Estimating production functions with control functions when capital is measured with error

Abstract

We revisit the production function estimators of Olley and Pakes (1996) and Levinsohn and Petrin (2003). They use control functions to address the simultaneous determination of inputs and productivity. Both assume that input demand is a monotonic function of productivity holding capital constant and then invert this function to condition on productivity during estimation. If the observed capital variable is measured with error, input demand will not generally be monotonic in the productivity shock holding observed capital constant. We develop consistent estimators of production function parameters in the face of this measurement error. Our identification and estimation results combine the nonlinear measurement error literature with Wooldridge (2009)'s joint estimation method to construct a proxy for productivity that addresses simultaneity. Our approach directly extends to the case where other inputs like intermediates or labor are observed with error.

Identification Properties of Recent Production Function Estimators

“…In this case, none of the procedures produce consistent estimates, but we illustrate (in at least one setup) that our procedure appears less affected by this misspecification than OP and LP. Note that since the original version of the paper, others have proposed newer methods of explicitly addressing measurement error in inputs; Huang and Hu (2011) proposed a method to explicitly deal with such measurement error in these approaches based on observing multiple proxies and deconvolution methods, and Kim, Petrin, and Song (2013) also allowed for measurement error in capital.…”

Production Function Estimation and Capital Measurement Error

“…While his focus is on the bias in the estimated coefficients, we provide an estimator that is robust to the presence of such measurement error, in the context of endogenous input choices. Kim, Petrin, and Song (2016) also study the identification of production function with measurement error in inputs, with an estimator that leverages recent work on non-linear measurement error models. Their estimator is more complex, which explains why, to our knowledge, it has not yet been used.…”

Estimating Production Functions with Fixed Effects

“…In contrast to this double measurement strategy, I use an instrumental variables strategy with a Berkson instrument (Schennach, 2007). Finally, Kim, Petrin and Song (2016) and Collard-Wexler and De Loecker 2017both focus on the case where capital is measured with error. Similar to Hu, Huang and Sasaki (2019), Kim, Petrin and Song (2016) use results form the nonlinear errors-in-variables literature and suggest an estimation procedure based on sieves.…”

“…Finally, Kim, Petrin and Song (2016) and Collard-Wexler and De Loecker 2017both focus on the case where capital is measured with error. Similar to Hu, Huang and Sasaki (2019), Kim, Petrin and Song (2016) use results form the nonlinear errors-in-variables literature and suggest an estimation procedure based on sieves. In contrast, Collard-Wexler Blundell and Bond (1998) BB98…”