Can We Reliably Identify the CES Preference Parameter from Firm Revenue and Cost Data? Evidence from Monte Carlo Experiments

In empirical studies involving the estimation of structural parameters, a commonly used strategy to identify the CES preference parameter is to assume that firms have a constant marginal cost (MC). This assumption allows one to utilize the link between the total variable cost and total revenue implied by profit maximization to recover the CES preference parameter. This paper explores the robustness of the constant MC assumption in Monte Carlo experiments, where the control group consists of simulated constant MC firms and the treatment group involves different degrees of violation of the assumption. The results of our experiments show that the constant MC assumption indeed has a high identification power. Nevertheless, researchers need to ensure that their samples contain a sufficient proportion of constant MC firms, which, in our experiments, must be around 20 percent. We also find that, irrespective of the actual proportion of constant MC firms in the sample, the constant MC assumption correctly identifies the CES preference parameter if the elasticity of substitution within the industry is 2.5 or lower.