Irregular identification of structural models with nonparametric unobserved heterogeneity

One of the most important empirical findings in microeconometrics is the pervasiveness of heterogeneity in economic behavior (cf. Heckman, 2001). This paper shows that cumulative distribution functions and quantiles of the nonparametric unobserved heterogeneity have an infinite efficiency bound in many structural economic models of interest. The paper presents general and precise conditions to prove such results. The usefulness of the theory is demonstrated with several relevant examples in economics, including, among others, the proportion of individuals with severe long term unemployment duration, Average Marginal Effects (AME) in a correlated random coefficient model without monotonicity, and the distribution and quantiles of random coefficients in linear, binary and the popular semiparametric Mixed Logit model.Financial support by MCI/AEI/FEDER/UE, grant PGC 2018-096732-B-100, and Comunidad de Madrid, grants EPUC3M11 (V PRICIT) and H2019/HUM-589, is gratefully acknowledged