We now turn to a more formal examination of factor price equality across economic regions.6 We introduce the theorems that motivate our empirical framework and develop the testable implications of the theory under a relatively general set of assumptions.
We start by restating the Factor Price Equality theorem of Leamer (1995) which provides the basis for our null and alternative hypotheses:
Proposition 1 The Factor Price Equality Theorem (FPEQ). Regions producing the same mix of products with the same technologies and the same product prices must have the same factor prices for identical factors.
This theorem contains the essential, relevant prediction from the Heckscher-Ohlin trade model for our purposes. At any point in time, regions making identical products with identical technologies should face the same factor prices. If prices for identical factors differed across the regions, then the techniques and/or the products would vary. An important component of the theorem is that the relevant factor prices are those for identical factors. Differences in factor quality across the regions may induce differences in nominal factor prices but should not be taken as evidence of the failure of the prediction of the theorem.
We also want to consider a related prediction on relative factor prices which allows for the possibility that there are region-specific productivity differentials such as those discussed in Trefler (1993):
Proposition 2 Relative Factor Price Equality Theorem (RFPEQ).
Regions with different productivity levels producing the same mix of products with the same product prices must have the same relative factor prices for identical factors.
This weakening of the original theorem allows for the likely possibility that there are region-specific differences in productivity that do not vary across factors or goods. Under this condition the price levels of the factors would differ but the relative prices would be identical. As is obvious, Proposition 2 is necessary but not sufficient for Proposition 1.