Production Function Estimation: Biased Coefficients and Endogenous Regressors, or a Case of Collective Amnesia?

42 Pages Posted: 3 Jun 2021 Last revised: 28 Sep 2021

See all articles by Jesus Felipe

Jesus Felipe

De La Salle University

John McCombie

University of Cambridge - Department of Land Economy

Aashish Mehta

University of California, Santa Barbara (UCSB)

Donna Faye Bajaro

Asian Development Bank

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Date Written: September 28, 2021

Abstract

The possible endogeneity of labor and capital in production functions, and the consequent bias of the estimated elasticities, has been discussed and addressed in the literature in different ways since the 1940s. This paper revisits an argument first outlined in the 1950s, which questioned production function estimations. This argument is that output, capital and employment, are linked through a distribution accounting identity, a key point that the recent literature has overlooked. This identity can be rewritten as a form that resembles a production function (Cobb-Douglas, CES, translog). We show that this happens because the data used in empirical exercises are value (monetary) data, not physical quantities. The argument has clear predictions about the size of the factor elasticities and about what is commonly interpreted as the bias of the estimated elasticities. To test these predictions, we estimate a typical Cobb-Douglas function using five estimators and show that: (i) the identity is responsible for the fact that the elasticities must be the factor shares; (ii) the bias of the estimated elasticities (i.e., departure from the factor shares) is, in reality, caused by the omission of a term in the identity. However, unlike in the standard omitted-variable bias problem, here the omitted term is known; and (iii) the estimation method is a second-order issue. Estimation methods that theoretically deal with endogeneity, including the most recent ones, cannot solve this problem. We conclude that the use of monetary values rather than physical data poses an insoluble problem for the estimation of production functions. This is, consequently, far more serious than any supposed endogeneity problems.

Keywords: accounting identity, endogeneity, monetary values, production functions, total factor productivity

JEL Classification: C18, C81, C82

Suggested Citation

Felipe, Jesus and McCombie, John S. L. and Mehta, Aashish Sunil and Bajaro, Donna Faye, Production Function Estimation: Biased Coefficients and Endogenous Regressors, or a Case of Collective Amnesia? (September 28, 2021). Available at SSRN: https://ssrn.com/abstract=3857565 or http://dx.doi.org/10.2139/ssrn.3857565

Jesus Felipe (Contact Author)

De La Salle University ( email )

2401 Taft Avenue
Manila, NCR 1004
Philippines

John S. L. McCombie

University of Cambridge - Department of Land Economy ( email )

19 Silver Street
Cambridge, CB3 9EP
United Kingdom

Aashish Sunil Mehta

University of California, Santa Barbara (UCSB) ( email )

South Hall 5504
Santa Barbara, CA 93106
United States

HOME PAGE: http://www.global.ucsb.edu/people/aashish-mehta

Donna Faye Bajaro

Asian Development Bank ( email )

6 ADB Avenue, Mandaluyong City 1550
Metro Manila
Philippines

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