Moment-based estimation of nonlinear regression models under unobserved heterogeneity, with applications to non-negative and fractional responses∗

In this paper we suggest simple moment-based estimators to deal with unobserved heterogeneity in nonlinear regression models that treat observed and omitted covariates in a similar manner. The results derived in the paper apply to a class of regression models that includes as particular cases exponential and logit and complementary loglog fractional regression models. Unlike previous approaches, which typically require distributional assumptions on the unobservables, a conditional mean assumption is enough for consistent estimation of the structural parameters. Under the additional assumption that the dependence between observables and unobservables is restricted to the conditional mean, consistent estimation of partial effects conditional only on the former is also possible without making distributional assumptions on the latter.