Identification of Gross Output Production Functions with a Nonseparable Productivity Shock (Revision Requested, The Review of Economic Studies)
We study the nonparametric identification of gross output production functions with a nonseparable productivity shock. Our nonseparable specification relaxes the traditional assumption of Hicks neutrality that has been shown to be inconsistent with a number of data sets. It can thus capture the bias in technical change, which recent research has found relevant to many important economic questions. We first generalize the identification approach of Gandhi et al. [2020] to nonseparable models and show the identification of output elasticities. To identify the entire production function, we then impose a homogeneity assumption, which is supported by the data. Given the fact that our nonseparable models nest Hicks-neutral models, we are able to document the misspecification bias of the latter. Using Chilean and Colombian plant-level data, our estimates suggest that Hicks-neutral models overestimate returns to scale, overestimate output elasticities of labor, and generate biased estimates of capital intensity. Our estimates also indicate that technological change is predominantly biased toward capital over labor and intermediate inputs.
Nonparametric Identification Using Timing and Information Set Assumptions with an Application to Non-Hicks Neutral Productivity Shocks with Daniel Ackerberg and Jinyong Hahn (Revision Requested, The RAND Journal of Economics)
A recent literature addresses endogeneity utilizing assumptions restricting agents' information sets when they chose endogenous variables. We consider using these identifying assumptions to identify a structural function (e.g. a demand or production function) in a fully nonparametric context. Using Imbens and Newey [2009]'s control function framework we show identification and illustrate how our model's structure permits weaker support conditions than used by Imbens and Newey. We apply our results to production function estimation, finding non-Hicks neutral shocks that generate interesting heterogeneity in output elasticities and biased technological change as defined in Acemoglu [2002] and studied in Doraszelski and Jaumandreu [2018].
Shape-Restricted Production Functions: An Application to Allocative Efficiency with Daniel Ackerberg
We propose a two-step nonparametric estimator of production functions. In the first step, we estimate the productivity shock from the input demand function using sieve MLE. In the second step, we estimate the production function using Bernstein polynomials after plugging in the estimated productivity shock. The use of Bernstein polynomials makes it easy to impose theory-based shape restrictions on the production function, such as monotonicity and concavity. With the shape restrictions, our second step is a disciplined convex programming (DCP) problem, which has attractive computational properties. Applying our estimator to commonly used production datasets, we find that, while the concavity restriction does not make much difference, imposing the monotonicity restriction can greatly reduce the dispersion of the estimated marginal productivity across firms, which implies much higher efficiency of resource allocation among firms.
Measuring Markups and Marginal Costs from Financial Statements (Draft Coming Soon!)
Tracking Down the Unobserved Prices: A Constrained GMM Approach to Production Function Estimation, with Daniel Ackerberg (Draft Coming Soon!)
Tracking Down the Unobserved Prices: A Constrained GMM Approach to Production FunctionEstimation, with Daniel Ackerberg (Draft Coming Soon!)
From Revenue to Production: Identification and Estimation, with Vincent Mastantuno and Lixue Zhou