Dissertation
Identification and estimation of production functions with unobserved heterogeneity
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Summer 2022
DOI: 10.25820/etd.006566
Abstract
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.
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.
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.
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.
Details
- Title: Subtitle
- Identification and estimation of production functions with unobserved heterogeneity
- Creators
- Justin C. Doty
- Contributors
- Suyong Song (Advisor)Luciano de Castro (Committee Member)David Frisvold (Committee Member)Seongjoo Min (Committee Member)Alexandre Poirier (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Economics
- Date degree season
- Summer 2022
- Publisher
- University of Iowa
- DOI
- 10.25820/etd.006566
- Number of pages
- 216 pages
- Copyright
- Copyright 2022 Justin C. Doty
- Language
- English
- Public Abstract (ETD)
Production functions represent the technology of a firm, and its inputs are assumed to be chosen optimally to maximize their profits. Inputs such as capital stock, employees, and intermediate inputs are determined by various observed and unobserved factors facing the firm. Production functions can be used to obtain estimates of productivity, infer trends in market power, and test whether inputs are allocated efficiently. Therefore, it is important to address econometric issues surrounding production function estimates as they may lead to incorrect inference by economists and policy makers. This thesis addresses how to estimate production functions when there are unobserved differences between firms, which can arise from unobserved differences in technology and unobserved inputs.
In the first chapter, we propose a new production function estimator that can recover estimates of technology for different firms. Standard approaches assume that technology within an industry is fixed across firms. Our results show that the proposed estimator captures unobserved heterogeneity in a simulation study and real data from manufacturing industries in the U.S., Chile, and Colombia. The second chapter can be seen as extension of the first. I consider an alternative pro-duction function specification that allows me to capture how a firm’s productivity may enhance the relative usage of inputs in production. In addition, I show asymmetric heterogeneity in a firms’ productivity evolution. Firms may react differently to random shocks to their productivity by choosing different input combinations. Previous approaches rely on a strict assumption on productivity evolution, which may not be supported by the data.
In the third chapter, I address another source of heterogeneity arising from unobserved inputs. Correct inference on production function estimates relies on the econometrician observing the inputs the firm uses. The production function model links optimal input choices to final output. When inputs are measured with error, the link between observed inputs and output is broken and estimates of the production function will be incorrect. I propose a method to identify and estimate a class of production functions in the presence of measurement error in inputs.
- Academic Unit
- Economics
- Record Identifier
- 9984285347602771
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