Heterogeneity in Panel Data: Are There Stable Production Functions?

We estimate separate productions functions for approximately 450 manufacturing firms each in France and the United States and for 850 manufacturing firms in Japan, covering the 13 year period 1967-1979, and focus on the wide dispersion in the estimated slope coefficients in all three countries. The main question asked Is: "Is this dispersion real?" Could it be just a reflection of sampling variability or is it an indication of real heterogeneity? We estimate the "true" dispersion using three different approaches: Maximum Likelihood, regressions of squares and cross-products of residuals, and Swamy's "residual" method, and try to interpret the somewhat different answers which emerge. In particular, we investigate the "reality" of the estimated heterogeneity by looking at its stability over time and by relating it to differences in capital shares and the industrial structure. We conclude that the observed heterogeneity is not "real." It is caused by some non-stable misspecification of our simple model, implying that we are unlikely to discern different but stable individual production relations in samples of this size which contain only a limited number of the economically relevant variables.