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 estima- tion. 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 pro- pose 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 numeri- cal challenges faced when using the Olley–Pakes and Levinsohn–Petrin estimators with the Ackerberg–Caves–Frazer correction in empirical applications, and we doc- ument how the generalized method of moments estimates vary depending on the optimizer or starting points used.