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Working Paper No. 994 | October 2021

Production Function Estimation

Biased Coefficients and Endogenous Regressors, or a Case of Collective Amnesia?
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.

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