Using Firm Optimization to Evaluate and Estimate Returns to Scale

73 Pages Posted: 19 Dec 2007 Last revised: 5 Nov 2022

See all articles by Yuriy Gorodnichenko

Yuriy Gorodnichenko

University of California, Berkeley - Department of Economics; National Bureau of Economic Research (NBER); IZA Institute of Labor Economics

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Date Written: December 2007

Abstract

At the firm level, revenue and costs are well measured but prices and quantities are not. This paper shows that because of these data limitations estimates of returns to scale at the firm level are for the revenue function, not production function. Given this observation, the paper argues that, under weak assumptions, micro-level estimates of returns to scale are often inconsistent with profit maximization or imply implausibly large profits. The puzzle arises because popular estimators ignore heterogeneity and endogeneity in factor/product prices, assume perfect elasticity of factor supply curves or neglect the restrictions imposed by profit maximization (cost minimization) so that estimators are inconsistent or poorly identified. The paper argues that simple structural estimators can address these problems. Specifically, the paper proposes a full-information estimator that models the cost and the revenue functions simultaneously and accounts for unobserved heterogeneity in productivity and factor prices symmetrically. The strength of the proposed estimator is illustrated by Monte Carlo simulations and an empirical application. Finally, the paper discusses a number of implications of estimating revenue functions rather than production functions and demonstrates that the profit share in revenue is a robust non-parametric economic diagnostic for estimates of returns to scale.

Suggested Citation

Gorodnichenko, Yuriy, Using Firm Optimization to Evaluate and Estimate Returns to Scale (December 2007). NBER Working Paper No. w13666, Available at SSRN: https://ssrn.com/abstract=1073648

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