The Productivity Bias in Purchasing Power Parity: An Econometric Investigation

A recent paper by the author (Officer, 1976) reviewed the various biases and limitations of the purchasing-power-parity (PPP) theory of exchange rates. It was shown that the imperfections of PPP theory fall into three categories: (1) those that reflect the fact that the PPP theory is subject to random error in its predictions; (2) those that emphasize the role of variables other than price levels in exchange rate determination; and (3) those that involve the hypothesis of a systematic bias in PPP as a measure of the equilibrium exchange rate.1 While the first type of weakness—random error—is common to all theories and the second type—other explanatory variables—can generally be corrected by a simple alteration or extension of the PPP theory, the third type—systematic bias—might require fundamental alterations in the theory to preserve its validity. Although the bias could be allowed for in empirical applications, the result might involve a theory of the exchange rate that was no longer recognized as being in the PPP tradition.

Abstract

A recent paper by the author (Officer, 1976) reviewed the various biases and limitations of the purchasing-power-parity (PPP) theory of exchange rates. It was shown that the imperfections of PPP theory fall into three categories: (1) those that reflect the fact that the PPP theory is subject to random error in its predictions; (2) those that emphasize the role of variables other than price levels in exchange rate determination; and (3) those that involve the hypothesis of a systematic bias in PPP as a measure of the equilibrium exchange rate.1 While the first type of weakness—random error—is common to all theories and the second type—other explanatory variables—can generally be corrected by a simple alteration or extension of the PPP theory, the third type—systematic bias—might require fundamental alterations in the theory to preserve its validity. Although the bias could be allowed for in empirical applications, the result might involve a theory of the exchange rate that was no longer recognized as being in the PPP tradition.

A recent paper by the author (Officer, 1976) reviewed the various biases and limitations of the purchasing-power-parity (PPP) theory of exchange rates. It was shown that the imperfections of PPP theory fall into three categories: (1) those that reflect the fact that the PPP theory is subject to random error in its predictions; (2) those that emphasize the role of variables other than price levels in exchange rate determination; and (3) those that involve the hypothesis of a systematic bias in PPP as a measure of the equilibrium exchange rate.1 While the first type of weakness—random error—is common to all theories and the second type—other explanatory variables—can generally be corrected by a simple alteration or extension of the PPP theory, the third type—systematic bias—might require fundamental alterations in the theory to preserve its validity. Although the bias could be allowed for in empirical applications, the result might involve a theory of the exchange rate that was no longer recognized as being in the PPP tradition.

The most important reason for a systematic divergence between PPP and the equilibrium exchange rate is the existence of productivity differences between countries. Although others had perceived the existence of such a “productivity bias,” 2 Balassa (1964) provided the most persuasive analytical argument for this bias. Elsewhere his reasoning is summarized as follows (Officer, 1976, pp. 18–19):

… A high-income country is more productive technologically than a low-income country; but the efficiency advantage of the former country is not uniform over all industries. Rather, it is greater for traded goods (especially manufactured goods and agricultural products) than for nontraded goods (taken by Balassa to be consumer services—he does not mention the public sector). Advances in productivity proceed in this asymmetric fashion for all countries.

Now, prices of traded goods are equalized across countries (abstracting from trade restrictions and transport costs); but this is not so for nontraded goods. With the wage rate higher in the more productive (higher-income) country and with wages equalized domestically across all industries, the internal price ratio [ratio of the price level of nontraded commodities to the price level of traded commodities] must be higher in the higher-income country.

The prices of nontraded goods (relatively higher in the more productive country) are not directly relevant for balance of payments equilibrium. Therefore, a price parity calculated from general price levels yields an exchange value of the high-income country’s currency that is lower than its true long-run equilibrium value, and this systematic bias increases with the overall productivity difference (represented by the per capita income difference) between the countries involved.

As Balassa (1964, pp. 586, 589) writes:

In other words, assuming that international productivity differences are greater in the production of traded goods than in the production of non-traded goods, the currency of the country with the higher productivity levels will appear to be overvalued in terms of purchasing-power parity. If per capita incomes are taken as representative of levels of productivity, the ratio of purchasing-power parity to the exchange rate [number of units of domestic currency per unit of the standard currency] will thus be an increasing function of income levels. … the higher level of service prices at higher income levels leads to systematic differences between purchasing power parities and equilibrium exchange rates.

The productivity bias and Balassa’s justification of it seem to have won general acceptance in the profession. Among those who have been persuaded of the existence and importance of the productivity bias are Gottfried Haberler, Harry G. Johnson, Charles P. Kindleberger, Angus Maddison, and Leland B. Yeager.3 The only challenge to Balassa’s theoretical argument was provided by Officer (1974) and rejected by Balassa (1974 a).4

The present study is not concerned with the analytical argument for the productivity bias but focuses on econometric testing of the existence and magnitude of the bias. Like any hypothesis, the productivity bias may be tested in two ways—through its operational impact and in terms of its assumptions. In this case, the first test investigates whether productivity is a variable that interposes itself in the relationship between PPP and the equilibrium exchange rate. The second test explores the theoretical underpinning of the bias, determining whether disparate productivity advances among countries do lead to divergent movements in their internal price ratios, where the internal price ratio is defined as the ratio of the price level of nontraded commodities to that of traded commodities. According to the productivity-bias hypothesis, the expected relationship is that the change in a country’s internal price ratio is positively related to the change in the country’s productivity.

Section I of the study is concerned with the first type of test of the productivity bias—its operational impact, and Section II with the second type—its theoretical underpinning. In each case the evidence from the existing econometric literature is outlined and evaluated, and the results of new investigations are presented. Section III provides a summary of the study’s findings and their implications for the validity of PPP theory. An Appendix describes the data sources and the construction of the variables used in the study.

I. Testing the Operational Impact of the Productivity Bias

Consider the following notation:

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Then a method of testing the operational impact of the productivity bias is to fit the following regression equation by ordinary least-squares estimation.

PPPi/Ri=α+βPRODi+εi(1)

for a sample of N countries, i = 1,…, N, where α and β are parameters and the error term εi is assumed to be normally, identically, and independently distributed for all i. The productivity-bias hypothesis is accepted if the estimate of β is significantly different from zero.5 The hypothesis also predicts a positive value for this coefficient.

previous tests of the operational impact of the bias

The above approach was followed by Balassa in testing the productivity-bias hypothesis. He took the United States as the standard country and per capita gross national product (GNP) at current prices as the measure of productivity. In his initial regression, Balassa (1964) converts GNP from domestic currency to U.S. dollars by means of the exchange rate (R). In a later study that makes use of revised data on the explanatory variable, Balassa (1973) presents results for GNP converted alternatively by means of R and PPP. The variables refer to the year 1960, and the absolute version of PPP is used.6 The sample consists of 12 industrial countries; it includes the standard country (the United States), which is inappropriate, as is pointed out in the next section.

Consider the following additional notation:

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Balassa’s regressions are presented in Table 1. In this and subsequent tables, the estimated coefficient and t-value (in parentheses) of α and of β are presented in the columns headed by “Constant” and the productivity variable (in this case “GNP/POP”), respectively. A double star following the t-value of the estimate of β denotes that the estimate is significantly different from zero at the 1 per cent level; a single star indicates significance7 at the 5 per cent level. One notes that in all three of Balassa’s regressions the estimate of β is significant at the 1 per cent level, lending strong support to the productivity-bias hypothesis.

Table 1.

Regressions ofPPP/RonGNP/POP, with the United States as the Standard Country, 1960 1

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The coefficient is significantly different from zero at the 1 per cent level.

Equation A is from Balassa (1964), and equations B and C are from Balassa (1973). Balassa provides standard errors of the coefficients, which are converted here into t-values.

In equations A and B, R rather than PPP is used to convert GNP from domestic currency to U.S. dollars.

In equation A, Balassa shows the coefficient for absolute per capita GNP as the explanatory variable. The coefficient is altered here to reflect the explanatory variable as defined in relation to per capita GNP for the United States.

The t-value is not provided.

R¯2 is not provided; the correlation coefficient = 0.92.

Attempts to reproduce Balassa’s findings using other data have not led to positive results regarding the existence of the productivity bias. De Vries (1968) reports on fitting equation (1) to a sample of 62 countries, including both developed countries (DCs) and less developed countries (LDCs), with the United States as the standard country. The explanatory variable is per capita gross domestic product (GDP) at current prices for the year 1958, with the exchange rate for that year used to convert GDP from domestic currency to dollars.8 The dependent variable involves a relative PPP measure, with the base period being 1955 and the current period being mid-1966. De Vries reports a t-value of 1.716 for the estimate of β; thus the coefficient is not quite significant at the 5 per cent level.

Clague and Tanzi (1972) estimate equation (1) for a sample of 19 Latin American countries, again with the United States as the standard country, for the year 1960. The absolute PPP concept is used, and, as the explanatory variable, per capita GDP (at current prices) is converted from domestic currency to dollars using, alternatively, R and PPP. Clague and Tanzi report R¯2 to be 0.24 in the first case and –0.05 in the second case. Thus, using PPP as the conversion factor results in a negative R¯2, that is, in a t-value below unity for the estimate of β.

A weaker test of the productivity bias than that provided by the fitting of equation (1) is offered by Grunwald and Salazar-Carrillo (1972). For ten member countries of the Latin American Free Trade Association, they perform a rank correlation of PPP/R and per capita GDP. For the former variable, the standard country is Venezuela and the time period is May 1968. On the other hand, GDP refers to the year 1963 and is converted to dollars using the exchange rate for that year.9 The rank correlation coefficient between the two variables is reported as –0.27 when R is the official exchange rate and –0.30 when it is the free exchange rate (which differs from the official rate for five of the countries). Thus, the rank correlation of PPP/R and per capita GDP is not only low in magnitude but has a sign opposite to that predicted by the productivity-bias hypothesis.

It should be a source of some amazement that the studies cited are apparently all the published econometric work on the operational impact of the productivity bias. It would be even more amazing that the conflicting findings regarding the bias—affirmative on the part of Balassa, not so on the part of the other authors—have not disturbed the profession’s general acceptance of the validity of the bias, except that Balassa (1973) has argued that equation (1) is not applicable to LDCs.10

At this stage it would appear a good procedure (a) to specify an optimum experimental design in using equation (1) to test the productivity-bias hypothesis, (b) to assess to what extent the previous studies have followed this experimental design, and (c) to provide a new test of the hypothesis following the specified experimental design as closely as possible.

the experimental design

1. In order to obtain a clear test of the productivity-bias hypothesis, the sample should be restricted to developed countries. As described earlier, the studies of Clague and Tanzi (1972) and Grunwald and Salazar-Carrillo (1972) show that a sample composed entirely of LDCs provides no evidence of a productivity bias, and in the work of de Vries (1968) a mixed sample of DCs and LDCs also failed to produce positive implications for the existence of such a bias. These results indicate that inclusion of LDCs in the sample would orient the test toward rejecting the productivity-bias hypothesis. However, it would be wrong to conclude that PPP is an unbiased measure of the equilibrium exchange rate for LDCs. On the contrary, Clague and Tanzi (1972) and Balassa (1973) provide analytical arguments that there exist systematic biases in representing the equilibrium exchange rate by the PPP in the case of LDCs, but that these biases are of a different nature from the productivity bias. Clague and Tanzi also offer econometric results suggesting the existence of such biases.

Of the authors considered, only Balassa observes the rule of using a sample composed exclusively of developed countries.

2. Both the dependent and independent variable should refer to the same time period, because the effect of productivity on PPP/R is a contemporaneous one.11 An implication of this precept is that absolute rather than relative PPP is the appropriate version to use in testing the productivity-bias hypothesis.

This rule is followed by Balassa and Clague and Tanzi but not by de Vries or Grunwald and Salazar-Carrillo.

3. All observations on the variables should be comparable in concept. In particular, the PPP should be computed in the same manner and using data of the same nature for all countries.

In contrast to the other authors, Balassa does not follow this rule, as his PPP measure emanates from a variety of sources and methods of computation, depending on the country. Although this procedure enabled Balassa to increase the size of his sample, it led to misleading regression results, as will be shown later.

4. Given that the absolute PPP concept is used, the PPP measure should be computed from individual prices in the domestic country and the standard country using a formula that incorporates the weighting patterns of both countries. If only one country’s weights are used, the computed PPP will be biased in the direction of an overvalued PPP for that country.12 A typical formula is Irving Fisher’s ideal index number—that is, the geometric mean of the parities calculated alternatively using the weighting pattern of the domestic country and that of the standard country.

This precept is followed by Grunwald and Salazar-Carrillo and by Clague and Tanzi, although their PPP measures are based on the average Latin American (rather than the individual country) weighting pattern and the U.S. weighting pattern. Balassa’s PPP measure is based on Fisher’s ideal index for 9 of the 12 countries in his sample; the rule stated here is not observed for the remaining 3 countries.

5. The optimum-price-level concept of the PPP measure is the GDP price level, because the GDP price level is the appropriate concept to use in computing the PPP as a representation of the equilibrium exchange rate (Officer, 1976, pp. 11–12).

The GDP-price-level concept is used by Clague and Tanzi, and a cost-of-living (COL) price level is used by Grunwald and Salazar-Carrillo. The concept employed by de Vries is a COL level, as COL indices are used to construct her relative PPP measure. As for Balassa, with 11 countries plus the standard country in his sample, a GNP-price-level concept underlies the PPP measure for 8 of the countries. The remaining 3 countries represent a mixture of concepts: a COL price level for Canada, an imprecise price level for Japan, and an unknown price level for Sweden.13

Obviously, the difference between a PPP founded on a GNP price level and one founded on a GDP price level would be minimal, although a purist would prefer the latter concept. A PPP based on a COL price level, however, can differ noticeably from one based on a GDP price level (Officer, 1976, pp. 12–13).

6. The standard country should not be included as an observation in the regression. With both the dependent and independent variable having a value identically equal to unity for this country, the degree of freedom gained is illusory, as the information concerning the standard country has already been used in constructing the variables for the other countries.14

This precept is observed by all authors except Balassa.

7. The income measure for an individual country (for use in the productivity variable) should be converted from domestic currency to the standard currency by using PPP rather than R. It is well known that the use of exchange rates rather than PPPs to convert national income data from one national currency to another misrepresents the relative positions of different countries’ real incomes. A substantial literature now exists on the application of PPP to intercountry comparisons of national income variables.15

De Vries and Grunwald and Salazar-Carrillo employ exchange rates for the conversion purpose,16 while Balassa and Clague and Tanzi show results for R and PPP used alternatively.

8. The appropriate income concept for the productivity variable is GDP rather than GNP. The reason is that the productivity-bias hypothesis concerns prices and production within the boundaries of a country. This point has been made elsewhere by Officer (1974, p. 874), with acknowledgment that its quantitative significance is small.

Of the authors considered, only Balassa does not use the GDP concept. However, as with point 5, the use of a GNP rather than a GDP concept would lead to only minor differences in the variable.

9. While per capita GDP is an acceptable concept of productivity, a better measure would be the ratio of GDP to total employment in the economy rather than to total population of the country—a point also made by Officer (1974, p. 874). A reasonable approach is to adopt both measures of productivity—per capita GDP and GDP per employed worker—alternatively, for the specification of the explanatory variable. None of the authors uses employment in place of population to construct an alternative productivity variable.

10. A still better measure of productivity can be employed to construct the explanatory variable. This measure is the ratio of productivity in the traded sector of the economy to productivity in the nontraded sector, where productivity in each sector is defined as the ratio of GDP (at constant prices) originating in the sector to total employment in the sector. Such a measure of productivity is closest to the productivity concept involved in the theoretical argument for the productivity bias.17 This third measure of productivity, which is not used by any of the authors, would provide another explanatory variable to be used alternatively in equation (1).18

11. Strictly speaking, the exchange rate (R) used in the dependent variable should be the equilibrium value of the exchange rate, as the productivity bias refers to the relationship between PPP and the equilibrium exchange rate (Officer, 1974, pp. 874–75; 1976, p. 36). Given that the actual exchange rate is to be employed as a proxy for the equilibrium exchange rate, equation (1) should be estimated for a number of years, preferably consecutive, so that periods in which exchange rates are close to equilibrium will be considered. Furthermore, the variables used should be comparable in concept and construction from year to year, so that year-to-year comparisons of results may be made. In other words, a moving cross-sectional regression, fitted independently over a number of years (and not pooling data of different years), is indicated.

All the previous authors estimated equation (1) for only one year.

tests using the experimental design

Consider the following notation:

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The traded sector consists of (1) agriculture, hunting, forestry, and fishing, (2) mining and quarrying, and (3) manufacturing. The non-traded sector encompasses all other industries (including government) in which GDP originates.19

The GDP measures in the PRODT/PRODNT variable are at constant prices in order to remove the effect of inflation on the productivity measures, thus facilitating year-to-year comparisons of results of the moving cross-sectional regression specified in point 11 above. In contrast, the GDP measures in the GDP/POP and GDP/EMP variables are correctly expressed in current prices, because the GDP of the domestic country is converted from domestic currency to the currency of the standard country by using the price levels of the two countries (i.e., the PPP) in the period (year) to which the GDP measures pertain.

The experimental design described earlier was applied to four sets of PPP/R data, two sets involving the Federal Republic of Germany as the standard country and two involving the United States in that role.

The Statistisches Bundesamt (Statistical Office) publishes exchange rate and PPP data for a number of countries in relation to the Federal Republic of Germany.20 For many of these countries, the Statistisches Bundesamt provides two PPP computations, one using the weights for the Federal Republic of Germany, the other the domestic country’s weights. The PPP concept employed is a cost-of-living level, with the weights referring to household consumption expenditure. Data are provided annually and monthly.21 For each country, the PPP series are obtained by extrapolation from a base period in which an absolute PPP computation is performed. Consumer price indices in the domestic country and in the Federal Republic of Germany are used in the extrapolation procedure.22

The sample selected for the first set of data consists of all members of the Organization for Economic Cooperation and Development for which the Statistisches Bundesamt provides the two PPP series, one with the weighting pattern of the domestic country and the other with the weighting pattern for the Federal Republic of Germany. The Fisher ideal index of the two PPP computations serves as the PPP measure for the variables in equation (1).23 The result is a sample consisting essentially of the industrial countries with a market economy: Canada, the United States, Australia, New Zealand, Austria, Belgium, Denmark, Finland, France, Italy, the Netherlands, Norway, Sweden, Switzerland, and the United Kingdom.24 The standard country, of course, is the Federal Republic of Germany, and equation (1) is estimated annually for the period 1950–73. Results are presented in Tables 2, 3, and 4. While the maximum size of the sample is 15, the degrees of freedom can fall below 13 because of missing observations in certain years.

Table 2.

Regressions of UnadjustedPPP/RonGDP/POP, with the Federal Republic of Germany as the Standard Country, 1950–73

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Table 3.

Regressions of UnadjustedPPP/RonGDP/EMP, with the Federal Republic of Germany as the Standard Country, 1950–73

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Table 4.

Regressions of UnadjustedPPP/RonPRODT/PRODNT, with the Federal Republic of Germany as the Standard Country, 1950–73

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It was mentioned above that the PPP computations of the Statistisches Bundesamt involve extrapolations from a base period. The base period (generally not the same for each country) can change from time to time, giving rise to inconsistencies in a country’s PPP series. To facilitate year-to-year comparison of results, the unadjusted PPP series are converted to adjusted PPP series for each country by linking the differently based subperiods by means of a year’s overlap or, when a full year is unavailable, by the maximum number of months’ overlap available. The base period to which alternatively based subperiods are linked is the one closest to the middle of the time period considered (1950–73). If a given country’s PPP series has an earlier subperiod with no overlap available for linking to a later subperiod, that country is dropped from the sample for the earlier subperiod. The PPP series resulting from this procedure are used to compute a new ideal-index PPP for each country, which is then used in re-estimating equation (1). The results are presented in Tables 5, 6, and 7.

Table 5.

Regressions of AdjustedPPP/RonGDP/POP, with the Federal Republic of Germany as the Standard Country, 1950–73

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Table 6.

Regressions of AdjustedPPP/RonGDP/EMP, with the Federal Republic of Germany as the Standard Country, 1950–73

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Table 7.

Regressions of AdjustedPPP/RonPRODT/PRODNT, with the Federal Republic of Germany as the Standard Country, 1950–73

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The results in Table 2 to 7 have totally negative implications for the existence of a productivity bias. With a total of 144 fitted regressions, not one estimate of β is significant at the 5 per cent level. Indeed, in only 30 of the regressions does the productivity variable yield even a positive R¯2.

Gilbert and associates (1958) provide absolute PPP computations (together with corresponding exchange rates) for eight European industrial countries for the years 1950 and 1955, using, alternatively, weights of the domestic country and of the standard country (the United States). The countries considered are Belgium, Denmark, France, the Federal Republic of Germany, Italy, the Netherlands, Norway, and the United Kingdom. The price-level concept used is the GNP, and the 1955 figures are obtained from the 1950 results by means of an extrapolation procedure.25

Taking the Fisher ideal index of the domestic-country-weighted and U.S.-weighted PPPs to measure the PPP, equation (1) was fitted to Gilbert and associates’ sample of countries for the years 1950 and 1955, with the results presented in Table 8. One observes that, again, in no case is the coefficient of the productivity variable significant at the 5 per cent level, and in only one of six regressions does this variable produce a positive R¯2.

Table 8.

Regressions ofPPP/Ron Productivity, with the United States as the Standard Country, 1950, 1955, and 1970

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The coefficient is significantly different from zero at the 5 per cent level.

The final set of PPP/R data that was considered emanates from Kravis and others (1975). These authors calculate, among other computations, absolute PPP measures for 9 countries for the year 1970, with the United States as the standard country and GDP as the price-level concept. For each country, they present the domestic-country-weighted, U.S.-weighted, and ideal-index PPPs, along with the corresponding exchange rate. Of the 9 countries, 5 are industrial market economies (France, the Federal Republic of Germany, Italy, Japan, and the United Kingdom), and they constitute the sample for fitting equation (1) to data for 1970. The ideal-index PPP is used, and the results of estimating equation (1) are shown in Table 8. In one of the three regressions, the coefficient of the productivity variable (GDP/EMP) is significant at the 5 per cent level. In the four sets of data to which equation (1) is fitted, this is the only result lending any credence to the existence of a productivity bias. The overwhelming evidence—from all other regressions of equation (1)—is that the productivity bias has no operational impact.

It might be objected that the PPP data obtained from the Statistisches Bundesamt and used in Tables 2 to 7 are based on a COL price level and therefore violate point 5 of the experimental design. Nevertheless, these data are used because they alone are available annually over a long time period, allowing conformity with point 11 of the experimental design. The question arises, however, as to how close these PPP measures are to corresponding PPP measures on a GDP (or GNP) price-level basis. The possible direct comparisons are limited to computations for the Federal Republic of Germany and the United States, and ideal indices of PPP are the logical measures to consider. Taking the PPP figures of Gilbert and associates as the norm for 1950 and 1955 and the measure of Kravis and others as the norm for 1970, the percentage deviation of the Statistisches Bundesamt PPP measure from the norm is 2.93 per cent in 1950, 1.34 per cent in 1955, and 6.58 per cent in 1970.

examination of research favorable to the productivity bus

How can Balassa’s positive results regarding the existence of a productivity bias be explained in light of the negative findings developed here? To begin answering this question, one should apply the experimental design of the present study to Balassa’s PPP/R variable. In particular, this procedure involves dropping the standard country (the United States) from the sample and replacing Balassa’s explanatory variable by the three alternative measures of productivity suggested in the experimental design. The results of estimating equation (1) under these conditions are presented as equations Al, Bl, and C1 in Table 9. Comparison with Balassa’s own regressions (Table 1) reveals that the explanatory power of the productivity variable is reduced, but that for the GDP/POP and GDP/EMP variables the estimate of β remains significant at the 1 per cent level.

Table 9.

Regressions ofPPP/Ron Productivity, with the United States as the Standard Country, 19601

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The coefficient is significantly different from zero at the 1 per cent level.

The dependent variable is from Balassa (1964). Equations A2, B2, and C2 exclude Canada, Japan, and Sweden.

The effect of dropping the United States from the sample is seen in a comparison of equation Al (where GDP/POP is the explanatory variable) in Table 9 with Balassa’s regressions (where GNP/POP is the explanatory variable) in Table 1. The reason for the noticeable reduction in the significance of the estimate of β when the United States is excluded from the sample (equation (Al)) is that, in Balassa’s sample (Table 1), the observation for the United States has the highest values for both the dependent and independent variable;26 it is an extreme observation that biases the results in favor of a more significant coefficient of the productivity variable. One must emphasize, however, that the United States is removed from the sample not because it provides an extreme observation but because its inclusion represents an illusory gain in degrees of freedom, as argued earlier in point 6 of the experimental design.

A closer look at the PPP data used by Balassa is warranted. These data fall into two groups:

Group A. Countries for which an ideal index of domestic-weighted and U.S.-weighted PPP measures is used, with the latter measures obtained by extrapolating the 1950 computations of Gilbert and associates (1958). Thus a GNP price-level concept applies for this group. The countries involved are (a) Denmark, France, the Federal Republic of Germany, Italy, the Netherlands, and the United Kingdom, for which the extrapolation is performed by Kravis and others who use a method described in Pincus (1965, pp. 87–91); and (b) Belgium and Norway, for which the extrapolation is carried out by Balassa himself.27

Group B. Countries for which the PPP measure is obtained from unique data sources, and for which an ideal index is not employed. These countries are Canada, Japan, and Sweden. In the case of Canada, Balassa uses the cross-PPP of the domestic-weighted PPPs (as distinct from that weighted for the Federal Republic of Germany) for Canada and the United States published by the Statistisches Bundesamt.28 It is recalled that cost of living (rather than GNP) is the price-level concept adopted by the Statistisches Bundesamt. For Japan, the PPP measure is developed by Kravis and Davenport (1963, p. 327), who use PPP calculations of Watanabe and Komiya (1958) and other information. For Sweden, the PPP measure is the cross-PPP between Swedish-U.K. and U.S.-U.K. PPPs computed by the National Institute of Economic and Social Research.29

The PPP measures for the countries in Group B not only are of a different nature from those for the countries in Group A but also differ conceptually from each other. Therefore, inclusion of Canada, Japan, and Sweden in the sample violates point 3 of the experimental design, and in four respects:

(1) Consider the price-level concepts underlying the PPP measures for the three countries in Group B. The PPP for Canada is based on a COL concept. The PPP for Japan is founded on an imprecise price-level concept, as the PPP measure is based on retail price comparisons, wholesale price comparisons, and wage comparisons between Japan and the United States.30 The price-level concept underlying the PPP measure for Sweden is not specified in the data source.31 In contrast, the PPP measures for the countries in Group A are all based on a GNP price level.

(2) The PPP measures for Canada and Sweden are computed from cross parities involving the United States and a standard country (the Federal Republic of Germany for the Canadian PPP, the United Kingdom for the Swedish PPP). For no other country in Balassa’s sample is the PPP measure of this nature. Furthermore, the PPP for Japan is derived from a variety of data and a unique method compared to computation of the PPPs for all other countries in the sample. Again, these properties of the PPP measures for the countries in Group B are in contrast to the measures for the countries in Group A. For the latter countries, the PPP measures are all of the same nature (assuming that Balassa’s extrapolation procedure for two countries is comparable to that of Kravis for the remaining six countries in the group).

(3) The PPP measures for the countries in Group A are Fisher ideal indices of domestic-weighted and U.S.-weighted PPP computations. In contrast, the PPP measures for the countries in Group B are not computed as a Fisher ideal index or any other index that takes into account the weighting patterns of both the domestic and the standard country (thus violating point 4 of the experimental design). Balassa could have taken the Fisher ideal indices of the PPPs for Canada and the Federal Republic of Germany and for the United States and the Federal Republic of Germany to compute the cross-PPP measure, but he chose to use the domestic-weighted PPPs. For Sweden and Japan, Kravis and Davenport (1963, p. 327) specifically state that the Fisher ideal indices are not employed to obtain the PPP measure. Indeed, for Japan, the retail and wholesale price comparisons made by Watanabe and Komiya (1958) are based only on the Japanese weighting pattern.32

(4) One might mention that, in light of the properties of the PPP measures for the countries in Group B, these measures can be presumed to be less accurate than the PPP measures for the countries in Group A.

For all of the above reasons, it is appropriate to drop Canada, Japan, and Sweden from the sample and to re-estimate equation (1), again using Balassa’s PPP/R data and the three alternative productivity variables. Thus the revised sample consists exclusively of the countries in Group A. Results of the regressions are shown as equations A2, B2, and C2 in Table 9. The coefficients of the GDP/POP and GDP/EMP variables lose significance at even the 5 per cent level. The coefficient of the PRODT/PRODNT variable now becomes significant at the 1 per cent level, an anomalous result in two respects: (1) the significant/insignificant pattern is opposite to that for the equations (in Table 9) involving GDP/POP and GDP/EMP; and (2) the significant result represents only the second such occurrence out of 156 regressions that are oriented to the experimental design and are estimated here.33

The reason why removal of Canada, Japan, and Sweden (along with the United States) from the sample eliminates the significance of the estimated coefficient of a Balassa-type productivity variable (GDP/POP and GDP/EMP) can be seen in the scatter diagram of PPP/R and per capita GNP provided by Balassa (1964, p. 590). These four countries constitute extreme observations, which play the dominant role in the least-squares fit of Balassa’s regression line. This explanation is reinforced in Table 12, where the rows for 1960 display the coefficient of variation (standard deviation as a percentage of the mean) of each of the variables that appear in the regressions using Balassa’s PPP/R data (Table 9). It is seen that the exclusion of Canada, Japan, and Sweden from the sample greatly reduces the variability of PPP/R, GDP/POP, and GDP/EMP.

Table 10.

Coefficients of Variation of Variables in UnadjustedPPP/R Regressions, with the Federal Republic of Germany as the Standard Country, 1950–73

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Table 11.

Coefficients of Variation of Variables in AdjustedPPP/R Regressions, with the Federal Republic of Germany as the Standard Country, 1950–73

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Table 12.

Coefficients of Variation of Variables inPPP/R Regressions, with the United States as the Standard Country, 1950, 1955, 1960, and 1970

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Excluding Canada, Japan, and Sweden.

Including Canada, Japan, and Sweden.

It should also be stated that the countries dropped from Balassa’s sample afford no special impetus to the operation of the productivity bias when the observations for these countries conform to the experimental design. The evidence for this statement is clear. Of the four countries removed from Balassa’s sample, three (Canada, the United States, and Sweden) are included in the first two sets of data to which equation (1) is applied in this study—that is, the samples in which the Federal Republic of Germany is the standard country.34 Thus, samples including three of the four countries dropped from Balassa’s sample nevertheless yield uniformly negative results concerning the existence of the productivity bias.

changing importance of the productivity bias

Finally, can one say anything about the changing importance of the productivity bias over time, given that the bias has existence? The regressions displayed in Tables 2 to 9 offer strong evidence that the bias does not exist; the general lack of significance of the coefficient of the productivity variable implies that a year-to-year comparison of the magnitude of this coefficient would be wrong.

If the coefficient of the productivity variable were significant in the regressions, the experimental design would have permitted direct comparisons of this coefficient over time for a given set of data. Expressing the domestic country’s productivity measure relative to that of the standard country results in a productivity variable without dimension, as is the dependent variable. A generally significant estimate of β would have allowed consideration of its changing magnitude, to aid in determining whether the productivity bias increased or decreased in impact over the period 1950–73. The lack of significance of the estimate of β effectively closes that approach to assessing changes in the importance of the productivity bias.

An alternative approach is to consider the changing values of the coefficients of variation of the dependent and alternative independent variables used in estimating equation (1) under the various sets of data. Tables 10 and 11 show, over the time period 1950–73, the movement of the coefficients of variation of the variables used in the unadjusted PPP/R and adjusted PPP/R regressions, respectively, with the Federal Republic of Germany as the standard country. There is a strong downward trend of the coefficient for the PPP/R, GDP/POP, and GDP/EMP variables in each set of data. There is a less strong, but nevertheless distinct, downward trend in the coefficient for the PRODT/PRODNT variable, if the years 1950–53 are eliminated from consideration. For these years there are only five or six observations on this variable (because of missing data), whereas succeeding years have at least eight observations.

The decreasing variability of the PPP/R variable implies that PPP is, over time, an ever better measure of the equilibrium exchange rate35 in a cross-country comparison, leaving ever decreasing scope for operation of the productivity bias—or indeed any bias—in representing the equilibrium exchange rate by the PPP. The decreasing coefficient of variation of the productivity variables means that the countries in the sample are converging over time in their productivity levels. The quantitative impact of a productivity bias—should one exist—thus would be decreasing over time. In other words, a given magnitude of the bias (represented by the value of β) would involve a reduced impact because countries’ productivity levels are converging.

For completeness, the coefficients of variation of the variables used in estimating equation (1) with the United States as the standard country are shown in Table 12. However, as only the data for 1950 and 1955 are comparable, trends in the coefficients cannot be discerned.

In summary, if there is a productivity bias, the available evidence suggests that its impact is steadily decreasing over time. However, the overwhelming conclusion from the findings of this study is that the bias does not exist.

implications for a bias under relative PPP

The experimental design was oriented to test for the existence of a productivity bias under absolute PPP. Indeed (following point 2 of the experimental design), the use of absolute rather than relative PPP was deliberate. Given that the results are strongly negative regarding the existence of a productivity bias under absolute PPP, are there any implications for the existence and impact of a corresponding bias under relative PPP?

Such a question is highly unusual. When Balassa (1964) estimated equation (1) and obtained results that supported the existence of a productivity bias for absolute PPP, he noted that the bias would pertain to relative PPP, given a reformulation of his analytical argument in terms of increases (rather than levels) of productivity. Such an approach is the usual one in considering the biases and limitations of the relative PPP theory. A weakness of absolute PPP is established—for example, the existence of trade restrictions or the neglect of the role of income—and the presumption is that this weakness can apply to relative PPP only if the relevant economic condition or variable has changed in some manner since the base period. Thus, in the examples cited, only a change in the severity of trade restrictions or in the level of income would give rise to a limitation of relative PPP corresponding to that of absolute PPP.36

Returning to the productivity-bias hypothesis, as Officer (1976, p. 22) has noted:

The Balassa argument of a nonuniform productivity advantage (greater for traded than for nontraded goods) enjoyed by the technologically advanced country involves a bias in absolute PPP. An increase (decrease) over time in the advanced country’s productivity advantage, as indicated by a higher (lower) rate of growth in per capita income compared with the less advanced country, imparts a similar bias to relative PPP.

In the present study, the opposite situation occurs. The productivity bias has been found to be inapplicable to absolute PPP, but the question remains as to its applicability to relative PPP. In line with the traditional approach to limitations of relative PPP, the answer is that the absence of a bias for absolute PPP provides no basis for a corresponding bias for relative PPP.

Nevertheless, a productivity bias may exist for relative PPP. The impact of productivity changes among countries might be significantly stronger than the impact of their productivity levels. Such a pattern is certainly possible. It would, however, be anomalous in light of the uniformly negative evidence concerning the existence of a bias under absolute PPP over a 24-year period (1950–73).

The reflections here concerning the existence of a productivity bias under relative PPP are not definitive. In Section II, direct econometric evidence is related to the question.

II. Testing the Theoretical Underpinning of the Productivity Bias

A necessary condition for the existence of a bias under relative PPP is that movements in a country’s internal price ratio be determined by the country’s productivity growth. One notes immediately that since this proposition is stated in terms of changes rather than in terms of levels of variables, it can have relevance only for relative PPP and not for absolute PPP.

One should further remark that fulfillment of the proposition is only a necessary condition for the existence of a productivity bias (under relative PPP) and not a sufficient condition. The reason for the latter statement is that the PPP theory, and therefore any impact of the bias, refers to an intercountry comparison. It is quite possible that, for a group of countries that may be considered: (a) there are disparate productivity advances among the countries, and (b) these advances lead to higher internal price ratios in the countries. Yet, the productivity-bias hypothesis might be inapplicable—as the internal price ratios of the countries might be converging while their productivity levels are diverging.

A reason for this result may be that the impact of a given increase in productivity on the internal price ratio might vary from country to country, contrary to the implicit assumption of the proposition. If this impact is inversely related to levels of productivity among countries, the convergence of internal price ratios may occur even if advances in productivity among countries are directly related to levels of productivity.37

However, the findings described in Section I indicate that both the productivity variables (representing the level of productivity) and the PPP/R variable (directly related to the internal price ratio) have converged over time. So, in practice, fulfillment of the proposition relating movements in a country’s internal price ratio positively to changes in the country’s productivity level may constitute both a necessary and a sufficient condition for the productivity-bias hypothesis to apply to relative PPP. How can this proposition be tested?

The approach is to calculate the change in each variable—internal price ratio and level of productivity—as an index number for a given country over a specified time period. The resulting index numbers constitute one observation in a cross-country sample of these index numbers. In other words, a comparative-static time-series computation is made to obtain an index-number observation from each country to be included in the sample. The sample is thus a cross section of these index-number observations, one for each country. Consider the following notation:

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Then the hypothesis may be tested by imposing the same base period and the same current period on the three variables defined above and fitting the regression

PNTi/PTi=ψ+γPRODi+ωi(2)

for a sample of N countries, i = 1, …, N, where ψ and γ are parameters and the error term ωi is assumed to be normally, identically, and independently distributed for all i. The theoretical underpinning of the productivity bias is confirmed if the estimate of γ is significantly different from zero. The productivity-bias hypothesis also predicts a positive value for this coefficient.

The preferred numerator of the dependent variable is the price index of nontraded commodities rather than the general price index (which incorporates both traded and nontraded commodities). The reason is explained by the following relationship:38

PPPiRiAi+Bi(PLNi/PLTi)As+Bs(PLNs/PLTs)(3)

where

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One notes that in relationship (3) the domestic country’s PPP/R ratio is directly related to its internal price ratio (that is, the ratio of the price level of nontraded commodities to the price level of traded commodities), indicating that the ideal numerator in the dependent variable in equation (2) is indeed the price index of nontraded commodities rather than the general price index.

previous tests of the theoretical foundation of the bias

Only two empirical studies of the theoretical foundation of the productivity bias have appeared in the literature. In both cases the authors specify the less preferred version of the dependent variable—that is, they use a general price index for the numerator of the dependent variable in equation (2).

Balassa (1964) fits equation (2) to a sample of seven industrial countries (Belgium, France, the Federal Republic of Germany, Italy, Japan, the United Kingdom, and the United States), using base year 1953 and current year 1961 to construct his variables. He uses the GNP deflator as the general price index, the wholesale price index of manufactured goods as the price index of traded commodities, and manufacturing output per man-hour as the measure of productivity. The estimate of γ is positive and significantly different from zero at the 1 per cent level.

McKinnon (1971, pp. 221–22) takes 1953 as the base period, the first quarter of 1970 as the current period, the consumer price index (CPI) as the general price index, the wholesale price index (WPI) and export price index (EPI) as alternative measures of the price index of traded commodities, and output per man-hour as the measure of productivity.39 He calculates the variables specified in equation (2) for six industrial countries, but he does not fit the regression, nor does he refer to Balassa’s earlier study. He does observe that the countries with high productivity growth (the Federal Republic of Germany, Italy, and Japan) have substantially higher CPI/WPI and CPI/EPI ratios than the countries with low productivity growth (Canada, the United Kingdom, and the United States). The divergence between the two sets of countries is greater for the CPI/EPI ratio—an expected result, because the WPI incorporates some nontraded goods.

new evidence on the theoretical foundation of the productivity bias

Both Balassa and McKinnon used a restricted sample of countries. In contrast, it is appropriate to fit equation (2) to a sample composed of all the countries (data permitting) included in samples to which equation (1) was applied in this study. Thus the present sample consists of the following industrial countries with a market economy: Canada, the United States, Japan, Australia, Austria, Belgium, Denmark, Finland, France, the Federal Republic of Germany, Italy, the Netherlands, Norway, Sweden, and the United Kingdom. The base period of 1953, common to both Balassa and McKinnon, is retained, and 1973, the final year of the analysis in Section I of this study, is selected as the current period. It is logical to choose as alternative explanatory variables the productivity measures developed in Section I, expressed as index numbers and without reference to a standard country. GDP is then expressed in constant prices for all three variables. Thus the new variables are as follows: 40

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If one follows the Balassa-McKinnon procedure of using a general price index in place of the price index of nontraded commodities, it is reasonable to try a variety of alternative measures: CPI, WPI, and PGDP (the GDP price deflator). Correspondingly, either the WPI or the EPI may be used to represent the price index of traded commodities, as the WPI represents a “general” price index only relative to a price index more heavily weighted with traded goods. Then alternative measures of the dependent variable in equation (2) are CPI/WPI, CPI/EPI, WPI/EPI, PGDP/WPI, and PGDP/EPI, where the numerator in each case is expressed as a percentage of the denominator.41

In light of relationship (3), a direct measure of the internal price ratio as an index number (that is, the ratio of the price index of non-traded commodities to the price index of traded commodities) is a preferred dependent variable, and such a measure is constructed for this study. The price index of traded commodities is obtained as the ratio of GDP at current prices originating in the traded sector of the economy to GDP at constant prices originating in that sector. A similar description applies to the price index of nontraded commodities. The traded and nontraded sectors are defined as in Section I of this study. Thus another alternative dependent variable (PNT/PT) is obtained, where again the numerator is expressed as a percentage of the denominator.42

Table 13 presents the results of fitting equation (2) to the various combinations of the specified dependent and independent variables. Consider, first, the regressions with GDP/POP or GDP/EMP as the explanatory variable. Because the WPI is heavily weighted with traded goods, the low significance of the estimate of γ in the regressions involving WPI/EPI as the dependent variable is to be expected. The high significance of the estimate of γ in the CPI/WPI, CPI/EPI, and PGDP/WPI regressions provides some positive evidence of the real-world existence of the theoretical underpinning of the productivity bias. However, the regressions for PGDP/EPI and PNT/PT involve a lesser significance (5 per cent rather than 1 per cent level) and no significance, respectively, of the estimate of γ. Conceptually, the latter variables are the optimal measures of the dependent variable; for PGDP is the most extensive general price index, EPI is the narrowest price index of traded goods, and PNT/PT is a measure especially geared to the theory underlying equation (2).

Table 13.

Regressions of Price-Index Ratios on the Productivity Index

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The coefficient is significantly different from zero at the 5 per cent level.

The coefficient is significantly different from zero at the 1 per cent level.

If the results for the GDP/POP and GDP/EMP variables are mixed, with a balance on the side inclined to verify the theoretical basis of the productivity bias, the regressions with PRODT/PRODNT as the explanatory variable involve totally negative findings. For none of the dependent variables is the estimate of γ significant at the 5 per cent level, and in four out of six cases the explanatory variable yields a negative R¯2. The results for PRODT/PRODNT are especially damaging to the productivity-bias hypothesis, as this variable is the productivity measure closest to the concept embodied in the hypothesis.

III. Summary and Conclusions

The evidence provided by this study indicates that the productivity-bias hypothesis lacks a firm empirical foundation, suggesting that the general acceptance of the hypothesis is unwarranted. With careful attention paid to the experimental design of the test, the productivity bias was found to have no operational impact on the PPP/exchange rate relationship, except in extremely rare cases. Furthermore, even if, contrary to these results, the existence of the bias was to be granted, then examination of the changing variability of the variables specified in the productivity-bias hypothesis suggested that the impact of the bias has been steadily decreasing in magnitude over time.

Regarding the theoretical underpinning of the bias—the hypothesis that changes in a country’s price ratio are related to changes in the country’s productivity—the evidence provided by the study is mixed. The result is contrary to the unambiguous positive findings of the previous studies on the topic. In any event, it should be reiterated that this theoretical underpinning relates only to the relative, and not the absolute, version of PPP.

On balance, the productivity bias does not survive empirical tests of its existence. Should one reject the theory or reject the econometric results? The author has argued elsewhere (Officer, 1974, pp. 873–74) that the productivity-bias hypothesis is questionable on analytical grounds because it ignores quality differences in nontraded commodities (specifically, consumer services) among countries. The more productive country would be expected to have an efficiency advantage in such services as education and medical care, where the labor involved embodies human capital and/or works with physical capital and advanced technology. Thus there exists some analytical support for the empirical findings of this study.

What are the implications for the validity of the PPP theory of exchange rates? An alleged powerful bias—one that overwhelmed the theory and constrained its applicability—has been shown to have little empirical foundation. However, for PPP to be considered an appropriate measure of the equilibrium exchange rate, the PPP theory must pass positive tests; it is not sufficient for it to survive negative tests. Elsewhere (Officer, 1976, pp. 51–54) the author has indicated shortcomings of the positive tests performed to date. There is much scope for improved testing of the PPP theory. The present study implies that avoidance of such testing because of an alleged “productivity bias” is unwarranted.

APPENDIX Data for Testing the Productivity Bias

The following annual time series were constructed for the time period 1950–73 (data permitting) for each country considered in the study:

National Accounts Series

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Labor Series

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For all series, consistent values over time are obtained by linking figures on a former basis to figures on a more recent basis by means of an overlap for the latest available year.43 In all cases, care is taken to use the most recently published data in preference to unrevised data or data on a former basis.

The basic source of the national accounts series is the Organization for Economic Cooperation and Development (OECD), National Accounts of OECD Countries. A secondary source is the United Nations, Yearbook of National Accounts Statistics. The basic problem with the national accounts data is a switch in concept from a former system to the present system of national accounts.44 The changeover occurs at different dates for individual OECD member countries, and a few countries have not yet provided data according to the new system. In order to obtain comparable series for all countries, all series are expressed on the former basis. The latest available data are used, as the values of a series under the present system are linked to the values under the former system by using the earliest year of overlap. The series at constant prices are then re-expressed in 1970 prices (if necessary) by multiplication by the ratio of the current price to the constant price value for the year 1970.

For the Federal Republic of Germany there is a minor problem of separating GDP originating in the mining and quarrying sector from that originating in the electricity, gas, and water producing sector. As the problem occurs in only a few years, typically the joint output is allocated to the two sectors on the basis of their relative shares in the preceding year.

With respect to the United Kingdom, GDP by industry of origin at constant prices as published by the OECD is based on indices of real output applied to output at current prices in a base year. For 1973, however, only the indices are published. For purposes of this study, the relevant indices are converted to GDP at constant prices, using a technique that approximates the procedure previously followed by the OECD.

The primary source of the labor series is the OECD, Labour Force Statistics. A secondary source is the International Labour Office, Yearbook of Labour Statistics. For the specific purpose of constructing early years of the ARM series for Australia, New Zealand, and France, the official yearbooks for Australia and New Zealand and The Statesman’s Year-Book are used.

The principal technique in constructing the series is to use as a basis the figures provided in the general (intercountry) tables on population, total civilian employment, employment in agriculture, and employment in industry (narrowly construed) as published in Labour Force Statistics. The OECD makes some attempt to achieve intercountry and intertemporal comparability in these tables. Employment in industry is then allocated to the traded sector (“mining and quarrying” and “manufacturing”) and the nontraded sector (“electricity, gas, and water” and “construction”) using data published in the individual country tables. Armed-forces data are obtained primarily from the latter tables.

The diverse sources of data are used to provide the maximum length for each series within the 1950–73 time period where overlaps are available to construct consistent series over time. Owing to data limitations, some gaps remain, principally in the early years.

A general problem in the data concerning the Federal Republic of Germany and the United States is the changes in their geographic boundaries that occurred during the time period of the study. The published national accounts series for the Federal Republic of Germany exclude West Berlin prior to 1960 and include it thereafter (with an overlap generally unavailable); therefore, the labor series are constructed according to the same principle as are the national accounts series, the discontinuity in 1960 occurring deliberately.

A slight discontinuity occurs in the national accounts series for the United States. From 1960 onward, the published series formally include Alaska and Hawaii, with no overlap provided. However, both the U.S. and the OECD authorities state that a portion of Alaskan and Hawaiian output was included in the U.S. national accounts prior to 1960.45 For this reason, the labor series for the United States are constructed to include Alaska and Hawaii in all years.

Then the following series, used directly to construct variables in the study, are computed for each country annually (data permitting) for the period 1950–73:

GDPC/POP: per capita GDP in domestic currency at current prices

GDPK/POP: per capita GDP in domestic currency at constant prices

GDPC/(EMPT + ARM): GDP in domestic currency at current prices per employed person

GDPK/(EMPT + ARM): GDP in domestic currency at constant prices, per employed person

AMK/(EMPA+EMPM)(EAKAMK)/(EMPT+ARMEMPAEMPM): ratio of productivity in the traded sector of the economy to productivity in the nontraded sector

GDPC/GDPG: GDP price deflator

(EACAMC)/(EAKAMK)AMC/AMK: internal price ratio as an index number

A remark is appropriate regarding the inclusion of the armed forces (ARM) in the employment measures for the total economy and the nontraded sector. In each case the corresponding measure of output is inclusive of all government production, including defense; therefore, it is incumbent to treat employment in the same manner.

The main limitation of the data concerns the division of the economy into traded and nontraded producing sectors. Allocation of GDP by industry of origin (especially at constant prices) is not available for any year for a number of countries, which explains the relatively small sample in regressions involving the PRODT/PRODNT variable (in either of its two versions) and/or the PNT/PT variable.

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*

Mr. Officer, professor at Michigan State University, was on leave as a consultant in the Research Department of the Fund at the time this paper was written. He is a graduate of McGill University and of Harvard University.

1

For the concepts of exchange rate equilibrium underlying the PPP theory, see Officer (1976, pp. 2–3).

2

For references and discussion, see Officer (1976, p. 18).

3

For references to their views on the matter, see Officer (1976, pp. 19, 22).

4

For a summary of their discussion, see Officer (1976, pp. 19, 36).

5

This test assumes that equation (1) is the correct specification of the impact of the productivity bias and that omitted variables (representing the effect of other biases), if any, do not affect the value of β.

6

Absolute PPP is the ratio of two countries’ price levels; relative PPP is the product of the exchange rate in a base period and the ratio of the countries’ price indices relative to that period.

7

The term “significant” will be used interchangeably with “significantly different from zero.”

8

Failure to express per capita GDP relative to the standard country does not affect the significance of the results.

9

However, Grunwald and Salazar-Carrillo indicate that a PPP measure would be a better conversion factor.

10

Balassa mentions as reasons the differences between DCs and LDCs in the importance of nontraded goods, endowment of natural resources, height of tariffs, and amount of capital inflow.

11

It is assumed that the variables are based on an annual rather than an intra-annual unit of observation.

12

For a discussion of this well-known result and references to the literature, see Officer (1976, pp. 15–16).

13

Further details on this aspect of Balassa’s sample are provided later.

14

The use of the standard country in constructing the PPP measure (for the dependent variable and the numerator of the productivity variable) is the crucial element here; expression of the productivity variable relative to the standard country does not affect the significance of the results.

15

The latest element in the literature, which contains references to its predecessors, is Kravis and others (1975). David (1972) provides the most systematic analysis of the bias involved in using exchange rates to convert national income data from domestic currency to a standard currency. For comments and elaboration on his approach, see Balassa (1973; 1974 b), David (1973), and Hulsman-Vejsová (1975).

16

Actually, their productivity variables are obtained in full from other sources.

17

This measure of productivity is unambiguously better than the others only if the classification of producing sectors into the traded and nontraded categories is correct. If, based on available data, these sectors do not fall clearly into one category or the other, it may be preferable to use a simpler productivity measure.

18

One notes that both numerator and denominator of the explanatory variable emanating from this measure—the ratio of productivity in the domestic country to productivity in the standard country—are without dimension, thus obviating the need for conversion of data from domestic currency to the standard currency.

19

In particular, the nontraded sector comprises (1) electricity, gas, and water, (2) construction, (3) wholesale and retail trade, restaurants, and hotels, (4) transport, storage, and communications, (5) finance, insurance, real estate, and business services, (6) community, social, and personal services, (7) government, (8) private nonprofit services to households, and (9) domestic services of households. Construction of the GDP/POP, GDP/EMP, and PRODT/PRODNT variables is described in detail in the Appendix.

20

The source is Federal Republic of Germany, Statistisches Bundesamt, Internationaler Vergleich der Preise für die Lebenshaltung.

21

The annual PPP data are unweighted averages of the monthly figures; the annual exchange rate data are weighted averages of the monthly figures, the weights being proportional to the number of days in which the foreign exchange market is open during the month.

22

For discussion of the extrapolation procedure and other aspects of the PPP series, see Federal Republic of Germany, Statistisches Bundesamt, Internationaler Vergleich der Preise für die Lebenshaltung 1974, pp. 5–11; and Wirtschaft und Statistik (November 1954, pp. 516–19; August 1961, pp. 443–49; June 1968, pp. 292–98).

23

Oddly enough, the Statistisches Bundesamt publishes the arithmetic mean rather than the geometric mean (Fisher ideal index) of its two PPP computations.

24

Japan is the most important exclusion from the sample.

25

The extrapolation procedure is described in Gilbert and associates (1958, pp. 157–58). The authors’ PPP results at the GNP level are presented in Table 5 (p. 30) of their study; but the 1955 domestic-country-weighted figure for the United Kingdom is listed wrongly as 0.272, whereas it should be 0.242. This reporting error was noticed by Pincus (1965, p. 88).

26

See the scatter diagram provided by Balassa (1964, p. 590) and the table that he presents in his later article (1973, p. 1261).

27

Balassa does not describe his own extrapolation procedure.

28

The data used are from the Federal Republic of Germany, Statistisches Bundesamt, Wirtschaft und Statistik (August 1961, p. 445).

29

The PPPs used in the cross computation are published in Needleman (1961, p. 61). Balassa takes the PPP measure for Sweden from Kravis and Davenport (1963, p. 327), who performed the cross computation of PPPs.

30

See the description provided by Kravis and Davenport (1963, p. 327). At best, these authors make a crude attempt to achieve a GNP price-level concept.

31

See Needleman (1961, pp. 60–61). Apparently, Needleman has a COL concept in mind, but the table he provides is in part based on data from Gilbert and associates (1958), where a GNP price-level concept is used.

32

Kravis and Davenport (1963, p. 327) state that both U.S. and Japanese weights are used in their computations, but they could not have done so below the level of aggregation of the product groups studied by Watanabe and Komiya. In any event, a Fisher ideal index or a similar type of index is not employed.

33

These regressions are those listed in Tables 2 to 8, inclusive, together with equations A2, B2, and C2 of Table 9.

34

Japan is excluded from these samples because the Statistisches Bundesamt publishes only a PPP that is weighted for the Federal Republic of Germany, and not a domestic-weighted PPP for that country, preventing the computation of a Fisher ideal index.

35

It is recalled that the equilibrium exchange rate is proxied by the actual rate.

36

For a systematic application of this approach in examining the limitations of absolute and relative PPP, see Officer (1976, pp. 16–22).

37

A symmetrical argument would apply to the case of diverging internal price ratios with converging productivity levels.

38

This relationship is demonstrated by Officer (1976, pp. 33–34).

39

McKinnon does not specify how output is defined.

40

One notes that the names of the variables are the same as in Section I but their definitions are different.

41

Data on the CPI, WPI, and EPI are obtained from the International Monetary Fund, International Financial Statistics (data tape). Construction of the PGDP variable is described in the Appendix.

42

Construction of the PNT/PT variable is described in greater detail in the Appendix.

43

There is one minor exception to this rule, as described below, in connection with the national accounts series.

44

See references cited in OECD, National Accounts of OECD Countries, 1962–1973, Vol. 1, p. 2.

45

See U. S. Department of Commerce, The National Income and Product Accounts of the United States, 1929–1965, p. vii; and the Organization for Economic Cooperation and Development, National Accounts of OECD Countries, 1953–1969, p. 69.