Production Function Estimation With Unobserved Input Price Dispersion

Abstract

We propose a method to consistently estimate production functions in the presence of input price dispersion when intermediate input quantities are not observed. The traditional approach to dealing with unobserved input quantities-using deflated expenditure as a proxy-requires strong assumptions for consistency. Instead, we control for heterogeneous input prices by exploiting the first order conditions of the firm's profit maximization problem. Our approach applies to a wide class of production functions and can be extended to accommodate a variety of heterogeneous intermediate input types. A Monte Carlo study 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 prediction 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 proxy methods.

On the Identification of Gross Output Production Functions

“…For example, unobserved serially correlated intermediate input price shocks violate the proxy variable assumption. However, this variation generates a measurement problem, since intermediate inputs are typically measured in expendi tures (see Grieco et al, 2016).…”

“…Second, the production technology exhibits constant returns to scale, which while not strictly necessary is typically assumed in order to avoid imputing a rental price of capital. Third, and most importantly for our More recently, and Grieco et al (2016) exploit the first-order conditions for labor and intermediate inputs under the assumption that they are flexibly chosen. Instead of using shares to recover input elasticities, these papers recognize that given a particular parametric form of the production function, the first-order condition for a flexible input (the proxy equation in LP/ACF) implies cross-equation parameter restrictions that can be used to aid in identification.…”

“…By exploiting the first-order conditions for both labor and intermediate inputs they are able to estimate a standard Hicks neutral and a labor-augmenting component to productivity. Grieco et al (2016) also use first-order conditions for both labor and intermediate inputs to recover multiple unobservables. In the presence of unobserved heterogeneous intermediate input prices, they show that the parametric cross-equation restrictions between the production function and the two firstorder conditions, combined with observed wages, can be exploited to estimate the production function and recover the intermediate input prices.…”

Techies, Trade, and Skill-Biased Productivity

“…De Loecker and Goldberg 2014give a clear exposition of the estimation and interpretation problems that arise when real input and output quantities are unavailable. Grieco et al (2016) [GLZ] show how to estimate the parameters of a CES production function even in the absence of real output or input data, by exploiting the firm's first-order conditions for profit maximization. In section 4.1 below, we extend the GLZ estimator to allow for factor-augmenting productivity differences.…”

Empirical models of firms and industries

“…Grieco et al. () use a translog to assess changes in economies of scale and other forms of efficiency that can be attributed to a merger.…”