Semiparametric identification and fisher information

Abstract

This paper provides a systematic approach to semiparametric identification that is based on statistical information as a measure of its “quality.” Identification can be regular or irregular, depending on whether the Fisher information for the parameter is positive or zero, respectively. I first characterize these cases in models with densities linear in an infinite-dimensional parameter. I then introduce a novel “generalized Fisher information.” If positive, it implies (possibly irregular) identification when other conditions hold. If zero, it implies impossibility results on rates of estimation. Three examples illustrate the applicability of the general results. First, I consider the canonical example of average densities. Second, I showirregular identification of the median willingness to pay in contingent valuation studies. Finally, I study identifica- tion of the discount factor and average measures of risk aversion in a nonparametric Euler equation with nonparametric measurement error in consumption.