The interpretation of cross-section regression tests of the heckscher-ohlin theorem with many goods and factors

Numerous authors have used cross-section regression methods to explain interindustry variations in net exports by means of factor-use ratios as one of the tests of the Heckscher-Ohlin theorem. This paper shows, via an algebraic proof, that the regression procedures used by these authors may be inappropriate tests of the Heckscher-Ohlin theorem. Specifically, the paper shows that in a framework of many goods and factors, inferences about the relative abundance of a particular factor cannot be made by looking at the signs of the regression coefficients unless very stringent requirements are met.