Global Factor Trade in Ohlin’s Time* Antoni Estevadeordal, Inter-American Development Bank† Alan M. Taylor, University of California at Davis and NBER†† July 2000 Abstract An empirical tradition in international trade seeks to establish whether the predictions of factor abundance theory match present-day data. In the analysis of goods trade and factor endowments, mildly encouraging results have been found by Leamer et al. But ever since the appearance of Leontief’s paradox, the measured factor content of trade has always been found to be far smaller than its predicted magnitude in the pure Heckscher-Ohlin-Vanek framework, the so-called “missing trade” mystery. Seeking a better fit with the data, recent work has contemplated considerable tinkering with the pure Heckscher-Ohlin theory. We wonder if this problem was there from the beginning. That is, we ask if the theory was so much at odds with reality at its time of conception. This seems like a fairer test of its creators’ original enterprise. We apply contemporary tests to historical data on goods and factor trade from Ohlin’s time, focusing on the major trading zone that inspired the factor abundance theory, the Old and New Worlds of the pre-1914 “Greater Atlantic” economy. Our analysis is set in a very different context than contemporary studies—an era with lower trade barriers, higher transport costs, a more skewed global distribution of the relevant factors (especially land), and comparably large productivity divergence. Thus, our work complements tests applied to today’s data and informs our search for improved models of trade. * Paper presented at the conference “Bertil Ohlin. A Centennial Celebration 1899–1999,” to be held October 14–16, 1999, at the Stockholm School of Economics. For superb research assistance we thank Brian Frantz. † Antoni Estevadeordal is a Research Economist at the Inter-American Development Bank. Address: Inter- American Development Bank, 1300 New York Avenue NW, Washington DC 20577. Telephone: 202-623-2614. Fax: 202-623-3030. Email: . †† Alan M. Taylor is an Associate Professor of Economics at the University of California at Davis and a Faculty Research Fellow at the National Bureau of Economic Research. Address: Department of Economics, University of California, One Shields Avenue, Davis, CA 95616-8578. Telephone: 530-752-1572. Fax: 530-752-9382. Email: . WWW: . 1. Factor Abundance Theory in Historical Context Some years ago, scholars in the field of international trade, and perhaps especially the empiricists, might have viewed an invitation to the Ohlin centennial with a sense of unease. Most of us saw factor abundance trade theory as possibly unparalleled in the realm of economic science in its elegance of form and powerful statements on the sources of comparative advantage. At the same time the theory was viewed as having been confounded by empirical contradictions in a series of studies dating back to the paradox unearthed by Leontief.1 Given such an environment, what kind of conference paper could one offer that would not mar the spirit of celebration? Happily, at least for the legacy of Ohlin, perspectives do change. In recent years, new approaches and extensions to this landmark theory and its empirical testing have attested to its durability and relevance for explaining modern-day trade patterns.2 In one tradition of empirical research, following Leamer (1984), scholars have constructed large datasets on national endowments and trade patterns so as to measure the link between factors and trade. This is predicted by the theory to be a linear relationship depending on technical coefficients, suggesting that, say, an increase in capital endowment should spill over into trade as an increase in the net export of capital-intensive goods. In another strand of work, following the notation and methodology of Vanek (1968), scholars have focused on the implicit factor trade alone and its relationship to factor abundance (Leamer 1980; Bowen, Leamer, and Sveikauskas 1987). This approach seeks to establish a pass thorough—in principle, a unit coefficient—relating increments in relative factor endowment directly to net exports of the same factor, as production shifts relative to a stable consumption pattern. Most of the very recent empirical contributions (for example, Trefler 1993, 1995; Davis and Weinstein 1999) have used the Vanek representation. These recent works point to a compromise position where the Heckscher-Ohlin theory, augmented in various ways, might better account for the contemporary pattern of factor trade. To deal with the Leontief paradox one can allow for differences in cross- country productivties, as suggested by Leontief, and implemented empirically by Trefler (1993; 1995). Still, this modification alone doesn’t get us very far towards narrowing the huge gap between measured and predicted factor trade. Trefler (1995) coined the term “missing trade” to depict the extent to which measured trade is still negligible compared to the prediction of the pure theory.3 To get an even closer fit, other modifications have been suggested by Trefler (1995) and Davis and Weinstein (1999) such as home bias in 1 Leontief (1953a) shocked everyone when he computed a U.S. input-output table for 1947 and discovered that the seemingly capital-abundant and labor-scarce United States was actually engaging in net labor export via trade, with a capital-labor ratio in imports 60% higher than exports. 2 We need not review the whole literature here, but direct the reader to the excellent survey by Helpman (1998) on which we have drawn extensively in what follows. 3 The same point has been forcefully repeated by Gabaix (1997) 1 consumption, an allowance for non-traded goods, and models without factor price equalization. However, before basking in fresh optimism over how the factor abundance theory has been thoroughly rehabilitated by these various devices, we should note that lurking here is a danger. After so much ornamentation has been added to the model, the skeptics might reasonably ask what is left of Heckscher and Ohlin’s original design. One wonders what Ohlin would make of all these developments and modifications to his theory given his original standpoint. Here was an economist working in the early twentieth century who was inspired to explain the international trade patterns previously witnessed in a largely free-trade regime—the trade of mostly commodity goods and manufactures in the Greater Atlantic economy during the first era of globalization before World War One.4 And when Heckscher and Ohlin made their seminal contributions most observers still hoped that this regime would soon be restored for the long run in the 1920s, though that was not be. Heckscher and Ohlin would not necessarily condone the use of their theory in today’s very different global economic environment. Today we see numerous barriers to trade (especially in agricultural commodities and simple manufactures), trade in differentiated products and services, and significant intra-industry trade.5 However, the duo still might be impressed by the substantial technical apparatus we have developed to evaluate their theory, even as they might regret that they never had easy access to the kinds of large datasets we now take for granted as we implement our sophisticated tests. Given all this, we can imagine one possible reaction from the fathers of factor abundance trade theory. Might they not call on us to take our considerably refined empirical skills back in time and at least give the theory—and its authors—some kind of a break by testing the model in the historical context for which it was first designed? Imagining that we heard such a call at the time of Ohlin’s centennial, and having a taste for economic history, we thought it would only be fair to him to do just that. Not only does this idea appeal for sentimental reasons, but also, we will argue, it helps resolve questions stimulated by the research on contemporary global factor trade. Testing the model in an earlier historical epoch might help us see the sources of difficulty in applying the model in the present. By bringing to the discussion new datasets from a different economic and political era, we can gain a new perspective. And in some ways, the pre- 1914 period offers a better testing ground for the pure Heckscher-Ohlin trade model, as economic historians love to remind us. Indeed, a strand of the economic history literature has already found strong support in that era for several features of standard theory, including predictions of factor price convergence and the pattern of goods trade.6 4 For a study of the era, encompassing trade and factor flows, see O’Rourke and Williamson (1999). 5 Still, in theories of differentiated products and intra-industry trade, the concepts of Heckscher-Ohlin trade theory endure in basic textbook formulations (Dixit and Norman 1980; Helpman and Krugman 1985). 6 On factor price equalization see O’Rourke, Taylor, and Williamson (1996) and O’Rourke and Williamson (1994). On goods trade and factor endowments see Estevadeordal (1993). We review the latter in the next Section 2. 2 What are the features of the pre-1914 era that make it a better laboratory for testing pure trade theory compared to today? And are there other aspects that favor the present? We know, first, that there were much lower trade barriers then than now, and this could be why the theory fails in the present. Even though trade reforms and tariff reductions have progressed in postwar decades, tariff levels are still high by nineteenth century standards and quotas now apply to many goods.7 Thus, the past epoch might more closely match the free-trade assumptions of the theory. Second, in the last century, certain endowments were very skewed in their distribution, most famously the agricultural land that differentiated the endowments of the New World from the Old. Today, in contrast, many of the countries in the samples studied have very similar endowment patterns, and this leaves little data variation from which to get a strong of fit.8 In the context of standard econometric tests of predicted- versus-measured factor content of trade such variation would strengthen the test enormously by offering a wide range in the independent variable. This could be another weak point in tests using modern data. Third, we note that there were considerable divergences in productivity across countries circa 1913, just as there are today. Over the course of the twentieth century we have seen dramatic productivity convergence within a narrow club of countries—mostly the OECD and, thus, much of the Greater Atlantic economy. Yet it is equally true that outside this subset productivity convergence of the unconditional variety has been weak or nonexistent.9 Thus, by doing our tests circa 1913, we are in no way making the problem simpler for ourselves by avoiding an essential ingredient in the “missing trade” puzzle: the possibility of international productivity differences. Raw differences in factor productivity were postulated by Leontief (1953a) as a possible solution to his paradox for the United States, and his idea was supported in international samples by Trefler (1993; 1995) and Davis and Weinstein (1999). However, as Helpman (1998) notes, this way out just creates another disturbing puzzle: namely, where do these differences in productivity originate? In historical work, this same disturbing idea was brought to the fore by the controversial work of Clark (1985). He found no comfort in any economic explanation of international variations in the 7 On trade barriers then and now see, for example, World Bank (1991). Tariff levels were in the single- or low-double-digit range before 1914, and much larger in the postwar period, especially in developing countries. Quotas were virtually nil before 1914, and considerable in the late postwar period. 8 For example, Davis and Weinstein (1999) find inevitably that OECD countries are clustered together with similar capital-labor ratios, a feature arising from those countries’ similar levels of development and industrial structures. Their Rest-of-the-World data point lies far away from the OECD group, but this gives a great deal of leverage to one point, so much so that it is thought prudent to exclude it from the tests as a sensitivity check. And in terms of data quality, the Rest-of-the-World point uses less consistent data, and the required measures have to be constructed by a more fragile procedure. 9 The first studies of long-run convergence (Abramovitz 1986; Baumol 1986) used the 16-country data of Maddison (1982). Baumol was the first to note the postwar failure of unconditional convergence in wider samples that included less-developed countries. The origin of this failure was first identified by Dowrick and Nguyen (1989); they found conditional convergence controlling for investment and population growth, narrowing the problem to a determination of these factor accumulation processes. 3 productivity of cotton mills in various countries circa 1913. There seemed to be no compelling economic reason why one New England cotton textile operative performed as much work as 1.5 British, 2.3 German and nearly 6 Greek, Japanese, Indian or Chinese workers. After controlling for capital intensities, breakdowns, human capital, learning, and other effects, Clark was forced to admit the possibility of a purely cultural origin of the differences, quite possibly exogenous to the economic system. If Clark’s idea holds in a wide range of sectors circa 1913, then, just as output would have been affected by these raw productivity differences, so too would the levels of trade and the factor content therein, with direct implications for our proposed tests. Finally, we should note a couple of characteristic that work against the earlier period as a good testing ground. First, we must consider the higher transport costs of the past. Like measuring true tariffs from actual import data, measuring true transport costs from trade data is problematic. Comparing CIF and FOB prices then and now might not lead to a big difference in the measured transport cost premium on goods actually shipped: goods too expensive to ship never make it into the sample, creating a serious selection problem.10 Data is scarce here, but it is a reasonable conjecture that many bulk goods shipped today move at a fraction of their cost a hundred years ago, and surely many exotic goods and services can now move more cheaply than they did in the past. The second problem for the earlier period—though it is by no means absent in the present—concerns factor mobility. It is well known that the theory predicts that trade and factor mobility are substitutes, and the late nineteenth century was a time of very fluid international factor markets. International labor mobility facilitated the migration of millions of people, especially in the great transatlantic waves from Europe to the New World (Easterlin 1961; Hatton and Williamson 1994, 1998; Taylor and Williamson 1997). The first era of global capital markets functioned very efficiently, reallocating vast sums of capital internationally (Obstfeld and Taylor 1998, 1999; Taylor 1996). The presence of endogenous factor movements could well interfere with empirical tests that treat factor endowments as exogenous independent variables. We will return to this issue in our conclusion. All of these comparisons of past and present reaffirm the need to fall back on theory to judge the issue. For example, it might be tempting to look at trade volumes and argue that the late nineteenth century was as much of an integrated trading economy as today’s, since, in many countries, trade-to-GDP ratios are no higher now than in the past. This misses the point. The factor abundance theory, for example, might counter this argument by pointing out that although the late nineteenth century trade (in goods or factors) was large, it was not large enough given the skewed distribution of world factor 10 This caveat must be kept in mind, even though plenty of evidence attests to the fact that on a wide range of goods shipped before 1914 transport costs in the Atlantic were collapsing over a span of several decades, both on primary products and manufactures. O’Rourke and Willamson (1994). See also North (1958) and Harley (1988). 4 endowments. Our proper interest here is not in the size of trade per se, but how large that trade is relative to what theory would predict, whether for goods of factors.11 But without tractable empirical tests and the right historical data we cannot attack this issue. The rest of this paper is organized around the steps we took to mount such an attack. We focus on the two different types of tests used, those based on goods trade and factor trade, respectively. We describe the historical data and its manipulation for the test at hand. Results are presented in the usual form for each test and the implications are discussed. A brief conclusion muses over some broader interpretations and suggests directions for future research 2. Factor Endowments and Product Trade circa 1913 Tests Consider the standard Heckscher-Ohlin theory, in a world of C countries, I industries, and F factors. Let the output in country c be Xc (I × 1). The factor content of Xc is BXc, where B is a matrix (F × I) of factor content coefficients.12 Full employment implies that BXc = Vc, where Vc is the factor endowment of country c. Consumption Cc (I × 1) in country c equals the country share of world expenditure (assumed equal to world output in this study) sc times world consumption CW. The latter, by world market clearing, equals world output, CW = XW = ΣcXc. Hence, Cc = sc XW, and the net goods trade Tc of country c equals Tc = Xc – Cc = Xc – sc XW. If we denote world factor endowment by VW = BXW, then Tc = B–1 (Vc – scVW). (1) This equation says that trade in each industry is linearly related to factor endowments. We assume that B is invertible (that is , square, with I = F). Leamer (1984) argued that the equation need not be restricted to the square case and he proposed it be tested by regressions for each industry i. Evaluation centers on the fit and reasonableness of these equations, allowing for both statistical and quantitative significance.13 This methodology was used to study trade circa 1913 by Estevadeordal (1993). The challenge was to construct new datasets on net trades (the left-hand side) and endowments (the right-hand side) for the econometric study. A detailed explanation of 11 Of course, switching from quantities to prices makes life no easier for the measurer of market- integration. Autarky prices can coincidentally equalize in two physically isolated economies, but prices can be far apart in two partially-integrated economies due to transaction costs barriers. 12 In detail, Bfi is the direct and indirect use of factor f per unit output of industry i. Direct use refers to factors used as inputs in the given industry; indirect use refers to the factors embodied in the intermediate products used as inputs in the given industry. 13 A potential weakness here is that we do not measure the matrix B–1, but rather estimate it. The specification is loose, and the estimated matrix has totally free parameters that may be unrelated to the true technological coefficients. This weakness is avoided in the factor-content approach we use in Section 3. 5 the data, coding, and aggregation is found in the appendix to Estevadeordal (1997). We provide a brief overview here. Data, Coding, and Aggregation Data on net trade for the period circa 1913 was collected for C = 18 countries: Argentina, Australia, Austria-Hungary, Belgium, Canada, Denmark, Finland, France, Germany, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom, and United States. The sources used were official national reports of trade statistics, originating from such agencies as the Board of Trade (U.K.) or the Department of Commerce (U.S). The principal problem in ensuring consistency across countries was to set up a universal classification scheme for industries, since, prior to World War Two, no standards had been developed and each country used its own classification. The solution was to laboriously construct country-specific concordances that would map each country’s sectors into selected sectors of the Standard International Trade Classification (SITC, Revised 1961) at the two-digit level. In this way the trade data Tc was rationalized into a database for C = 18 countries and I = 55 sectors expressed in U.S. dollars at market exchange rates. 14 National product estimates were taken from Mitchell (1980, 1983) and Maddison (1995) and expressed in U.S. dollars at market exchange rates, providing the basis for expenditure shares sc.15 Endowment data Vc for all countries were collected for F = 5 types of factor: capital stock, skilled and unskilled labor force, agricultural land, and mineral resources. In Estevadeordal (1993) a proxy for capital stock based on energy consumption of solid fuels was used. The data on energy consumption refers to apparent consumption of primary sources, including net imports of secondary as well as primary energy forms. Because of data availability only solid fuels had been considered (hard coal, brown coal, lignite and coke). In order to permit aggregation and comparison, data were expressed in thousands of hard-coal equivalents. However, in order to carry out the subsequent factor content analysis in Section 3 we made new capital stock estimates for 1913 using a perpetual-inventory method applied to pre-1913 annual investment rates and real outputs, as described in the appendix. The results gave capital-output ratios for the terminal year 1913, and multiplying by national products yielded capital stocks in U.S. dollars at market exchange rates. In this section of the paper we report results based on Estevadeordal (1993) which uses the original capital measure. The labor force figures originate in Maddison (1982) and Mitchell (1980, 1983), using interpolation between 14 For all the data described in this section, figures were collected for the year closest to 1913. Exchange rates were taken from international compendia of exchange rates, where available, or from national sources. 15 We do not calculate consumption or expenditure shares directly, but rather assume they are equal to income or output shares. That is we set sc = GDPc/GDPw, and not, following the trade-balance correction of Trefler (1995) as sc = Cc/Cw. This correction makes no material difference to our results. 6 census years as necessary. Agricultural land is measured in hectares and the data is largely from a study by the League of Nations (1927). Mineral resources are estimated using as a proxy the U.S. dollar value of the annual production of petroleum plus twelve other minerals and ores; quantities are drawn principally from Mitchell (1980, 1983) and prices from Potter and Christy (1962).16 Results The Heckscher-Ohlin equation (1) expresses trade in terms of excess endowments (Vc – sc VW). For empirical purposes, following Leamer (1984), we can regress trade on endowment supplies alone.17 We report results at two different levels of aggregation (six and forty-six commodity groups). Table 1, Panel (a), reports the estimates for the following six commodity groups: agricultural products, raw materials, capital-intensive goods, labor-intensive goods, machinery and chemicals. The R2 measures of fit are typically very high and most of the estimated coefficients are correctly signed and statistically significant. The coefficients still depend on the units of the explanatory variables. Since we are not only interested in the statistical significance of a coefficient but also in knowing how important each of the variables is in explaining the trade pattern, Panel (b) reports β values for each of the five explanatory variables for each trade aggregate considered.18 If we select arbitrarily, as in Leamer (1984), 1.0 to define a significant β value, then capital is significant five times, land four times, and labor-skilled and minerals three times. 16 The twelve ores are bauxite; copper; iron; lead; manganese; nickel; phosphate; potash; pyrites; sulphur; tin; and zinc. Some data was also drawn from Rothwell (various issues) and national sources of mineral production for various countries. 17 The Heckscher-Ohlin model of trade can express trade in terms of endowment supplies or in terms of excess endowment supplies. In a 2 × 2 version the equations of the model are T1 = β1L (L – Y Lw/Yw) + β1K (K – Y Kw/Yw); T2 = β2L (L – Y Lw/Yw) + β2K (K – Y Kw/Yw); Y = wLL + wKK; where T1 and T2 are net exports of the two commodities, Y is GNP, L is labor, K is capital, wL and wK are factor returns, the w subscripts refers to the world, and the β are Rybczynski coefficients. This form of the model expresses net trade as a linear function of excess supplies of factors. However, excess factor endowments are a linear function of all factor supplies: that is, L – Y Lw/Yw = L – (wLL + wKK) Lw/Yw. Thus, for almost all distributions of K and L these excess supplies are correlated, and a regression of trade on a subset of the excess supplies will yield biased and inconsistent estimates. This problem will be compounded if there are measurement errors. Because of this problem a reduced form of the model is preferred in empirical studies. This reduced form is found inserting the GNP equation into the net exports equations: T1 = β1LL + β1KK; T2 = β2LL + β2KK; Y = wLL + wKK. 18 A β value is equal to the estimated coefficient times the ratio of the standard deviation of the explanatory variable divided by the standard error of the dependent variable (Maddala 1977; Leamer 1978). These β values are directly proportional to the contribution that each variable makes to a prediction of net trade. These values indicate the amount of change in standard deviation units of the net trade variable induced by a change of one standard deviation in the factor endowment. A β value of 0.1 is small, since a change of one standard deviation in the resource would have a hardly perceptible effect on net exports, but a value of one can be regarded as large. 7 Table 1 Tests of Factor Endowments and Product Trade Labor- Labor- Agricultural Adjusted (a) OLS estimates Capital skilled unskilled land Minerals R2 R2 Agricultural products -7.6*** -26.3 -31.9 8.5** 4.5*** .81 .73 (-5.22) (-1.74) (-0.55) (2.38) (4.50) Raw materials 2.7*** -20.6*** 41.6* -3.0*** 0.4 .78 .69 (5.22) (-4.61) (2.14) (-4.91) (1.67) Capital-intensive goods 2.1*** 18.4*** 13.3 -6.5*** -0.7* .83 .77 (5.98) (4.21) (0.66) (-4.98) (-2.08) Labor- intensive goods -0.9*** 17.8*** -9.8 -4.0*** 0.8** .65 .51 (3.20) (8.89) (-1.24) (-3.79) (2.59) Machinery 1.1*** 5.0* -9.6 -3.1*** 0.08 .91 .88 (4.73) (2.12) (-1.05) (-5.87) (0.54) Chemicals -0.1 6.7*** -6.3 -2.3*** 0.38 .69 .56 (-1.08) (5.87) (-1.62) (-2.53) (1.72) Labor- Labor- Agricultural (b) β values Capital skilled unskilled land Minerals Agricultural Products -1.83 -0.51 -0.11 0.72 1.64 Raw Materials 2.36 -1.45 0.50 -0.92 0.53 Capital Intensive-Goods 1.30 0.92 0.11 -1.42 -0.65 Labor Intensive-Goods -1.10 1.76 -0.17 -1.73 1.48 Machinery 1.22 0.45 -0.15 -1.22 0.13 Chemicals -0.24 1.29 -0.21 -1.93 1.37 Notes: t-ratios in parentheses, (***) denotes significant at the 1% level. (**) denotes significant at the 5% level. (*) denotes significant at the 10% level. Commodity groups based on SITC Rev.1, 2 digit codes (see Appendix Table A3): Agricultural products (Groups 0, 1, 2 except 27 and 28, 4); raw materials (Groups 27, 28, 3 and 68); Capital-intensive goods (Groups 61, 62, 63, 64, 651-655, 67 and 69); labor-intensive Generally speaking, using the estimates from Table 1, comparative advantage in agricultural products is associated with abundance of land and mineral resources and is negatively related to capital. Trade in raw materials owes comparative advantage to the availability of capital and unskilled labor; land and skilled labor contribute to comparative disadvantage. The sources of comparative advantage in manufacturing are, in general, as expected: capital is a source of comparative advantage for capital-intensive goods and machinery. Mineral resources are important for labor-intensive and chemicals groups. Skilled labor also contributes to comparative advantage in all manufacturing groups. The β values indicate, again, that the contribution is most important in labor- intensive and chemicals products, followed by capital-intensive goods and machinery. Net exports of all manufacturing groups are negatively associated with the supply of land.19 We also performed some sensitivity analysis on these results.20 19 Results such that agricultural land have a negative impact on the comparative advantage of all manufacturing groups should not be surprising. Although the model used here appears to require that all factors be used in all industries, this is not the case. The existence of industry-specific factors implies that particular elements of the factor requirements matrix B may be zero. For example in a model with two inputs, labor (L) and land (M), and two goods, agricultural (X1) and industrial (X2), if land is not used to produce the industrial commodity, the BM2 element of matrix B will be zero. It can be easily shown that even though both labor and land are used to produce the agricultural good, the output of agricultural goods depends only upon the endowment of land. And although land is not used to produce industrial goods, the level of output of industrial goods depends on both the endowment of labor and the endowment of land. This apparently paradoxical result stems from the fact that full employment requires that land must be fully 8 Table 2, Panel (a), reports results from Estevadeordal (1997) where a more disaggregated Heckscher-Ohlin model was estimated with the goal of obtaining measures of trade protection by sector. Based on the reported F-statistics, thirty-seven out of the forty-six net trade regressions are significant. Moreover, most of the R2 measures of fit are very high. For individual factor endowments, out of forty-six estimated equations, capital has significant coefficients (at the 10% confidence level) in twenty-six cases, skilled labor in fourteen, unskilled labor in only seven, land in twenty-nine, and mineral resources in twenty-seven. The β values are reproduced in Panel (b). In general, capital and skilled labor are sources of comparative disadvantage for primary product trade. Capital is a source of comparative advantage in most capital- intensive goods; it is a source of disadvantage in labor-intensive commodities, where skilled labor contributes to comparative advantage. Agricultural land is consistently a source of advantage for primary products and creates comparative disadvantage in manufacturing. Interestingly, mineral resources are a source of comparative advantage in the processed agricultural products group and in almost all manufactures. Using the conventional 0.5 level to define a significant β value, capital is significant in thirty-six out of forty-six net trade equations. 21 Skilled labor is significant twenty-four times, unskilled labor only four times, agricultural land thirty-eight times, and mineral resources thirty-six times. Summary In this section we have shown how it is possible to implement a test circa 1913 of the Heckscher-Ohlin prediction that there exists a linear relationship between factor endowments and the net trade of goods. The results are very favorable to the hypothesis. For most goods the fit is acceptably good and many coefficients have statistical significance. Moreover, once we compare the signs of the coefficients for each type of good with what we expect—based on whether certain goods are intensive in certain types of factor—we also find a reassuring correspondence between the econometric results and our intuition. Finally, using the technique of β coefficients to see how much the variation in factor endowments explains the variation in net trade, we find that the quantitative significance of the model is also very high. In short, having appealed to the 1980s vintage of empirical trade tests of the form pioneered by Leamer (1984), we have found a good utilized in the agricultural sector. This fact, together with the fixed input requirement BM1, determines the level of agricultural output M /BM1. Since the labor residual left over for industrial production is then dependent upon the endowment of land (that is, L – X1 BL1 = L – M BL1/BM1), it becomes obvious that the level of industrial output is also dependent upon the endowment of land. 20 To test for the robustness of these estimates a sensitivity analysis was performed. Influential observations were identified using the extreme t-statistics of dummy variables that select a single country and that are included in the equation one at a time. In general, however, the coefficients in Table 1 with high t-statistics are insensitive to the omission of those observations. 21 In this highly disaggregated studies, 0.5 is usually used as a threshold for a β value to be considered significant (see Leamer 1984 and Saxonhouse 1986). 9 deal of correspondence between the empirical results of the past and present. In both cases the fit of the model is good, and it is quite a bit stronger in the historical data from Ohlin’s time. Thus, viewed from a 1980s empirical perspective, the factor abundance theory seems to work very well in its own time. We now ask whether the same holds true from a 1990s perspective, where attention has shifted to tests based on factor content. 10 Table 2 Tests of Factor Endowments and Product Trade (Disaggregated Data) Labor- Labor- Agricultural Adjusted (a) OLS estimates Capital skilled unskilled land Minerals R2 R2 F(6,11) SITC Group 0: Food and Live Animals 00 0.06* -0.67** -0.25 0.80** -0.21** 0.66 0.48 2.52 01 -1.34** 0.60 -12.12* 1.88** 0.54** 0.79 0.69 7.30** 02 -1.03** 0.18 -8.37 1.79** 0.20* 0.75 0.62 5.62** 03 0.10** -1.13** -1.41** 0.33** -0.10* 0.39 0.06 1.17 04 -1.16** -8.52** -17.8* 5.2** 0.18 0.90 0.85 17.53** 05 -0.42** -0.74 7.21* 1.26 -0.20 0.68 0.50 3.90** 06 -0.64** 1.11 -4.02 -0.29 0.45** 0.58 0.35 2.55 07 -0.28** -2.13** 1.50* 0.08** 0.06** 0.98 0.97 137.11** 08 -0.00 0.09 0.07 0.43** -0.06** 0.70 0.54 4.36** 09 -0.28** 0.51* -2.33* 0.16** 0.12** 0.73 0.59 5.08** SITC Group 1: Beverages and Tobacco 11 0.06* -1.22** 6.45** -0.24** 0.039* 0.70 0.54 4.41** 12 -0.06** -0.43** -0.16 0.07 0.06** 0.78 0.66 6.70** SITC Group 2: Crude Materials, Inedible (Except fuels) 21 0.20** -0.40* -0.56 0.88** -0.22** 0.96 0.94 46.34** 22 0.13* -5.80** 3.72 1.27** -0.15 0.74 0.61 5.48** 23 -0.59** 1.44** -3.28** 0.08 0.16** 0.96 0.94 49.54** 24 0.06 -3.83** -3.0* 1.76** -0.21** 0.72 0.57 4.83** 25 -0.16** 0.27 -2.80** 0.16** 0.06** 0.58 0.35 2.55 26 -1.27** -17.24** -4.11 5.64** 0.66* 0.79 0.68 7.25** 27 0.00 -1.04** 2.02** 0.07 0.01 0.22 0.10 0.53 28 -0.46** -0.28 -4.29** 1.46** -0.08 0.84 0.76 10.06** 29 -0.02 -2.27** 2.87 0.66** -0.06** 0.62 0.41 3.04 SITC Group 3: Mineral Fuels, Lubricants and Related Materials 32 2.02** -8.33** 22.71** -2.64** -0.21** 0.89 0.83 15.04** 33 0.17** -4.13** 2.15 0.88** 0.04 0.86 0.78 11.42** SITC Group 4: Animal and Vegetable Oils and Fats 41 -0.03 -0.44 -1.43 0.68** -0.11** 0.70 0.53 4.31** 42 -0.20** 0.73** -0.46 -0.11* 0.12** 0.80 0.69 7.35** 43 -0.03** 0.03 -0.21 0.02** 0.01** 0.74 0.60 5.40** SITC Group 5: Chemicals 51+52+53+55+59 0.04 0.82* -0.17 -0.54** 0.03* 0.74 0.59 5.23** 54+56+57+58 0.03** -0.04 0.45 -0.24** 0.05** 0.66 0.47 3.58** SITC Group 6: Manufactured Goods Classified Chiefly by Material 61 -0.42** 2.49** -5.08** -0.20* 0.25** 0.82 0.73 8.71** 62 -0.06** 1.04** -0.61* -0.19** 0.05** 0.80 0.69 7.35** 63 -0.90** 2.24** -6.96* 0.23 0.41** 0.77 0.64 6.14** 64 -0.21** 1.08** -2.18** -0.39** 0.21** 0.70 0.54 4.42** 65 2.25** 10.86** 17.1 -3.74** -1.23** 0.86 0.79 12.22** 66 -0.11 1.31 -8.69** -0.80** 0.18** 0.69 0.52 4.12** 67 0.73** 0.80 10.93 -3.28** 0.37** 0.83 0.74 9.15** 68 -0.15** -3.98** 1.60 0.94** 0.11 0.77 0.65 6.35** 69 0.21** 1.16* 2.61 -1.95** 0.38** 0.84 0.76 10.23** SITC Group 7: Machinery and Transport Equipment 71 0.84** -2.82** 5.18** -1.50** 0.17** 0.94 0.91 29.85** 72 0.08** 0.30 0.44 -0.75** 0.16** 0.87 0.80 12.49** 73 0.24** 2.21** -0.12 -0.48** -0.06** 0.94 0.91 31.32** SITC Group 8: Miscellaneous Manufactured Articles 81+83+85 0.11** -0.08 1.19* -0.40** 0.06** 0.88 0.82 14.65** 82 0.02** -0.04 0.52** -0.05** -0.00 0.59 0.38 2.72 84 -0.04 4.29** 0.79 -1.17** 0.10* 0.80 0.69 7.39** 86 -0.15** 0.73** -3.26** 0.10 0.06** 0.49 0.22 1.82 89 -0.41** 4.74** -7.66* -1.23** 0.24** 0.34 0.01 0.99 SITC Group 9: Commodities Not Classified According to Kind 95 0.08** 0.16 0.35 -0.06** -0.04** 0.83 0.73 8.96** 11 Table 2 (continued) Tests of Factor Endowments and Product Trade (Disaggregated Data) Labor- Labor- Agricultural (b) β values Capital skilled unskilled land Minerals SITC Group 0: Food and Live Animals 00 0.46 -0.41 -0.03 2.14 -2.41 01 -2.26 0.08 -0.24 1.13 1.38 02 -2.29 0.03 -0.25 1.4 0.67 03 1.04 -0.95 -0.2 1.21 -1.57 04 -1.19 -0.68 -0.18 1.87 0.28 05 -0.79 -0.11 0.22 0.83 -0.57 06 -2.25 0.31 -0.2 -0.36 2.39 07 -0.86 -0.53 0.06 0.09 0.28 08 0 0.09 0.01 1.82 -1.09 09 -2.72 0.4 -0.3 0.55 1.76 SITC Group 1: Beverages and Tobacco 11 0.7 -1.15 1.03 -0.98 0.68 12 -1.13 -0.65 -0.04 0.46 1.71 SITC Group 2: Crude Materials , Inedible (Except Fuels) 21 0.62 -0.1 -0.02 0.96 -1.03 22 0.47 -1.68 0.19 1.63 -0.82 23 -2.32 0.46 -0.16 0.11 0.95 24 0.23 -1.19 -0.15 2.38 -1.22 25 -2.31 0.32 -0.56 0.82 1.31 26 -0.84 -0.86 -0.04 1.3 0.66 27 0 -1.01 0.34 0.3 0.18 28 -1.56 -0.08 -0.21 1.75 -0.41 29 -0.11 -1.04 0.23 1.32 -0.51 SITC Group 3: Mineral Fuels, Lubricants and Related Materials 32 3.37 -1.08 0.45 -1.56 -0.53 33 0.57 -1.12 0.11 1.03 0. 2 SITC Group 4: Animal and Vegetable Oils and Fats 41 -0.28 -0.33 -0.19 2.26 -1.57 42 -3.02 0.89 -0. 1 -0.59 2.74 43 -2.35 0.19 -0.23 0.55 1.18 SITC Group 5: Chemicals 51+52+53+55+59 0.43 0.71 -0.03 -2.06 0.49 54+56+57+58 0.55 -0.06 0.11 -1.54 1.38 SITC Group 6: Manufactured Goods, Classified Chiefly by Material 61 -2.81 1.34 -0.46 -0.47 2.52 62 -1.09 1.53 -0.15 -1.22 1.38 63 -3.04 0. 6 -0.35 0.27 2.09 64 -1.62 0.67 -0.24 -1.06 2.45 65 1.73 0.65 0.17 -1.01 -1.43 66 -0.52 0. 5 -0.52 -1.34 1.29 67 1.36 0.12 0.33 -2.16 1.04 68 -0. 6 -1.27 0.08 1.33 0.66 69 0.58 0.26 0. 1 -1.91 1.59 SITC Group 7: Machinery and Transport Equipment 71 1.75 -0.48 0.16 -1.1 0.53 72 0.56 0.17 0.04 -1.87 1. 7 73 1. 1 0.82 -0.01 -0.78 -0.42 SITC Group 8: Miscellaneous Manufactured Articles 81+83+85 1.2 -0.07 0.18 -1.54 0.99 82 1.26 -0.2 0.45 -1.11 0 84 -0.18 1.54 0.05 -1.85 0.68 86 -2.09 0.82 -0.62 0.49 1.26 89 -0.87 0.81 -0.23 -0.92 0.77 SITC Group 9: Commodities Not Classified According to Kind 95 1.93 0.31 0.12 -0.51 -1.46 Notes: t-ratios not reported. (***) denotes significant at the 1% level. (**) denotes significant at the 5% level. (*) denotes significant at the 10% level. See Appendix Table A3 for a description of SITC Rev. 1 (2 digit) codes. Source: Estevadeordal (1997) 12 3. Factor Endowments and Factor Trade circa 1913 Tests The factor content test is based on the immediate precursor of Equation (1) that does not depend on any assumptions about the dimensions or invertibility of the matrix B, namely BTc = Vc – sc VW. (2) Here, the left-hand side vector is the measured factor content of trade (denoted MFCTf) and the right-hand side is the predicted factor content of trade (denoted PFCTf). In this methodology all parameters in Equation (2) are measured, none are estimated econometrically, and the test centers on whether the equation holds. Thus, the method is harder to implement since its data requirements are considerably larger, which might explain why cross-country tests of this type have only appeared relatively recently. Testing Equation (2) can take a variety of forms, as outlined by Davis and Weinstein (1999, Table 3). Four tests have been deployed, usually one factor at a time and using the set of countries c of their sample: • The sign test focuses on whether, the direction of MFCTf matches that of PFCTf. In Equation (2) this amounts to asking whether the sign of the left- and right-hand sides are equal. The results are displayed in terms of the fraction of correct predictions. In contemporary data using the pure Heckscher-Ohlin model, the successful prediction rate is very poor, typically no better than a coin flip (Bowen, Leamer, and Sveikauskas 1987; Trefler 1995; Davis and Weinstein 1999). • The variance ratio test asks on whether the variance of MFCT is as large as PFCT. Of course, if the theory were a perfect fit, the ratio of the variances of the left- and right-hand sides of Equation (2) would be unity, but typically it is much less. In contemporary data using the pure Heckscher-Ohlin model, the “missing trade” problem pushes the variance ratio is less than 5 percent (0.03 in Trefler 1995; 0.0005 in Davis and Weinstein 1999). • The slope test depends on a regression of MFCT on PFCT. One can calculate the slope coefficient and its significance level from a regression of the left-hand side of Equation (2) on the right-hand side. Again, if the theory were a perfect fit the slope would be unity In contemporary data using the pure Heckscher-Ohlin model, the “missing trade” problem pushes the slope to small, even negative, albeit insignificant, values (Gabaix 1997; Davis and Weinstein 1999). • The t-test reports the t-statistic for the slope test where the null is a zero slope. This test can detect a positive and significant relationship of endowments to trade, although the relationship need not be one-for-one. 13 Data, Coding, and Aggregation As in the previous tests, we will still need each country’s trade and factor endowment data (Tc and Vc), and for these we draw on the data described in the previous section for C = 18 countries, I = 55 sectors, and F = 4 factors. We also need a factor use matrix B. In general, when there are intermediate goods, B depends on the direct factor use matrix Bd and the input-output matrix A. Using a Taylor expansion we see that, for any vector of outputs Z, the factor content of Z is given by BZ = BdZ + BdAZ + BdA2Z + BdA3Z + … = Bd(I – A)–1Z. Here, in the middle expression, the first term is direct use, the second term is direct use in intermediates, the third term is direct use in the intermediates used to make the intermediates, and so on. Thus, calculating B = Bd(I – A)–1 is straightforward if data on technology can be found to construct Bd and A. In the pure version of the theory and empirics it is assumed that B is constant across countries. The objective can then be easily met if we can construct B for just one country, and, like Trefler (1993, 1995) we pick the United States as the source of the B data.22 Construction of a historically useful direct factor use matrix Bd for the U.S. is possible using the study of Eysenbach (1976).23 She used the BLS-Leontief 1947 input- output table as the basis of her 165-industry classification scheme. Her capital and labor coefficients came from the census of 1899, and her natural resource coefficients, via Vanek (1963), from the 1947 input-output table. Already, the composite nature of her sources alerts us to the fact that her estimated Bd is not built from a consistent database at one point in time, and this drawback should be kept in mind. However, with this matrix available, it was straightforward to construct a concordance mapping the 165 industries into the aggregated classification based on I = 55 industries codes of the SITC scheme. For our purposes, another inconsistency problem with Bd arises in the factor classification. The categories (and the figures for the U.S.) do not exactly match the endowment data Vc. Eysenbach measures six types of labor: male and all, with each broken down into three wage levels to proxy skill levels. As a first pass at the problem we looked at all labor aggregated, so as to correspond to our endowment data on labor force. For capital input, Eysenbach has a single stock measure expressed in U.S. dollars that we take as corresponding to our factor endowment definition of capital. She measures 22 A less restrictive but very data-intensive formulation would examine allow B to vary across countries. See Davis and Weinstein (1999), who were fortunate to find this information easily to hand in a consistent form in the OECD input-output database. If B varies across countries then the relevant country- specific B must be used to calculate the factor-content of each countries exports and imports, radically changing Equation (2). Unfortunately, we have no consistent source of input-output tables circa 1913. 23 Wright (1990) used Eysenbach’s data in his study of resource abundance and U.S. industrial success from 1879 to 1940. The methodology in Wright’s study followed in the Heckscher-Ohlin-Vanek tradition and examined the renewable and nonrenewable resource factor contents of exports and imports at the benchmark dates. 14 nonrenewable resource inputs in the same units (dollars) as our endowment measure of mineral resources. However, her renewable resources measure is not the same (neither in definition nor in units) as our endowment category of agricultural land. Thus, in the construction of B from Bd we will have four factors, but not an exact match to the structure of the endowment data. The above discussion highlights the inconsistencies between the definitions of the endowment V on the right-hand side of Equation (2) and the factor use B on the left-hand side. This is a serious issue: if MFCT and PFCT, the two sides of Equation (2), are not commensurate then any tests that rely on consistent units will be rendered useless. Having taken care to make the units of labor (number of workers), capital (U.S. dollars), and nonrenewable resources (U.S. dollars) consistent, the problem should be avoided for these factors, notwithstanding the usual problems of measurement error, and all tests should be valid. However, in the case of renewable resources we note that there is likely to be an insurmountable discrepancy between the measurement concepts of the two sides. This will invalidate some of our tests for this case: consistent units are needed for a meaningful benchmark of unity in the slope coefficient and variance ratio tests. However, even with the discrepancy in measurement, we can still deploy the sign test to see if the directions of factor trade accord with theory. We can also examine the significance of the slope coefficient to see if there is any statistically significant linear relationship between factor endowment and trade, albeit the slope is meaningless. Fortunately, then, the problem with units does not afflict all of the factor content tests. Unfortunately, it does rule out the more interesting tests that have the strongest bearing on questions of quantitative significance, though in this study this will only be a problem for the case of renewable resources. Our final data collection task was to find a suitable input-output matrix A. Leontief’s 1947 input-output table is well known, and was the source for Eysenbach’s resource coefficients, but he also constructed an input-output table for 1919 that we can employ here (Leontief 1953b). However, the 1919 input-output table was built around a smaller classification scheme of only 41 industries, so yet another concordance problem had to be solved in order to usefully align this dataset with the 55-sector SITC classification scheme used in all the previous calculations. Considering the extent of the overlap and consistency between these two classifications, it was decided to settle finally on a 25-industry aggregation scheme for the present exercise. Thus, two new sets of concordance mappings were constructed, one from the 165- industry classification to the new 25 industry classes, and one from the 41-industry classification to the 25 new classes. Our previously constructed vectors and matrices Tc and Bd were converted to this I = 25 classification by some simple arithmetic aggregation, and then B = Bd (I – A)–1 was calculated. 15 Results Table 3, Panel 1, shows the results of applying the four basic tests (sign, t, variance ratio, and slope) to the raw data for 18 countries. We applied the tests to six individual factor types plus two sets of pooled factor types. A word on definitions and units is in order, although an appendix gives full details. Capital is measured in 1913 dollars, and uses Eysenbach’s U.S. census measure of factor use on the left-had side and a perpetual- inventory estimate of 1913 capital stocks on the right. Labor is measured as the size of the workforce, and skilled and unskilled are based on Eysenbach’s census data on the left, and on literacy rates across countries on the right. Nonrenewable resources are in dollar terms from Eysenbach’s census data on the left, and from Estevadeordal’s minerals measure on the right. Renewable resources are not commensurate on the left and right, being based on Eysenbach’s dollar-value census data on the left and Estevadeordal’s measure of agricultural land areas on the right. In cases where the factors are pooled, we need to worry about the commensurability not only on each side of the equation, but also from one type of factor to the next. Units of, say, labor and capital, will never be commensurate in a physical sense, but econometric adjustments are needed to permit valid estimation, specifically to ensure homoskedasticity. Following Trefler (1995), we weight each observation by ωfc = 1/(σf sc1/2) where the σf are the standard deviations of the pure Heckscher-Ohlin- Vanek error MFCTfc–PFCTfc for each factor f, and where sc is an adjustment for country size. This is our preferred specification in what follows, although alternative weighting schemes do not dramatically change the results. In Table 3 we show unweighted results and results using the Gabaix (1997) weights ωfc = 1/sc; we have also tried the Davis- Weinstein (1999) weights ωfc = 1/VWf and found little difference. The results are, at best, mixed, and perhaps a little disappointing. For capital and labor (total and disaggregated) all the tests offer almost no support for the theory. The sign test reveals a predictive power no better than a coin flip. The t-tests are insignificant and often of the wrong sign. The exceptions are the unweighted results, but these are clearly driven by country-size effects and should be ignored. The variance ratio and slope tests confirm that the fit is very poor, the slope is almost a horizontal line, and overall the model can explain maybe 1% of the overall variance of the dependent variable. So far so bad, but our hopes pick up a little bit when resources are considered. For renewable resources, the non-commensurability problem confines us to the sign test and the t-test, but the results are more favorable. The sign test rises to 67% and the slope is always significant and positive. For non-renewable resources, we can run the full battery of tests, and we find the best fit of all. Consider the Trefler-weighted results. The sign test shows that we get the direction of trade right in almost 4 out of every 5 cases, the t ratio is a respectable 1.7, the variance ratio is 60% and the slope is 0.33.24 Finally, what the 24 The Gabaix-weighed results are weaker, we think, because the big resource exporters are big countries, like the United States. An additional weight of 1/(sc1/2) severely downplays these observations. 16 Trefler weights Gabaix weights Unweighted Factors in the sample sign t VR slope t VR slope t VR slope Productivity correction: None K Capital 0.50 1.4 0.01 0.03 0.0 0.00 0.00 2.2 0.01 0.04 L Labor 0.44 -1.1 0.00 -0.02 -0.8 0.00 -0.01 -3.1 0.00 -0.03 Ls Labor-Skilled 0.50 -0.6 0.01 -0.01 -0.5 0.01 -0.01 -2.8 0.00 -0.03 Lu Labor-Unskilled 0.50 -1.0 0.00 -0.01 -0.8 0.00 -0.01 -2.4 0.00 -0.02 Rr Resources-Renewable 0.67 2.6 — — 1.4 — — 4.8 — — Rn Resources-Nonrenewable 0.78 1.7 0.60 0.33 0.5 0.26 0.08 2.0 0.69 0.37 K, L, Rn Pooled 0.57 1.9 0.29 0.14 — — — — — — K, Lu, Ls, Rn Pooled 0.57 1.8 0.21 0.10 — — — — — — Productivity correction: GDP per capita K Capital 0.72 2.4 0.01 0.06 1.4 0.01 0.04 6.5 0.01 0.10 L Labor 0.44 0.2 0.18 0.02 1.0 0.26 0.15 -1.5 0.19 -0.15 Ls Labor-Skilled 0.56 1.2 0.02 0.04 0.7 0.01 0.02 1.2 0.03 0.04 Lu Labor-Unskilled 0.44 -1.1 0.01 -0.03 -0.7 0.01 -0.02 -2.2 0.01 -0.05 Rr Resources-Renewable 0.83 3.0 — — 2.0 — — 3.2 — — Rn Resources-Nonrenewable 0.78 2.6 1.00 0.61 1.8 0.90 0.49 3.3 0.63 0.50 K, L, Rn Pooled 0.65 3.4 0.63 0.35 — — — — — — K, Lu, Ls, Rn Pooled 0.62 3.4 0.52 0.29 — — — — — — Productivity correction: Real Wage K Capital 0.78 1.5 0.01 0.03 0.3 0.01 0.01 4.7 0.00 0.05 L Labor 0.61 0.1 0.02 0.01 -1.1 0.03 -0.06 3.4 0.01 0.07 Ls Labor-Skilled 0.56 0.7 0.01 0.02 -0.6 0.01 -0.01 4.7 0.00 0.05 Lu Labor-Unskilled 0.39 -1.3 0.02 -0.05 -0.9 0.02 -0.03 -1.3 0.03 -0.05 Rr Resources-Renewable 0.72 2.3 — — 1.4 — — 2.9 — — Rn Resources-Nonrenewable 0.67 2.2 1.07 0.56 1.2 0.96 0.36 3.4 0.51 0.46 K, L, Rn Pooled 0.69 2.5 0.51 0.24 — — — — — — K, Lu, Ls, Rn Pooled 0.60 2.6 0.45 0.21 — — — — — — Notes: For description of tests, see text; sign = sign test; t = t test; VR = variance ratio test; slope = slope test. Sources: See text. Minimal concordance (for more details see authors' appendix): Capital: Perpetual inventory endowment (own, PFCT); total capital usage (Eysenbach-Leontief, MFCT). Labor: workforce endowment (Estevadeordal, PFCT); total labor usage (Eysenbach, MFCT). Labor-Skilled: literate workforce endowment (Estevadeordal, PFCT); skilled labor usage (Eysenbach, MFCT). Labor-Unskilled: Labor minus Labor-Skilled (PFCT, MFCT). Resources-Renewable: Agricultural land endowment (Estevadeordal, PFCT); usage (Eysenbach-Leontief, MFCT). Resources-Nonrenewable: Mineral endowment (Estevadeordal, PFCT); usage (Eysenbach-Leontief, MFCT). regressions are telling us we can also show graphically, and Figure 1 depicts the scatter plots for the eight cases in Panel 1, using no productivity correction and Trefler weights. The poor fit for labor and capital is immediately apparent given the diffuse cloud of dots seen in each case. For resources, the basis for a tighter fit is also clearly visible, and the pooling is a mélange of the two. Such results, though disappointing, are not too surprising given the equally weak findings of the recent literature using the basic, unadorned specification of the Heckscher-Ohlin-Vanek hypothesis. Accordingly, various enhancements of the basic specification have been proposed. These looser specifications appeal to theory as a basis for adding additional parameters that allow for a better fit: for example, adjustments for factor productivity differences and home bias in consumption. We now apply each of these refinements to the historical data. 17 Figure 1 Measured versus Predicted Factor Content of Trade Capital Labor Labor-Skilled Labor-Unskilled Extensions: Factor Productivity Adjustment Could the poor results be simply a manifestation of the Leontief problem? That is, could we be measuring factor endowments incorrectly in raw units instead of in effective units, controlling for productivity? Trefler (1993; 1995) showed that a way to correct for this problem is to rescale the endowment vector Vfc by some measure of relative productivity. If such a productivity correction δc is common to all factors in one country, then we ˜ would arrive at a productivity-corrected endowment vector of the form Vfc = δc Vfc , and 18 Figure 1 (continued) Measured versus Predicted Factor Content of Trade Resources-Renewable Resources-Nonrenewable K, L, Rn K, Lu, Ls, Rn Notes: MFCT on vertical axis, PFCT on horizontal. Trefler weights, no productivity correction. See text and Table 4. Units on each axis are non-commensurate for renewable resources, hence 45-degree line is omitted. the analysis can then proceed as before. We use two proxies for δc, the relative GDP per capita (like Trefler) and the relative real wage.25 Table 3, Panels 2 and 3, show these results. By our reading, these productivity adjustments do help the model fit better, confirming the findings on contemporary data (Trefler 1993, 1995; Davis and Weinstein 1999). The sign tests starts to rise well above the coin-flip level for capital, and improves somewhat for both types of resources. The 25 In each case we set U.S. equal to 1, since we are using the U.S. factor-use coefficients on the left side. GDP per capita measures were taken from Maddison (1991) and real wages from Williamson (1995). 19 slope for non-renewable resources also rises, doubling to the level of about 0.6; and the variance ratio rises to unity. However, the joy is short-lived, since the slope and variance ratio tests are still demoralizingly low for both capital and labor. The pooling of the results does not add a great deal to the analysis in any of the cases shown in the three panels of Table 3. With pooling the tests come out somewhere in between the good results for nonrenewable resources and the poor results for labor and capital, as expected. Are we justified in using incomes and wages as productivity proxies? If these were imperfect measures of factor productivity, either due to measurement error, market failures, or deviations from pure Hicks-neutral technological shifts, then our results might be polluted. One way around this is to “let the data speak” by estimating the implied technology shift parameters, rather than imposing them. In this method, the parameters δc are chosen to maximize the fit of Heckscher-Ohlin-Vanek equation, subject to the normalization that δUS = 1.26 Accordingly, we estimate the corresponding variant of equation (2): BT c = Vc − sc VW = δ c Vc − sc ∑δ c' V c' . ˜ ˜ (2′) c' Here, the implied slope and other tests are based on a regression of measured (left-hand side) versus predicted (fitted values on right-hand side). Clearly, this method cannot be attempted on the data for a single factor type since it would exhaust all degrees of freedom.27 We must pool across factors to make the method workable, implying that we must use Trefler weighting and omit the non-commensurate data on renewable resources. The results appear in columns (1) and (2) of Table 3, with the labor both aggregated and disaggregated. Here the findings are somewhat encouraging. We use up 17 out of 54 degrees of freedom (17 parameters, 54 observations), but to good effect. The sign test shows successful predictions in 3 out of 4 cases, the t ratio is very significant, the variance ratio is exactly one (no “missing trade” at all by that measure) and the slope of 0.56 is not to be sneezed at. Column (2) looks very similar, though the variance ratio is slightly below one. So much for the better fit, and the ability to dramatically reduce missing trade through this correction. But do the implied δc make sense? In a sharp theoretical insight that illuminated some confusion in the debate Gabaix (1997) warned of the pitfalls of comparing the implied δc to seemingly-independent measures of productivity, such as GDP per worker, and using these results for inference about the fit of the HOV theory. The measures are not independent at all. In fact, if there is complete missing trade, the productivity correction turns out to be exactly a weighted total productivity measure. We can report that our δc look quite reasonable upon inspection, and they have a correlation 26 Obviously, in a less interesting exercise, if we can scale each factor and each country independently, with a free choice of δfc, then we can obtain a perfect fit in the HOV model by using all degrees of freedom. (Trefler 1993; 1995). 27 Actually, there would be one degree of freedom, because the U.S coefficient is not free, 20 Table 3 Productivity and Home Bias Parameters (1) (2) (3) (4) (5) (6) Factors {K,L,Rn} {K,Ls,Lu,Rn} {K,L,Rn} {K,Ls,Lu,Rn} {K,L,Rn} {K,Ls,Lu,Rn} Productivity Implied Implied None None Imposed Imposed correction Hicks-Neutral Hicks-Neutral GDP per capita GDP per capita Home Bias No No Yes Yes Yes Yes sign 0.76 0.72 0.74 0.62 0.67 0.60 t 4.7 4.2 6.9 7.3 8.2 8.9 VR 1.00 0.71 2.01 2.22 1.64 1.79 slope 0.56 0.39 1.00 1.00 1.00 1.00 Coefficient δ δ α* α* α* α* Argentina 0.97 (0.365) 0.85 (0.317) 0.79 (0.510) 0.59 (0.378) 0.65 (0.397) 0.57 (0.290) Australia 0.74 (0.208) 0.72 (0.196) 0.80 (0.335) 0.81 (0.284) 0.55 (0.229) 0.58 (0.193) Austria 0.34 (0.136) 0.34 (0.130) -0.12 (0.444) -0.13 (0.375) -0.13 (0.279) -0.23 (0.235) Belgium 0.58 (0.189) 0.56 (0.175) -0.43 (0.905) -0.37 (0.718) -0.23 (0.487) -0.60 (0.392) Canada 0.57 (0.247) 0.56 (0.219) -0.45 (0.321) -0.39 (0.247) -1.03 (0.696) 1.90 (1.107) Denmark 0.72 (0.417) 0.63 (0.343) 1.86 (1.141) 1.71 (0.944) 1.72 (0.920) 1.49 (0.755) Finland 0.56 (0.451) 0.43 (0.371) 0.43 (0.939) 0.28 (0.670) 0.32 (0.736) 0.31 (0.515) France 0.66 (0.112) 0.59 (0.094) 0.63 (0.315) 0.62 (0.265) 1.00 (0.341) 0.99 (0.212) Germany 0.62 (0.090) 0.58 (0.080) 0.40 (0.423) 0.30 (0.327) 0.29 (0.275) -0.07 (0.242) Italy 0.59 (0.126) 0.52 (0.109) 0.33 (0.278) 0.25 (0.204) 0.33 (0.234) 0.32 (0.160) Netherlands 0.76 (0.286) 0.71 (0.247) 2.22 (0.651) 2.06 (0.538) 2.98 (0.612) 2.39 (0.501) Norway 0.09 (0.202) 0.11 (0.189) -0.23 (0.439) -0.22 (0.372) -0.18 (0.443) -0.16 (0.382) Portugal 0.27 (0.175) 0.17 (0.146) 0.31 (1.075) 0.13 (0.577) 0.20 (1.103) 0.04 (0.408) Spain 0.66 (0.172) 0.51 (0.147) 0.04 (0.306) 0.04 (0.221) 0.14 (0.303) 0.21 (0.171) Sweden 0.68 (0.309) 0.56 (0.239) 0.37 (0.856) 0.26 (0.609) 0.35 (0.544) 0.50 (0.492) Switzerland 0.53 (0.253) 0.51 (0.225) 0.82 (0.663) 0.73 (0.542) 0.58 (0.496) 0.34 (0.395) United Kingdom 1.18 (0.165) 0.99 (0.131) -0.18 (0.186) -0.16 (0.155) -0.15 (0.190) -0.23 (0.134) United States 1.00 1.00 0.34 (0.116) 0.30 (0.094) 0.56 (0.156) 0.57 (0.143) Correlation with: GDP per capita 0.65 0.77 — — — — Real wage 0.32 0.46 — — — — Notes: Trefler weights. Standard errors in parantheses. with GDP per capita of about 0.7; but (to repeat) this says nothing at all about the fit of the HOV theory: only missing trade tests can do that. But the correlation is not irrelevant: it should reassure us that the good fit we have found was achieved without the data having to be manipulated through implausible productivity corrections.28 We should not overlook the main points here. The results look quite good. For comparison, the variance ratio was about 0.25 (or 0.59) in Table 2 without (respectively, with) the imposed productivity correction. There is a dramatic improvement over the results on contemporary data: according to Trefler and Zhu (2000, Table 1), the best variance ratio result was 0.33 by Trefler (1995), with five other benchmarks less than 0.09. Hence, our historical study provides much stronger support for the idea that an allowance for the Leontief hypothesis will play an important part in reconciling the HOV theory to the data. But the results are not perfect, and we know that the fit for some individual factors, especially capital and disaggregated labor, is poor, whilst the fit for resources is much better. 28 Another check involves simple inspection of the implied δc, and an appeal to introspection to determine whether they look reasonable. They do, but with some exceptions. It might be questioned, for example, whether Norway really languished with a productivity of merely 10% of the U.S. level. 21 Extensions: Home Bias in Consumption A second extension to the basic model, also due to Trefler (1995), allows for home bias in consumption. This extension admits Armington preferences where country c consumption is now a weighted combination of home goods and foreign goods, Cc = sc[αcXc + αc*(XW – Xc)], with αc >1 and αc*<1. National budget balance requires αc sc + αc*(1 – sc) = 1, so one can eliminate the αc. Here, the estimating equation (1) becomes BTc = αc*(Vc – sc VW). (2″) and world market clearing in each factor imposes F restrictions of the form Σcαc*(Vc – sc VW) = 0. 29 In the case (1 – αc*) = 0, we have no home bias and we revert to the standard theory. In the case (1 – αc*) = 1 we have complete home bias. A range of values of (1 – αc*) between zero and one is assumed to correspond to a varying degree of home bias. Already, we can intuitively see what is going to happen. Suppose the home bias were constant across countries, with αc* = α*. Clearly, a regression based on (2″) will then set α* equal to the slope from (2) and the fit will improve dramatically. A corollary of the OLS algebra is that the implied slope of measured (left-hand side) versus predicted (fitted values on right-hand side) will be unity by construction! This eliminates the slope test as a meaningful criterion. However, the other tests are still good—for example, the variance ratio is not necessarily equal to unity in these regressions, nor is the R2. The result of applying these tests is shown in columns (3) through (6) of Table 4. Again, if we want to allow for country-specific parameters we can only gain sufficient degrees of freedom by pooling, and we repeat both types of pooling (with and without labor disaggregation). The results show promise of a better fit, though it does not seem to matter whether an (imposed) productivity correction is included or not (columns 5 and 6 versus 3 and 4).30 This is worrying. But of greater concern are the implied home bias parameters themselves, with αc* shown for each country. Judging whether these are reasonable parameters is again a matter for our introspection, but some of these estimates seem implausible, and beyond the bounds of what theory permits. It is not clear what is implied by a value of αc* that is outside the interval [0,1]. We cannot dismiss this is a case of imprecision—the standard errors are fairly small. Thus, we react to the home-bias extension rather pessimistically. Like Trefler (1995), we find some strange implied values for the αc* coefficients that make little sense in theory. Undoubtedly some kind of home-bias effect will be a necessary part of a complete trade theory, but, given that the results here are not markedly better as judged 29 For simplicity, we omit the (empirically less-relevant) adjustments for trade imbalances discussed by Trefler (1995). Equation (1″) is estimated by OLS with the F linear restrictions imposed. 30 Though feasible, there would be few degrees of freedom left if we estimated both a productivity correction (17 paramaters) and a home bias correction (18 parameters). 22 by fit, we doubt the usefulness and relevance of the home-bias correction for our sample, at least in this form. Summary In this section we have shown how it is possible to implement a test circa 1913 of the Heckscher-Ohlin-Vanek prediction that there exists a linear relationship between factor endowments and the net factor content of trade. The results are very unfavorable to the hypothesis. For labor and capital the fit of the model is close to nonexistent. For resources, there is evidence that the model fits well—though we are hampered by a units problem that prevents us from fully testing the predictions for renewable resources. For all factors the fit of the model is much improved by a Leontief-style productivity correction, whether by direct proxy such as incomes or wages, or indirect via an estimated technology coefficient. If home bias is allowed the model fits very well, by construction, but the implied home bias parameters appear, in most cases, quite implausible. In short, having appealed to the 1990s vintage of empirical trade tests of the form pioneered by Trefler (1993; 1995) we have found a good deal of correspondence between the empirical results of the past and present. Missing trade is everywhere, though it is less absent in the case of resources than in the cases of labor and capital (Gabaix 1997). The fit of the model in the latter cases is poor, and productivity and home bias corrections do not solve the problem in an entirely satisfactory way. Thus, the simple factor-content approach seems to work as well in its own time as it does today—that is, not very well at all. Our study brings us to a point that corresponds to the year 1995 in the contemporary empirical literature—the year Trefler announced the mystery of the “missing trade.” In the conclusion we ponder where we can go from here 4. Conclusion: Give Heckscher and Ohlin a Break! This work has looked very broadly at the applicability of modern tests of the Heckscher- Ohlin trade theory to the historical data for 1913, an earlier period of relatively well- integrated goods markets, and a time in history that inspired the creators of the factor- abundance model. The results of this exercise have been mixed. The relationship between factor endowments and goods trade appears strong, even stronger than that found in contemporary data. But the factor content tests perform as poorly as they do on recent data, although a Leontief-style productivity correction can go some way towards correcting the problem. Even then, the best fit in 1913 seems to be for resource endowments, rather than for capital and labor. Though we are disappointed to find such weak evidence, is this cause to dismiss the Heckscher-Ohlin model? We think not. First, on empirical grounds, we are not fully satisfied with the methodology adopted here and, compared to the most recent advances in the field that have attained a close match between theory and data, we have many gaps in our data. The Davis and Weinstein (1999) analysis goes further than any previous 23 work in achieving a satisfactory fit. They extend the model in new ways, allowing for factor productivities and home bias, but adding the possibility of differing technologies across countries and deviations from factor-price equalization. They are fortunate to have a wealth of OECD data that allows them to investigate different factor-use matrices B for each country. They can also directly test for home bias and productivity differences using production and consumption data, and then test for the fit of the trade model. In contrast, we have only one factor-use matrix B for the U.S. in 1913, and even that was a struggle to construct, needed much manipulation, and had to draw on data from a variety of sources at different points in time. It is clearly a strong assumption to impose the U.S. technology matrix on all countries in 1913, and it is likely to be rejected as an assumption, just as Davis and Weinstein reject the constancy of B across countries today. In terms of production and consumption data, we have nothing like the OECD data to work with, so our productivity and home bias parameters fall out from the factor-content regressions themselves. It might then be no surprise that some of these parameters look odd since we have had to estimate them indirectly. Could one do better in a historical setting? This would be a major archival and data-gathering exercise, though we think it would be very profitable for all of us if someone did it. As historians are painfully aware, there are no CD-ROMs with OECD data for 1913. Only in the postwar period was even (single-sector) national accounting beginning to be standardized. It may be a vain hope, then, to imagine we might build full set of input-output tables and production-consumption accounts for even just these 18 countries at a 25-sector level circa 1913. However, it is clear to us that such basic work expanding the range of our data would be necessary to advance beyond the circa 1995 econometric vintage that we have been confined to work with here. Notwithstanding these methodological constraints, what can we say about the interpretation of our results when they are taken at face value? The fact that we can only get really strong support for the case of natural resource trade need not be a fatal weakness—at least not in 1913. Gabaix (1997) protested that the good fit of the Heckscher-Ohlin-Vanek model on natural resources today was cold comfort, since such endowments constitute such a paltry share of world output in the modern, service- oriented, knowledge-based economy. In this world most of factor rewards accrue to capital and labor (mostly skilled, i.e. human capital). Such objections are clearly less relevant in 1913, when much of the basis of world trade, and still significant portions of world output, were based on primary-producing activities. The role of resources, and the good fit of the model there, also brings us back to the point made in the introduction: the Heckscher-Ohlin theory supposes that factors are not mobile and endowments are exogenous. Only then would estimation be valid. In a paper entitled “Give Heckscher and Ohlin a Chance!” Wood (1994a) raised this concern in connection with contemporary tests of the theory that ignore the fact of considerable international capital mobility that can equate rates of return across countries; instead, he 24 argues, we must restrict attention only to the factors that are basically immobile. Land being problematic to measure, his research agenda has focused on skilled and unskilled labor as the key contrast in his “North-South” view of the global economy (1994b). Note that these shortcomings are econometric problems, not a failure of the theory itself: indeed, the theory very usefully predicts that trade and factor migration can be substitutes. This brings us back to the nature of the world economy in 1913: it was not just a world of relatively free trade, it was also a world with a high degree of factor mobility. If we think just capital mobility is a problem today for factor content tests, then in 1913 we will have an even bigger problem for both labor and capital were highly mobile then. These are the factors for which the fit of the Heckscher-Ohlin-Vanek model is weakest in our data—a coincidence? We think not. The fit of our model is strongest for the immobile factors that have long been considered the key source of comparative advantage in the late-nineteenth and early-twentieth centuries.31 In summing up, we urge caution before interpreting poor static regression results as providing evidence against the theory for this historical period. A large literature in economic history has sought to model endogenous capital and labor flows in the Greater Atlantic economy of that era (Taylor and Williamson 1994; Hatton and Williamson 1994, 1998; O’Rourke and Williamson 1999; Edelstein 1982). Until an econometric strategy can be found that adapts the factor-content tests to cope with this simultaneity problem we should, perhaps, give Heckscher and Ohlin a break. 31 In a paper entitled “Give Heckscher and Ohlin a Chance!” Wood (1994a) raised this concern in connection with contemporary tests of the theory that ignore the fact of considerable international capital mobility that can equate rates of return across countries. Instead, he argues, we must restrict attention only to the factors that are basically immobile, resting his case on the theoretical work of Ethier and Svennson (1986). Land being problematic to measure, Wood’s research agenda has focused on skilled and unskilled labor as the key contrast in his “North-South” view of the global economy (1994b). 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Explorations in Economic History 32 (April): 141–96. Wood, A. 1994a. Give Heckscher and Ohlin a Chance! Weltwirtschaftliches Archiv 130 : 20–49. Wood, A. 1994b. North-South Trade, Employment, and Inequality: Changing Fortunes in a Skill-Driven World. Oxford: Clarendon Press. Wright, G. 1990. The Origins of American Industrial Success, 1879–1940. American Economic Review 80 (September): 651–68. 28 DATA APPENDIX Endowment Data (Table A1) a. Capital (1): Variable used in tests of Section 2. It is calculated as apparent energy consumption (production plus net imports) of solid fuels (Hard Coal, Brown Coal, Lignite, and Coke). Data are in thousands of hard-coal equivalents. See Estevadeordal (1993) for a detailed description. b. Capital (2): Variable used in tests of Section 3. The capital stock estimates are constructed using a perpetual inventory method applied to pre-1913 annual investment rates and real outputs. Our approach here was to use a 3% constant depreciation rate, calculating the contribution of real investment in each year as the investment share times real GDP times the depreciation factor. Alternative depreciation methods were tried, such as 30- and 50-year straight line and 5% constant rates, but although these altered the levels in 1913, they did not markedly change their cross-country variation, as expected. Summing up the weighted investments from each year and dividing by the terminal year real GDP gave an estimate of the 1913 capital-output ratio, which was then multiplied by country GDP to obtain capital stock estimates in 1913 dollar terms. This procedure was possible for 14 countries in our sample, but 4 countries lacked pre-1914 investment time series. These were Austria-Hungary, Belgium, Portugal, and Switzerland. For these 4 countries, extrapolations were made on the basis of Estevadeordal’s 1913 proxy for capital stock (the correlation between Estevadeordal’s data and the resulting capital stock estimates for the 14 countries for which we had investment data was .9575). All investment data were taken from the database of Obstfeld and Taylor (1999). Data are 1913 dollars. c. Total Labor: Data for all countries except Argentina, Spain, and Portugal is total labor force (in thousands) estimated at mid-year and is taken from A. Maddison (1982), Phases of Capitalist Development (Oxford, UK: Oxford University Press). Data for Argentina, Portugal, and Spain refers to the economically active population as reported in B.R. Mitchell (1980), European Historical Statistics 1750-1975, 2nd edn (London: Macmillan) and (1983), International Historical Statistics: The Americas and Australasia (London: Macmillan). Linear interpolation between census years was used when needed. d. Skilled Labor: Computed as Labor times literacy rate. Data are in thousands of workers. e. Unskilled Labor: Computed as Labor minus Skilled Labor. Data are in thousands of workers. f. Agricultural Land: Agricultural land for all countries except Portugal are available in League of Nations (1927), Population and Natural Resources, (Geneva). For Portugal data on agricultural land is taken from P. Lains (1989), Foreign Trade and Economic Growth in the European Periphery. Portugal, 1850-1913 (Florence: European University Institute, mimeo). Data are in thousands of hectares. g. Mineral Resources: Computed as the value of petroleum production plus ore production of a composite of 12 minerals: Bauxite, Copper, Iron Ore, Lead, Manganese, Nickel, Phosphate, Potash, Pyrites, Sulfur, Tin, and Zinc. Data are in thousands of 1913 dollars. See Estevadeordal (1993) for detailed sources. h. GDP Data: Real GDP per capita data in 1990 U.S. dollars comes from Maddison (1995), Monitoring the World Economy, 1820-1992 (Paris: OECD). These figures are then normalized to the U.S. and multiplied by U.S. real GNP per capita in 1913 U.S. dollars, as given by U.S. Department of Commerce, Bureau of the Census (1975), Historical Statistics of the United States: Colonial Times to 1970 (Washington, DC: Bureau of the Census), to get real GDP per capita in 1913 U.S. dollars for all countries. To calculate country GDP, the resulting figures are then multiplied by the 1913 population data found in Maddison. Data are in 1913 dollars. Trade Data (Table A2) Net export data was constructed from national trade records and originally aggregated in fifty-six commodity groups. Commodities were classified according to the Standard International Trade Classification (Revised, 1961) at the two- digit level (See Table A3). All data is for 1913 except for a few countries for which the closest year to 1913 was used. Data are in 1913 dollars. See Estevadeordal (1993) for detailed sources. Technology Data (Tables A4-A5) We make use of Leontief’s 1919 U.S. input-output table as found in W.W. Leontief (1953), The Structure of the American Economy, 1919-1939 (Oxford, UK: Oxford University Press). Data are in millions of dollars. (Table A4). Data on factor coefficients come from M.L. Eysenbach (1976), American Manufactured Exports, 1879-1914: A Study of Growth and Comparative Advantage (New York: Arno Press). Eysenbach industry data follows the classification scheme as outlined in U.S. Department of Labor, Bureau of Labor Statistics (1953), Industry Classification Manual for the 1947 Interindustry Relations Study (Washington, DC: BLS). Direct use renewable- and nonrenewable-resource coefficients can be found on pages 297-301. Labor and capital coefficients can be found on pages 302-6. We convert labor and capital coefficients into per dollar terms. Skilled labor coefficients can be found on pages 307-11. Unskilled labor coefficients are given by column (3), the share of males, women, and children as a fraction of all employees. We calculate skilled labor coefficients as one minus the unskilled labor coefficient for each industry. (Table A5) Concordance (Tables A6 and A7) Due to the range of data sources, the first task was to create a concordance mapping relating the 165 BLS industry codes used by Eysenbach, the SITC Rev. 1 codes used to report the net trade data, and the 41 industries that comprise Leontief’s U.S. 1919 input-output table. Each BLS industry was first assigned to a related SITC Rev. 1 category. Each SITC Rev. 1 category was subsequently assigned to one of the Leontief industries. In some cases BLS industries 29 proved difficult to classify according to the SITC Rev. 1 system. This is due to the fact that the BLS codes identify particular industries while the SITC Rev. 1 codes identify products. Likewise, it proved difficult in some cases to classify SITC Rev. 1 products according to the Leontief industries. Generally speaking, this problem was resolved by going directly from the BLS industrial classification system to the Leontief industry classification. It also proved useful to “collapse” the 41 industries given by Leontief’s input-output table into 25 industries, as occasionally a product classified according to the SITC Rev. 1 system belonged to multiple Leontief industries. For example, SITC Rev. 1 product 32 is “Coal, coke, and briquettes.” Leontief separates “Coal” and “Coke” into two separate industries. It thus seemed logical to combine “Coal” and “Coke” from the input-output table to better accommodate the trade data. In addition, some of the original input-output industries appeared rather indistinguishable from one another, so it was decided to combine such related categories for the sake of simplicity. An example is the case of “Lumber & timber products” and “Other wood products.” Finally, it should be noted that two industries, “Electric utilities” and “Construction” were removed entirely from the original input-output table. Calculating Factor Content of Trade Before calculating the factor content of trade, it was first necessary to compute direct use factor content coefficients for each of our 25 industries. All relevant Eysenbach coefficients were first grouped on the basis of our 25-industry classification scheme and averaged. Eysenbach’s labor and capital coefficients are reported as “Labor per unit of Value Added” and “Labor per unit of Capital,” so in order to make use of her numbers, it was then necessary to calculate the value added as a fraction of total output for each of the 25 industries. This was done by first converting the collapsed input-output table from absolute numbers into fractions of industry gross total output. To obtain value added as a share of output for a given industry, we simply subtracted the sum of the contributions of each input industry to the output industry from one. We were then in a position to calculate the direct use factor content coefficients for each of our 25 industries according to the following formulas: Labor: (labor / value added) × (value added / output) = (labor / output) Capital: [1 / (labor / capital)] × (labor / value added) × (value added / output) = (capital / output) In addition, by multiplying the solutions to each industry’s Labor equation by the share of unskilled labor in total labor, as given by Eysenbach, and by one minus this share, we were able to obtain the direct use factor content coefficients for unskilled and skilled labor, respectively. Eysenbach’s raw material coefficients are reported in per-output terms, so no further calculations were needed to obtain direct use coefficients for renewable and nonrenewable resources. To complete the construction of our technology matrix, B, we had to account for the indirect usage of each factor in each industry. To do so, the following formula was employed: B = B0 (I – A) -1 where B0 is the (6 × 25) matrix of direct use coefficients, I is the identity matrix, and A is the (25 × 25) input-output table expressed in terms of input industry shares of gross total output. Multiplying B by our vectors of trade data yields the factor content of trade for each of our 18 countries. Appendix Table A1 Factor Endowments and GDP in 1913 Countries Capital Capital Total Skilled Unskilled Agricultural Mineral GDP (1) (2) Labor Labor Labor Land Resources Argentina 3801 3433222006 3162 2052 1110 18780 580 2228525624 Australia 8145 4932800511 2076 2030 46 7260 95787 2035353163 Austria 40257 11793779639 3186 2644 542 18420 43583 1810164212 Belgium 28312 9634472145 3484 3017 467 2010 25149 2428086689 Canada 25725 6990369775 3107 2921 186 35730 34715 2536980164 Denmark 3590 2264699287 1358 1315 43 2950 0 861089294.1 Finland 586 927410885.1 1338 740 598 2840 0 475895505.9 France 64266 31519795903 21225 18699 2526 36800 88969 11036922774 Germany 189259 44300847086 17638 17373 265 34810 327139 12000803764 Italy 10853 18691927041 16632 10445 6187 20770 29056 6947871078 Netherlands 10479 5415075831 2365 2330 35 2180 0 1867261089 Norway 2516 1269658875 999 984 15 990 51783 426933950.4 Portugal 1417 4772640831 2545 791 1754 5037 2952 623142844.9 Spain 7169 5772694763 7675 3669 4006 40680 121084 3515841163 Sweden 5739 2320033742 2631 2592 39 5010 35622 1338900699 Switzerland 3387 5128759354 1923 1894 29 702 0 1246679882 United Kingdom 216315 26863944809 18964 18300 664 18200 69682 16448253048 United States 498102 97713161627 42509 39236 3273 193620 790512 39725642000 Source: All data come from Estevadeordal (1993) with the exception of Capital (2) and GDP, which are calculated as described in the appendix. 30 31 AppendixTable A2 Aggregated Net Trade Data industry Argentina Australia Austria Belgium Canada Denmark Finland France Germany 1 262729078 24713358 -35245400 -50189375 -7715612 -16332940 -7347680 -113819988 -449456340 2 29783816 46378436 -4604200 -94890796 111106412 -27276340 -18439690 -123061754 -184988310 3 -2786537 -6760430 58675200 6102272 -20349974 945100 -3735590 8767140 61264410 4 -13982211 -9724345 5843200 -10878459 -7461685 -965640 -2202670 -5175114 -922760 5 -7199793 -5066915 -9476200 -3144875 -7187749 -1935180 -1325060 -7704661 -3662520 6 44155620 36650028 3039200 -1038004 1087594 47221200 -936320 75703 -19234900 7 -2516019 17751641 8759000 -8955112 16545352 64432680 6639930 -4150317 -88429940 8 -9930061 -13410690 -29060400 -19748011 -1279668 -5218200 -4473930 -59241682 -95651020 9 103773 51660546 -8844600 -404434 42850417 -420940 0 -1329598 -99568840 10 -30771219 -26619309 -4253000 30944458 -114208547 -7189260 319200 9094757 167501640 11 -50931051 -57602499 -18118400 -5411796 -43253975 -7093320 -5782080 -32309826 367096330 12 -25449768 -19619499 -994200 21297067 -18923271 -2548000 -693310 36507793 29545110 13 -3761695 -4737494 -18996600 2948531 -21060619 -2634580 -6931580 -42193281 -67737070 14 -41554782 -8788333 15534800 2781045 -21054578 -1426100 -4872550 -8287471 32670810 15 -10921625 -7075358 10526800 -11558376 -13230032 -19053580 -1442290 -34886820 -29753720 16 1394286 5306824 -32594400 -13528352 -37134578 -2635880 139080 -102117972 99590230 17 -8008836 -7673949 -15072000 -8892821 -25172602 -9396660 -4211540 3877913 4392080 18 -21474811 -12583177 50784400 -24191654 17208108 -12013820 42423770 -7405877 -76829660 19 -7072163 -9779652 4965200 3851134 3294813 -1723800 13024120 8459327 53550900 20 24874641 56245732 -93602000 -1049362 -76075062 -23457460 -12121620 -52277768 -278086330 21 -9855328 -22136838 10812000 -857960 -28041440 -77480 0 52875132 77806240 22 -2331430 372169 -7654000 3200187 -9547428 -3258580 -800470 21944554 47137810 23 -1055082 -4057488 0 0 -4612682 0 0 0 35384120 24 -1172967 -4642102 -6143600 -4152152 -11007837 -1720680 -2401790 10621380 -2765980 25 -20448524 -45082090 -11641400 -2558650 -39122047 -2709460 -2029010 148921589 99059620 industry Italy Netherlands Norway Portugal Spain Sweden Switzerland United Kingdom United States 1 59440453 -45142041 -645325 -662978 29399006 -12417245 -16371917 -305123912 -230173551 2 -74820263 -98790313 -15976750 -4288024 -19994046 -14480834 -30403622 -387522214 194716287 3 601132 19603896 -3914600 -1875528 245014 -873841 -5952892 -115871498 4543660 4 16177567 -505826 -2380000 8435380 28767670 -2430773 -6940337 877803 -16326757 5 -6473583 -1140492 -1088675 -483210 0 -3071769 -1794590 -22628597 12667153 6 7814 13329802 4512100 62191 381488 1721462 -5829881 -268394176 127302854 7 21798344 24226459 2755575 51881 -3125106 12294954 8810831 -203740619 -3259296 8 -22389974 24621517 25181225 -1447071 -2089516 -13693790 -1311993 -137604237 -150977884 9 -2033406 -2773496 6737700 1058932 27972461 17590060 -11569575 -82836163 -33849493 10 -21716980 -85477893 -8583825 -3590762 -10669193 12054407 -8891995 144940033 66954708 11 -23374892 -19178107 -13599825 -2530138 -22704268 6402305 3393865 212117222 259669692 12 -1035003 -2728239 -6701650 -1338856 -15926407 -2833996 -524158 78327619 53081824 13 -20487763 -11157714 1689500 -1203797 18472634 -6556729 -2985329 -97521358 47678995 14 -69543598 -24744369 -604675 -1275552 -3531411 4281636 -3892699 -9181254 -59993216 15 -10842442 -6491365 -2679500 -692416 -3073517 -7619373 -2395216 -40202182 139622325 16 0 -33056118 -10418175 -3600640 -12245756 -27119399 -18012908 260607586 63623548 17 -23785048 -22609783 -5028550 -1984111 -6253757 -14916308 -4825764 -29565533 -15594989 18 -20557320 -33283782 16718550 2423431 1079650 50602041 -6548819 -177089886 48717279 19 -5399686 30798803 7172500 -732444 -519098 35837194 -1640590 -43023597 23287590 20 11900701 -16959667 -14361725 -9723827 -18916657 -31575793 26319929 50143716 230353846 21 9713860 -10354121 -1563200 -229295 -387951 -3393982 -5252617 57623518 -13028488 22 -13623499 3787985 -2040825 -1970879 -1022017 -4475349 -4109474 -46069529 28355886 23 -32411 -2338175 0 58645 2711274 353385 -192104 24540653 19818804 24 -1623512 113807 -662800 -336748 -2342751 -3148295 -1116946 -96943878 -89838545 25 -19258467 197033280 -3433600 -1496908 1850857 516767 11961131 50822128 -83861946 Source: Estevadeordal (1993). 32 Table A3 Description of Standard International Trade Classification codes (2 Digit, Rev.1) SITC Group 0: Food and Live Animals 56 Fertilizers, manufactured 00 Live Animals 57 Explosives and pyrotechnic products 01 Meat and meat preparations 58 Plastic materials, regenerated cellulose and 02 Dairy products and eggs artificial resins 03 Fish and fish preparations 59 Chemical materials and products, n.e.s. 04 Cereals and cereal preparations 05 Fruit and vegetables SITC Group 6: Manufactured Goods Classified 06 Sugar, sugar preparations and honey Chiefly by Material 07 Coffee, tea, cocoa, spices and manufactures 61 Leather, leather manufactures, n.e.s., and thereof dressed furskins 08 Feeding stuff for animals (not including 62 Rubber manufactures, n.e.s. unmilled cereals) 62 Wood and cork manufactures (excluding 09 Miscellaneous food preparations furniture) 64 Paper, paperboard and manufactures thereof SITC Group 1: Beverages and Tobacco 65 Textile yarn, fabrics, made-up articles and 11 Beverages related products 12 Tobacco and tobacco manufactures 66 Non-metallic mineral manufactures, n.e.s. 67 Iron and Steel SITC Group 2: Crude Materials, Inedible, Except 68 Non-ferrous metals Fuels 69 Manufactures of metal, n.e.s. 21 Hides, skins and furskins, undressed 22 Oil-seeds, oil nuts and oil kernels SITC Group 7: Machinery and Transport 23 Crude rubber Equipment 24 Wood, lumber and cork 71 Machinery, other than electric 25 Pulp and waste paper 72 Electric machinery, apparatus and appliances 26 Textile fibres 73 Transport equipment 27 Crude fertilizers and crude minerals (excluding coal and petroleum) SITC Group 8: Miscellaneous Manufactured 28 Metalliferous ores and metal scrap Articles 29 Crude animal and vegetable materials, n.e.s. 81 Sanitary, plumbing, heating and lighting fixtures and fittings SITC Group 3: Mineral Fuels, Lubircants and 82 Furniture Related Materials 83 Travel goods, handbags and similar articles 32 Coal, coke and briquettes 84 Clothing 33 Petroleum and petroleum products 85 Footwear 34 Gas, natural and manufactured 86 Professional, scientific and controlling instruments; photographic and optical goods; SITC Group 4: Animal and Vegetable Oils and watches and clocks Fats 89 Miscellaneous manufactured articles 41 Animal oils and fats 42 Fixed vegetable oils and fats SITC Group 9: Commodities not Classified 43 Animal and vegetable oils and fats, processed, According to Kind and waxes 95 Firearms of war and ammunition thereof SITC Group 5: Chemicals 51 Chemical elements and compounds 52 Mineral tar and crude chemicals from coal, petroleum and natural gas 53 Dyeing, tanning and couloring materials 54 Medicinal and pharmaceutical products 55 Essential oils and perfume materials 33 Appendix Table A4 Aggregated Input-Output Table industry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 9102 1792 163 57 202 3033 797 261 0 0 0 0 0 0 0 0 308 0 4 1117 0 30 0 0 0 2 686 354 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 27 50 11 6 0 0 30 140 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 4 0 0 0 35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 19 92 0 0 0 354 17 0 0 0 0 0 0 0 0 0 79 0 0 20 0 247 0 0 0 7 0 27 0 0 0 0 0 36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 22 0 0 0 0 0 67 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 7 274 0 0 267 0 0 0 0 0 0 0 0 0 0 0 0 10 46 0 0 0 0 0 0 0 43 1157 1315 189 0 13 76 89 0 0 0 0 0 0 0 2 0 11 522 28 1 11 0 0 51 101 15 17 503 1812 0 7 76 30 11 50 24 110 7 19 14 17 47 12 744 82 26 11 0 77 0 0 99 121 165 1002 17 187 131 763 9 337 0 0 0 0 0 0 0 13 0 0 0 0 5 0 0 13 0 24 287 47 622 0 0 0 41 0 0 0 0 0 0 0 0 14 7 0 1 21 0 0 0 19 0 26 22 29 3 20 3 0 54 0 9 0 0 1 0 0 0 15 2 6 6 2 0 5 1 4 5 50 40 85 18 36 1029 1 23 4 5 5 0 0 0 1 10 16 0 14 15 10 1 15 5 9 19 342 105 449 29 80 84 228 49 15 37 41 2 6 2 8 24 17 356 0 0 0 0 159 0 0 13 3 0 10 0 1 13 23 194 0 6 58 0 47 0 2 25 18 258 0 0 0 13 0 0 0 15 0 110 139 0 0 35 36 48 975 0 0 0 0 25 0 14 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 287 0 0 0 0 0 233 20 47 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 61 0 1205 1255 1 6 189 1 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 145 0 0 0 0 22 75 0 0 0 0 0 0 0 0 0 0 19 0 0 0 0 8 17 0 6 4 120 482 0 3 23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 233 0 0 24 0 0 0 0 0 0 0 0 0 0 1 153 0 0 0 0 0 0 0 0 0 0 0 19 0 25 21 0 0 0 0 0 0 0 0 0 10 30 0 0 0 0 0 14 0 3 20 0 0 0 184 Output 22147 3810 1201 615 1013 4576 1148 2028 648 3652 10459 8930 1812 806 3004 2471 3272 3432 1244 6163 3371 1309 1379 1138 3445 Source: Leontief (1953b) and authors' calculations. AppendixTable A5 Aggregated Eysenbach Coefficients our Labor per dollar Labor per dollar Unskilled Labor as a Skilled Labor as a Direct Use Direct Use classification of value added of Capital share of Total Labor share of Total Labor Renewable Resources Nonrenewable Resources 1 0.00067 0.000 1.000 1.000 0.001 2 0.00069 0.00058 0.310 0.690 0.495 0.001 3 0.00078 0.00009 0.550 0.450 0.153 0.008 4 0.00024 0.00029 0.459 0.541 0.128 0.004 5 0.00086 0.00094 0.366 0.635 0.653 0.002 6 0.00077 0.00055 0.317 0.683 0.878 0.000 7 0.00070 0.00055 0.275 0.725 0.771 0.002 8 0.00121 0.00082 0.550 0.450 0.211 0.002 9 0.00019 0.000 1.000 0.005 1.000 10 0.00095 0.00049 0.412 0.588 0.000 0.054 11 0.00106 0.00058 0.377 0.623 0.000 0.002 12 0.00097 0.00051 0.370 0.630 0.000 0.001 13 0.00072 0.00034 0.403 0.597 0.000 0.152 14 0.00119 0.00063 0.369 0.631 0.000 0.335 15 0.00094 0.00039 0.405 0.595 0.000 0.512 16 0.00113 0.00066 0.309 0.691 0.007 0.705 17 0.00081 0.00033 0.463 0.537 0.066 0.024 18 0.00128 0.00082 0.265 0.735 0.153 0.001 19 0.00113 0.00069 0.350 0.650 0.099 0.014 20 0.00129 0.00072 0.364 0.636 0.234 0.002 21 0.00128 0.00130 0.747 0.253 0.004 0.001 22 0.00111 0.00056 0.324 0.676 0.002 0.002 23 0.00161 0.00143 0.688 0.312 0.000 0.001 24 0.00091 0.00041 0.553 0.447 0.000 0.004 25 0.00112 0.00080 0.321 0.679 0.001 0.005 Source: Eysenbach (1976) and authors' calculations. 34 Appendix Table A6 Concordance Mapping Our Input-Output SITC Rev. 1 1947 BLS classification classification classification classification 1 1 00,05,08,21,22,29 1,7-10 2 2,4 04 4,24,25 3 5 06 27 4 6 11 28 5 7 12 6,29 6 8 01 2,21 7 9 02 3,22 8 3,10 03,07,09 23,26 9 11,16 28 11-15 10 12,13 67 78-81,92 11 14 69,71,72 94-96,98-102,104-144 12 15,41 73 145-152 13 17,18 68 82-91,93 14 19 27,66 18-20,70-77 15 20,21,24 33,34 17,62,64 16 22,23 32 16,63 17 26 41-43,51-59 48-50,52-61 18 27,28 24,63,82 36-43,162 19 29,30 25,64 44-46 20 32,34 26,65,83 5,30-33,35 21 33 84 34 22 35,37 61 67,68 23 36 85 69 24 38 23,62 51,65,66 25 31,39 81,86,89,9 47,97,103,153-161,163-165 Notes and sources: Authors’ mapping to reconcile the Eysenbach-BLS, Leontief-IO and SITC classification. Appendix Table A7 Industry Classification Descriptions our Leontief's 1919 U.S. Input-Output table classification categories 1 Agriculture 2 Flour & grist mill products; Bread & bakery products 3 Sugar, glucose & starch 4 Liquors & beverages 5 Tobacco manufactures 6 Slaughtering & meat packing 7 Butter, cheese, etc. 8 Other food industries; Canning & preserving 9 Iron mining; Non-Iron metal mining 10 Blast furnaces; Steel works & rolling mills 11 Other iron, steel & electric manufactures 12 Automobiles; Transportation 13 Smelting & refining; Brass, bronze, copper, etc. manufactures 14 Non-metal minerals 15 Petroleum & natural gas; Refined petroleum; Manufactured gas 16 Coal; Coke 17 Chemicals 18 Lumber & timber products; Other wood products 19 Paper & wood pulp; Other paper products 20 Yarn & cloth; Other textile producs 21 Clothing 22 Leather tanning; Other leather products 23 Leather shoes 24 Rubber manufactures 25 Industries, nes; Printing & publishing Note: For Leontief-category numeric equivalents see Leontief (1953b). 35