The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Leontief Paradox

  • Edward E. Leamer
Reference work entry


Using 1947 US input–output tables and data on exports and imports, Leontief (1953) found, to the surprise of the profession, that the capital per worker of US exports was less than the capital per worker of US import substitutes. The response to this empirical ‘paradox’ was the formulation of theory that might explain why a capital abundant country had labour-intensive exports. These were the first (confused) steps in an ongoing process of making the theory and data conform sufficiently to enable us comfortably to claim to understand the basis for international trade.


Factor content of trade Factor mobility Heckscher–Ohlin–Samuelson trade model Leontief paradox 

JEL Classifications


The Heckscher–Ohlin–Samuelson (HOS) model of international trade with two factors of production and two commodities implies that a country will export the commodity that is produced intensively with the relatively abundant factor. Leontief (1953) discovered, to the surprise of the profession, that 1947 US exports were more labour-intensive than US imports in the sense that the capital per man required to produce a $1 million of exports was less than the capital per man required to produce a $1 million in import substitutes. This seemed to conflict sharply with the presupposition that the USA was abundant in capital compared with labour. Leontief’s finding was so startling that it has been called a ‘paradox’, even though the result amounted to at most a single contradiction of the theory and even though no alternative model could be said to conform better with the facts.

Leontief’s finding preceded and apparently stimulated a search of great breadth and intensity for a new theory of trade that could account for his result. It is in fact difficult to find another empirical result that has had as great an impact on the intellectual development of the discipline. Among the explanations of the finding are: (a) high productivity of US workers; (b) capital-biased consumption; (c) factor-intensity reversals; (d) tariffs; (e) abundance of natural resources; ( f) abundance of human capital; (g) technological differences. These developments are surveyed in Chacholiades (1978, pp. 298–306).

It is surprising in retrospect that no one thought to examine the theoretical foundation for Leontief’s inference that the factor content of US trade revealed the United States to be scarce in capital compared with labour, though a clear theory of the factor content of trade was not laid out until Vanek (1968). Vanek’s model of the factor content of trade was first used in an overlooked article by Williams (1970) to criticize Leontief’s inference. The very simple theoretical foundation for the Leontief calculation was clearly laid out in Leamer (1980), which shows that Leontief’s data in fact reveal the United States to have been abundant in capital compared with labour.

Theoretical relationships that can serve as a foundation for studying the relative factor abundance revealed by international trade are the Heckscher–Ohlin–Vanek equations. These equations are derived from the simple identity that net exports of the services of a factor f are the difference between home supply and home demand: Tf= Xf− Mf= Sf− Df, where Tf is the amount of factor f embodied in net exports, Xf is the amount of factor f required to produce the exported commodities, Mf is the amount required to produce the imported commodities, Sf is the domestic supply and Df is the domestic demand. This identity is given empirical content by assuming identical homothetic tastes which implies that domestic demand for factor f is proportional to world supply, Df= sWf, where Wf is the world supply and s is the country’s share of world consumption. With the use of this assumption, the net export equation can be written as
$$ {T}_f/{S}_f=1{-} s\left({W}_f/{S}_f\right). $$
In words, net exports as a share of domestic supply is positively related to factor abundance defined as the share of the world’s total supply Sf/Wf. Accordingly, the relative scarcity of the factors is revealed by the ordering of the net export ratios Tf/Sf. Leamer (1980) shows that, although the net export of both capital and labour services were positive in 1947, the share of domestic supply of capital that was exported exceeded the share of labour exported, and consequently the United States was revealed by trade to be relatively abundant in capital compared with labour. In addition, Leamer (1980) shows that Leontief’s finding that the exports were more capital intensive than imports is compatible with either ordering of factor abundance.

This fully resolves the apparent paradoxical ordering of capital and labour abundance, but a new problem arises. Brecher and Choudhri (1982) note that, if net exports are positive, the overall consumption share s must be less than the abundance ratio Sf/W. If trade is balanced, the consumption share is the ratio of home to world GNP, s = GNP/GNPw. The inequality Sf/Wf> s = GNP/GNPw can be rewritten as GNPw/Wf> GNP/Sf. Thus the United States is revealed by its positive net exports of labour services embodied in commodities to have had a per-capita GNP that is less than the rest of the world. Even after adjusting for the trade surplus, this is impossible to square with the facts. Another way of expressing this new paradox is that the positive export of labour services reveals that labour is abundant compared with other resources on the average since the consumption share s is an average of the abundance ratios.

It is ironic that this is one of the few empirical findings that can be said to have had a decided impact on the course of the profession and at the same time is based on a simple conceptual misunderstanding. The error that is implicit in Leontief’s paradox is the use of an intuitive but false theorem which states that the ordering of capital per man in exports compared with imports reveals the relative abundance of capital and labour. This is true for the simple two-good model, but it is not the case for a multi-commodity reality. There is a lesson to be learned from this experience.

Empirical work requires a fully articulated theoretical foundation. Intuition alone is not enough.

Although the precise form that Leontief’s calculations took is inappropriate, the calculation of flows of factor services embodied in trade remains an interesting activity since these flows can be used to form a proper test of the Heckscer–Ohlin–Samuelson theorem and since the net effect of trade on the demand for factors of production can be an important input into trade policy that is intended to affect the distribution of income.

As it turns out, measurements of 1967 factor contents of trade reported in Bowen, Leamer and Sveikauskas (1987) rather badly violate the HOS model, thus reinvigorating the message of the Leontief paradox: there is something wrong with this model. One thing that is wrong is emphasized by Trefler’s (1995) title: ‘The Case of the Missing Trade’. Given the world’s apparent unequal geographic distribution of capital, labour and land, the HOS model suggests that there should be much more trade than actually occurs. Trefler’s solution to this puzzle is to allow in the model both home bias in consumption and also international productivity differences (for example, the United States is not so labour-scarce when allowance is made for the intensity of work). Also, Conway (2002) finds problems with the measurement of factor scarcity and calls for the model to include factor-specific differences in domestic factor mobility. It seems likely that we have not seen the end of the search for a model that most fully explains the nature of international trade.

See Also


  1. Bowen, H., E. Leamer, and L. Sveikauskas. 1987. Multicountry, multifactor tests of the factor abundance theory. American Economic Review 77: 791–809.Google Scholar
  2. Brecher, R., and E. Choudhri. 1982. The Leontief paradox, continued. Journal of Political Economy 90: 820–823.CrossRefGoogle Scholar
  3. Chacholiades, M. 1978. International trade theory and policy. New York: McGraw-Hill.Google Scholar
  4. Conway, P. 2002. The case of the missing trade and other mysteries: Comment. American Economic Review 92: 394–404.CrossRefGoogle Scholar
  5. Leamer, E. 1980. The Leontief paradox, reconsidered. Journal of Political Economy 88: 495–503.CrossRefGoogle Scholar
  6. Leontief, W. 1953. Domestic production and foreign trade: The American capital position re-examined. Proceedings of the American Philosophical Society 97: 332–349. Reprinted in Readings in international trade, ed. H. Johnson and R. Caves. Homewood: R.D. Irwin. 1968.Google Scholar
  7. Trefler, D. 1995. The case of the missing trade and other mysteries. American Economic Review 85: 1029–1046.Google Scholar
  8. Vanek, J. 1968. The factor proportions theory: The N-factor case. Kyklos 21: 749–756.CrossRefGoogle Scholar
  9. Williams, J. 1970. The resource content in international trade. Canadian Journal of Economics 3: 111–122.CrossRefGoogle Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Edward E. Leamer
    • 1
  1. 1.