Production Function Estimation Robust to Flexible Timing of Labor Input

27 Pages Posted: 9 Apr 2019

See all articles by Kyoo il Kim

Kyoo il Kim

Michigan State University - Department of Economics

Yao Luo

University of Toronto - Department of Economics

Yingjun Su

Jinan University - Institute for Economic and Social Research

Date Written: March 17, 2019

Abstract

Control function approaches to estimating production functions rely on a proxy that is monotone in an unobserved scalar productivity conditioning on other state variables. Ackerberg, Caves, and Frazer (2015) point out a potential functional dependence problem when conditioning only on capital. They provide a simple solution by conditioning on both capital and labor. This approach allows flexible timing of labor input for when firms learn all or part of their productivity. However, we demonstrate that ACF's moment condition may suffer from weak identification, and its significance depends on the timing of labor input. We then propose easy-to-implement modified procedures that remedy these issues, and provide Monte Carlo evidence. Estimation of production functions with flexible timing assumption of inputs is important because it can allow for unobserved, serially correlated, firm-specific wage shocks, labor being chosen prior to other variable inputs, or labor having dynamic implications. Moreover, since the exact timing of input choices is unknown and even may differ across firms in practice, our proposal is valuable as it fully incorporates the flexible framework but avoids weak identification.

Keywords: Production Function, Weak Identification, Control Function, Monte Carlo Simulation

JEL Classification: C14, C18, D24

Suggested Citation

Kim, Kyoo il and Luo, Yao and Su, Yingjun, Production Function Estimation Robust to Flexible Timing of Labor Input (March 17, 2019). Available at SSRN: https://ssrn.com/abstract=3354067 or http://dx.doi.org/10.2139/ssrn.3354067

Kyoo il Kim (Contact Author)

Michigan State University - Department of Economics ( email )

East Lansing, MI 48824
United States

Yao Luo

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S3G7
Canada

Yingjun Su

Jinan University - Institute for Economic and Social Research ( email )

601 West Whampoa Road
Tianhe District
Guangzhou, 510632
China

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