Trade Patterns Among Industrial Countries
Their Relationship to Technology Differences and Capital Mobility
Author: Mika Saito1
  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund

Contributor Notes

Author’s E-Mail Address: msaito@imf.org

This paper compares two alternative measures of technology differences across industrial countries during 1970-92: one measures differences in labor productivity (the Ricardian measure), and the other differences in total factor productivity (the Hicksian measure). The distinction between the two measures is important to the extent that trade patterns are inconsistent with comparative advantage revealed by the Hicksian measure, but not necessarily with that by the Ricardian measure. The distinction becomes more important in the period with high capital mobility across countries.

Abstract

This paper compares two alternative measures of technology differences across industrial countries during 1970-92: one measures differences in labor productivity (the Ricardian measure), and the other differences in total factor productivity (the Hicksian measure). The distinction between the two measures is important to the extent that trade patterns are inconsistent with comparative advantage revealed by the Hicksian measure, but not necessarily with that by the Ricardian measure. The distinction becomes more important in the period with high capital mobility across countries.

I. Introduction

Recent papers such as Bowen, Leamer, and Sveikauskas (1987), Trefler (1993, 1995), Harrigan (1997), Davis and others (1997), and Davis and Weinstein (2001) have emphasized the importance of cross-country differences in technology in explaining trade patterns within the Heckscher-Ohlin framework. Despite the growing interest in technology differences across countries, the choice of the measure of technology differences has received little attention in the literature. In particular, one has a choice between cross-country differences in total factor productivity (the Hicksian measure) and those in labor productivity (the Ricardian measure).2

Although it has been more standard to measure technology differences with the former than the latter, if capital is allowed to move across countries in a two-factor model of the Heckscher-Ohlin type, then the latter, which is more easily measured, can be used as an alternative measure to summarize the supply side of the economy. For example, Kemp (1966) and Jones (1967) showed that if capital is mobile across countries and technology differs across countries, then trade patterns can be summarized by cross-country differences in labor productivity (see Ruffin, 1984, for more discussions). Given the well-established evidence of high capital mobility across industrial countries since the mid-1980s (Graham and Krugman, 1993), examining the role of the Ricardian measure in comparison with the Hicksian measure in explaining trade patterns is an important exercise.

This paper shows that trade patterns are inconsistent with comparative advantage revealed by the Hicksian measure, but not necessarily with that by the Ricardian measure. This result holds regardless of the different estimators used to obtain the total factor productivity (TFP) differences; two estimators used in this paper are the panel fully modified ordinary least squares (panel FMOLS) estimator of Pedroni (2000) and the three-stage least squares (3SLS) estimator of Boskin and Lau (1992).

II. Literature Review

Recent papers in the international trade literature have found that one of the key requirements for finding evidence supportive of the Heckscher-Ohlin model is to allow for cross-country differences in technology. For example, Bowen, Leamer, and Sveikauskas (1987), using data on 12 resources and the trade of 27 countries in 1967, showed that the Heckscher-Ohlin-Vanek (HOV) equations are rejected in favor of weaker models that allow for technological differences and measurement error. Trefler (1993) allowed for factor-augmenting international productivity differences in the HOV model and showed that this modification can explain much of the factor content of trade. Trefler (1995), using 1983 data for 33 countries and 9 factors, rejected the Heckscher-Ohlin model in favor of alternative models that took account of international technology differences and home bias in consumption. Maskus and Webster (1995) looked at differences in technology and consumption behavior between two countries (the United States and the United Kingdom), but for a finer disaggregation of factors; they also rejected the Heckscher-Ohlin theorem in favor of alternative models. Harrigan (1997) found differences in both relative technology and endowment differences to be important determinations of specialization. He used TFP to capture cross-country differences in technology among industrial countries. Davis and others (1997) showed that, when one controls for technology differences across countries, the Heckscher-Ohlin model performs much better empirically; they showed this using interregional trade in Japan. Most recently, Davis and Weinstein (2001) demonstrated in the most comprehensive manner that the HOV theory, when modified to permit technical differences, a breakdown in factor price equalization, and the existence of nontraded goods and costs of trade, is consistent with data from 10 OECD member countries and a rest-of-world aggregate. In all of these studies, one of the key elements in explaining the pattern of trade is cross-country differences in technology.

III. Two Measures of Technology Differences

A. The Ricardian Measure

Denote the price of a good in a given country by pitm, where superscript m (or n) represents countries and subscript i (or j) stands for goods. The law of comparative advantage says that if

pitmpjtm<pitnpjtn,(1)

then country m must export good Xi, if trade exists at time t.3

The Ricardian model (Ricardo, 1817) assumes that production is a function of a single factor, labor. Therefore, if pitm=citm, where citm is a unit cost of producing good i in country m, then

pitm=citm=witmlitmXitm,(2)

where witm,litm, and Xitm are the wage rate, labor, and output, respectively. The Ricardian theorem of comparative advantage says that if

witmlitmXitmwjtmljtmXjtm<witnlitnXitwjnljtnXjtn,(3)

then country m exports good Xi, if trade exists. Typically, the Ricardian model treats a labor input requirement, limXim, as a constant, aLim. It also assumes that the labor market clears in each country, and hence that wage rates are equal across sectors; for example, wim=wjm. Thus equation (3) is often expressed as aLimaLjm<aLinaLjn. Since factor prices are not necessarily equalized in the real world, we define and compute the Ricardian measure of technology differences as follows:

RICARDOijtmn=lnwitmlitmXitmwjmljmXjmlnwitnlitnXitwjtnljtnXjtn.(4)

If RICARDOijtmn is negative, then country m has comparative advantage in producing goods in sector i and thus exports good Xi to country n.

This Ricardian measure is computed for every bilateral combination of 14 OECD member countries m and n for 10 sectors at the two-digit International Standard Industrial Classification (ISIC) level for 1970-92 using production data from the International Sectoral Data Base.4 Details of the data used in this study are discussed in Section V.

B. The Hicksian Measure

A component that is attributed to Hicks-neutral technological progress, called the Hicksian measure, is extracted from the Ricardian measure.

The extraction takes two steps. First, the Ricardian measure is decomposed into a relative labor productivity component and a relative wage component:

RICARDOijtmn=(lnXjtmljtmXjtnljtnlnXitmlitmXitnlitn)+(lnwitmwitnlnwjtmwjtn)(5)or=(Δ lnXjtljtΔ lnXitlit)+(Δ lnwitΔ lnwjt),

where Δ lnXitlit(=lnXjtmljtmlnXjtnljtn) is the cross-country difference in labor productivity in sector i expressed in percentage terms at time t, and Δ lnwit(=lnwitmwitn) is the cross-country difference in wage rates in sector i expressed in percentage terms at time t. Notice that the first term captures the relative labor productivity differences across countries and the second term the relative wage rate differences across countries.

To extract the Hicksian measure HICKSijtmn from the first term of equation (5), we estimate the production function described as follows:

lnXitclitc=lnX0i+lnAic+λic.t+αkilnkitclitc+lnuitc,(6)

where c = m or n. Notice that Aic and λic are country-specific technological parameters, respectively. Aic captures differences in the initial level of technology across countries (relative to that of a particular country X0i), and λic captures differences in the rate of technical progress across countries. kitc and litc are country-specific capital and labor inputs, respectively. αki is without a country superscript, indicating that this technological parameter is commonly shared across countries.5 ln uitc is the disturbance term, capturing unobservable productivity shocks.

This specification makes two implicit assumptions. First, technological progress is Hicks-neutral across factors (capital and labor) within each sector. This assumption is implied by the common shift parameter Aic and the common rate of technical progress λic for both factors, capital and labor. Second, technological progress is not necessarily Hicks-neutral across sectors. This assumption is revealed by allowing for AicAjc and λicλjc.

With the estimates of parameters, the cross-country difference in labor productivity Δ ln Xitlit for each sector i at time t (in percentage terms) can be decomposed as follows:

Δ ln Xitlit=Δ ln Ai+Δλit+αkiΔ lnkitlit+Δ lnuit.(7)

Notice that Δ ln Ai(=ln Aimln Ain) and Δλi(=λimλin) together capture cross-country differences in technology. Δ ln kitlit(=ln kitmlitmln kitnlitn) represents cross-country differences in factor intensity, and Δ ln uit(=ln uitmln uitn) represents cross-country differences in unobservables.

Together with the first step of the decomposition in equation (5), the Ricardian measure (aside from the unobservables) is decomposed into the following two components:

RICARDOijtmn=HICKSijtmn+CAPijtmn,(8)

where

HICKSijtmn=(Δ lnAjΔ lnAi)+(ΔλjΔλi)  t(9)
CAPijtmn=(αkjΔ lnkjtljtαkiΔ lnkitlit)+(Δ lnwitΔ lnwjt).(10)

IV. Relationships Between the Two Measures: Theory

When there is an exogenous and observable change in technology in a world with capital mobility across countries, one can show that the Hicksian measure captures cross-country differences in relative productivity, whereas the Ricardian measure captures those in relative prices, which reflect differences in both relative productivity and relative factor intensity across countries.

Consider a 2 × 2 × 2 model with capital mobility and technology differences across countries. That is, there are two countries, home country m and foreign country n; two factors, labor and capital; and two goods, a labor-intensive good Xi (a numeraire good) and a capital-intensive good Xj.

Suppose that two countries are identical initially, so that neither has comparative advantage in either sector. We focus on a one-period change in the home country by assuming that the foreign country remains unchanged.6

Let aLi(=liXi) and aKi(=kiXi) denote the labor and capital requirements, respectively, for good i. When two goods are both produced, we know that competitive pricing requires

aLiw+aKir=1(11)aLjw+aKjr=p,

where w and r are wage rates and rental rates, respectively. Note that w and r no longer have sector subscripts as in the earlier section. p is the price of the capital-intensive good Xj relative to that of the labor-intensive good Xi.

Let θLi and θKi be the labor cost share and the capital cost share, respectively. For example, θLi = aLiw and θLj=aLjwp. By totally differentiating equation (11) and letting carets indicate a proportionate change in a variable, we obtain

θLiw^+θKir^=πi(12)θLjw^+θKjr^=πj+p^,

where πi=(θLia^Li+θKia^Ki) is the factor-weighted rate of technical progress in sector i.7

Provided that both goods are produced before and after, the evolution in factor returns can be obtained by solving equation (12) for w^ and r^, and therefore the percentage change in the wage-rental ratio w^r and that in the price of capital-intensive goods p^ take the form

w^r=πiπjp^θ(13)
p^=θLjπiθLiπjθLi,(14)

where θ = θLiθLj = θKjθKi > 0.8

In this simple framework, the Hicksian measure in equation (9), the capital-intensity component in equation (10), and therefore the Ricardian measure in equation (8) can be expressed as follows:9

HICKSij=πjπi,(15)
CAPij=πiπjp^,(16)
RICARDOij=HICKSij+CAPij=p^.(17)

Equation (15) shows that the Hicksian measure captures comparative advantage through cross-country differences in relative productivity. If an increase in the rate of technical progress is higher in the capital-intensive good sector (πj > πi) in country m (and country n remains unchanged), then the Hicksian measure will be positive, implying that country m has comparative advantage over country n in producing the capital-intensive good Xj.

Equation (16), which can also be expressed as CAPij=θθLiπi, shows that the sign of the capital-intensity component depends only on the rate of technical progress in the labor-intensive goods sector (the sector that uses the immobile factor more intensively).10 The intuition is as follows. When capital is mobile across countries, the cost of capital inputs is constant. Thus, even if the capital-intensive good sector becomes more productive, the relative price of factors (and therefore the factor intensity) remains unchanged. When the labor-intensive goods sector becomes more productive, however, labor inputs become relatively more expensive, and hence both sectors become more capital intensive.

Finally, equation (17) shows that the Ricardian measure captures comparative advantage through cross-country differences in relative prices, which reflect both cross-country differences in relative productivity and those in relative capital intensity. For example, when the relative price of the capital-intensive good falls (p^<0) in country m (and that in country n remains unchanged), the Ricardian measure is positive, implying that the home country has comparative advantage over the foreign country in producing the capital-intensive good.

Notice that the sign of the Ricardian measure (which is given by p^><0 or, alternatively, πjθLj><πiθLi) and that of the Hicksian measure (which is given by πj><πi) do not necessarily coincide. For example, when the sectoral bias in technical progress is toward the capital-intensive goods sector (πj > πi > 0), the Ricardian and the Hicksian measures both take a positive value because θLj < θLi. When the sectoral bias in technical progress is toward the labor-intensive goods sector (πi > πj > 0), however, it is not clear whether both measures take a negative value. The Hicksian measure would always be negative, but the Ricardian measure would be negative if and only if the relative price of the labor-intensive good is actually falling.11

V. Issues in the Empirical Analysis

A. Econometric Issues

The econometric estimation of the technological parameters of production functions is necessary to extract the Hicksian measure from the Ricardian measure as discussed in Section II. A problem arises in estimating the industry-level production function in equation (6) because of the possible correlation between the regressor ln kitclitc and the disturbance term ln uitc.12 Such correlation is likely for two reasons: measurement error especially in capital inputs kitc, and a possible simultaneity between unobservable productivity shocks uitc and the choice of factor inputs kitc and litc.

Two solutions will be implemented. One is to use an instrumental variable (IV) estimator. Specifically, the three-stage least squares (3SLS) estimator used in Boskin and Lau (1992), which introduces instrumental variables into a system of equations, is used.13 The other is to use the panel fully modified ordinary least squares (FMOLS) estimator (Pedroni, 2000). This estimator is the panel version of the Phillips and Hansen (1990) procedure.14 Although the parameter estimates obtained from these two estimators are somewhat different, the qualitative results of the paper do not change with the choice of estimators.

B. Difficulties in Testing the Law of Comparative Advantage

To compare the Ricardian and the Hicksian measures in terms of how well they can explain trade patterns, this paper attempts to test the law of comparative advantage using these two measures. There are two difficulties in doing so.

First, applying the law of comparative advantage in a higher dimension than the 2 × 2 × 2 world is difficult; see Drabicki and Takayama (1979) and Dixit and Norman (1980). We therefore refer to the general law of comparative advantage suggested by Deardorff (1980). This weaker version of the law is unable to predict the direction of movement of a particular good or factor or a particular country, but it is able to predict the direction of trade on average. Specifically, the null hypothesis to test is

H0:correlation (Pa,E)  0,(18)

where Pa is a column vector containing autarky prices (normalized to a unit simplex) for all countries and industries, and E is a column vector containing net exports for all countries and industries arranged in the same order as in Pa.

Second, a more serious limitation is in finding data in autarky.15 As a second-best solution, we test the following condition:

H0:correlation (Pc,E)  0,(19)

where Pc is a column vector containing the prices paid (if importing) or received (if exporting) by domestic traders (normalized to a unit simplex).16

A rejection of equation (19) implies a rejection of equation (18) since the latter holds if and only if condition (19) and the remaining feasibility, maximal, and preferred assumptions made in Deardorff (1980) are satisfied. Not rejecting condition (19), however, does not imply not rejecting condition (18) and hence the test results must be interpreted cautiously.

C. Data

Industry data at the two-digit ISIC level are taken from the International Sectoral Data Base. The 14 OECD member countries included are Australia, Belgium-Luxembourg, Canada, Denmark, France, Finland, (West) Germany, Italy, Japan, the Netherlands, Norway, Sweden, the United Kingdom, and the United States. The abbreviations and descriptions of the data are given in Table 1. This table also shows how trade data at the two-digit Standard International Trade Classification (SITC) taken from the OECD’s International Trade by Commodities Statistics are matched with the production data. The details of the data used for each variable in this study are given in Appendix I (see p.15).

Table 1.

Concordance Between Industry Data (ISDB) and Trade Data (ITCS)

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Source: Created by author.

Subcategories in these sectors are divided between ISIC categories 1 (AGR) and 31 (FOD).

To use the panel FMOLS estimator, both variables in equation (6), ln Xitclitc and ln kitclitc, must be nonstationary. Results of unit root tests on these variables are reported in Tables 2 and 3, respectively. The group mean unit root test of Im, Pesaran, and Shin (1997) is used, since it has an advantage over the pooled unit root test in that, under the alternative hypothesis, the autoregressive parameter is not required to be the same among different countries in the panel. The t-bar statistics reported in Tables 2 and 3 show that the null of a unit root cannot be rejected for lnXitclitc and lnkitclitc in all sectors, except for lnXitclitc in agriculture.

Table 2.

Heterogeneous Panel Unit Root Tests on the Left-Hand-Side Variable, ln(X/1) 1/

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Source: Author’s calculations.

Heterogeneous panel unit root tests of Im, Pesaran, and Shin (1997) are implemented for each industry indicated in the first column (see Table 1 for explanation of industry abbreviations). For example, in agriculture (AGR), there are 14 members in the panel. Each member’s augmented Dickey-Fuller (ADF) test statistic is reported in the first row. Here, heterogeneous trends are included. Also heterogeneous lag truncation (up to the maximum lag of 4) is allowed (see the second row for the number of lags). The null hypothesis is that the time-series has a unit root. The t-bar (group-t) statistic is reported in the last column (for example, the group-t statistic for agriculture is −2.64). An asterisk indicates that the null is rejected.

Table 3.

Heterogeneous Panel Unit Root Tests on the Right-Hand-Side Variable, ln(k/1) 1/

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Source: Author’s calculations.

Heterogeneous panel unit root tests of Im, Pesaran, and Shin (1997) are implemented for each industry indicated in the first column (see Table 1 for explanation of industry abbreviations). As in Table 2, heterogeneous trends are included and heterogeneous lag truncation (up to the maximum lag of 4) is allowed (see the second row for the number of lags). The t-bar (group-t) statistic is reported in the last column (for example, the group-t statistic for agriculture is 0.61). There is no asterisk next to the group-t statistics. This indicates that the null of unit root cannot be rejected in any of the industries at the two-digit ISIC level.

In addition to the nonstationarity of lnXitclitc and lnkitclitc, there must be a cointegrating relationship between the two in order to apply the panel FMOLS estimator. The cointegration between the two variables is therefore tested using the group mean cointegration tests (Pedroni, 1999), and the test results are reported in Table 4. As with the group mean unit root tests, the group mean cointegration tests have an advantage over pooled tests in that they allow the autoregressive parameter in the estimated residuals to be heterogeneous under the alternative. The group mean test statistics in Table 4 show that the null of no cointegration is rejected by at least one test statistic in all industries, except for textiles and machinery and equipment.17 The cointegration relationship between the left-hand side and the right-hand side of equation (6) confirms that we can use the FMOLS estimator to take care of the endogeneity problem.18

Table 4.

Heterogeneous Panel Cointegration Tests Between ln(X/1) and ln(k/1) 1/

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Source: Author’s calculations.

Heterogeneous panel cointegration tests of Pedroni (1999) are implemented for each industry indicated in the first row (see Table 1 for explanation of industry abbreviations). The null hypothesis is that there is no cointegration between the left-hand-side variable ln(X/l) and the right-hand-side variable ln(k/l). An asterisk next to the various test statistics indicates that the null is rejected. Except for the textile and machinery and equipment industries, at least one test statistic rejects the null of no cointegration.

The instrumental variables, provided by Boskin and Lau (1992), are the relative price of cotton to wheat, the relative price of oil to wheat, the relative price of iron to wheat, world population, male population, female population, arable land, permanent crops, male life expectancy, and female life expectancy.

Finally, our sample size (14 countries, 10 industries, and 23 years) implies that the Ricardian measure RICARDOijtmn is computed for (142) combinations of countries for each of (102) combinations of industries for 23 years. That is, there are 94, 185 = 91 × 45 × 23 observation points. Each of them is decomposed into three components: the Hicksian measure HICKSijtmn, the capital-intensity component CAPijtmn, and the residuals. Moreover, to avoid choosing an arbitrary sector as a numeraire, for each sector i we compute RICARDOitmn by taking an average over all ji, that is, RICARDOitmn=1141jiRICARDOijtmn (which reduces the observation points to 20, 930 = 91 × 10 × 23). HICKSitmn and CAPitmn are computed in the same manner.

VI. Empirical Findings

A. Estimates of Structural Parameters

The panel FMOLS estimates of the structual parameters are presented in Table 5. There are a few points to note on these estimates. First, the mean of the rate of technical progress λi is 0.006, which is relatively low for the industrialized countries during this period.

Table 5.

Structural Parameters Estimated with the Panel FMOLS Estimator

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Source: Author’s calculations using the panel FMOLS estimator (Pedroni, 2000).

See Table 1 for explanation of industry abbreviations.

No inferences are done on the estimate of these parameters.

A group-mean estimate for the parameter αk is obtained by averaging the estimates for individual countries. An asterisk indicates that the estimate is significant at the 5 percent level.

Second, the average of the group mean FMOLS estimates for αki across 10 sectors is 0.50, which seems to represent a reasonable capital cost share. Individual estimates for αki however are hard to interpret. For example, in the mining and basic metals products industries, estimates for αki exceed 1, and that in the nonmetallic mineral products industry takes a negative value.

Third, the assumption that αki is common to all the countries in the sample is tested for the panel FMOLS estimates. The null hypothesis cannot be rejected for all sectors except the agriculture and nonmetallic mineral products industries.

The parameter estimates using the 3SLS estimator (Boskin and Lau, 1992) are presented in Table 6. The estimates for the rate of technical progress (the average of λic for each industry i) are on average 4.0 percent. These estimates are much more reasonable than in the case of the FMOLS estimates. Some of the individual estimates, however, are again hard to interpret.

Table 6.

Structural Parameters Estimated with the 3SLS Estimator

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Source: Author’s calculations using the 3SLS estimator (Boskin and Lau, 1992).

See Table 1 for explanation of industry abbreviations.

The asterisk indicates that estimates are significant at the 5 percent level.

Heterogeneous intercept term is estimated as a residual for the initial period.

B. Case Study: Japan Versus the United States

To provide an example of the actual values computed for the Ricardian and the Hicksian measures, Table 7 presents these measures for the Japanese industries relative to the corresponding U.S. industries for 1970 and 1990. In other words, RICARDOitmn in this particular case study is computed for m = Japan, n = the United States, i = industries listed in the first column of the table, and t = 1970 or 1990.

Table 7.

Measures of Technology Differences Between Japan and the United States, 1970 and 1990 1/

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Source: Author’s calculations.

The Ricardian measure (RICARDO) is decomposed to two subcomponents, the Hicksian measure (HICKS) and the capital-intensity component.

See Table 1 for explanation of industry abbreviation.

A positive value indicates a higher unit labor cost in Japan than in the United States in the indicated industry and period.

A positive value indicates a higher unit labor cost in Japan than in the United States had capital intensity been the same in the two countries in the indicated industry and period.

Includes the residuals (unobservables) so that the sum of two subcomponents equals the Ricardian measure in each industry.

A positive value indicates a higher unit labor cost in Japan than in the United States had technology been the same in the two countries in the indicated industry and period.

The Ricardian measure The Japanese textile and basic metals industries (such as steel) became competitive and began to enjoy comparative advantage over the United States in the 1960s. This phenomenon can be observed in the negative signs on the Ricardian measure in 1970: the Ricardian measure for the textile industry is −0.241, and that for the basic metals industry is −0.113. The magnitude is expressed in natural logarithms, so that these values imply that the corresponding relative unit labor costs in Japan were 78 and 89 percent of those in the United States, respectively. Machine tools, autos, videos, semiconductors, and other products belonging to the machinery and equipment industry still had comparative disadvantage in the early 1970s. The Ricardian measure in the machinery industry in 1970, 0.517, indicates that the relative unit labor cost in Japan was approximately 1.677 times as high as that in the United States.

During the 1970s and 1980s, some Japanese industries such as the food products and the textile industries lost comparative advantage. The Ricardian measures for these industries in 1990 are 0.171 and 0.241, respectively. These values imply that the relative unit labor cost in the food products and the textile industries in Japan were approximately 1.186 and 1.273 times as high as those in the United States, respectively. On the other hand, the machinery and equipment industry began to enjoy comparative advantage by the beginning of the 1990s. The negative value, −0.070, indicates that the relative unit labor cost in Japan was 93.2 percent of that in the United States in this industry.

Two Subcomponents of the Ricardian measure Japan’s comparative advantage in the textile industry in 1970 is not revealed in the Hicksian measure, indicating that the United States had comparative advantage over Japan as far as technology was concerned. Japan’s comparative advantage in this industry in 1970 is, however, revealed in the capital-intensity component: the value of −0.523 for this component reveals that had technology been the same in the two countries, the relative unit labor cost in Japan would have been 59.3 percent of that in the United States because of the heavy use of capital inputs. The relatively higher allocation of capital in this industry is consistent with the industrial policies implemented during this period (Komiya, Okuno, and Suzumura, 1988).

In the case of the machinery and equipment industry in 1970, Japan’s comparative disadvantage is also revealed in the Hicksian measure: the value of 0.992 implies that the relative unit labor cost in Japan was more than twice that in the United States, had capital intensity been the same in the two countries. What is revealed in the Ricardian and the Hicksian measures, however, is not revealed in the capital-intensity component. The relative capital intensity indicated by the capital-intensity component value of −0.475 reveals that had technology been the same in the two countries, the relative unit labor cost in Japan would have been 62.2 percent of that in the United States. This is again consistent with the industrial policies implemented during this period.

C. Relationships Between the Two Measures: Empirical Evidence

Here we examine the general tendency in the relationships between the Ricardian measure and the Hicksian measure. Specifically, we classify each observation into one of three cases. Case 1 is the case where the signs of RICARDO, HICKS, and CAP are the same (for example, when πj > πi > 0, the signs of all three are positive). Case 2 is the case where the signs of RICARDO and HICKS are the same, but not the sign of CAP (for example, when πj > 0 > πi, the two technology measures are positive, but because of the negative productivity in the labor-intensive good sector, the capital-intensity component is negative). Case 3 is the case where the two measures of technology differences are of opposite sign (for example, when πi > πj > 0, but πiθLi<πjθLj, or p^<0, the Hicksian measure is negative but the Ricardian measure is positive).19

Table 8 shows that approximately two-thirds of observations for the whole sample period belong to either case 1 or 2. That is, in two-thirds of the cases, comparative advantage revealed by the Ricardian measure and that by the Hicksian measure are not the same. With the panel FMOLS estimates the corresponding share is 61 percent, and with the 3SLS estimates it is 56 percent. Moreover, these shares tend to fall toward the period when capital becomes more mobile; with the panel FMOLS estimates, it falls from 65 percent in 1970 to 58 percent in 1990, and with the 3SLS estimates, it falls from 74 percent in 1970 to 52 percent in 1990.

Table 8.

Empirical Relationships Between the Two Technology Measures 1/

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Source: Author’s calculations.

Cases 1, 2, and 3 are classified as follows: Case 1, the signs of RICARDO, HICKS, and CAP are the same; Case 2, the signs of RICARDO and HICKS are the same, but not the sign of CAP; Case 3, the signs of RICARDO and CAP are the same, but not the sign of HICKS.

D. Correlations Between the Two Measures and Net Exports

The fact that comparative advantage revealed by the two measures of technology differences coincide at most two-thirds of the time raises the question of which of the two is more closely related to trade patterns.

Table 9 presents the correlation coefficients between the technology measures and net exports. The first column presents the correlation coefficients between RICARDO and net exports. The second and third columns present those between HICKS and net exports (the difference between the two is the estimator used to obtain the parameters of the production functions). The sample period becomes 1970-90 instead of 1970-92 because the OECD trade data we use end in 1990.

Table 9.

Pearson Correlation Coefficient 1/

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Source: Author’s calculations.

An asterisk indicates statistical significance at the 5 percent level.

The sample period is 1970–90 instead of 1970–92 because the trade data used in this study end in 1990.

Table 10.

A Complete Set of Possible Outcomes

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Source: Author’s analysis.

The correlation coefficients in the first row in Table 9 are computed using the whole sample (that is, 91 bilateral country combinations, 23 years, and 10 industries). An asterisk next to a correlation coefficient indicates that it is statistically significant at the 5 percent level.

The correlation coefficient between the Hicksian measure and net exports is positive and statistically significant at the 5 percent level. We therefore reject the general law of comparative advantage, since the rejection of condition (19) implies the rejection of condition (18). The correlation coefficient between the Ricardian measure and net exports, however, is negative with statistical significance at the 5 percent level and therefore we cannot reject condition (19). The rejection of the general law of comparative advantage therefore becomes questionable. What we find in the whole sample period (1970-90) is also found in 1990 but not in 1970 (see the second and third rows of Table 9).

Empirical evidence found in this paper implies that the weak relationship between comparative advantage revealed by TFP differences (the Hicksian measure) and trade patterns may not necessarily mean that the supply side of the economy cannot explain trade patterns. It may instead mean that comparative advantage should be captured by labor productivity differences (the Ricardian measure), especially in the period with high capital mobility across countries.

VII. Conclusion

We first showed that, in the simple 2 × 2 × 2 model with capital mobility and technology differences across countries, the Ricardian measure exactly captures the change in the relative price of capital-intensive goods. Moreover, we showed that in theory the Hicksian measure does not have to coincide with the Ricardian measure. Empirically, we found that the two measures coincide only in half of the cases in the period when capital has become highly mobile across countries. The distinction between Hicksian and Ricardian is important to the extent that the general law of comparative advantage is rejected with the Hicksian measure, but not necessarily with the Ricardian measure.