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.