Distinguishing Between Signal and Noise in the Measurement of the Firm Wage Premium

There is a growing interest about firm-side drivers of wage differentials, as different studies show that this component is driving the increase in inequality in many developed countries. In this paper, I contribute to this literature in three respects. First, I reconsider the widely used model from Abowd, Kramarz and Margolis (1999) used to decompose the respective contributions of firm and individual heterogeneity. I suggest an easily applicable split-sample procedure to uncover the extent of overfitting in this model. Using French administrative data, I find evidence of sizeable overfitting: conservative estimates suggest that the contribution of firm heterogeneity to wage inequality is overestimated by at least 25%. Second, I provide a simple procedure to recover the correct signal variance of firm effects and the covariance between individual and firm effects. Third, I show how to recover better prediction of the firm effects using shrinkage estimators. This matters quantitatively: due to shrinkage, half of the firm effects are shrunk by 38% or more, and 40% of firms end up in different deciles when ranked according to their firm effects.