This paper is the first application of the singular value decomposition in general equilibrium theory. Every technology matrix can be decomposed into three parts: (1) a definition of composite commodities; (2) a definition of composite factors; and (3) a simple map of composite factor prices into composite goods prices. This technique gives an orthogonal decomposition of the price space into two complementary subspaces: (1) vectors that generate the price cone; and (2) a basis that describe the flats on the production possibility frontier. This decomposition can be used easily to compute Rybczynski effects.

This paper will be published in the International Journal of Economic Theory.



Measuring factors services, not quantities, we examine the technologies and endowments of thirty-nine countries and five factors in 2005. We conduct three tests of the Heckscher-Ohlin-Vanek paradigm: (1) the conventional one; (2) a benchmark where every country has America’s technology; and (3) a test that converts foreign endowments into international efficiency units. The first predicts the direction of trade better than any former study. The second shows no statistically significant evidence of missing trade. The third performs just as well, and it accounts for international differences in both factor prices and unit input requirements.



We develop two simple modifications of Heckscher-Ohlin-Vanek theory for countries with heterogeneous technologies: virtual endowments and modified Rybczynski effects. Virtual endowments predict factor trade using a reference country’s technology. Modified Rybczynski effects show the domestic factor content of changes in foreign endowments. The empirical implications are striking. There is no missing trade, and we predict the direction of trade with significance levels exceeding 99%. We make no assumptions about home bias in consumption, not traded goods, trade costs, or trade in intermediate inputs. We make no corrections to measured endowments and estimate nothing; the data speak for themselves.



Exploiting recent international data on factor usage by sector, we provide the first direct test of Leontief’s notion of factor-specific productivity differences. This test strongly rejects Trefler’s (1993) generalization of Leontief’s idea. Hence tests of the Heckscher-Ohlin paradigm cannot be based upon such simple technological differences across countries.



Technology matrices are measured with error when researchers combine data on intermediate inputs with those on direct factor requirements from disparate sources. This error is compounded when factor prices differ across countries, since it is no longer appropriate to measure factors in homogeneous physical units. It is more accurate empirically and more cogent theoretically to compute flows of factor services, measured at local factor prices that incorporate international productivity differences. In the long run, production techniques adapt so that every country is competitive in almost every good. Since capital and labor are complementary inputs in
almost every industry, a country that is physically scarce in a factor may well be measured as abundant in its services.