Panel data estimates of the production function and product and labor market imperfections

Embedding the efficient bargaining model into the R. Hall (1988) approach for estimating price-cost margins shows that both imperfections in the product and labor markets generate a wedge between factor elasticities in the production function and their corresponding shares in revenue. This article investigates these two sources of discrepancies both at the industry level and the firm level using an unbalanced panel of 10646 French firms in 38 manufacturing industries over the period 1978-2001. By estimating standard production functions and comparing the estimated factor elasticities for labor and materials and their shares in revenue, we are able to derive estimates of average price-cost mark-up and extent of rent sharing parameters. For manufacturing as a whole, our estimates of these parameters are of an order of magnitude of 1.17 and 0.44 respectively. Our industry-level results indicate that industry differences in these parameters and in the underlying estimated factor elasticities and shares are quite sizeable. Since firm production function, behavior and market environment are very likely to vary even within industries, we also investigate firm-level heterogeneity in estimated mark-up and rent-sharing parameters. To determine the degree of true heterogeneity in these parameters, we adopt the P.A. Swamy (1970) methodology allowing to correct the observed variance in the firm-level estimates from their sampling variance. The median of the firm estimates of the price-cost mark-up ignoring labor market imperfections is of 1.10, while as expected it is higher of 1.20 when taking them into account and the median of the corresponding firm estimates of the extent of rent sharing is of 0.62. The Swamy corresponding robust estimates of true dispersion are of about 0.18, 0.37 and 0.35, showing indeed very sizeable within-industry firm heterogeneity. We find that firm size, capital intensity, distance to the industry technology frontier and investing in R&D seem to account for a significant part of this heterogeneity.