Olley and Pakes-style Production Function Estimators with Firm Fixed Effects

We show that control function estimators (CFEs) of the firm production function, such as Olley–Pakes, may be biased when productivity evolves with a firm-specific intercept, in which case the correctly specified control function will contain a firm-specific term, omitted in the standard CFEs. We develop an estimator that is free from this bias by introducing firm fixed effects in the control function. Applying our estimator to the data, we find that it outperforms the existing CFEs in terms of capturing persistent unobserved heterogeneity in firm productivity. Our estimator involves minimal modification to the standard CFE procedures and can be easily implemented using common statistical software.