Capital-Labor Substitution Heterogeneity with Endogenous Switching Regression

The aim of this paper is to show that it would be easier, for firms, to substitute capital for low skilled labor than to substitute capital for high skilled labor. To test this conjecture, we use panel data spanned from 1980 to 1987 on nearly 800 French manufacturing firms. We first propose a semi-reduced form obtained conditionally to a specific price setting rule as, at the micro level, the selling price is not observed. We next argue for estimating a system of two equations as the production function alone is not the best way to reveal the elasticity of substitution in production. Our system can be interpreted as the following recursive firms' behavior. On the one hand, firms choose the optimal capital per worker level; on the other hand, the optimal production and price levels. We also can capture the between-firms heterogeneity by means of individualizing a deep production function parameter. Finally, we propose to trace heterogeneity in elasticity of substitution by considering the presence of two groups of firms. The first group includes the low elasticity of substitution firms; the second group includes the high elasticity of substitution firms. We develop a switching regression model to carry out firms classification, by endogenous selection. Eventually, we find that the average skills of the work force is a factor which contributes to accounting for the probability that a firm belongs in either one group or another. This paper then gives a (soft) evidence to support the French current policy to subsidize the "low wages jobs".