Revisiting the Omitted Price Bias in the Estimation of Production Functions

The lack of information on quantities presents significant challenges for estimating production functions. As shown by Klette and Griliches in 1996, deflating nominal variables using aggregate price indices leads to biased estimators. In this paper, we show that a similar problem arises when firm‐specific prices are recovered from reported firm‐specific price changes via a recursive formula. This recursion formula depends on an initial condition given by the unobserved price level in the base year, which then appears in the empirical production function as a firm‐specific fixed effect. The standard practice is to ignore these fixed effects by setting the firm‐specific prices in the base year to a constant value common to all firms, usually unity (zero in logs). We show that this practice generates biased estimators. We examine this bias via Monte Carlo simulations and with an empirical application. Solving this problem is not straightforward and requires further assumptions because these fixed effects generate nonlinear measurement errors.