Production Function Estimation with Unobserved Input Price Dispersion
Paul Grieco, Shengyu Li, and Hongsong Zhang
[Abstract] We propose a method to consistently estimate production functions when intermediate inputs are not observed in the presence of input price dispersion. The traditional approach to dealing with unobserved input quantities--using deflated expenditure as a proxy--requires strong assumptions for consistency. In particular, we show that the traditional approach tends to underestimate the elasticity of substitution and bias estimates of the distribution parameters. Our approach applies to a general class of production functions with a mild identification restriction. As a demonstration, we apply our approach to the CES production function. A Monte Carlo experiment illustrates that the omitted price bias is significant in the traditional approach, while our method consistently recovers the production function parameters. We apply our method to a firm-level data set from Colombian manufacturing industries. The empirical results are consistent with the predictions that the use of expenditure as a proxy for quantities biases the elasticity of substitution downward. Moreover, using our preferred method, we provide evidence of significant input price dispersion and even wider productivity dispersion than is estimated using traditional methods.