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.