NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Production Function Estimation with Measurement Error in Inputs

Allan Collard-Wexler, Jan De Loecker

NBER Working Paper No. 22437
Issued in July 2016, Revised in August 2016
NBER Program(s):Industrial Organization, International Trade and Investment, Productivity, Innovation, and Entrepreneurship

Production functions are a central component in a variety of economic analyzes. However, these production functions often first need to be estimated using data on individual production units. There is reason to believe that, more than any other input in the production process, there are severe errors in the recording of capital stock. Thus, when estimating production functions, we need to account for the ubiquity of measurement error in capital stock. This paper shows that commonly used estimation techniques in the productivity literature fail in the presence of plausible amounts of measurement error in capital. We propose an estimator that addresses this measurement error, while controlling for unobserved productivity shocks. Our main insight is that investment expenditures are informative about a producer’s capital stock, and we propose a hybrid IV-Control function approach that instruments capital with (lagged) investment, while relying on standard intermediate input demand equations to offset the simultaneity bias. We rely on a series of Monte Carlo simulations and find that standard approaches yield downward-biased capital coefficients, while our estimator does not. We apply our estimator to two standard datasets, the census of manufacturing firms in India and Slovenia, and find capital coefficients that are, on average, twice as large.

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Document Object Identifier (DOI): 10.3386/w22437

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