In econometrics some nonparametric instrumental regression models and nonparametric demand models with endogeneity lead to nonlinear integral equations with unknown integral kernels. We prove convergence rates of the risk for the iteratively regularized Newton method applied to these problems....

Estimation of polynomial regression equations in one error-ridden variable and a number of error-free regressors, as well as an instrument set for the former is considered. Procedures for identification, operating on moments up to a certain order, are elaborated for single- and multi-equation...

The linear IV estimator, in which the dependent variable is a linear function of a potentially endogenous regressor, is a major workhorse in empirical economics. When this regressor takes on multiple values, the linear specification restricts the marginal effects to be constant across all...

This paper is concerned with inference on the coefficient on the endogenous regressor in a linear instrumental variables model with a single endogenous regressor, nonrandom exogenous regressors and instruments, and i.i.d. errors whose distribution is unknown. It is shown that under mild...

We explore the validity of the 2-stage least squares estimator with l_{1}-regularization in both stages, for linear triangular models where the numbers of endogenous regressors in the main equation and instruments in the first-stage equations can exceed the sample size, and the regression...

This paper develops Wald type tests for general possibly nonlinear restrictions, in the context of heteroskedastic IV regression with many weak instruments. In particular, it is first shown that consistency and asymptotically normality can be obtained when estimating structural parameters using...

[enter Abstract Body]This paper derives the limiting distributions of alternative jackknife IV (JIV ) estimators and gives formulae for accompanying consistent standard errors in the presence of heteroskedasticity and many instruments. The asymptotic framework includes the many instrument...

This paper studies robustness of bootstrap inference methods for instrumental variable regression models. In particular, we compare the uniform weight and implied probability bootstrap approximations for parameter hypothesis test statistics by applying the breakdown point theory, which focuses...

We present a methodology for estimating the distributional effects of an endogenous treatment that varies at the group level when there are group-level unobservables, a quantile extension of Hausman and Taylor (1981). Standard quantile regression techniques are inconsistent in this setting, even...

This paper employs conditional second moments to identify the impact of education in wage regressions where education is treated as endogenous. This approach avoids the use of instrumental variables in a setting where instruments are frequently not available. We employ this methodology to...