Estimating production functions when prices are partially observed

Resumo

The unobservability of quantities and prices is a typical limitation in the estimation of .rms pro- duction functions. In the absence of price information, the standard practice has been to approximate output as the .rm.s revenue de.ated by an industry price index. Some recent .rm-level datasets report information on .rm price rate of change, which is used to recover a .rm speci.c price index in order to de.ate revenue. However, a strong assumption is needed to circumvent the problem that the base year price level is not observed when constructing this price index: all .rms in all industries should have the same base year price level. In this paper we consider the unobserved base year price level as a .xed e¤ect in the estimation of the production function. As a consequence, the .rst step of Olley and Pakes (1996) under Ackerberg.s et al. (2006) assumptions turns out to be a semiparametric partially linear panel data .xed e¤ect model. Moreover, the .xed e¤ect assumption can be tested by means of a nonparametric Hausman test. We apply this method to a survey of Spanish manufacturing .rms and do not reject the .xed e¤ect assumption.on.