  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.
