Labor demand and wage inequality in Europe - an empirical Bayes approach

To what extent can changes in the distribution of wages be explained by changes in labor supply of various groups (due to demographic change, migration, or expanded access to education), and to what extent are other factors (technical and institutional change) at work? We develop a flexible methodology for answering this central question of labor economics, using an empirical Bayes approach, without imposing the restrictions on heterogeneity and on cross-elasticities of labor demand assumed by the literature. Our approach allows to reduce the variance of estimates by exploiting the information embodied in economic structural models, while avoiding the inconsistency and non-robustness of misspecified structural models.This approach also allows to overcome the issues associated with pretesting and the conventional duality of testing theories / imposing theories. We characterize the geometry and the mean squared error of our estimator. One of our key theoretical results explicitly describes the risk-function of empirical Bayes under an asymptotic approximation. Simulations confirm our characterizations and the fact that our estimator uniformly dominates unrestricted estimation over a large space of parameter values. In our empirical application, we analyze changes since 2003 of the wage distribution in the countries of the European Union, using the EU-SILC data. We find inverse elasticities of substitution which are significant but much smaller than comparable estimates for the US. CES-production functions seem to fit reasonably well, but fit declines with the number of types considered.