Untested Assumptions and Data Slicing: A Critical Review of Firm-Level Production Function Estimators

This paper surveys the most popular parametric and semi-parametric estimators for Cobb-Douglas production functions arising from the econometric literature of the past two decades. We focus on the different approaches dealing with 'transmission bias' in firm-level studies, which arises from firms' reaction to unobservable productivity realisations when making input choices. The contribution of the paper is threefold: we provide applied economists with (i) an in-depth discussion of the estimation problem and the solutions suggested in the literature; (ii) a detailed empirical example using FAME data for UK high-tech firms, emphasising analytical tools to investigate data properties and the robustness of the empirical results; (iii) a powerful illustration of the impact of estimator choice on TFP estimates, using matched data on patents in 'TFP regressions'. Our discussion concludes that while from a theoretical point of view the different estimators are conceptually very similar, in practice, the choice of the preferred estimator is far from arbitrary and instead requires in-depth analysis of the data properties rather than blind belief in asymptotic consistency.