Production function estimation using observed price changes

The estimation of production functions with firm-level data is hampered by the non-observability of real quantities (output and inputs). An increasing number of papers use reported price changes to construct firm-specific price indices which are then used to deflate nominal quantities. We argue that this procedure does not address the fundamental problem of the non-observability of prices because it introduces an initial condition given by the price level in the base year chosen to construct the price index. Because this price level is unobserved, this procedure generates an omitted variable bias (OVB) whose importance can be gauged by the non-robustness of the estimated production function parameters to the choice of base year. The OVB disappears when firm-specific fixed effects are incorporated in the estimation of the production function. We illustrate using simulations and a panel of Spanish manufacturing firms.