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International capital mobility, the factor content of trade and Leontief paradoxes
Joumdof INTERNATIOWAL ECOfNitilCS EL%VIER
Journal of International Economics 39 (1995) 175-183
International capital mobility, the factor content of trade and Leontief paradoxes James D. Gaisford Department
of Economics, University of Calgary, 2500 University Drive NW, Calgary, Alberta
T2N lN4, Canada
Received July 1991, revised version received January 1995
Abstract In a world where capital is internationally mobile, care is required in interpreting data on the factor content of trade. US data for the 1960sseems to suggest that the US should have been abundantly endowed with labour relative to capital in comparison with the world as a whole. Ethier and Svensson’s (1986, J. International Economics 20, pp.21-42) work on international factor mobility provides the basis for an interesting re-examination of such Leontief paradoxes. Given that the US exports capital services directly, its exports of goods would, on average, be intensive in its relatively abundant internationally immobile factors and, thus, need not be capital intensive. Key words: Capital mobility; Factor content of trade; Foreign investment; International factor mobility; Leontief paradox JEL classification:
Fll; F21
1. Introduction
In a world where capital is internationally mobile, care is required in interpreting data on the factor content of trade. For example, Leontief paradoxes in the post-war US trade pattern require a significant reinterpretation in the light of capital mobility. In the absence of capital mobility, the data in Baldwin (1971) and Bowen et al. (1987) on the factor content of trade in goods in the 1960s would predict that the US was abundantly 0022-1996/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDZ 0022-1996(95)01373-3
176
J.D. Gaisford
I Journal of International
Economics 39 (1995) 175-183
endowed with labour relative to capital in comparison with the world as a whole. This prediction, which is at odds with both perceptions and observations of factor endowments, does not follow if the US was exporting capital directly (via “foreign investment”) as well as indirectly (via the capital content of trade in goods). Given that the US exports capital services directly, its exports of goods would, on average, be intensive in its relatively abundant internationally immobile factor(s) and, thus, need not be capital intensive. The Leontief paradox, however, does not vanish. When capital is internationally mobile, the traditional tests, which focus exclusively on factors indirectly exported through trade in goods, imply that the endogenously determined capital-labour deployment ratio for the US should have been less than that of the world. Such paradoxes, however, may be the result of non-prohibitive costs associated with capital mobility. The second section of the paper connects Ethier and Svensson’s (1986, p.39) mobile-factor extension of the Heckscher-Ohlin-Vanek (HOV) theorem with Learner’s (1980) analysis of “trade-revealed factor abundance”. The third section identifies some potential pitfalls in empirical data on the factor content of trade and reinterprets Leontief paradoxes. The fourth section concludes the paper. 2. Capital mobility and the factor content of trade: Theory Ethier and Svensson (1986, esp. p.39) provide the key point of departure for re-examining Leontief-type paradoxes by adapting the HOV theorem (see Vanek, 1968) in a manner that accommodates international factor mobility. The extended HOV theorem can be formulated and supported as follows. Extended HOV Theorem. Suppose that: Al. All goods and a subset of factors can be internationally traded without cost. AZ. There are at least as many international markets (i.e. for goods plus internationally mobile factors) as there are (internationally immobile plus mobile) factors. A3. All markets are perfectly competitive and all countries utilize the same constant-returns-to-scale, single-output production technologies. A4. All countries’ domestic endowments of internationally immobile factors lie within the same cone of diversification. And A5. All individuals have identical homothetic tastes. Then, a country’s overall-direct plus indirect-net exports of a factor are positive if and only if it is abundantly endowed with that factor.
Since assumptions Al-A4 are sufficient to establish international factor price equalization (see Ethier and Svensson, 1986, pp.2529), all countries
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will adopt the same cost-minimizing factor proportions. Thus, there will be a matrix of (mobile and immobile) factor utilization coefficients, A, that is common to all countries. The standard model links the factor content of trade to factors deployed in the Home country. AT=uh-wW
(1)
Here, T is the vector of net exports of goods by the Home country, uh is the vector of factors deployed in Home, uw is the factor deployment (and endowment) vector for the world as a whole and s is Home’s share of world expenditure. Measures of the stocks of internationally mobile factors can be adjusted for inflows or outflows. In particular, cumulative domestic savings may be greater than or less than domestic capital accumulation. u = uh + uf
(2)
Here, u is Home’s “factor endowment” or ownership vector and cf is the vector of (net) quantities of Home’s factors that are deployed abroad. The model can now be adjusted to explicitly allow for international factor mobility. AT+v’=u-su”
(3)
For any factor i, indirect net exports, n
2, = C ai,T, g=l (i.e. the factor content in goods g = 1, . . . . n), plus direct net exports, r~f, must be equal to the difference between domestic factor ownership, ui, and domestic factor consumption, WY. Since the Home country is abundantly endowed in a particular factor if and only if its share of the world endowment of that factor exceeds its share of world expenditure (i.e. ui/uw > s), the extended HOV theorem is confirmed.’ The extended HOV theorem implies that a capital-abundant country could have negative indirect net exports of capital provided that its direct exports of capital through foreign investment were sufficiently large. None the less, HOV system (3) implies that a country must indirectly export its abundant immobile factors.
’ Further, suppose that Home is said to deploy a factor extensively in its domestic production whenever its domestic deployment of the factor relative to that of the world as a whole exceeds its share of world expenditure (i.e. $1~: >s). According to HOV system (1). a country indirectly exports a factor if and only if it deploys the factor extensively.
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The possibility of international factor mobility can now be incorporated into Leontief-Learner links (see Learner, 1980) between a country’s exogenous relative factor endowments and its endogenous overall net factor exports. Corollary 1. Given assumptions Al -A5, a country is abundantly endowed with factor i relative to factor j (i.e. uilui > v~/u~) if and only if its overall-indirect plus direct-net-export to endowment ratio for factor i exceeds that for factor j (i.e. (zi + v~,)lui > (zj + u~)/uj). This Corollary follows from HOV system (3) which implies that Home is abundantly endowed in capital relative to labour if and only if its capitallabour endowment ratio exceeds its capital-labour ratio in consumption, i.e. ‘i
2, I
uj
-q-v;
VW =I
-
zi
-
u;
u,y
With capital (IS) but not labour (L) internationally mobile, Home would be abundant in capital relative to labour if and only if its overall net-export to endowment ratio for capital exceeds its indirect net-export to endowment ratio for labour (i.e. (zk + u~)/u, >z,/u,). Thus, Home must be abundantly endowed with capital relative to labour in the simple case where it has positive overall net exports of capital but negative net exports of labour. If Home is abundantly endowed with capital relative to labour and it has positive (negative) overall net exports of both factors, then its ratio of overall net exports of capital to indirect net exports of labour, (zK + r&/z,, must be greater (less) than its capital-labour endowment ratio, u,Iu,. Whenever the data violates Corollary 1, it can be said that there is a trade-versus-endowment Leontief paradox. There are also Leontief-Learner relationships between a country’s endogenous factor deployment levels and its endogenous indirect net factor exports. Corollary ly relative net factor for factor
2. Given ~surnp~o~ Al -A$ a county deploys factor i extensiveto factor j (i.e. $1~~ > ~~~u~) if and only if the ratio of its indirect exports to its domestic factor deployment for factor i exceeds that j (i.e. .zilu~ > zilu~).
Corollary 2 follows from HOV system (1) in the same way that Corollary 1
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follows from system (3).* Given that capital is internationally mobile but labour is not, Home would deploy capital extensively relative to labour if and only if the ratio of its indirect net exports of capital to its capital deployment exceeds the ratio of its indirect net exports of labour to its labour endowment (i.e. z,/vh, > zt/vL). When Home has positive indirect net exports of capital but negative net exports of labour, it must deploy capital extensively relative to labour in domestic production. If Home deploys capital extensively relative to labour and it has positive (negative) indirect net exports of both factors, then its ratio of indirect net exports of capital to labour, zK/zL, must be greater (less) than its capital-labour deployment ratio, r&/v;. Whenever the data are found to violate Corollary 2, there is a trade-versus-deployment Leontief paradox. 3. Leontief paradoxes and capital mobility: Evidence It appears that economists who have used data on trade and endowments to test either the weak, inequality implications of the factor proportions theory (e.g. Leontief, 1953; Baldwin, 1971; Learner, 1980) or the strong, equality implications (e.g. Learner, 1984; Maskus, 1985; Bowen et al., 1987) have always implicitly assumed that capital is internationally immobile. Given the premise of internationally immobile capital, Learner (1980) has shown that Leontief’s (1953) data concerning the factor content of US trade for 1948 actually imply that the US is abundant in capital relative to labour as one would expect.3 Nevertheless, Learner also notes that Leontief-type paradoxes do exist in Baldwin’s (1971) trade data from the early 1960s. The data of Bowen et al. (1987) for the mid 1960s would reveal a similar paradox. There is a serious danger that such Leontief-type paradoxes will be misinterpreted unless the implications of international capital mobility are taken into account. The 1967 data in Table 1 is drawn primarily from Bowen et al. (1987, pp.806-807). They calculated capital stocks by adding up a country’s gross domestic investment net of 13.33% depreciation starting in 1949 and they treated the resultant capital stocks as if they were “capital endowments” because they implicitly assumed that capital was internationally immobile.
* In any case where the two factors in question are internationally immobile, it is clear that Corollaries 1 and 2 would be equivalent because factor endowment and deployment levels coincide and direct factor exports would be absent. The applicability of HOV relationships in such cases has been examined in an interesting recent paper by Wood (1994). 3Brecher and Choudhri (1982) indicate that other paradoxes persist in Leontiefs data.
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Table 1 US factor endowments, factor deployment levels and net factor exports, 1967
1. “World” factor endowment 2. US Domestic factor deployment 3. US national factor endowment 4. US direct net exports of factors 5. US indirect net exports of factors 6. US overall net exports of factors 7. US indirect-net-export to deployment ratio 8. US overall-net-export to endowment ratio
Capital (Millions of US dollars)
Total labour (Millions of person-years)
Ratio of capital to total labour (US dollars per person-year)
1,905,647 785,933 834,708 +48,775 +5,761 +54,536 +0.73303%
355.893 76.595 76.595 0 +0.764413 +0.764413 +0.99799%
5,355 10,261 10,898 7,537 71,344
+6.53356%
+0.9979970
-
-
Sources: Rows 1, 2, and 5 are from Bowen et al. (1988, pp.806-807, table Al). The “World”
factor endowments pertain to the restricted world comprised of the 27 countries in the Bowen et al. data set. Many less-developed countries and oil-producing countries are omitted as are all communist countries. US direct exports of capital in row 4 are calculated by subtracting foreign long-term investments in the US of $27,006m from US private long-term investments abroad of $75,78lm for the 1966 year end (US Bureau of the Census, 1970, p.765, table 1207).
With international capital mobility, these reported capital stocks must be reinterpreted as endogenous capital deployment levels. Measures of US direct exports of capital were obtained by deducting (cumulative) foreign long-term investments in the US from US long-term investments abroadP The US capital endowment was then calculated by adding the direct net export of capital to the capital deployment level. When capital is internationally mobile, the 1967 data in Table 1 does not provide grounds for inferring that the US was abundantly endowed in labour relative to capital. Since the US overall (direct plus indirect) net-export to endowment ratio for capital (i.e. +6..53%) easily exceeds its overall-netexport to endowment ratio for labour (i.e. +l.OO%), the US is revealed via Corollary 1 to be abundantly endowed in capital relative to labour. Since the
‘While it would be desirable to exclude long-term government bonds from the portfolio component of long-term investments on both the asset and liability sides, the data would only permit the desired correction for the liability side. Alternatively, if direct net exports of capital were measured using only cumulative foreign direct investment, inaccuracies would arise because firms are not 100% domestically owned. The qualitative findings of the paper, however, would be unaltered if the foreign-direct-investment method of calculation were used.
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US capital-labour endowment ratio (i.e. $l0,898/person-year) does in fact exceed that of the world (i.e. $5,355/person-year), there is not a tradeversus-endowment paradox.5 Table 1 indicates that the US indirect-net-export to deployment ratio for capital (i.e. +0.73%) is less than its indirect-net-export to deployment ratio for labour (i.e. +l.OO%). Consequently, factor proportions theory predicts via Corollary 2 that the US should not deploy capital extensively relative to labour in comparison with the world as a whole. Since the US capitallabour deployment ratio (i.e. $10,26l/person-year) is, in fact, far greater than the world’s capital-labour endowment ratio (i.e. $5,355/person-year), Corollary 2 is violated and there is a trade-versus-deployment paradox.6 Those who mistakenly treat capital as if it were internationally immobile would incorrectly conclude that such data on the factor content of trade indicate that the US should have been poorly endowed with capital. The real paradox, however, concerns why the endogenous domestic deployment of capital in the US remained so high while simultaneously the endogenous indirect net exports of capital by the US were so low in comparison with labour. The situation in 1962 appears to have been similar to that in 1967. In 1962, US direct net exports of capital were $34.069 billion (US Bureau of the Census 1970, 765, table 1207). US indirect net exports of capital were $4.319 billion and US indirect exports of labour were 787,371 person-years (see Baldwin, 1971 and Learner, 1980). These data are consistent with Corollary 1. The ratio of US overall (direct plus indirect) net exports of capital to net exports of labour was $48,773/person-year. This number is easily in excess of the US capital-labour endowment ratio of $10,898/ person-year for 1967 (Table 1) and, thus, it would also be far in excess of any estimate of the US capital-labour endowment ratio for 1962. The data, however, are inconsistent with Corollary 2. The ratio of US indirect net exports of capital to indirect net exports of labour was $5,485/person-year which was less than the capital-labour deployment ratio of $6,949/personyear for 1947 (Travis, 1964) and, in all likelihood, less than the capital-
’ For other countries in the Bowen et al. (1987) data set such as Canada and the UK, it could be shown that there are endowment-versus-trade paradoxes that have not previously been noticed because direct net exports of capital have been ignored (see Gaisford, 1993). ‘The Bowen et al. (1987) data on the factor content of trade also suggests that the US is abundantly endowed in capital relative to skilled (scientific/technical plus managerial) labour which, somewhat surprisingly, is in accord with the endowment data. Nevertheless, the trade data indicate that the US deployment of capital relative to skilled labour should be less than that of the world which is in contradiction with the data.
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labour deployment ratio in 1962. Once again, there is a trade-versusdeployment paradox, but there is not a trade-versus-endowment paradox. 4. Conclusion The persistence of paradoxes in the trade data probably should not be surprising. Ultimately, any of these paradoxes indicate that assumptions that underlie the Heckscher-Ohlin-Vanek theorem do not adequately describe the world economy. Markusen and Melvin (1984, pp.194-195) have argued that it is rash to expect that the factor-proportions theory of trade could fully explain all observed trading patterns. For example, economies of scale and differences in tastes and technologies are likely to be empirically important causal factors even though they must be assumed away in order to isolate the effects of differing factor endowments. This paper has shown that when capital is internationally mobile, a careful reassessment of paradoxes in the trade data would be necessary even if the other assumptions of factor proportions theory were valid. International capital mobility appears to have been extremely important during the post-war period. Certainly, this era has witnessed the rapid proliferation of multinational enterprises (MNEs). During the first two decades after the war, the MNEs were especially important facilitators of international capital mobility. European capital markets were a much less important source of financing for US direct investment than is currently the case. Since the US direct exports of capital services were large in the 1960% it certainly seems reasonable to argue that US exports of goods need not have been capital intensive. Rather, US exports of goods should have tended to be intensive in its relatively abundant internationally immobile factors. It has also been shown that when the 1960sdata on US indirect net factor exports are evaluated in the light of the factor proportions theory of trade, the US capital-labour deployment ratio would be expected to be less than the capital-labour endowment ratio of the world despite the evidence to the contrary. It seems likely that this type of trade-versus-deployment paradox may, at least in part, be related to the nature of capital mobility. Although capital is mobile between countries, there are significant barriers to international capital mobility. Many countries still place restrictions on foreign direct investment and there are typically differences in the tax treatment of capital which is invested domestically and that which is invested abroad. Further, subsidiaries that are under the jurisdiction of foreign governments typically face a higher risk of expropriation and portfolio investments abroad may also be subject to additional risks from foreign exchange controls and the like. Thus, impediments to capital mobility may help
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explain why the domestic deployment of capital remained so high in the 1960~~ Given that the natural and policy barriers to capital mobility seem to be declining over time, tests of the factor proportions theory using more recent data might lead to fewer anomalies. Acknowledgements
The author is grateful to Professor J. Black and two anonymous referees for a series of extremely useful and insightful suggestions. The author, however, is responsible for any remaining short-comings in the paper. References Baldwin, R.E., 1971, Determinants of the commodity structure of US trade, American Economic Review 61, 126-146. Bowen, H.P., E.E. Learner and L. Sveikauskas, 1987, Multicountry, multifactor tests of factor abundance theory, American Economic Review 77, 791-809. Brecher, R.E. and E.U. Choudhri, 1982, The Leontief paradox, continued, Journal of Political Economy 90, 820-823. Ethier, W.J. and L.E.O. Svensson, 1986, The theorems of international trade with factor mobility, Journal of International Economics 20, 21-42. Gaisford, J.D., 1993, International capital mobility, the factor content of trade and Leontief paradoxes, presented at the Canadian Economics Association meetings, Ottawa. Learner, E.E., 1980, The Leontief paradox, reconsidered, Journal of Political Economy 88, 495-503. Learner, E.E., 1984, Sources of international comparative advantage: Theory and evidence (MIT Press, Cambridge, MA). Leontief, W.W., 1953, Domestic production and foreign trade: The American capital position re-examined, Proceedings of the American Philosophical Society 97, 332-349. Markusen, J.R. and J.R. Melvin, 1984, The theory of international trade and its Canadian applications (Butterworths, Toronto). Maskus, K.E., 1985, Tests of the Heckscher-Ohlin-Vanek theorem: The Leontief commonplace, Journal of International Economics 19, 201-212. Travis, W.P., 1964, The theory of trade and payments (Harvard University Press, Cambridge, MA). US Bureau of the Census, 1970, Statistical Abstracts of the United States (Washington, DC). Vanek, J., 1968, The factor proportions theory; The n-factor case, Kyklos 21, 749-754. Wood, A., 1994, Give Heckscher and Ohlin a Chance! Weltwirtschaftliches Archiv 130, 20-49. ’ It can also be observed that when there are barriers to trade and capital mobility, factor price equalization will not occur and each country will use different cost-minimizing production techniques. Ethier and Svensson (1986) show that the extended Heckscher-Ohlin results for such situations are only correlations.
Journal of International Economics 39 (1995) 175-183
International capital mobility, the factor content of trade and Leontief paradoxes James D. Gaisford Department
of Economics, University of Calgary, 2500 University Drive NW, Calgary, Alberta
T2N lN4, Canada
Received July 1991, revised version received January 1995
Abstract In a world where capital is internationally mobile, care is required in interpreting data on the factor content of trade. US data for the 1960sseems to suggest that the US should have been abundantly endowed with labour relative to capital in comparison with the world as a whole. Ethier and Svensson’s (1986, J. International Economics 20, pp.21-42) work on international factor mobility provides the basis for an interesting re-examination of such Leontief paradoxes. Given that the US exports capital services directly, its exports of goods would, on average, be intensive in its relatively abundant internationally immobile factors and, thus, need not be capital intensive. Key words: Capital mobility; Factor content of trade; Foreign investment; International factor mobility; Leontief paradox JEL classification:
Fll; F21
1. Introduction
In a world where capital is internationally mobile, care is required in interpreting data on the factor content of trade. For example, Leontief paradoxes in the post-war US trade pattern require a significant reinterpretation in the light of capital mobility. In the absence of capital mobility, the data in Baldwin (1971) and Bowen et al. (1987) on the factor content of trade in goods in the 1960s would predict that the US was abundantly 0022-1996/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDZ 0022-1996(95)01373-3
176
J.D. Gaisford
I Journal of International
Economics 39 (1995) 175-183
endowed with labour relative to capital in comparison with the world as a whole. This prediction, which is at odds with both perceptions and observations of factor endowments, does not follow if the US was exporting capital directly (via “foreign investment”) as well as indirectly (via the capital content of trade in goods). Given that the US exports capital services directly, its exports of goods would, on average, be intensive in its relatively abundant internationally immobile factor(s) and, thus, need not be capital intensive. The Leontief paradox, however, does not vanish. When capital is internationally mobile, the traditional tests, which focus exclusively on factors indirectly exported through trade in goods, imply that the endogenously determined capital-labour deployment ratio for the US should have been less than that of the world. Such paradoxes, however, may be the result of non-prohibitive costs associated with capital mobility. The second section of the paper connects Ethier and Svensson’s (1986, p.39) mobile-factor extension of the Heckscher-Ohlin-Vanek (HOV) theorem with Learner’s (1980) analysis of “trade-revealed factor abundance”. The third section identifies some potential pitfalls in empirical data on the factor content of trade and reinterprets Leontief paradoxes. The fourth section concludes the paper. 2. Capital mobility and the factor content of trade: Theory Ethier and Svensson (1986, esp. p.39) provide the key point of departure for re-examining Leontief-type paradoxes by adapting the HOV theorem (see Vanek, 1968) in a manner that accommodates international factor mobility. The extended HOV theorem can be formulated and supported as follows. Extended HOV Theorem. Suppose that: Al. All goods and a subset of factors can be internationally traded without cost. AZ. There are at least as many international markets (i.e. for goods plus internationally mobile factors) as there are (internationally immobile plus mobile) factors. A3. All markets are perfectly competitive and all countries utilize the same constant-returns-to-scale, single-output production technologies. A4. All countries’ domestic endowments of internationally immobile factors lie within the same cone of diversification. And A5. All individuals have identical homothetic tastes. Then, a country’s overall-direct plus indirect-net exports of a factor are positive if and only if it is abundantly endowed with that factor.
Since assumptions Al-A4 are sufficient to establish international factor price equalization (see Ethier and Svensson, 1986, pp.2529), all countries
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will adopt the same cost-minimizing factor proportions. Thus, there will be a matrix of (mobile and immobile) factor utilization coefficients, A, that is common to all countries. The standard model links the factor content of trade to factors deployed in the Home country. AT=uh-wW
(1)
Here, T is the vector of net exports of goods by the Home country, uh is the vector of factors deployed in Home, uw is the factor deployment (and endowment) vector for the world as a whole and s is Home’s share of world expenditure. Measures of the stocks of internationally mobile factors can be adjusted for inflows or outflows. In particular, cumulative domestic savings may be greater than or less than domestic capital accumulation. u = uh + uf
(2)
Here, u is Home’s “factor endowment” or ownership vector and cf is the vector of (net) quantities of Home’s factors that are deployed abroad. The model can now be adjusted to explicitly allow for international factor mobility. AT+v’=u-su”
(3)
For any factor i, indirect net exports, n
2, = C ai,T, g=l (i.e. the factor content in goods g = 1, . . . . n), plus direct net exports, r~f, must be equal to the difference between domestic factor ownership, ui, and domestic factor consumption, WY. Since the Home country is abundantly endowed in a particular factor if and only if its share of the world endowment of that factor exceeds its share of world expenditure (i.e. ui/uw > s), the extended HOV theorem is confirmed.’ The extended HOV theorem implies that a capital-abundant country could have negative indirect net exports of capital provided that its direct exports of capital through foreign investment were sufficiently large. None the less, HOV system (3) implies that a country must indirectly export its abundant immobile factors.
’ Further, suppose that Home is said to deploy a factor extensively in its domestic production whenever its domestic deployment of the factor relative to that of the world as a whole exceeds its share of world expenditure (i.e. $1~: >s). According to HOV system (1). a country indirectly exports a factor if and only if it deploys the factor extensively.
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The possibility of international factor mobility can now be incorporated into Leontief-Learner links (see Learner, 1980) between a country’s exogenous relative factor endowments and its endogenous overall net factor exports. Corollary 1. Given assumptions Al -A5, a country is abundantly endowed with factor i relative to factor j (i.e. uilui > v~/u~) if and only if its overall-indirect plus direct-net-export to endowment ratio for factor i exceeds that for factor j (i.e. (zi + v~,)lui > (zj + u~)/uj). This Corollary follows from HOV system (3) which implies that Home is abundantly endowed in capital relative to labour if and only if its capitallabour endowment ratio exceeds its capital-labour ratio in consumption, i.e. ‘i
2, I
uj
-q-v;
VW =I
-
zi
-
u;
u,y
With capital (IS) but not labour (L) internationally mobile, Home would be abundant in capital relative to labour if and only if its overall net-export to endowment ratio for capital exceeds its indirect net-export to endowment ratio for labour (i.e. (zk + u~)/u, >z,/u,). Thus, Home must be abundantly endowed with capital relative to labour in the simple case where it has positive overall net exports of capital but negative net exports of labour. If Home is abundantly endowed with capital relative to labour and it has positive (negative) overall net exports of both factors, then its ratio of overall net exports of capital to indirect net exports of labour, (zK + r&/z,, must be greater (less) than its capital-labour endowment ratio, u,Iu,. Whenever the data violates Corollary 1, it can be said that there is a trade-versus-endowment Leontief paradox. There are also Leontief-Learner relationships between a country’s endogenous factor deployment levels and its endogenous indirect net factor exports. Corollary ly relative net factor for factor
2. Given ~surnp~o~ Al -A$ a county deploys factor i extensiveto factor j (i.e. $1~~ > ~~~u~) if and only if the ratio of its indirect exports to its domestic factor deployment for factor i exceeds that j (i.e. .zilu~ > zilu~).
Corollary 2 follows from HOV system (1) in the same way that Corollary 1
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follows from system (3).* Given that capital is internationally mobile but labour is not, Home would deploy capital extensively relative to labour if and only if the ratio of its indirect net exports of capital to its capital deployment exceeds the ratio of its indirect net exports of labour to its labour endowment (i.e. z,/vh, > zt/vL). When Home has positive indirect net exports of capital but negative net exports of labour, it must deploy capital extensively relative to labour in domestic production. If Home deploys capital extensively relative to labour and it has positive (negative) indirect net exports of both factors, then its ratio of indirect net exports of capital to labour, zK/zL, must be greater (less) than its capital-labour deployment ratio, r&/v;. Whenever the data are found to violate Corollary 2, there is a trade-versus-deployment Leontief paradox. 3. Leontief paradoxes and capital mobility: Evidence It appears that economists who have used data on trade and endowments to test either the weak, inequality implications of the factor proportions theory (e.g. Leontief, 1953; Baldwin, 1971; Learner, 1980) or the strong, equality implications (e.g. Learner, 1984; Maskus, 1985; Bowen et al., 1987) have always implicitly assumed that capital is internationally immobile. Given the premise of internationally immobile capital, Learner (1980) has shown that Leontief’s (1953) data concerning the factor content of US trade for 1948 actually imply that the US is abundant in capital relative to labour as one would expect.3 Nevertheless, Learner also notes that Leontief-type paradoxes do exist in Baldwin’s (1971) trade data from the early 1960s. The data of Bowen et al. (1987) for the mid 1960s would reveal a similar paradox. There is a serious danger that such Leontief-type paradoxes will be misinterpreted unless the implications of international capital mobility are taken into account. The 1967 data in Table 1 is drawn primarily from Bowen et al. (1987, pp.806-807). They calculated capital stocks by adding up a country’s gross domestic investment net of 13.33% depreciation starting in 1949 and they treated the resultant capital stocks as if they were “capital endowments” because they implicitly assumed that capital was internationally immobile.
* In any case where the two factors in question are internationally immobile, it is clear that Corollaries 1 and 2 would be equivalent because factor endowment and deployment levels coincide and direct factor exports would be absent. The applicability of HOV relationships in such cases has been examined in an interesting recent paper by Wood (1994). 3Brecher and Choudhri (1982) indicate that other paradoxes persist in Leontiefs data.
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Table 1 US factor endowments, factor deployment levels and net factor exports, 1967
1. “World” factor endowment 2. US Domestic factor deployment 3. US national factor endowment 4. US direct net exports of factors 5. US indirect net exports of factors 6. US overall net exports of factors 7. US indirect-net-export to deployment ratio 8. US overall-net-export to endowment ratio
Capital (Millions of US dollars)
Total labour (Millions of person-years)
Ratio of capital to total labour (US dollars per person-year)
1,905,647 785,933 834,708 +48,775 +5,761 +54,536 +0.73303%
355.893 76.595 76.595 0 +0.764413 +0.764413 +0.99799%
5,355 10,261 10,898 7,537 71,344
+6.53356%
+0.9979970
-
-
Sources: Rows 1, 2, and 5 are from Bowen et al. (1988, pp.806-807, table Al). The “World”
factor endowments pertain to the restricted world comprised of the 27 countries in the Bowen et al. data set. Many less-developed countries and oil-producing countries are omitted as are all communist countries. US direct exports of capital in row 4 are calculated by subtracting foreign long-term investments in the US of $27,006m from US private long-term investments abroad of $75,78lm for the 1966 year end (US Bureau of the Census, 1970, p.765, table 1207).
With international capital mobility, these reported capital stocks must be reinterpreted as endogenous capital deployment levels. Measures of US direct exports of capital were obtained by deducting (cumulative) foreign long-term investments in the US from US long-term investments abroadP The US capital endowment was then calculated by adding the direct net export of capital to the capital deployment level. When capital is internationally mobile, the 1967 data in Table 1 does not provide grounds for inferring that the US was abundantly endowed in labour relative to capital. Since the US overall (direct plus indirect) net-export to endowment ratio for capital (i.e. +6..53%) easily exceeds its overall-netexport to endowment ratio for labour (i.e. +l.OO%), the US is revealed via Corollary 1 to be abundantly endowed in capital relative to labour. Since the
‘While it would be desirable to exclude long-term government bonds from the portfolio component of long-term investments on both the asset and liability sides, the data would only permit the desired correction for the liability side. Alternatively, if direct net exports of capital were measured using only cumulative foreign direct investment, inaccuracies would arise because firms are not 100% domestically owned. The qualitative findings of the paper, however, would be unaltered if the foreign-direct-investment method of calculation were used.
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US capital-labour endowment ratio (i.e. $l0,898/person-year) does in fact exceed that of the world (i.e. $5,355/person-year), there is not a tradeversus-endowment paradox.5 Table 1 indicates that the US indirect-net-export to deployment ratio for capital (i.e. +0.73%) is less than its indirect-net-export to deployment ratio for labour (i.e. +l.OO%). Consequently, factor proportions theory predicts via Corollary 2 that the US should not deploy capital extensively relative to labour in comparison with the world as a whole. Since the US capitallabour deployment ratio (i.e. $10,26l/person-year) is, in fact, far greater than the world’s capital-labour endowment ratio (i.e. $5,355/person-year), Corollary 2 is violated and there is a trade-versus-deployment paradox.6 Those who mistakenly treat capital as if it were internationally immobile would incorrectly conclude that such data on the factor content of trade indicate that the US should have been poorly endowed with capital. The real paradox, however, concerns why the endogenous domestic deployment of capital in the US remained so high while simultaneously the endogenous indirect net exports of capital by the US were so low in comparison with labour. The situation in 1962 appears to have been similar to that in 1967. In 1962, US direct net exports of capital were $34.069 billion (US Bureau of the Census 1970, 765, table 1207). US indirect net exports of capital were $4.319 billion and US indirect exports of labour were 787,371 person-years (see Baldwin, 1971 and Learner, 1980). These data are consistent with Corollary 1. The ratio of US overall (direct plus indirect) net exports of capital to net exports of labour was $48,773/person-year. This number is easily in excess of the US capital-labour endowment ratio of $10,898/ person-year for 1967 (Table 1) and, thus, it would also be far in excess of any estimate of the US capital-labour endowment ratio for 1962. The data, however, are inconsistent with Corollary 2. The ratio of US indirect net exports of capital to indirect net exports of labour was $5,485/person-year which was less than the capital-labour deployment ratio of $6,949/personyear for 1947 (Travis, 1964) and, in all likelihood, less than the capital-
’ For other countries in the Bowen et al. (1987) data set such as Canada and the UK, it could be shown that there are endowment-versus-trade paradoxes that have not previously been noticed because direct net exports of capital have been ignored (see Gaisford, 1993). ‘The Bowen et al. (1987) data on the factor content of trade also suggests that the US is abundantly endowed in capital relative to skilled (scientific/technical plus managerial) labour which, somewhat surprisingly, is in accord with the endowment data. Nevertheless, the trade data indicate that the US deployment of capital relative to skilled labour should be less than that of the world which is in contradiction with the data.
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labour deployment ratio in 1962. Once again, there is a trade-versusdeployment paradox, but there is not a trade-versus-endowment paradox. 4. Conclusion The persistence of paradoxes in the trade data probably should not be surprising. Ultimately, any of these paradoxes indicate that assumptions that underlie the Heckscher-Ohlin-Vanek theorem do not adequately describe the world economy. Markusen and Melvin (1984, pp.194-195) have argued that it is rash to expect that the factor-proportions theory of trade could fully explain all observed trading patterns. For example, economies of scale and differences in tastes and technologies are likely to be empirically important causal factors even though they must be assumed away in order to isolate the effects of differing factor endowments. This paper has shown that when capital is internationally mobile, a careful reassessment of paradoxes in the trade data would be necessary even if the other assumptions of factor proportions theory were valid. International capital mobility appears to have been extremely important during the post-war period. Certainly, this era has witnessed the rapid proliferation of multinational enterprises (MNEs). During the first two decades after the war, the MNEs were especially important facilitators of international capital mobility. European capital markets were a much less important source of financing for US direct investment than is currently the case. Since the US direct exports of capital services were large in the 1960% it certainly seems reasonable to argue that US exports of goods need not have been capital intensive. Rather, US exports of goods should have tended to be intensive in its relatively abundant internationally immobile factors. It has also been shown that when the 1960sdata on US indirect net factor exports are evaluated in the light of the factor proportions theory of trade, the US capital-labour deployment ratio would be expected to be less than the capital-labour endowment ratio of the world despite the evidence to the contrary. It seems likely that this type of trade-versus-deployment paradox may, at least in part, be related to the nature of capital mobility. Although capital is mobile between countries, there are significant barriers to international capital mobility. Many countries still place restrictions on foreign direct investment and there are typically differences in the tax treatment of capital which is invested domestically and that which is invested abroad. Further, subsidiaries that are under the jurisdiction of foreign governments typically face a higher risk of expropriation and portfolio investments abroad may also be subject to additional risks from foreign exchange controls and the like. Thus, impediments to capital mobility may help
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explain why the domestic deployment of capital remained so high in the 1960~~ Given that the natural and policy barriers to capital mobility seem to be declining over time, tests of the factor proportions theory using more recent data might lead to fewer anomalies. Acknowledgements
The author is grateful to Professor J. Black and two anonymous referees for a series of extremely useful and insightful suggestions. The author, however, is responsible for any remaining short-comings in the paper. References Baldwin, R.E., 1971, Determinants of the commodity structure of US trade, American Economic Review 61, 126-146. Bowen, H.P., E.E. Learner and L. Sveikauskas, 1987, Multicountry, multifactor tests of factor abundance theory, American Economic Review 77, 791-809. Brecher, R.E. and E.U. Choudhri, 1982, The Leontief paradox, continued, Journal of Political Economy 90, 820-823. Ethier, W.J. and L.E.O. Svensson, 1986, The theorems of international trade with factor mobility, Journal of International Economics 20, 21-42. Gaisford, J.D., 1993, International capital mobility, the factor content of trade and Leontief paradoxes, presented at the Canadian Economics Association meetings, Ottawa. Learner, E.E., 1980, The Leontief paradox, reconsidered, Journal of Political Economy 88, 495-503. Learner, E.E., 1984, Sources of international comparative advantage: Theory and evidence (MIT Press, Cambridge, MA). Leontief, W.W., 1953, Domestic production and foreign trade: The American capital position re-examined, Proceedings of the American Philosophical Society 97, 332-349. Markusen, J.R. and J.R. Melvin, 1984, The theory of international trade and its Canadian applications (Butterworths, Toronto). Maskus, K.E., 1985, Tests of the Heckscher-Ohlin-Vanek theorem: The Leontief commonplace, Journal of International Economics 19, 201-212. Travis, W.P., 1964, The theory of trade and payments (Harvard University Press, Cambridge, MA). US Bureau of the Census, 1970, Statistical Abstracts of the United States (Washington, DC). Vanek, J., 1968, The factor proportions theory; The n-factor case, Kyklos 21, 749-754. Wood, A., 1994, Give Heckscher and Ohlin a Chance! Weltwirtschaftliches Archiv 130, 20-49. ’ It can also be observed that when there are barriers to trade and capital mobility, factor price equalization will not occur and each country will use different cost-minimizing production techniques. Ethier and Svensson (1986) show that the extended Heckscher-Ohlin results for such situations are only correlations.