  One of the most important empirical findings in microeconometrics is the
pervasiveness of heterogeneity in economic behaviour (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 a relatively
simple check of this fact. 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, the average
marginal effect and the proportion of individuals with a positive marginal
effect in a correlated random coefficient model with heterogenous first-stage
effects, and the distribution and quantiles of random coefficients in linear,
binary and the Mixed Logit models. Monte Carlo simulations illustrate the
finite sample implications of our findings for the distribution and quantiles
of the random coefficients in the Mixed Logit model.
