How Firms Affect Wages: a Structural Decomposition

There is a long literature that has studied the link between firm productivity and the wage they pay their workers. The typical finding is that more productive firms pay higher wages, and are larger in size. A recent stream of papers including Lopes de Melo (13), Eeckhout and Kircher (10) and Lise, Meghir and Robin (12) has emphasized a different aspect of the productivity-wages relationship. These papers have stressed that in assignment models, after you condition on worker skill, wages are non-monotone in firm productivity. The explanation for this is that each worker has an ideal firm that he should be matched and the price system (wages) is what induces matching. While these papers have used this prediction of the theory to explain some empirical regularities they have not provided direct evidence of those non-monotonicities. In this paper, we estimate a conditional wage function using a matched employer-employee dataset from Brazil to shed light on this question. In particular, we are interested in how much wages vary in firm productivity conditional on worker skill, and if that function is monotone or not. The idea is to use restrictions from the theory to construct an index of worker skill, an index of firm productivity and a third index which we label compensating differentials. This last index captures systematic differences in pay across firm, and are consistent with the compensation for a job amenity. Our indexes capture both observed and unobserved characteristics of firms and workers and they can be computed for subsets of workers within establishments. Once we compute those indexes we estimate the conditional wage function using non-parametric methods. Applying this method to a Brazilian matched employer employee dataset yields a number of results. First, we find that there is strong assortative matching in the Brazilian economy, as the worker and firm indexes are highly correlated. Second, after conditioning on worker skill the share of wage dispersion due to differences in productivity is very small - less than 2% of overall wage dispersion. Third, for most levels of worker skill, the wage function is non-monotone in firm productivity. However, the peak of the wage function seems to be not increasing in worker skill, which goes against the theory. Fourth the estimated wage function only accounts for around 60% of overall wage dispersion, and it's residual is highly clustered across firms. This last observation is what motivates us to consider the extended model with compensating differentials, but the results with the augmented model are work in progress.