Firm size and the entire distribution of wages: a semiparametric approach

Abstract

In this article we argue that parametric regression analysis might well provide only partial evidence on the firm size-wage effect and propose a methodology that focuses on the entire distribution of wages. Results for a sample of Spanish workers show that the size premium is almost completely concentrated in the middle of the distribution.

Acknowledgements

We are grateful to Rita Gol for her collaboration in the initial phases of our research on the size-wage effect in Spain. EL-B acknowledges financial support from the Ministerio de Ciencia y Tecnología, Programa Nacional de I+D+i, SEC2005-07814.

Notes

¹ Sophistications have progressively been considered in such analyses to account, for instance, for the influence of worker sorting across firms of different size.

² See also DiNardo and Lemieux (1997) and Butcher and DiNardo (2002).

³ The kernel density estimate of a univariate density f based on a random sample i = 1, 2, … , n, with weights θ _i (), is where h is the bandwidth and K(·) the kernel function. See Silverman (1986) for further details.

⁴ A Gaussian kernel has been used in all the estimates, while the bandwidth, h, has been selected according to the ‘plug-in’ method of Sheather and Jones (1991). Optimal bandwidths for the different densities range from 0.036 to 0.051, though we have fixed h = 0.041 to guarantee comparisons between them. It should be stressed that neither the selection of the kernel nor the value of the bandwidth in the aforementioned range alters significantly the shape of the distributions.

⁵ Actually, Kolmogorov–Smirnoff tests confirm that both distributions differ, and that the wage distribution of large firms stochastically dominates the one for the small firms. Results are available from the authors upon request.