This paper provides a systematic approach to semiparametric identi fication that is based on statistical information as a measure of its quality. Identi fication 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) identi fication 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 identi fication in a structural model for unemployment duration with two spells and nonparametric heterogeneity. Second, I show irregular identi fication of the median willingness to pay in contingent valuation studies. Finally, I study identi fication of the discount factor and average measures of risk aversion in a nonparametric Euler Equation with nonparametric measurement error in consumption.
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