In this paper, we provide a general methodology to test for factor price equality across economies. Under the usual HO assumptions of common products, common product prices, and common technologies, we develop testable implications of the Factor Price Equality Theorem and the Relative Factor Price Equality Theorem for a broad class of production technologies. Unlike previous attempts to formulate tests for FPEQ and RFPEQ, our testing methodology is robust to sources of unobserved heterogeneity that are likely to be present in any cross-country or cross-region data, including differences in regional productivity, unobserved regional factor quality, and variations in production technology. Our empirical methodology can be applied to any cross-region data set with factor payment information and sufficient industry detail.
We test for relative factor price equality across labor markets in the US in both 1972 and 1992. In both years, we soundly reject the null hypothesis that all regions face the same relative factor prices. In particular, we find that relative wages vary considerably across the US. Using a methodology to group regions into cones of factor price insensitivity, we find at least three such cones in the US in both years. Over time, numerous regions have switched cones with most moving to one of the extreme factor price groups. However, on balance regions are slightly closer together in terms of relative factor prices in 1992 than in 1972 as the cones themselves have moved closer together.
Sorting regions into cones, we look for the predicted relationship from HO trade theory between industry mix and factor prices. While most labor market areas have substantial numbers of industries in common, regions in different factor price cones have 9-19 percent fewer industries in common. Regions that switch cones over time have greater churning of industries. This variation in industry mix provides a direct mechanism for variation in the transmission of external shocks. In particular, our results suggest that we should not expect to find homogenous responses to external shocks throughout the US.