Semiparametric Identification and Fisher Information

TL;DR

This paper introduces a systematic approach to semiparametric identification using Fisher information, distinguishing regular and irregular cases, and proposes a new generalized Fisher information to analyze identification and estimation limits.

Contribution

It develops a novel generalized Fisher information concept and characterizes conditions for regular and irregular semiparametric identification across various models.

Findings

Positive Fisher information implies regular identification.

Zero Fisher information indicates impossibility of certain estimation rates.

Examples demonstrate applicability to economic models and valuation studies.

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 a nonparametric 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 find necessary conditions for semiparametric regular identification in a structural model for unemployment duration with two spells and nonparametric heterogeneity. Second, I show irregular identification of the median willingness to pay in contingent valuation studies. Finally, I study identification of the discount factor and average measures of risk aversion in a nonparametric Euler Equation with nonparametric measurement error in consumption.