  We study identification and estimation of endogenous linear and nonlinear
regression models without excluded instrumental variables, based on the
standard mean independence condition and a nonlinear relevance condition. Based
on the identification results, we propose two semiparametric estimators as well
as a discretization-based estimator that does not require any nonparametric
regressions. We establish their asymptotic normality and demonstrate via
simulations their robust finite-sample performances with respect to exclusion
restrictions violations and endogeneity. Our approach is applied to study the
returns to education, and to test the direct effects of college proximity
indicators as well as family background variables on the outcome.
