Theory and practice of total-factor productivity estimation: The control function approach using Stata

Alongside instrumental-variables and fixed-effects approaches, the control function approach is the most widely used in production function estimation. Olley and Pakes (1996, Econometrica 64: 1263-1297), Levinsohn and Petrin (2003, Review of Economic Studies 70: 317-341), and Ackerberg, Caves, and Frazer (2015, Econometrica 83: 2411-2451) have all contributed to the field by proposing two-step estimation procedures, whereas Wooldridge (2009, Economics Letters 104: 112-114) showed how to perform a consistent estimation within a single-step generalized method of moments framework. In this article, we propose a new estimator based on Wooldridge's estimation procedure, using dynamic panel instruments a la Blundell and Bond (1998, Journal of Econometrics 87: 115-143), and we evaluate its performance by using Monte Carlo simulations. We also present the new command prodest for production function estimation, and we show its main features and strengths in a comparative analysis with other community-contributed commands. Finally, we provide evidence of the numerical challenges faced when using the Olley-Pakes and Levinsohn-Petrin estimators with the Ackerberg-Caves-Frazer correction in empirical applications, and we document how the generalized method of moments estimates vary depending on the optimizer or starting points used.