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Moment-based estimation of nonlinear regression models with boundary outcomes and heterogeneity, with applications to non-negative and fractional responses

Ramalho, E.A., J.J.S. Ramalho (2017), "Moment-based estimation of nonlinear regression models with boundary outcomes and heterogeneity, with applications to non-negative and fractional responses", Econometric Reviews, 36(4), 397-420.
Abstract:

In this paper we suggest simple moment-based estimators to deal with unobserved heterogeneity in a special class of nonlinear regression models that includes as main particular cases exponential models for nonnegative responses and logit and complementary loglog models for fractional responses. The proposed estimators: (i) treat observed and omitted covariates in a similar manner; (ii) can deal with boundary outcomes; (iii) accommodate endogenous explanatory variables without requiring knowledge on the reduced form model, although such information may be easily incorporated in the estimation process; (iv) do not require distributional assumptions on the unobservables, a conditional mean assumption being enough for consistent estimation of the structural parameters; and (v) under the additional assumption that the dependence between observables and unobservables is restricted to the conditional mean, produce consistent estimators of partial effects conditional only on observables.