Restoring Identification in the Olley-Pakes Estimator: A Timing Assumption Approach

The production function estimation method proposed by Olley and Pakes (1996) to correct for selection bias suffers from an identification problem concerning the capital elasticity parameter. This paper proposes a simple solution to this problem. Our approach introduces an unanticipated, idiosyncratic firm-level demand shock into the firm’s dynamic decision-making process. Under a key timing assumption, this demand shock serves as a valid exclusion restriction: it affects the selection mechanism but is independent of the firm’s productivity. This exogenous variation restores the identification of the capital elasticity parameter. We validate the performance of our proposed estimator through Monte Carlo simulations and an empirical application using Japanese manufacturing data. We demonstrate that while the standard Olley-Pakes estimator is inconsistent and systematically biased, our proposed estimator is consistent and performs well.