Identification and estimation of production functions with unobserved heterogeneity
Creators: name: Doty, Justin C.
Publisher: name: University of Iowa
Year: 2022
Subjects: public abstract

description: Production functions are a component of many economic models and inform economists on how firms make decisions under environments of uncertainty, market restructuring, and technological change. Accordingly, there has been substantial effort dedicated to resolving econometric limitations of production function estimates. One crucial limitation is the significant amount of unobserved heterogeneity among firms. These unobserved sources of variation in technology are important because an incorrectly specified production function will bias estimates of other models for which it relies on. This thesis proposes new methodologies to control for unobservables in firm production functions. I propose new quantile regression techniques to capture heterogeneity between firms as well as techniques for addressing heterogeneity that arises from unobserved inputs in the production function.
description: In the first chapter, we propose a new approach for estimating production functions when elasticities are heterogeneous across the conditional distribution of output. We provide a quantile regression framework which controls for unobserved productivity as an extension of the extant control function approaches. Parameters are estimated in a simple two-stage approach which relies on a location-shift assumption on unobserved productivity. We show that this method allows us to capture heterogeneity in output elasticities which may not be found in the conditional mean estimates. Empirical applications to U.S., Chile, and Colombia data confirm that the proposed method captures substantial unobserved heterogeneity in output elasticities.
description: In the second chapter, I study identification and estimation of a nonseparable model for production functions with unobserved heterogeneity. Nonparametric identification results are established for the production function and productivity process under stationarity conditions. This framework allows for heterogeneous effects of output elasticities and factor efficiencies in addition to nonlinear productivity persistence. It also allows for additional unobservables in the input demand functions, which would violate the scalar unobservability requirement in proxy variables under previous approaches. This extension is used to show firms' heterogeneous responses to productivity shocks corresponding to their productivity history. This paper illustrates these results in an application to U.S. manufacturing firms where the proposed model is estimated using nonlinear quantile regression.
description: The third chapter studies the identification and estimation of gross-output production functions when inputs are unobserved. Prior approaches correct for the simultaneity bias of unobserved productivity and mismeasured inputs by combining the proxy variable approach with nonparametric identification of conditional densities under nonclassical measurement error. However, the production functions in those models are still subject to the non-identification critique of Gandhi et al. (2020) (GNR). I show that under similar assumptions as those papers, identification of the parameters can still be achieved by extension of the GNR estimator. Therefore, this methodology corrects for two sources of identification failure in the production function literature. This paper provides a consistent estimator that is robust to these sources of non-identification and shows that measurement error remains an important limitation for obtaining unbiased estimates of output elasticities and productivity.