the system, like building blocks. For this latter type of purpose, it is desirable to value quantities in an inter- national-price system which , while having the essential properties of our Pr system , has the dimensions of some familiar national currency unit such as the dollar. This is done by the ICP in Appendix Table 4.5, having the dimen- sions m x n, in which each element such as mik can be derived from the fore- going system by the operation ,

ik Pirjij (2i8) where p$r signifies the ith element of Pr multiplied by the average dollar price ol the reference conmodity , at the official exchange rates of the bench- mark year averaged with quantity weights over all n countries in that year.

As already indicated in ICP Phase II, because the countries studied are not necessarily representative for the calculation of world prices , a sys- tem of stratified weighting is used (the so-called "super-country" technique) in order to make the averages more effectively representative. - 11 -

7) Significance of the Log Transformation

Characteristically, following familiar practice, the ICP publications present results as index numbers with a particular country, actually the Un-ted States, acting as base in each benchmark year. In binary comparisons this method is not signifi'cantly different from our logarithmic method. In multi- lateral comparisons, the method produces a linear, as against a proportional, indicator. The two methods converge, however, if, as will be suggested below, economic welfare is conveniently regarded as a function of the logarithms of commodity quantities.

III. PURPOSES AND USES OF THE DATA

1) First Account of Purposes

Building on Beckerman's short but rather classic discussion of the subject in 1966, 1/ we can discuss the main uses of this type of data at an increasing level of generality. It is essential to emphasize, however, that any such discussion must be necessarily incomplete, owing to the very wide variety of the uses to which the data will in fact eventually be put. To ask the question, "what are the uses of these data" is, to the economics pro- fession as a whole, rather similar to asking what is the use of any national income data. In the present writer's opinion, applied economics, over a wide range of topics, has in the past been severely handicapped by a lack of cer- tain types of cross-section data, of which international real GDP was a major example; new applications of the ICP data are being found almost every day. In this report, we concentrate on the uses of the data for an aid-granting agency, which is also a substantial international economic research organiza- tion and a major influence on international development policy.

A first list of uses and purposes, therefore, is as follows:

(i) To the extent that the national income figures are used for determining aid terms and aid allocations, to pro- vide more accurate data for this purpose. The ICP results now show that exchange deviations are large. Exchange deviations are normally correlated with GDP per capita, so it is often comforting to think that the bias involved in using official rates is monotonic, but it is one thing to show (as many have done, KHS particularly) that the correlation between GDP and exchange deviation is strong, it is another to feel confident that relationships thus inferred will give

1/ Wilfred Beckerman, International Comparisons of Real Incomes, OECD, Paris, 1966. - 12

an adequately accurate result for a particular country in a particular year, given all that is known to have happened in the international market for her currency in the preceding five years or soo For example, at official exchange rates, both Germany and Sweden have now overtaken the U,S. in real GDP per capita. Some people might think it unimportant to know that this conclusion is wrong by a significant amount, but others find tuch information intensely interesting. They may also find it equally interesting to learn that the per capita real GDP of India is one fifteenth, rather than one fiftieth, of that of the U.S.

(ii) To increase understanding of the phenomenon of eco- nomic growth by permitting comparisons of countries at different stages of growth without the distortion of exchange deviations: among the 16 ICP Phase II countries: errors caused by using official exchange rates range from 200-300 percent when comparing developing countries with developed countries, from 30 to 50 percent when comparing among devel- oping countries, and from 20 to 40 percent when comparing among developed countries.

(iii) More specifically to test economic growth theories in which the level of present or past per-capita income, relative to other countries, is an explana- tory or dependent variable. Dennison's classic studies 1/ included attempted explanations of the relative international levels, as well as of rates of growth0 The latter appear to have been based on official rates, a fact which may appear to explain the rather high correlations between the residuals and explanatory variables. It would seem that errors due to exchange deviations may have been thrown into the residuals, which would thus in turn be auto-correlated. More recent writers, such as CrEpps, Tarling and John Cornwall, 2/ have tested "technology gap" or "catching up" models in which GDP per capita, at official rates, is an explanatory

1/ Edward Dennison, Why Growth Rates Differ, Brookings, 1967.

2/ F. Cripps and R. Tarling, Growth in Advanced Industrial Countries, Cambridge University Press, 1973; John Cornwall, "Diffusion, Con- vergence and Kaldor's Laws," Economic Journal, June 1978; John Cornwall, Modern Capitalism, Its Growth and Transformation, 1978. - 13 -

variable. The present writer, using a combination of data from ICP Phase II and KHS, has been experimenting with a model in which the dependent variable is a country's growth rate during a five-year period relative to the U.S. growth rate, and the main explanatory variable is the ratio of the level of US GDP per capita to the corresponding figure for the country in question at the beginning of the period. Results so far have been encouraging in the sense of improved t-values and rising R2's, and thus suggest that the ICP data do indeed contribute to considerable reduction of noise.

(iv) In development planning, it is important to be able to predict structural changes associated with expected future growth, from international cross-section studies in which real per capita income levels are the driving explanatory variable.

(v) Studies of income distribution and growth 1/ are enriched if systematic changes in employment and production patterns associated with growth can likewise be made using cleaner cross-section data.

(vi) A variety of problems in applied economics which have in the past only been permitted study in time-series or from household-budget data can now be studied in international cross-section. Kravis is proposing to study a variety of consumer-demand systems and has already derived demand-equations for a large number of commodities from the 16-country data. The present writer has also computed from Phase II some 150 demand equations in a particular normalized form required for the analysis of index-number problems to be presented later in the present paper. These proved well-behaved. Without constraint, income elastici- ties averaged unity and an unweighted average of substitution elasticities came out at the rea- sonable figure of -1.5. Negative income elastici- ties were obtained mainly for commodities that are plausible inferior goods. And etc.

See for example Simon Kuznets, "Economic Growth and Income Inequality," American Economic Review, March 1955, or Hollis Chenery and Moises Syrquin, Patterns of Development, Oxford University Press, for World Bank, 1975. - 14 -

2) Product Comparisons or Welfare Comparisons?

The ICP publications are semantically oriented to measurements of concepts of "product" (e.g., the titles of the publications and the use of GDP). But it may be noticed that, in our above account of the potential uses of the data, we have repeatedly implied concepts of real income or welfare. The distinction between production concepts and welfare concepts has a dis- tinguished pedigree 1/ but nevertheless deserves some reconsideration or re- exposition.

If two countries had each only one citizen and produced only the same one commodity, their outputs could be compared in units of this commodity while their welfare levels could be regarded respectively as some function of these outputs. However, if this function was for some reason to differ between the countries, it would be customary to say that they could not be compared. 2/ If there is more than one person in either country, a Social Welfare Function is required and a significant distinction between production and welfare imme- diately arises. But, in international comparisons, we usually abstract from intra-national deviations. 3/ In effect, one may envisage a two-part eval- uation of World Welfare; one part considers the distribution of per capita

1/ See for example Kenneth Arrow, Social Choice and Individual Values, 1950; Graham Pyatt (Bank memo circulated in November 1978).

2/ Some aspects of the doctrine of non-comparability of non-homogeneouss populations are criticized in Section IV below.

3/ See A.K. Sen, "The Welfare Basis of Real Income Comparison," Journal of Economic Literature, March 1979, subsection on "The Nation as a Person," page 18. - 15 - aggregates (such as GOP). the other considers internal distributions of these aggregates. 1/

See, for example, Alhluwalia, Carter and Chenery, "Growth and Poverty in Developing Countries," World Development Report, Background Paper No. 6, Sept. 1978.

Thinking about that interesting paper has provoked some questions in this writer about the logic'of World Welfare measurements which are a little digressive in the present context but worth pursuing en passant. Should World Welfare be derived directly from the welfare levels of each of the world's inhabitants, or should it be derived indirectly from assessments of the welfare levels of nations, which latter would in turn be expected to be derived from the welfare levels of their respec- tive citizens? Or should we accept only welfare functions which guaran- tee both methods to produce consistent results? Clearly the answers to these questions depend on the philosophical premises upon which the welfare function is based: e.g. if distribution is an argument in the function, are we concerned only with the absolute extent of world poverty or are we also concerned with the extent of "relative deprivation" within individual countries? Intra-national relative deprivation is clearly sub- jective: poor Americans supposedly are more conscious of rich Americans than of much poorer people in Pakistan. Political realities apart, how- ever, it might be regarded as questionable whether the welfare function of an international aid organization should take cognizance of intra- national envy. The paper of Ahluwalia, et al, for example, is clearly based on an absolute concept of world poverty, since it applies the same standard of poverty - derived from one of the poorest countries - to all countries.

Whichever philosophy is followed, it is important to appreciate how results of the two ma-y differ. For example, imagine a world inhabited by four people, a, b, c, d, whose real-income levels are respectively 1, 2, 4, 8. Consider a general welfare function which is to be applied appropriately either to the four individuals directly or, if the indirect method is used, for evaluating the welfare levels of nations. Let this function take the form:

W = aZn -Vn (3.1)

for any group of 1....i....n individuals with real income levels Yl....Yi....Yn; n signifying world population in the direct case, or national population in the indirect case; Vn signifying the var- iance of Log yi over all i from 1 to n and,

i=n Zn = (1/n) Z (Log yi) (3.2) i=-I - 16 -

Reverting to the single-person country, let each country now pro- duce two commodities, but, owing to differences in material or human resource endowments, let each face different isoquants. With the same tastes in each they will country - represented by a common set of indifference curves -- reach different welfare levels, produce and consume the two commodities in different quantities, and may well have different relative prices. 2/

1/ (continued): a is always a positive number. If an egalitarian philosophy is adopted, B is also positive. (Optimum income distributions can be derived by maximizing W subject to a constraint such as F(Zn, Vn) - 0, eg. implying feasibility trade-offs between equity and efficiency. Such optimum distributions are closely related to ideas such as John Rawls' pragmatic principle of justice, or to recent theories of optimum taxa- tion.)

Now consider three cases:

Case (1) (World Welfare signified as WI)

World welfare is assessed directly from the four individuals;

Case (2) (World Welfare signified as W2)

Individuals a and b are in one country, c and d in another. World welfare is the mean of the two nation's separate welfare levels, which are in turn calculated by applying the general welfare function to the respec- tive pairs of individuals;

Case (3) (World Welfare signified as W3)

As Case (2) except that the nations are now (a,d) and (b,c).

Suppose a moderately egalitarian outlook, e.g. a = .75 and 6 - .25. only do the direct and Then W1 = 0.56, W2 = 0.66 and W3 - 0.47. Not indirect methods produce different cardinal results, but the ordinal comparison with the results of the direct method varies, in the indi- rect method, with the way in which individuals are arranged in coun- tries. Is this an irrelevant factor or is it not? The answer depends, in turn, on, inter alia, the legitimacy of considering intra-national envy.

2/ A distinction does arise, however, if relative consumer prices differ from relative producer prices, e.g., due to differential incidence of expenditure taxes. See Sen. op. cit., at page 20. - 17 -

This is simply illustrated in Diagram 3.1 below, with the better- off country at A and the other at B. If there were accepted conventions for enumerating indifference curves and isoquants, we could say that Country A, as a result of possessing, e.g., isoquant 10 (whereas B possesses only iso- quant 6) has been permitted to reach welfare-level 400, whereas B can achieve only e.g., 200. Lacking such measurements, points A and B can be compared by conventional index numbers, using either A's prices, B's prices (indicated by respective tangent slopes) or by some combination of the two such as the Ideal index. As points A and B lie both on indifference curves and isoquants, with such indices, no distinction between production variation and welfare variation is possible. 1/ The same appears to the writer to be the case with any indices based-on observed quantities. This does not rule out the possibility that some other kinds of indices, not based on observed quanti- ties, might not create a valid technical distinction between measured pro- duction changes and measured welfare-indicator changes. The philosophical implications would, however, seem to remain somewhat murky: how else can one usefully evaluate a change in production other than by reference to the change in welfare that it makes possible?

3) A More General Discussion of the Purpose of the ICP Data

In addition to the data themselves, the need for Kravis and his collaborators to resolve in practical terms a number of problems with impor- tant theoretical implications has significantly advanced knowledge. For example, many people have the idea that it is impossible to make any mean- ingful "quantitative" comparison of economic welfare between e.g., the United States and India; the idea of this impossibility has an honorable pedigree which includes such disparate names as Keynes and Lionel Robbins. Kravis, however, questions whether the supposed "utter differentness" of the in- habitants of the Indian sub-continent from those of e.g., North America is due mainly to intrinsic factors or whether it is due mainly to the fact that the two groups are, indeed, at very different per capita GDP levels. If the latter is the main cause of observed behavior difference, the effects are automatically incorporated in the weighting system (subject to major index- number problems, see below), provided that careful attention is given to the measures of quantity employed and to problems created by the greater consumption of own-produce by rural populations and by other special fea- tures of rural populations.

More generally, the uses of the ICP data can be classified as either Casual, Policy-Oriented or Scientific. The Casual purposes are of the miscellaneous kind exemplified in the previous sub-section. The Policy- Oriented purposes are such as aid allocations, assessment or contributions to international organizations; resources allocation within international economic confederations such as EEC, and etc. The Scientific purposes are in applied economics or other social science where it is desired to test

1/ In the diagramatic example below, the prices are rather close, but this is coincidental. - 18 -

DIAGRAM4 3 .1

Commodity

"914

600

Comiodit 1 * - 19 - theories by means of international cross-section studies in which real income per capita is expected to be an important explanatory variable0 This, of course, applies to any theory where income per capita has an important influ- ence, even if that influence is not the central object of study; because, if income per cdpita is omitted, econometric results may be biased by the effects of the omitted variable.

Thus, the fundamental overall purpose of the ICP data is to make cardinal international comparisons of welfare.

There is no escape from this statement. Students are conventionally taught that inter-personal comparisons of utility are impossible, although it is accepted that utility may for some purposes be regarded as cardinal up to a linear transformation (i.e., in the manner of Von Newman and Morgenstern); but, since the coefficients (constant and units) of the transformation equa- tion are necessarily arbitrary, the data of different individuals are not commensurable. This position was originally asserted by V. Pareto in a little-read passage in his Cours, in which he said little more than how can we compare the ophelimity of the lion with that of the ant? 1/

The traditional ordinalist position has been attacked from two quarters: from political scientists 2/ who assert that, in matters of pol- icy, we (i.e., economists and others) in fact make and apply inter-personal comparisons every day, and more recently from economic theorists such as A.K. Sen 3/ who has shown that virtually the entire "agnostic" theoretical structure of modern welfare economics (including the famous Impossibility theorems) depends virtually on a single obstruction: once one accepts the impossibility of inter-personal comparisons, Sen shows, one has already accepted the impossibility of any kind of non-dictatorial Social Welfare Function. Consequently (paralleling the argument of political scientists), Sen argues that one cannot for example decide what to do about poverty, because one does not know who are the poor people. In international com- parisons, one might add that one cannot decide what to do about poor coun- tries because one does not know which countries they are.

1/ V. Pareto, Cours d'Economie Politique, Lausanne, 1897, Vol. II, p. 47. "Comment peut-on decider si l'homme prehistorique etait plus ou moins heureux que l'homme civilise moderne? En poussant plus loin la com- paraison, pourrait-on decider si la fourmi est plus ou momns heureuse que l.'homme; le lion, que la gazelle?"

2/ See, e.g., Brian Barry, Political Argument, 1967.

3/ See, e.g., Sen "Rational Fools: A Critique of the Behavioral Foundations of Economic Theory," Philosophy and Public Affairs, Summer 1977. - 20

The ozthodox answer to such criticism is that the issue is not in fact founded on the validity or otherwise of interpersonal or international comparisons but only on the validity of cardinal comparisons. The orthodox school would argue that we were entitled to adopt a Social Welfare Function that ordered the welfare levels of different countries according to some acceptable criteria, a.go according to ICP-type index numbers, especially if these displayed the necessary properties that a shift from Country A, with a low indey9 to Country B, with a higher index, would be Pareto-optimal for the citizens of Country A0 Thus, the international development community could arrange countries in an order according to, e.g. the ICP Multilateral index (such an oTderingD see above, meeting the required transitivity con- ditions) and then allocate IDA money to successive countries, starting from the bottom, until the funds available were exhausted. On further investiga- tion, however, this apparent "solution" turns out to be subject to two weak- nesses, each sufficiently severe as virtually to destroy it. In the first place, it is inevitable that as one moves up the list it will become in- creasingly impossible to treat the relationship between three countries ordered A, B, C as if one could have absolutely no knowledge as to whether the excess of A's over B's welfare level was in some sense greater or smaller than the excess of B's over C's. 1/ For example, if one had the intuitive idea that A's level was ten times B's, but B's was only 50 percent greater than C's, one would surely want to redistribute aid that might otherwise have been granted to A to other countries further down on the list. The second weakness followys from the first: the suggested approach might con- ceivably tell one which countries to aid, it could not tell one anything useful about how much aid each should receive. The proof of the pudding is in the eating; for the past twenty years aid-giving agencies, using official exchange rate data have, in fact, been adopting an explicitly cardinalistic approach (eOgo. the $100 per capita criterion) in their policy guidelines. Unfortunately, it was subject to very grave measurement errors.

Thus, given that aid and economic research is every day based on cardinal, inter-personal, international comparisons of apparent welfare, the object of the ICP study is to reduce irrelevant noise incorporated into the measurements that are actually employed. For this purpose, the Kravis studies have provided three kinds of binary proxies (Laspeyres, Paasche and Ideal) which have sore or less well understood theoretical connotations in their own contexts, but as we have seen in Section II, are unstable and poten- tially intransitive; together with the transitive index provided in the multi- lateral comparisons. However, as will be discussed below, the theoretical properties of the multilateral index are less well understood. In fact, the four types of index by no means exhaust the possibilities among potentially useful welfare proxies. To put the point another way, if an enlightened committee of aid administrators and economists were to attempt to agree on a Social Welfare Function to be imposed on the international data for purposes of guiding aid policy and/or for the purposes of economic research, neither

I/ See RoGoDo Allen, Mathematical Economics, 1959, Ch. 11. - 21 - the conventional Ideal Index, nor the ICP multilateral index would necessa- rily be selected. The relevant theory, alternative indices and the theore- tical and emprirical relations between them in the ICP dat will thus be a major subject of this report.

IV. THEORETICAL PROBLEMS IN INTERNATIONAL COMPARISONS OF ECONOMIC WELFARE

1) The Theory of International Welfare Comparisons

Imagine that the President of the World Bank, the Secretary General of the United Nations and/or the Chairman of the OECD Development Assistance Committee have set up a technical committee on international welfare compari- sons. The members would in our view face three immediate questions,-namely:

- What type of utility function, if any, should lie behind the recommendations?

- How should the question of diminishing marginal utility of goods in general (leisure included) be treated?

- How should international differences in tastes be treated?

We discuss these in turn here.

2) Index Numbers and Utility Functions

Many people would argue that no specific utility function is possible or desirable. In comparing two countries, all that is necessary to measure, by means of some appropriate constant-utility index number, is the percentage in- crease in country A's money income (measured in a standard currency unit) that would be necessary to put its representative citizens on the same indifference- curve as the representative citizen of country B. Or, as Franklin Fisher has stated the position "That theory (of the true cost of living index) does not seek to make inter-temporal comparisons of utility ... Rigorous statements of the theory have avoided them. Such statements run as follows: 'Given an in- difference map, we compare two hypotheticl situations, A and B. We ask how much income the consumer in B would require to make him just indifferent between facing B's prices and facing A's prices with stated income.' Note that the question of whether the consumer has the same utility in A as in B never arises. So long as we remain on this level of abstraction, the point in time and space at which the consumer has the indifference map used in the comparison may be A, or it may be B or it may be any other single point dif- ferent from both of these." 1/

In the present writer's view, several reasons would compel the imagi- nary committee to reject this conventional approach. Firstly, the conventional

1/ Price Indexes and Quality Change, Zvi Grilliches (ed.), Harvard Press, 1971; Franklin Fisher and Karl Shell, "Taste and Quality Change", pp. 18-19. violates the committee'8 imsiagi y bhLgf D tho CoFItteG wai OXplcitly approach utilaies asked to do juot that which conventiou den±eus, oaly to coaapre the of countrica sch as A and B. Secondlyg as Fisheg eooiroetly implies, a con- tinuous pceoavence ordering creates an i mite oaugbpa og alternative "true" indexes, because there is an infinity of valid referoonco points withiu the relevant opac5o The two problems are ilstrated In tho g4olowing lax.

Diagram 4.1 considers a "true" price iuden0 It depicts indifference curves for a representative citizen In two countriSo with identical tasteoo B, Consider one country at point A on the curve Indicated and another at point is on another curve. Since the tangent-slopes at A and B arQ different, it evident that the two countries are not only at different welfare levels, but have different price structures. If the vertical axio represents some kind of international numeraire cocmodity which has the same price in both coun- tries (for simplicity of argument, it is convenieut to imagine that the two countries have a common currency), it is apparent that the price of the other commodity is higher in terms of the numeraire in B than in A. In fact, the diagram has been drawn in such a way that the projected tangents intersect at the vertical axis, thus, by simplifying assumption, the higher price of the non-numeraire commodity is the whole reason for country B'es inferior welfare levGlO DIAGRAM 4.1

Commodity 2

Al

b K~~~~~~~

Commodity 1 - 23 -

Take the tangent at A and slide it round the indifference curve on which A is located until it is a tangent to the same curve parallel to the tan gent at B, i.e., until (at point A') prices are the same in both countries. The ratio of the quantity of numeraire now intercepted by this new tangent on the vertical axis, to the quantity intercepted by the original A-tangent 1/ is a true price index based on point A. Familiarly, it is lower than Laspeyres and higher than Paasche (both of which can also be derived from the diagram in the usual way). An alternative would have been to do the same gymnastics on B's indifference curve. Another justifiable procedure would do the exer- cise on another curve, i.e., take an arbitrary point on another curve and rotate the tangent by the amount necessary to produce the same price change. Yet another would be to do the last-mentioned exercise on the original A-curve, but starting from a different point than A. And so on.

In Diagram 4.2 the problem is represented as that of defining a "true" quantity index. Starting from point A, we want a true index of the cost of elevating ourselves to the welfare level implied in point B. Draw the tangent at A and shift it with constant slope until it is tangent to B's curve at A" (the result will not, of course be point B, because we are using the price-weights of country A). The movement of the intercept reads off a true index. The same process can be reversed from point B. Or we can take any tangent to the original curve and move it up to the original B-curve, and so on. 2/ None of the methods necessarily produces the same result.

Thus the essential difference between a true index and either a Laspeyres or a Paasche index is that it is calculated not from observed quan- tities but from the quantities that would be expected to be observed if the assumed prices were actual prices. In Paasche or Laspeyres the assumed prices differ from actual prices in one or other of the countries, therefore the ob- served quantities are expected to differ from the hypothetical quantities. Oa account of the systematic influence of substitution effect, the Laspeyres index tends to exceed the true index calculated from the Laspeyres reference point, and the Paasche index has a similar but inverted relationship to a true index calculated from the Paasche reference point.

The familiar "biasses" of the Laspeyres and Paasche indexes there- fore relate to a particular pair of true indexes only. The Ideal index, which averages Laspeyres and Paasche, tends to cancel the bias. In fact, if indif- ference curves are homothetic, the bias thus defined is cancelled completely. So, on certain assumptions (of which homotheticity is the most significant), the Ideal index is one true index.

The foregoing may be given precision in the notation of Section II. Let the matrix Qh signify the quantities of each commodity that would be consumed in each country if the prices in each country were the prices of

1/ The ratio represented by (a+b)b. 2/ The literature on "true" or constant-utility indexes is quite large, but in our view a good deal of this literature makes the subject seem unneces- sarily abstruse. A precise account, only moderately taxing to the mathe- matically literate, can be found on pp. 134-135, of Philips (1974) op. cit (below). This account is entirely consistent with our diagramatic exposi- tion, but does not emphasize the infinity of possible true indexes. - 24 -

DIAGRAM 4.2

Commodity 2 X

A

Commodity 1 country h. Let Q continue to stand for the quantities consumed at actual prices. Then, by reason of substitution-effect, not only Q # Qh # Qs etc., but the differences are systematic. (Given a set of demand equations one could of course in principle derive expected matrix Q from actual matrix P, and expected Qh from actual vector Ph). The vector qh in Q is however identical to qh.T

Now let th be a vector in which the hypothetical quantities qh are aggregated at the prices Ph. That is to say,

th - Ph Qh (matrix multiplication) (4.1)

Therefore, there is a set, T

T - tl ... th ... tn (4.2) - 25 -

By the same operations as were performed upon the matrix K (see Section II) to obtain the general binary set B, we may obtain a "true" binary set, BT, containing not all possible true indexes, but all possible binary comparisons using true indexes that may be based on the prices of some country among the n countries. In terms of the exposition given in Diagram 3, where the true index is defined by parallel-shifting of tangent-slopes, the com- parisons in BT are restricted to comparisons which may be based on actual tangents to national indifference curves.

As in the case of B, so in the case of BT, the set contains (1/2)m (m2 - m) elements. It will also display similar properties with respect to intransiL.i,_'eb, ad to cardinal and ordinal instability.

T. .is also apparent that the multilateral indexes are not true indexes. The vector of true indexes that would be based on the international prices Pr would be defined as Pr Qr which is clearly different from the definition of the multilateral indexes, and for the following reasons the dif- ference may be expected to be systematic and potentially non-monotonic.

Suppose there is one country whose prices closely approximate the international prices. We have found that the variance of relative prices as between a pair of countries increases with the magnitude of the gap in their per capita real product in a manner which is quite well predicted in a single-variable regression equation. 1/ Consequently the country with the representative prices is likely to be a country that minimizes the mean abso- lute sum of differences between its own per capita GDP and other countries' per capita GDP's, in other words it will tend to be a country near the middle of the international per capita-income hierarchy0 Consider that country as a point of reference and consider the pairwise comparisons between it and all other countries0 Let these first be made by true indexes based on the inter- national prices Pr and let the resulting cardinal system for the sake of argument be regarded as the "true" system0 Multilateral indexes calculated as in the ICP will then differ systematically from the true system because, although based on the same prices, these are applied to actual, rather than hypothetical quantities0 The extent of the bias depends on the average degree of elasticity of substitution, on the one hand, and the degree to which an individual country's prices differ from the representative prices, on the

1/ Let xik be the price of commodity i in country k calculated in dollars at the official exchange rate expressed as a ratio of the corresponding U.S. price0 Let Vk signify the normalized variance of xik (over all i from 1 to m) defined as the variance divided by the square of an ICP index of the overall price-level (in dollars at official exchange-rates) in country k as compared to the U.S. Then we obtained the cross-section equation,

Vk = 607 + o56 Yk R2 = 077; n = 15; (4.3)

from ICP Phase II, when Vk is defined in percentage terms and Yk stands for ideal index of per capita real product, U.S. = 1000 - 26 -

other. 1/ We have just seen, however, that the latter increase with the per- capita-GDP-distance between two countries and will therefore be greatest for the countries with the greatest distance from the representative country, i.e., lying at the top and bottom of the international hierarchy. Therefore, if the actual multilateral indexes were corrected to this "true" system, some more distant countries may change places with some less-distant countries. Given the quantitative relationships suggested by the regression equation referred to above, and given quantitative evidence of plausible values for the average elasticity of substitution, significant order reversals of this kind do not seem very likely in the actual ICP data, but the implied cardinal ambiguities remain, of course, serious.

3) Why Not A Direct Utility Function?

The foregoing considerations suggest a paradox: it is clear that proper use of this type of data inexorably predicates the existence of an inter-personal/international/utility function, yet in deploying conventional index numbers (Paasche-Binary, Laspayres-Binary, Ideal or Multilateral), we are essentially ambiguous as to the actual utility function implied: none of the four indexes implies a unique function. Perhaps, therefore, the time is ripe for a radical departure from conventional procedures. Rather than the conventional indexes, perhaps we should first estimate and then employ a car- dinal welfare measure based on one of the several specific utility functions that have been investigated in the modern literature of applied consumption analysis. j/ More precisely, suppose we specify some function such as

Wk = W (k) (4.4) where q signifies the vector of the ratios of quantities consumed in country k, in a given year (e.g. 1970) to the quantities of the corresponding commo- dities consumed in a reference country. Having chosen a form for this func- tion that seemed to represent a satisfactory balance between theoretical and practical desiderata, the ICP data could be employed to estimate it and, thus estimated, it would then be used to evaluate the welfare levels of individual countries.

To such a revolutionary suggestion, the following objections are likely to be raised:

1/ In other words, in the notation of the previous footnote, on Vk, when this is defined not by reference to the United States but to the repre- sentative country.

2/ For references, see below. - 27 -

(i) to asumse any specific functional form (for the utility function) is arbitrary , since we have no reason to believe that any form is nearer the truth than any other form, or for that matter that any utility function exists at all;

(ii) even if we can pazs hurdle (i) we cannot estimate the rele- vant weights or coefficients;

(iii) it is irpossible to deploy a utility function unless the two 9 populations are homogenous (ioeo, have the same " tastes' and probably the saae incoae distribution)o

We will attempt to deal with these objectione seriatim.

Objection (i) is basically an argument whose time has passed. We have already demonstrated that anyone using these kinds of data for almost any conceivable purpose1 , whether they like it or not , is engaged in an overt act of Benthamismo To be true to their principles , committed Paretians would abandon this type of work altogether; instead they should travel the world advocating the proposition that there is no more reason for giving aid to India than there is-for giving it to Japan. For others , there is no way of staying in the business without implying the enistence of some utility function. Once this proposition is accepted, however reluctantly , it only remains to consider whether a function can be selected that will be a reasonable approximation to a description of the preference patterns implied by actual consumer behavior.

Objection (ii) could be made with honesty only by persons who are not familiar with the enormous strides that have been made in the estima- tion of demand systems. It may be argued that the fact that the assumption of a particular utility-function form which can be estimated to provide a good fit to the international data does not imply that this form is true. Indeed it does note However , what we are trying to do here is to assign weights (in a welfare index) to the commodities that people actually con- sume. In choosing to consume the quantities they do consume1 , people can validly be said to be revealing , virtually axiomatically the weights they do themselves perceive or feel. In other words1 , in the present problem we do have justification for crossing the rainbow bridge from Positivism to I9ormativism. For , although the construction of index numbers of real GDP -er capita is not an immediately normative act , it is clear that the international develpoment community intends to use the figures for spe- cifically normative purposes , such as policy recommendations or aid allocations.

4) Taste Differences and Utility Theory

Finally objection (iii) concerning taste differences , -apparently the most telling , may be less serious than most people suppose. There are basically two grounds of counter-argument , which we will call (a) and (b) as follows: 28 -

(a) (Pace Phase II, p. 18). Taste differences as between the populations of different countries may be less significant than expected. We certainly observe large differences in relative quantities actually consumed of different commo- dities in different countries, and it is easy to fall into the trap of attributing these to differences in "habits." What has to be established is that such differences are not explicable by differences in relative prices or welfare levels. This, of course, is not the way the problem was seen by Lionel Robbins, whose essay on the Nature and Meaning of Economic Science sparked the Paretian Revival in the late 1930s. In a famous passage (whose profundity was in truth little better than that of the passage in Pareto already cited) he asked how he could argue with an Indian mystic who claimed to obtain far more sublime sensations from his meagre consumptions than could ever possibly be exper- ienced by a materialistic LSE professor. We deal with the problem of the relation between total consumption and total utility in the next sub-paragraph. But in the meantime it is necessary to remind ourselves of the sad fact that when people such as Lionel Robbins' imaginary Brahmin (for exam- ple, people such as refugees from South Asia) are, in real life, suddenly transported to places like California, they quite rapidly begin to behave like Californians. Given Californian incomes, they consume more of everything, and, of course proportionately more of some things than others. But most likely - after reasonable time for gathering information -- they will tend to consume relatively more of things which are cheap in California, relative to South Asia, and vice versa. We would no doubt think better of mankind if Robbins' Brahmin on reaching California, repaired directly to Monterrey and continued to devote his time to contemplation. But the sad truth is, he will more likely be found slaking his thirst with Coca-Cola and warming his psyche with bad television.

The foregoing should not, however, be interpreted as an argument that all international taste differences are insignificant. That some important differences indeed exist is indicated by the fact that in international demand equations containing only price and income as explanatory variables, although regression coefficients are strongly significant, R2's are moderate, lying mostly in the range .2 to .4 for fifteen observations. We therefore proceed to the second counter-argumento

(b) Following my earlier work in this field, 1/ I assert that it is wrong to rule out all comparisons where there are 'any

1/ R. Marris, "Professor Hicks' Index Number Theorem," Review of Economic Studies, 1957. - 29 -

kinds of taste differences. I continue to claim that some kinds of taste differences may be permissible. Permissible differences are commodity-specific. Impermissible differ- ences are "people-specific" or, in the present context, "country-specific." One way of characterizing the imper- missible differences is to say that they arise when indi- viduals are considered to vary in their efficiencies as transformers of commodities, including leisure, 1/ into happiness. 2/ Such differences could be random or syste- matic. "Diminishing marginal utility of money" - interpreted as diminishing marginal utility of consumption in general - is an example-of systematic differences: with education, information, etc., held constant (and ignoring Duesenberry- type effects 3/), poor people are supposed to be more effi- cient marginal consumers than rich people. Random differences may result from the cumulative accidents of cultural history or of adaptive experience, but many apparently random differ- ences will in practice be caused by ommitted explanatory variables such as climate or demographic structure. A Committee on International Welfare Comparisons might in some cases wish to take account of objective explanatory variables, in other cases not.

In any event, if the world contained only one commodity, the Com- mittee, unlike Lionel Robbins, would almost certainly insist that the selected index assumed that every world citizen obtained equal welfare from a given quantity. In practice the Committee would need to go further than this, and

1/ In principle, leisure, including leisure taken at the work-place, should be included in the commodity set, because, if leisure is not an inferior good, we expect diminishing marginal utility of goods-other-than-leisure except for goods that are complementary to leisure. -Except for leisure at work- place, it should not be too difficult to provide estimates of leisure time in the international commodity set. Wilfred Beckerman has been doing some work on this, in the inter-temporal context, for OECD.

2/ This has been described as the individual's efficiency as a pleasure machine, an efficiency which may change, without a change in tastes. We are saying that our imaginary committee should not attempt to take account of real or supposed international differences in pleasure machine produc- tivity. See Franklin Fisher or Karl Shell, "Tastes and Quality Change in the Theory of the True Cost-of-Living Index", in Value, Capital and Growth: Papers in Honouring Sir John Hicks, J.N. Wolfe (ed.), 1968.

3/ James Duesenberry, Income, Saving and the Theory of Consumer Behaviour, Harvard, 1949. 30 - rule out systematic country-specific effects, such as diminishing marginal utility of consumption in general, as wellg they could recognize that such differences occur but would lack the capacity to make the experiments required for quantification. Account of the possible implications of such effects could be taken at a later stage. Thus, in an m-commodity world, the Committee would impose the condition of "constant returns to general consumption," or CRGC, implying that whatever the initial real-income level, a 10-percent increase in all quantities would at all times and in all places produce a 10-percent increase in the welfare index.

The definition of CRGC then leads directly to a more explicit defini- tion of permissible, or commodity-specific, taste differences, namely that a country may have a relatively strong taste for a particular commodity provided this is offset, in some sense or other, by a weaker taste for other commodi- ties: loosely, the indifference curves may vary in the sense of "twisting" but not in the sense of "shifting". 1/

5) The Cobb-Douglas Utility Function

The Cobb-Douglas Utility Function is a convenient vehicle for expressing the foregoing ideas. It has the twin merits of having been well investigated by empirical demand theorists 2/ and of providing a more pre- cise definition of CRGCo Let the representative individual in the k'th country have a utility function such as, l-m

Wk = kik' (4.5)

where 7ike signifies the log of the indicated per-capita quantity minus the log of the corresponding per-capita quantity in some reference country, e.g., in the U.S.; and where the eik are coefficients representing the k'th coun- try's tastes. Then in order to preserve CRGC, we impose the familiar condi- tion,

e e (4.6) ik

1/ See R. Marris, Economic Arithmetic, 1958, po 251253.

2, See L. Phlips, Applied Consumption Analysis, North-Holland, 1974, pp. 89-160, 172-9 and Ch. 9. - 31 -

It can be proved that individuals maximizing this function in face of actual national relative prices will spend the proportion eik Of their income on commodity i, at all income levels and with any relative-price structure: thus by implication all income and substitution elasticities are unity. 1/ Since the eik are observable, the function can be estimated from data such as provided by the ICP in Appendix Table 4.2.

Then we define QN, an m x n matrix whose elements are qik and also E, an n x m matrix whose elements are the eik.

Now consider the matrix EQN. It is similar to the matrix K except that taste-weights have now replaced prices in the aggregation process. Any column vector consists of each country's consumption evaluated at some one country's tastes. We could also create a vector in which they had been eval- uated at "representative" tastes, i.e. at some er perhaps similarly calcu- lated like Pr. So we would have either yet another multiplicity of order- ings, or we could settle on some one ordering, such as that based on the tastes of a particular country, or that based on the representative tastes.

There is another ordering available, however, namely the set of indexes that may be calculated from the leading diagonals. Let each country be evaluated at its own tastes! To put the point less provocatively, let us say that the consumption of individual countries is influenced by omitted variables which we cannot for the moment observe. These variables, whatever they are, are creating some observable commodity-specific taste differences. What logical objection is there, therefore, to taking the revealed differences into account? Why evaluate French welfare as if French people had the tastes of Americans, when we have good reason to believe that they do not. 2/

1/ Stone and Geary have provided a classic modification designed to pre- serve the linearity and "adding-up" properties of the system while removing the unrealism of unit income elasticities. Unit substitution elasticities, however, remain (in our international demand equations, referred to in Section III, mean substitution elasticities were 1.5 and they displayed considerable inter-commodity variation). See J.R.N. Stone, "Linear Expenditure Systems," Economic Journal, 1954; R.C. Geary, "A Note on the Constant-Utility Index of the Cost of Living," Review of Economic Studies, 1950-1; F.M. Fisher and K. Shell, "Taste Change and Quality Change," in Value, Capital and Growth (essays in honor of John Hicks), N. Wolfe (ed.), Oxford, 1969. For a general survey, see L. Phlips, loc. cit.

2/ The present writer is thus in head-on conflict with Afriat, The Price Index, Cambridge University Press, 1977, ibid. 32 -

6) Taste Differences and Index Numbers

In some circumstances, this controversy may matters in others not. We may illustrate the difference by reviving some aspects of the analysis of index-number problems originally developed by this writer in 1957. 1/ For the purpose, it is necessary to employ a separate notation, inconsistent with the notation of the previous sections, even where concepts overlap, as follows:

There are two countries, country j and an unsignified reference country;

There are 1.,..i....m commodities, consistently defined for the two countries;

Wi - the proportion of total expenditure in the reference country devoted to commodity i (Ewi - 1);

Pij - the price of i in i divided by the price of i in the reference country;

qij - the corresponding quantity ratio;

a foiwi pij ("Laspeyres" price index);

Q - Z'wi qij ("Laspeyres" quantity index);

esi u the elasticity of substitution of i (defined as pro- portionate variation of quantities divided by the pro- portionate variation in ratio of prices);

-e s m C-wi esi (mean substitution elasticity);

= pij - P (deviation price-relative);

q ij = qij - Q (deviation quantity-relative);

evs9i = esi - Es (deviation substitution-elasticity);

eyi= income elasticity of commodity i, minus 1 (N.B. Ewie'yi - 0);

tjj = the effect on the relative consumption of i, in j, of taste differeBee between country j and the reference country (N.B. twitij - 0);

1/ R. Marris, Economic Arithmetic, London, 1957, Part III and Rev. Ec. Studs., 1957 op. cit. - 33 -

Qj Diwi pi qij/i wi pi ("Paasche" quantity index)

Z = (Qj -Q/Q)

-2- vp, wwPi= p 2 (normalized variance of prices); p ji j _ ~~~-2 v a v P p rpes X first order correlation coefficient between price relatives and substitution elasticities;

rpey - corresponding coefficient relating to income elas- ticities;

rpt - corresponding coefficient relating to taste-effects;

Ves = wi ei, (variance of substitution elasticities);

vt 3= i w ti/Q (normalized standard deviation of taste effects);

S3 = coefficient of skewness of substitution elasticities defined as wi - weighted sum of cubed deviations divided by wi - weighted sum of squared deviations;

FQ - (Q - l)/Q.

From the foregoing definitions, it follows that the deviation quan- tity relative for any given commodity breaks down as follows:

qi = (eCe + e )(p'j)Q / P + (1 + e',)(Q 1) + tij (5.1) ij si s iiyii -

Consistent with our conception of permissible taste differences we restrict the distribution of the tj to have mean zero. They also have no obvious reasons to be correlated with the other explanatory variables, which is not the same as saying that we necessarily assume the expected values of such correlations to be zero. - 34 -

Given (5.1), it can be shown I/ that t:he proportionate difference between the two quantity indexes, Laspeyres (Q) and Paasche (Qj) is Z where,

-2- -2 3 -- z V e + v r v S3 + v r F + v r v- (5.2) p 9 p pes es es p pey Q p pt r

Equation (5.2) is a way of partitioning the proportionate difference between Paasche and Laspeyres index numbers, which is also applicable to inter-tem- poral comparisons.

Let us consider some possible conditions, namely:

(1) Either price relatives and substitution elasticities are uncorrelated or (a weaker condition) substitution elastici- ties are symmetrically distributed (in either case the second term of the partitioning is zero), 2/

(2) price relatives and income elasticities are uncorrelated, 3/

(3) price relatives and taste effects are uncorrelated. 4/

.If all the above hold, Z becomes the product of the normalized variance of prices and mean substitution elasticity, and the ideal index is a true index, In the absence of these conditions neither the ideal nor any conventional index will be a true index, If is my contention that the breakdown of the conditions would not, however, destroy the validity of comparisons based on a specific utility functions using for each country the weights (and hence implied tastes) appropriate to that country. Thus, if there are causes of correlations (e.g. between prices and income elasticities or prices and tastes) breaking down the conditions, the direct-utility-function approach is superior to the conventional approaches not only because, as argued pre- viously, there is an infinity of true indexes of which the ideal would be only one,.!but now because, with such correlations, the Ideal is no longer True.

1/ Marris, Rev, Ec. Studs., 197_, op. cit.

2/ In the first case, rpes 0; in the second, S3es =0

3/ rpey = 0.

4/ rpt =° 35 -

The validity of the conditions can be considered both theoretically and empirically. The most obvious a priori cause of non-zero correlation co- efficients between prices and income-elasticities or taste-effects, would be the prevalance of economies or diseconomies of scale; but, as I also showed in the 1957 article 1/, such effects are complex. After a decade or more of quiescence , interest in this subject, especially empirical interest , has recently revived0 It was investigated by Y. Toda (of Western Ontario) in 1971 /1, by Kravis ICP Phase II (p. 249) and more recently has attracted the attention of none other than Paul Samuelson 3/. Kravis and Toda conclude that price-relatives do not appear to be correlated with income elasticities in a damaging manner but neither author, of course , is able to investigate taste-effect correlations.

We have , however , discovered an indirect method of making infe- rences on this point from a rather simple simultaneous-equations econometric model applied to the ICP Phase II data which enables us to identify an appa- rent measurement of the mean elasticity of substitution and the mean amount of residual gap between Paasche and Laspeyres for the 15 countries using USA as numeraire. This residual gap, in turn, must be explained by correlation between prices and income elasticities or between prices and taste effects , or both. If we accept the various direct measurements (Kravis, Toda) that there is no significant correlation in respect of income elasticities, any non-zero residual must be due to taste correlations. In effect , the resi- dual then by inference becomes the normalized co-variance of taste-effects and relative prices. According to our calculations this is distinctly non- zero. Of course, there are so many sources of slippage along the path to the validity of this inference (i.e. offsetting violations of some of the intermediate assumptions) that the result can be regarded as no more than suggestive. It is suggestive, nevertheless, and therefore reinforces the case for our direct utility index.

1/ RES, 1957, op. cit.

2/ Yasushi Toda "An Index Number Approach to the International Comparison of Consumption", Review of Income and Wealth , December 1971.

3/ Paul Samuelson "Analytical Notes on International Real Income Measures", Economic Journal, September 1974. - 36 -

V. PROBLEMS OF QUALITY DIFFERENCES AND THE SERVICES SECTORS

There is no need to spell out the nature of the problem of compar- ing quantities of products where significant differences in "quality" are suspected. The problem has been much discussed in thee context of inter- temporal comparisons, 1/ where the main fear is that persistent upward or downward trends in the quality of goods in general may lead to bias, in some meaningful sense, in our estimate of the rate of change of the economic welfare of a given population through time. The international problem is analogous, but in my view probably sharper, because as the normalized variance of prices tends to be large in international comparisons; so also, one suspects, international variation in the quality of particular products may also be greater. In addition, the quality problem has an analogy with the problem of taste differences. A French cost-of-living expert visiting the United States might well refuse to weigh a pound of beef until all the fat had been trimmed off, but would in practice find it very difficult to get the fat out of "marbled" USDA beef. An American expert visiting France might (and, if she or he came from the FDA almost certainly would) complain that French beef was, in fact, insufficiently marbled and therefore insist on downgrading it!

That there are some genuine effects here that are not explicable by factors connected with intrinsic differences in relative costs of different types of beef production in the two countries' agricultvral sectors may be suggested by the fact that "lean" beef offered for sale in some American supermarkets does not, in fact, seem able to command a premium price.

The "index-number-problem" faced here would conventionally be posed as a choice between making comparisons based on French or on US "weights", where "weight" is now being interpreted as the shadow price of a quality characteristic. Then, because there is co-variance between the consumption of particular quality characteristics and the incidence of the characteristics themselves, there will be the usual "gap" between the two index numbers. Thus, in Phase I pp. 104-111, which is an account of com- plex and sophisticated quality analyses undertaken by the ICP team for the case of motor cars, reference is made (on p. 114) to the apparence of this problem, even in the case of multilateral comparisons, because small cars are relatively cheap in France and large cars relatively cheap in America. And after all price effects have been removed it turns out that the French like their beef and Americans like theirs. Many Europeans prefer small to large cars. Consequently, attempts to solve the car problem (see below) are affected by the difficulty (which is not entirely removed by the otherwise -excellent-and ingeneous methods adopted by Kravis to take each country's car

1/ See e.g. Price Differences and Quality Change edited by Zvi Giliches, Harvard Press, 1971. - 37 - market at its own face value) that a feature that is regarded as a posit:ive quality attribute in one country may be regarded as a negative attribute in another. 1/

1) Alternative Treatments of the Quality Problem

There are three basic methods of dealing with quality differences all of which have been used in various ways by Kravis and his associates. The first may be called the "representative-price method", the second the "Hedonic Index" method and the third the "stratified input method", this last being especially used in the services sectors.

In the "representative price" method one first obtains from national data total expenditure in national currency on each sub-category which is known to contain a variety of detailed components of varying quality. One then attempts to sample particular items which are thought to be truly comparable in quality. One can sample either for quantities or for prices. If one samples for quantities, one uses the sample quantity ratios to make the quantity comparison between the two countries, with the expenditure figures serving mainly to provide information for weights. If one samples for prices, one uses the sample prices to deflate the exenditure aggregates to obtain aggregate estimates of the quantity ratios in the usual way. Because it is believed that the within-category variance of prices is likely to be less than the within-category variance of quantities, sampling for prices is usually preferred.

This method (representative-price) is used by the ICP for example for transport; total expenditure on transport is compared and deflated by what is hoped to be the price of a standard journey of standard length for a ticket bought on standard terms (although problems are caused by the con- siderable variety of special fares available in some countries).

1/ On page 104 Kravis describes the conventional "matching models" method by posing a comparison of an American car and a Japanese car which are similar except that the Japanese is considerably lighter and slightly narrower. The question is posed whether the inferiority of the Japanese car should be assessed by the difference in width or by the difference in weight. R. L. Marris's answer is that the Japanese car is superior to the US car because it has a higher power-weight ratio and, given other characteristics, probably higher acceleration per unit of power- weight ratio. There is the further difficulty that there are obviously associated relationships between tastes and relevant features of the environment. It is impossible to say whether one reason why Americans have big cars is because owing to climate and methods of local government it is very difficult to maintain the roads without huge potholes, or whether the roads are tolerated in this condition because the majority of Americans still do, in fact, drive big cars. - 38 -

The "Redonic Index" method stems from the work of Lancaster and and Grilliches. For one country it is fairly straightforward. One draws up a list of characteristics relating to the complex of needs the commodity is believed to serve, one then searches for measurable proxies for these, for example, "speed" is represented by horsepower, "comfort" by weight and width etc., etc. and finally one includes these in a regression equation for a large number of specimens of the commodity sold in that country in that year, with the price actually fetched by that model as the dependent vari- able. The resulting regression coefficients reveal the relative monetary valuations apparently placed by consumers on the different characteristics. So long as it is applied with care and imagination the method is clearly a powerful one. 1/ The careful application of as much of the method as was feasible, and especially the application of the quantitatively important field of automobiles is a major feature of the ICP study. Apart from the rather casual comments (plus the suggestion for dynamic applications in the above footnote) we have no further comment to make.

2) The Special Problems of Services

Our special interest lies in those commodities where the third method, which we have called "stratified input method," was mainly applied i.e. to services. The basic problem with services is that they are intrinsi- cally less likely to yield satisfactory proxies suitable for inclusion in Hedonic regressions. The problem is not so much that no indicators exist as that the interpretation of those that do exist is frequently very prob- lematic. The classic example is the classrom teacher. If she or he teaches a large class, has she or he become more productive or has the quality of service been so severely reduced that this individual's total annual output of the service "education" may actually have been reduced? It is often customary to call these professions "constant-productivity" sectors because it is thought they are intrinsically incapable of mechanization without debasement.

The problem must be clearly divided into a problem of weights and a problem of quantity-measurement. The latter is universal, the former not. If all goods and services were produced in a perfectly competitive free-enter- prise system with a perfectly desirable income distribution, the amount that society chose to spend on a particular service would be its weight. But the problem of quantity comparison for international purposes would still remain, because without a quantity comparison we have no price deflator and vice versa.

1/ There could be scope for the application of dynamic demand analysis of the type classicaly surveyed and applied in Houthakker and Taylor (1965). "Taste" for a quality characteristic is likely to be acquired as a result of consuming it. If Americans are forced by prices and regulations to drive smaller cars, they may get to like them. - 39 -

It happens, however, that a large proportion of the most difficult service categories are either public goods or are publically-provided goods, e.g. Defence, Public Administration, Education and Health. As publically- provided goods they are provided on a not-for-profit basis (which may under- weight them) and, owing to the "failures" of the public-decision-making system, may be provided in arbitrary quantities. If then the government is also a major monopsonist in the labor market (or if it adopts conscription), the use of unit labor incomes as a proxy for the marginal value product of the factors in question (an assumption implicit in all National Income work, including the ICP) may be seriously in error. It is for this reason that many people from time to time have recommended simply eliminating these kinds of commodities from the GNP, a step which, however, at least in the West, has never actually been officially adopted. Thus for these goods, as well as the problem of quantity measurement, there may be significant errors in the weights.

Errors in weights, however, are of significant consequence only if they are correlated with relative quantity differences. 1/ At first sight, at least, the most serious problem therefore appears to be that of the quantity comparisons themselves. What is the ICP treatment? Kravis force- fully argues that so long as the level of education (primary, secondary, college) and the qualifications of the teacher are held constant, there is no way he (Kravis) can say whether a schoolteacher in Nairobi, with a class of size x is producing more education per annum than a school teacher in Berkeley, California, in a class of size Y. Therefore, throughout the ICP study it is assumed that teachers, doctors, dentists, nurses and civil servants have the same annual output per head of their particular profes- sional product, in whatever country they may operate, subject to a small adjustment for differences in cooperating capital. We call this method "stratified" input because each commodity category, e.g. "public administra- tion," is quantified as if its output- were equal to its labor input strati- fied for differences in the professional and educational qualifications of the participants. The weights attached to each stratum are related to dif- ferences in annual earnings.

1/ The difference between alternative weighted averages of the same set of numbers, where the form of the average is the same but the weights are different, is equal to the number of items, multiplied by the cor- relation coefficient between the quantity differences and the weight differences, multiplied by the variance of the quantity differences, multiplied by the variance of the weight differences. (See R. Marris, Economic Arithmetic, 1958, p. 217.) In international comparisons, associations of this kind may well occur, i.e. the relevant correla- tion may well be non-zero. A country which appears to like certain types of publicly provided goods will suffer in international compar- ison if the absence of profit margin causes these to be underweighted. - 40 -

The significance of these very strong assumptions can be seen by comparing the ICP GDP index (multilateral comparisons) for each country as published in Phase II with similar indexes from which all the problematic service items have been eliminated. (The fact that we are able to do this on a multilaterally commensurable basis is, of course, yet another example of the value of those tables.) If this is set out in a scatter-diagram (Diagram 5.1) which shows the percentage difference between the two indexes for each country in 1970 with US 1970=100, plotted against the "Adjusted GDP" (i.e. GDP with problematic items removed), adjustments range from more than plus 10% for very poor countries to minus 5 to 10% for affluent countries. As will be seen, the deviation is systematic. If the "Adjusted" figure were true, and the "Unadjusted" (i.e. ICP actual) were intended as a proxy for it, the proxy systematically overstates the real GDP per capita of the poor countries relatively to rich countries. But, of course, it is quite wrong at this stage of the argument to assume that the "Adjusted" figure is "better" than the Unadjusted. Because we have not been able to adjust employment and population figures (used to obtain per capita data from aggregate data), we imply that the entire output of these services should be treated as intermediate goods; clearly an extreme assumption. An alternative method would reduce population figures by the proportion that services employment bears to total civil employment: this will treat the items as all final goods with productivity levels proportionate to produc- tivity in the rest of the economy, another extreme assumption.

In the constant search for noise reduction, these limits may seem too wide. It could be, therefore, appropriate to try and look a little further into some of the assumptions implicit in the ICP stratified input method.

3) Implicit Assumptions of the Input Method

The first question is whether the assumption of constant produc- tivity across countries is justifiable, and whether, without committing absurdities, if should not be possible to obtain more accurate assumptions. For example, it is common observation that, partly by the use of more capital, but considerably by the use of superior organization, a good Washington dentist can effectively treat more people in a day than his London counter- part. Similarly, the education assumptions, despite their sympathetic cul- tural overtones, are also very strong. Some people think they can teach large classes quite well: students appear to dislike large classes but do not necessarily learn worse or experience inferior total education from them. Lecturing to large audiences is a genuine face-to-face operation which can- not, in fact, be fully replicated e.g., by Videotapes.

The "Kravis" assumption in education implies a highly specific mathematical form to the relationship between educational quality and size of classes: in fact it is a rectangular hyperbola! If I teach a class of zero size my productivity is infinite! (Kravis would answer that he would hope, if I am not teaching this semester, that I am doing other useful - 41 -

DIAGRAM 5.1 EFFECT OF REMOVING SERVICE ITEMS FROM REAL GDP

Deviation (Unadj. less Adj. as Z Adj.)

7/I6 4 Y = 23.3 - ~6.7LnX R2 .85,

eKenya

Z w K~~~~~~~~~~orea-

l ~~~~~~~~~~~~~~~~~~Hungary . e~~~~~~~~~~~~~~~ Etc.'

Get '

2.5 5 10 20 07

ADJ. REAL GDP PER CAP, U.S., 1970 - 100; LOG SCALE

N.B.: Adj. GDP excludes Dom. Service, Doctors, Dentists, Nurses, Teachers, all other government employees and some miscellaneous services. Populations are not adjusted. - 42 - things, such as research, which are part of my general professional output.) Surely it should be possible to attempt e.g. to measure the annual produc- tion of students who have reached certain defined standards, as e.g. measured by national tests, and etc.? Where students do not take national tests, could not experts (perhaps not expert educationists!) be assembled to try to sample for the educational quality of the outputs of different countries systems? 1/ If it is argued that such work would involve extraordinary labor, one wonders whether this labor would actually be any greater than the work that has gone into, e.g. assembling cost-of-living experts to judge quality differences (as the ICP study, with great credit, did) or into the task of constructing hedo- nic indexes, or many of the other indexes (e.g. rent and etc.) that created important special problems.

The cases of public administration and defence are much more intract- able (as Kuznets, in calling them "regrettable necessities" long ago recog- nized). Some parts of public administration (e.g. the "service" of redis- tributing income) should be capable of quantitative assessment of some kind, but other parts, far more than we usually recognize, are intermediate goods which should not, repeat not, be included in final output.

4) Implications of Stratification Methods

To the above critique Kravis and associates would probably reply firstly that no better assumptions and methods are currently available and that part of the potential "error" is reduced by the method of stratifying. To this latter point, which is particularly important in public administra- tion, in defense and in education, we must now turn. ICP divides public employees, other than teachers, into four categories: Unskilled Blue Collar, Skilled Blue Collar, White Collar, and Professional. The total government payroll in each category is then internationally deflated by price indicators intended to be representative of the hourly compensation of a worker of stan- dard quality in each category, resulting in input indicators that are to some degree adjusted for within-category "quality" changes due to within-category shifts in employment structure. The result is, not a quality-adjusted meas- ure of output, but a partly quality adjusted measure of input. "Accordingly" (Phase I, p. 162), "we assumed not that the productivity of all government employees was the same internationally, but rather that the productivity of government employees having the same level of education was the same." In

1/ One of the problems here is that large-scale painstakZing work in applied economics tends to be undertaken by Americans, e.g. Edward Dennison and Irving Kravis. Such persons may be especially conscious of the diffi- culty of measuring educational output in a large diverse country without standardized exams for High School graduates. (Dennison measured educa- tional qualifications by the age at which the individual ceased full time education!) a problem which is compounded by co-variance with the fact that this same country also displays an unusually large proportion of its population attending High School and College. - 43 -

turn, level of education was defined (see above) not by educational quali- fications, but, in effect, by the number of years of full-time education experienced.

Such assumptions, however reasonable in face of the considerable difficulties of the problem, create some rather remarkable paradoxes. Here, for example, are the proportionate distributions of input-expenditure in these categories, valued at the international prices, in the total Central, State and Local Government in India, UK, Germany and the US:

Percentage Share of Various Groups in the Public Services of Four Countries, from ICP Data, International Prices. 1970

US Germany UK India

Unskilled Blue-Collar 12 4 38 38 Skilled Blue Collar 14 21 8 3 White Collar 37 62 37 41 Professional 37 13 17 17

Total 100 100 100 100

A similar table may be drawn up for education (as Kravis found that school teachers at different levels in most countries were paid much the same, we need only look at the distinction between school teachers and college teachers):

Percentage Shares of School and College Teachers in Total Educational Employment, Data otherwise as Above

School Teachers 72 91 90 89 College 28 9 10 11

The cultural difference between the US and most other countries comes out most clearly in the second table, which reflects, of course, the vast output of US undergraduate education. It would be interesting to be able to test whether this output has caused the US to be technically more productive, and/ or educationally better endowed in the sense that the average citizen is "better educated" than, for example, her or his European counterpart. We would like to be able to test for the technical effect by comparing the GDPs of countries with different educational systems (as, of course, did Dennison). But we cannot use the ICP data for the purpose because its method has already answered the question for us.

Further study of the above figures illustrates the difficulty in more detail. The second table virtually explains the first. Britain has a particular educational system which has been so closely copied by India that the column vectors in the first table for the two countries (with the obvious small exception in skilled Blue Collar) are almost identical. It follows that the ICP data have automatically told us that the average output per head of - 44 -

all public employees is higher in the US than in the UK - clearly an intui- tively implausible though not necessarily wrong presumption -- while their average productivity in India is automatically assumed to be the same as in the UK. In the case of Germany, that country has a law that requires that all employers, including the Government, send out any unskilled employee to a part-time trade school to learn the trade of his or her current employment. Consequently, very few Germans in Germany are statistically classified as unskilled, and the "guest workers," outside this system, who may be very unskilled, are not much employed in the government sector. Similarly, in Germany, many people who are classified as White Collar are in the US classi- fied as Professional. The effect, again, is that in the ICP data, the average German public employee is rated as less productive than the average American. Whatever may be guessed about the relative productivity of British, Indian and US civil servants, common observation makes the proposition that German civil servants are inherently less productive than American civil servants rather implausible.

5) Possible Solutions to the Problems

The foregoing remarks should be sufficient to show why we believe there is a problem, which is far from saying we have the solution. We have hinted that the solution might lie along the line of finding proxies for e.g. educational output, along the lines of the proxies used in Hedonic indexes: as we move into post-industrial society, with probably less than a third of the population engaged in industry and agriculture (the current US figure is 34%), if we want to continue to measure real product, either internationally or inter-temporarily, we shall be increasingly dependent on trying to find some solutions to these problems. We, therefore, conclude this discussion on a slightly more whimsical note.

Suppose as a proxy for the "consumer-good" aspect of the output of education we took the figure for real expenditure on books, newspapers and mag- azines. Let us take this as the quantity index, for educational output or "end product" and give it the weight of total expenditure on education! Among the three rich countries in the above table the quantity-relatives for this item in the ICP data are, US 100, Germany 71, UK 151. But, of these three countries, the UK has the most "elitist" system of education, Germany next and the US least! (France which has also a rather elitist system has a reading-material quantity index of 112.) In the light of this, one hesitates to carry out the suggested calculation, but given the large weight of education expenditure, the procedure would obviously have a rather dramatic effect on the positions of France and the UK in the GDP League Tables. An even more dramatic effect would be if using "English weights" one tried to measure the educational out- put of the United States by the number of High School students who annually reached a standard equivalent to the appropriate grades of the British General Certificate of Education (0-level, A-level, etc.), and similarly, with the French "Bachot." Clearly, there is a problem here almost exactly analogous to the problem of comparing American and French beef, discussed above, i.e. a problem of strong cultural associations between "tastes" and "qualities". It may be necessary to be bolder in future in finding the means to quantify such - 45 - differences, in a manner that will, as argued above, be increasingly sensi- tive to the measurement problems of societies in which conventional consumer hardware has decreasingly relative importance. 1/

6) The Relationship Between the Treatment of Services and Other Problems

In a previous section we have seen that index-number problems are closely connected with the international dispersion of price-relatives. In the next and final section we discuss the theory of the relationship between GDP per capita and the dispersion and character of price structures. These problems in turn are closely connected with the problems of finding efficient short-cut methods for extending ICP to other countries.

Clearly, to test hypotheses in these areas, it is desirable to have appropriate empirical correlates. A familiar argument concerning the develop- ment of price structures is that there exist intrinsically labor-intensive or constant-productivity commodities (i.e. services) whose prices must necessa- rily rise relatively to others, as real wages rise in conformity with growth of productivity in the hardware sectors. But we cannot test this idea if in fact our data have assumed the existence of constant productivity in certain sectors. Thus the assumption of constant productivity generates apparent relative-price structures. So it would at least in theory be possible that the positive statistical association between price dispersion and GDP per capita which we have observed and discussed above, would disappear or be sig- nificantly reduced, if, in fact, some other measurements concerning the actual productivity of the sectors whose productivity had been assumed constant had found their way into the implicit price relatives from which our data on var- iances were calculated. Finally, this would mean that if the problem we dis- cuss in this section is to be tackled, the sampling of "prices" in short-cut methods would have also to find means for sampling coefficients of produc- tivity in the service sectors. It is most unlikely that to fail to make some such attempt would generate only random errors.

1/ Clearly, the implications of Fred Hirsch's The Social Limits to Growth, Harvard, 1976, are of some relevance here. - 46 -

VI. PRICE STRUCTURE, ECONOMIC DEVELOPMENT AND EXCHANGE RATES

It has for some time been accepted that there are reasons for expecting systematic changes in price structure with economic development. The theory was initiated by Milton Gilbert and Kravis in 1954 and has been continued by Balassa, Samuelson, Clague and Tanzi. The latter group was especially concerned with the implications for the theory of exchange deviations. More recently "KHS" reviewed and synthesized this body of theory and Sultan Ahmad has done likewise in a Ph.D. disseration which is under consideration for publication as a World Bank Monograph. 1/

1) A Model Without Trade

In what follows, we first investigate two economies which cannot trade, for which, therefore, there is only one exchange rate, the ppp exchange rate. We then relate the results to the classic findings of Balassa which relate to two economies which may trade some goods but not others: the latter are typical labor-intensive "services" which also by assumption display smaller differences in output per worker (as between the two countries) than the average differences in the traded sectors - the assumptions which lead to the prediction that market exchange rates, as compared with ppp exchange rates will undervalue the currency of the poorer country.

First, imagine two countries in a state of nature with Leontief/Sraffa- type economies (i.e., fixed coefficients in production) at generally low levels of labor productivity. Initially they are identical both in respect of the list of goodds with strictly positive outputs and in respect of all corresponding coefficients. The real wage and the rate of profit are the same in all sectors and in both countries. Relative prices are those that equalize the rate of profit. The rate of profit itself is exogenous, consequently, the real wage is endogenous. The two countries, however, have different currencies, and nominal wages are therefore arbitrary.

1/ Milton Gilbert, Irving Kravis and Associates, Comparative National products and Price Levels, OECD, Paris, 1958; Bela Balassa, "The Purchasing Power Parity Doctrine: A Re-appraisal", Journal of Political Economyi 1964; Paul Samuelson, "Theoretical Notes on Trade Problems", Q,ev. Ec. and Stats., 1964; CO Clague and V. Tanzi, "Human Capital, Natural Resources and the Purchasing Power Parity Doctrine: Some Empirical Results", Economia Internazionale, 1972. The present author also has reason to believe that some anonymous published work of S.N. Marris (then a junior memeber of the OECD economic staff) incorporated into the Milton Gilbert-Kravis publications of the 1950's, is also rather explicitly relevant. Stephan Marris, in fact, appears to have been one of the first to recognize the significance of so-called "constant pro- ductivity" sectors. - 47 -

Now suppose, skirting round the various consistency problems of non-linear expansion paths, that one country "takes off" into a process where labor productivity, on account of technical progress, grows at different pro- portional rates in different sectors. Let the process occur in such a way that the rate of profit remains constant through time and equal in all sectors (we fudge the question of whether it would need to show a once-and-for-all increase at the start of the process 1/). In the other country, however, no growth occurs and everything remains constant. In the take-off country, given perfect labor markets, the real wage will grow at the same proportional rate in all sectors, this rate being some appropriate average of the sectoral productivity growth rates. Relative prices in the take-off country will therefore fall in the sectors with relatively fast productivity growth. Since relative prices in the other country will remain constant, the international set of commodity price- relatives, which had all been initially unity, will become dispersed. Whether the normalized variance of these ratios will increase, however, is another question, to answer which we need a more precise model.

2) An Analysis of the Variance of Productivity and Prices During Economic Growth

(i) Notation

Compare two countries j and k, and let p' be the relative price if i in J, defined as in Uction IV, subsection (6) above, with k treated as the reference country (i.e., Pi is the ratio of the price if i in j to the correspo4ding price in k, less the Laspeyres overall price-index between the t'1o countries). As also in that subsection, define v , the normalized variance of prices, as the k-weigRted sum of the squares of the p' 's divided by the square of the laspeyres price inlax. Then define additional variables as follows: w,j = the nominal wage in sector i in country j;

Lij = the labor required per unit of output;

1/ In a neo-Keynesian system, where the rate of saving depends on the dis- tribution of income between wages and profits, the general rate of profit will have to be higher in the growing country. Interestingly, this will disturb the Sraffa equations and create different relative prices, a pos- sible cause of relative price dispersion that has not, I think, been discussed in the literature. Notice, however, that this prediction refers only to a growing country. If we imagine that we are examining a situation after the "rich" country has stopped growing, we can continue to assume that the rate of profit remains the same in both countries, as can also be done in a Neo-Classifical system, even during the growth process, if the savings rate is independent of income distribution. - 48 -

m - a mark-up factor defined as,

mij 1 + (bi1 + kij zih)/(wij ij (6.1)

where bij is the dollar value of intermediate input per dollar of output, and kij is the capital coefficient.

w L m - Pij -*ij - ;itn'J Pjk (6.2) ik ik ik This for convenience may be written,

pij RWi * RLi * Rmi jk (6.3)

Where R = w /w etc. wi ij ik (ii) Simplifying Assumption

All Rmi ' 1. Hence (6.3) becomes

Pj' Rw * R -P (6.4) ~ij Wi Li jk

Define Rw as a k-country-weighted average of the Rvi and similarly RL

Also define,

rvi = (Rw -Rw)/Rw (6.5)

and similar, rLI

- these are proportionate deviations from means.

(iii) Economic Assumption

Labor markets are to some degree imperfect in both countries; as a result, part of the difference between the relative labor pro- ductivity of the two corresponding sectors in the two countries is captured by a difference in relative wages and part is not. But as between two sectors with identical productivities (in the two - 49 -

countries) there may be additional differences between relative wages due to institutional factors and other miscellaneous imper- fections. These residual elements in the wage equation are more or less random in their incidence.

The economic assumption may more precisely be expressed in a regression equation based on the data of the two countries, namely,

-1 rwi , b.rLi + ui (6.6)

The economic -assumption expects b to be significantly positive (as the variables are defined Is pure numbers, if the association were perfect, b would be unity, and also R ; hence we may think of b as a positive number of the order of 0 to 0.5) and the ui normally distributed and uncorrelated with rLi.

(iv) Results

It can be proved that the normalized variance of prices is governed by the folowing general equation:

-2 -2 3 v 2a (b + b) p L

-4 - 4 + b^2 aLa-L)) (6.7)

L L -2 A2 + a (1 + 2b + b2)

+ -2 `2

where:

b is the least squares estimate of b, based on observations over all sectors in two countries;

-2 aL is weighted variance of rLi;

-3 L is weighted third moment of the rLi divided by -3 (R); in other words, a measure of the skewness of rLi; - 50 - -4~~ ~ ~ ~~s

aL a similar normalized measure of the Kurtosis of the labor productivity distribution defined so that if the distribution is Normal, this measure - 4 equals (a L)

-2 a the variance of the disturbance term in the regression equation, i.e., that part of the variation in wages that is not explained by productivity differences.

It is unlikely that labor productivities will be normally distri- buted. If they are, however, Equation (6.7) becomes:

-2 -2 2 -..2 -_2 v . a (1 + 2b + b ) + au (1 4 OL) (6.8)

Given the likely magnitude of b, (see above), this could be approximated: -2 -2 -2 -2 -2 - vp L (1 + 2b) d au + au a L (6.9)

If there is no correlation between wages and productivities, we obtain,

_-2 -2 -2 -2 -2 v = aL + au 4 au a L (6.10)

Finally, if relative wages in the two countries are everywhere the same, we have:

-2 _-2 vp aL (6.11)

3) Implications of the No-Trade Model

It will be noitced that at every level of complexity or simplifica- tion, from Equation 6.7 through 6.11, the average level of real wages in the one country as compared to the other (and hence comparative real GDP per capita) does not enter the equations. The driving force in the dispersion of prices, evidently, is the dispersion of labor productivities, enhanced or not as the case may be by other factors such as correlation between wages and - 51 - productivities and non-normalities in the distribution of the productivity relatives. This is the justification for the earlier statement that we are left with a further need for a theory to explain why the normalized dispersion of labor productivities between two countries increases with their economic distance.

4) Possible Scenarios for Labor-Productivity-Structure and Development

It is, therefore, time to investigate some possible models, or "scenarios" for the development of the sectoral pattern of labor produc- tivities during the course of economic growth.

(a) A Classical Scenario

Suppose each sector in each country were endowed with a more or less conventional production function, the same for both countries, but with inter-sectoral varia- tion in the rate at which the marginal productivity of capital declined with increased capital per man. 1/ No technical progress is permitted, but Ricardian capital accumulation proceeds throughout the economy and is dis- tributed throughout sectors in such a way that the rate of profit is at all times equalized; the marginal pro- ductivity of capital, everywhere declining (but at different rates) is kept everywhere the same because accumulation goes faster in industries where the marginal

1/ E.g., in a Cobb-Douglas case we could, with full generally, write:

Log qik Aik + Bik Log Lik + (1-Bik)Log Lik (6.12)

then assume that the Aik are constant over all i and k, but the Bik, though constant over k, vary over i; the equation becomes,

Log qk = A + Bi Log Lik + (1LBo) g ik (6.13) - 52 -

productivity of capital declines least sharply 1/; in the limit case of "pure" constant-productivity sectors, the marginal productivity of capital is zero from the outset (or declines infinitely rapidly), so in these sectors no capital accumulation occurs at all. Labor productivity grows fastest in those industries where capital accumulation is fastest, and continues until by some appropriate mathematical trick the marginal productivity of capital becomes zero in all sectors at the same moment, profits become zero, accumulation ceases and we have the condition of multi-sectoral Bliss.

Now suppose that for some unknown reason overall capital accumula- tion proceeds faster in one country than in another. Thus if we examine the two countries at a later point in time, one will have lower real wages and a higher rate of profit than the other. Evidently, labor productivi- ties will also have become dispersed and so also, it can be shown, relative prices. However, when we used arithmetic examples of this model to simulate the normalized variance of price relatives (as between two countries through time) we found that this tended to remain constant unless there was, in fact, a large pure constant-productivity sector in the sense defined above. Alter- natively, it was necessary to assume a skew distribution of the production- function coefficients. 2/

1/ In Equation (6.14) define

Kik 3 Kik/Lik (capital-labor ratio) (6.14)

and mik as the partial derivative of q with respect to K (the mar- ik ik ~~~~~~~~~~~~ik ginal productivity of capital), then we have:-

m A.K iB(1-B (6.15) mik= ,Kik (1B 1 hence,

d(mik) A. (B 2 -B ) k (I+Bi) (6.16) d(kik) i i ik

Since B must be less than one, the negative value of (B -B ) increases i ii with Bi itself, so the fast-growing-productivity industries are those with relatively low values of this coefficient; they are in fact industries with relatively high values of the marginal productivity of labor.

2/ In the algebra of Equation (6.14), this means a skew distribution of the Bi. - 53 -

(b) A Keynesian Scenario

We then tried Harrod-neutral technical progress. It turns out that in such a model, somewhat analogously to the case of the classical scenario, for the normal- ized price-relative variance to increase through time, it is necessary that technical progress rates vary inter-sectorally in some kind.of skew distribution.

(c) A Random-Walk Scenario

I can see no natural reason why skewness of the kind required to create increeasing normalized variance in either the Classical or in the Keynesian Scenarios should not occur, but neither can I immediately see any obvious reason why it should occur. I have there- for proceeded towards a stochastic model of a type that is known to be capable of producing the kinds of results we are trying to explain, although this is not yet rigorously proved.

Write,

LogLijt aij(t-q)+ cLik(t-q)+dv t+ei (6.17) where Lijt represents labor per unit of output in sector i, in country j at time t.

Lij(t ) is a vector of lagged logarithmic values from q time t through q of labor productivities in country J,

Lik(t ) is a corresponding vector for country k,

vijt is a stochastic disturbance term.

a, c and d are vectors of coefficients.

The interpretation is that the labor producitivity of a sector in a particular country depends on its own lagged values on the lagged values of productivity in the other country (owing to a degree of technology transfer) and to choice effects.

If we set the above equation to work for both countries it will predict in a probablistic fashion the development of the structure of pro- ductivity relatives between the two countries, although owing to the known complexity of these kinds of models, simulation may be required.

The model may tend towards a log-symmetrical distribution. In a very simple case where all the higher-order lags are absent, and there is no technology transfer, it will predict the development of a log-normal - 54 - distribution of labor productivities, with normlalized logarithmic variance of productivity relatives apparently declining rather than increasing with economic development. However, this condition could be consistent with an increasing development of the natural (non-log) normalized variance.

More generally, we shall want (see equation 6.9) to develop the model to predict the general characteristic (log-normal or what have you) of the distribution of labor productivity relatives, to be compared with observable data. These distributions will be of considerable importance in the study of the efficiency of sampling methods of extending the GDP estimates, as discussed elsewhere.

5) The Perfect Trade Model

Let the previous model operate for a time, with no trade. Now let the two countries stop growing and let trade be permitted. There are no tariffs, no economies or diseconomies of scale, and no transport costs for any sector including labor-intensive or services sectors: a Kenyan hairdresser can daily commute costlessly to New York. The theory of comparative advantage tells us that one country will totally specialize on one group of commodities and the other on another. At any exchange rate, the price of each commoddity will be the same in both countries. Variations in the exchange rate will, however, vary the relative prices of commodities, and the exchange rate will manipulate these prices to produce a pattern of demands that balances the balance of payments. This equilibrium exchange rate will also be a ppp exchange rate.

What does this really mean? It means that since relative prices are the same in both countries, the Laspeyres and Paasche volume indexes of per capita GDP will give the same answer and will also be true indexes defined from these prices as reference points. Nominal GDP at the equilibrium exchange rate will also give this answer.

6) The Belassa Effect

Now modify the perfect-trade model by having some sectors where international transport costs are infinitely high. The result must be a mixture of the two previous models, and we are all set for the theorem developed by Balassa. 1/ To obtain his result, however, we cannot have a random mixture of tradable/non-tradable with high/low productivity attri- butes among sectors. There must be a correlation between the non-tradability ai.tribute, which can be called NT, with the attribute of having comparatively low labor/productivity in the rich country, which may be called RCLP. To preserve semantic neutrality we will call goods which combine the two attri- butes, Beta-goods. It is often supposed that Beta goods are a synonym for "Services". But in reality, pace Clague and Tanzi, it is not evident that all kinds of services are necessarily Beta goods.

1/ Op cit. - 55 -

In order to understand this distinction it is necessary to empha- size that RCLP is not necessarily the same thing as "labor-intensive in both countries". Again following Clague and Tanzi, a poor country may be at a significant comparative disadvantage in a sector which is, in fact, labor intensive in both countries. The significance of this point is that we tend to assume, of course, that it is the attribute of labor intensity (rather than RCLP) which makes goods non-transportable because, despite the activi- ties of Vidal Sassoon, we recognize that international commuting is in prac- tice expensive. L/

However, in both the Classicial and Keynesian scenarios set out above, and apparently also in the random-walk case, it appears that if the relevant skew distribution of coefficients is appropriately random 2/ an association between RCLP and capital intensity (and hence inversely with labor-intensity) will develop in the rich country over time.

Some rather hard thinking is required, however, to convince oneself that this necessarily creates a well-defined class of Beta goods in both countries.

There are some other possibilities, for example, that the poor country remains so backward that most of its goods are so labor intensive (like subsistence agriculture) that they are all non-tradable; in which case little trade occurs and we are back to square 1. But if the poor country pays for imports with a narrow range of primary products. which by definition are not Beta goods, we have a condition in which the remaining goods in the poor country, matching corresponding goods ("services") in the rich country, become genuine Beta goods. In honour of the person who drew attention to the significance of the distinction between traded and non-traded goods in this context, and hence by implication invented Beta goods, we may call a state of affairs where for one reason or another a substantial class of Beta goods has in fact developed, a Belassa-condition. Then the resulting undervaluation of the poor country's currency in the international market we may call the Belassa-effect.

When we come to define the effect precisely, however, we find we have an index-number problem. It is probably impossible to prove that the nominal-exchange-rate GDP index, in the presence of the Belassa effect, will necessarily lie between Paasche and Laspeyres quantity indexes or even that the poorer country will lie below the Ideal index. Similar ambiguities probably apply to the range of true indexes lying between the Paasche and Laspeyres reference points.

When multilateral studies are in progress, however, the situation is better. Given any one index, it would be expected that on average, the poorer countries' nominal indexes would deviate downwards from it, and this, of course, is what has been observed. But the nature of the regression

1/ The Swiss and the Mexicans have an answer, however.

2/ E.g., the Bi in (6.12). - 56 - relationship thus obtained will be significantly affected by the choice of index. As Sultan Ahman has shown, previous investigators who relied on Laspeyres were trapped into believing they had found large and robust relationships between GDP and exchange deviation, but these results on further investigation proved to be artifacts of the index-number bias, which was, in effect, being absorbed in substantial amounts into the regression coefficients.

Finally, there is the possibility, which this author does not personally believe, that the empirical phenomenon of the Belassa effect is entirely due to systematic underestimating of the comparative productivity of service activities in rich countries. While Section V has demonstrated that some such possibilities indeed exist, it seems rather unlikely, though not necessarily impossible, that the phenomenon should be sufficiently pervasive. Clearly, some relatively simple experiments on the ICP data would be required to test this question and should be carried out as soon as possible.

7) Conclusions

The systematic underevaluation of the currencies of poor countries, seen as the outcome of multi-sectoral models of economic growth, requires the existence of a class of goods, which we call Beta goods, which are both non-traded and display comparatively low labor productivity in the rich countries. When present, we call this the Belassa effect. It is empirically and intuitively strong, but on examination, theoretically quite complex. It is just conceivable that more accurate measurements of labor-productivity in the service sectors of rich countries might eliminate the effect. Alterna- tively, the interpretation of the effect might become somewhat ambiguous in the light of a more rigorous development of the required associated index- number theory.

However, if by chance the weight of the Belassa effect, empirically or theoretically, were to become significantly reduced, this would by no means imply that the problem of exchange deviations has disappeared or that we do not need estimates of ppp exchange rates. It would merely mean that a systematic form of deviation has become less powerful, leaving us with our evident knowledge of large and economically important non-systematic devia- tions; it would, however, weaken the force of short-cut methods of estimating the ppp's.

To repeat, the author does not believe this will happen. One has only to recollect how much greater intuitive sense has been imparted by the ICP results into comparisons between developed and developing countries, to believe that such a development is unlikely. One might guess that a more accurate measurement of services productivities will widen the gaps between rich and poor countries, but will fall far short of returning these gaps to anywhere near the levels provided by nominal indexes. RECENT PAPERS IN THIS SERIES

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