User Cost of Capital & Cost Function : Does the Margin of Freedom in the Modelling Yield Robust Results?

In this paper we report results of a rather successful attempt to provide evidence on the substitution possibilities between capital, labour, and energy in the three branches of French manufacturing industry. In order to assess the sensitivity of results to the choice of the functional form and to data construction procedures, alternative specifications of the cost function are estimated, based on three flexible functional forms (i) the Translog, (ii) the Generalized Leontief, and (iii) the Symmetric Generalized McFadden - while two different series of the user cost of capital are constructed (i) the implicit ex ante price (including fiscality parameters), obtained by extending the theoretical model of Jorgenson and (ii) the ex post price computed as the residual rate of return to capital, when zero profits are imposed at full equilibrium position.We show that the choice of the regressors is even important in the context of the choice of the functional form. We also consider the validity of the ex post approximation of the user cost of capital, frequently used in studies of production and investment behaviour, and find that our data do not support it.Our most important innovation is then in confronting results and interpretations yielded by three flexible approximations of the cost function when the two measures of the user cost of capital are alternatively used. In cases where we can precisely estimate an elasticity, our results seems robust to the choice of the functional form and the method of calculating the user cost of capital. Nevertheless, inconsistencies are enough frequent since this circumstance is scarce with the ex post approximation. This explain the fact that regressions with the ex post price of capital yield elasticities that can diverge from theirs true values and discrepancies between the estimates suggests that care should be taken during the interpretation of the econometric results