A production function estimator with proxy variables and firm fixed effects

We show, in a very plausible theoretical setting, that control function estimators (CFEs) of firm production function, such as Olley-Pakes, may be biased. The bias will occur, in particular, when investments respond differently to short- and long-lasting changes in productivity. We modify the original CFE approach to allow for this differential response by introducing firm fixed effects to the control function. Applying our modified CFE to the data, we find that it does better than the existing CFEs in terms of controlling for persistent unobserved heterogeneity in productivity. Our findings imply that allowing firm fixed effects in the control function enhances its ability to capture firm productivity, and hence improves statistical quality of productivity estimates.