On estimating firm-level production functions using proxy variables to control for unobservables

In the common case where polynomial approximations are used for unknown functions, I show how proxy variable approaches to controlling for unobserved productivity, proposed by Olley and Pakes Olley, S. and Pakes, A., 1996. The dynamics of productivity in the telecommunications equipment industry. Econometrica 64, 1263–1298.] and Levinsohn and Petrin (Levinsohn, J. and Petrin, A., 2003. Estimating production functions using inputs to control for unobservables. Review of Economic Studies 70, 317–341.], can be implemented by specifying different instruments for different equations and applying generalized method of moments. Studying the parameters within a two-equation system clarifies some key identification issues, and joint estimation of the parameters leads to simple inference and more efficient estimators.