Semiparametric Identification and Fisher Information

58 Pages Posted: 31 Jul 2016 Last revised: 18 Apr 2018

Date Written: April 5, 2018


This paper provides a systematic approach to semiparametric identification that is based on statistical information. Identification can be regular or irregular, depending on whether the Fisher information for the parameter is positive or singular, respectively. I first characterize these two cases in models with densities linear in a nonparametric parameter. This analysis leads to simple-to-check necessary conditions for regular identification in many linear and nonlinear models. 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. The usefulness of the theory is illustrated by showing that distributions and quantiles of unobserved heterogeneity are not regularly identified in many economic models of interest. Similarly, I show that average marginal effects (AME) and the proportion of individuals with positive AME cannot be regularly identified in a correlated random effects model. I also obtain primitive conditions for regular identification of the discount factor and average measures of risk aversion in a nonparametric Euler Equation with nonparametric measurement error in consumption.

Keywords: Identification, Irregular Identification, Semiparametric Models, Fisher Information.

JEL Classification: C14, C31, C33, C35

Suggested Citation

Escanciano, Juan Carlos, Semiparametric Identification and Fisher Information (April 5, 2018). Available at SSRN: or

Juan Carlos Escanciano (Contact Author)

Universidad Carlos III de Madrid ( email )

CL. de Madrid 126
Madrid, Madrid 28903
653686785 (Phone)
28907 (Fax)

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