Are Good Workers Employed by Good Firms? A Simple Test of Positive Assortative Matching Models

In this article, we test a simple version of Becker's (1973) marriage model for wage setting. This model predicts positive assortative matching. We estimate this model using linked employer--employee data for the France and the United States. We reject the simple version for both countries. The zero or negative correlation between person and firm effects is not explained by estimation biases due to a lack of mobility in the data. Several other potential explanations are proposed, including Shimer (2001) style coordination friction models. We focus on direct evidence that good workers are employed by good firms. This provides a direct empirical test of the simplest version of the Becker matching model. We start by constructing a very simple structural model of production and pay that implies positive assortative matching between a worker and her employer, exactly in the spirit of Becker. We do structural estimation using both French and American matched longitudinal employer-employee data. Because the structural model implies that the log-wage of workers is the sum of a person-specific effect and a firm-specific effect, recently developed techniques (Abowd, Creecy and Kramarz 2002) can be used to estimate its parameters. Because the Becker model predicts positive assortative matching, the person and firm effects should be positively correlated. We examine this correlation and find that it is either negligibly positive (United States) or negative (France). The article discusses one possible interpretation -- biases in the estimated parameters because the mobility process that helps identify the structural parameters is not active enough. Even though this interpretation contains a grain of truth, the bias-corrected correlations are still, respectively, negligibly positive and negative. Therefore, these results must be taken at their face value. The remainder of the article tries to understand the implications of the rejection of this model. In particular, it discusses various hypotheses that are used in order to derive and estimate the structural model. First, a true and meaningful firm effect must exist. Second, the log-wage must be the sum of a person component and of a firm component. The first hypothesis that is needed in order to generate a true and meaningful firm effect is the absence of a perfectly competitive labor market. The second hypothesis -- the absence of comparative advantage in the economy -- comes from the structure of the compensation in the model: the log-wage is the sum of a person component and of a firm component.