Semiparametric Identification and Fisher Information

This paper offers a systematic approach to semiparametric identification based on statistical information in semiparametric and nonparametric models. It first establishes a generalized rank condition that is sufficient and necessary for semiparametric identification in models with densities that are affine in a possibly unidentified nonparametric parameter. "Irregularly identified" parameters, i.e. identified parameters with zero semiparametric Fisher information, are characterized in this setting. Sufficient conditions for irregular identification are given for nonlinear models in terms of a novel "generalized Fisher information". The paper also establishes a generic zero information result, and uses it to prove that the non-random parameters of the widely used semiparametric mixed Logit model are irregularly identified. Other example applications include regular identification of average marginal effects in binary choice panel data models with fixed effects, and irregular identification of the cumulative distribution and quantiles of the distribution of unobserved heterogeneity in nonparametric structural models of unemployment duration and random coefficient models.