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

In this comment I illustrate that in the model of (Lee et al. (2019). Oxford Bulletin of Economics and Statistics. Vol. 81, pp. 80-97), firm profit maximizing implies that Assumption 2 and Equation 14 may be contradictory. More specifically, there is generally a contradiction when investment is used as the control variable, but there is generally not a contradiction when a static input like material input is used as the control variable (both types of control variables are discussed in Lee et al.). While the Lee et al. model and techniques are an interesting way to incorporate fixed effects into Olley and Pakes-style production function estimators, this observation suggests that their application should be restricted to cases where static inputs are used as control variables.