ABSTRACT
In this article, 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.
Acknowledgment
The authors thank the Editor, the Associate Editor, the referees, and Joao Santos Silva for their valuable suggestions and remarks.
Notes
1We use the term “neglected heterogeneity” to designate the case where the unobserved and the included covariates are independent.
2See Heckman (Citation2000) for a rigorous definition of Marshallian causal functions.
3For example, if G2(⋅) is an exponential function, then we may redefine the constant 𝜃0 and the error term as and 𝜀 = exp(u)∕E[exp(u)], respectively.
4Note that as π1 is fixed independently of the number of instruments, more instruments imply a higher overall fit of the instruments to the endogenous regressor x1.
5Note that the highest value that we could add to y is any positive value below 0.002, given that the maximum value for Leverage in the sample is 0.998, see .
6R code to compute all estimators and tests discussed throughout the article is available at http://evunix.uevora.pt/∼jsr/ FRM.htm