In nonparametric instrumental variables estimation, the mapping that identifies the function of interest, g, is discontinuous and must be regularized to permit consistent estimation. The optimal regularization parameter depends on population characteristics that are unknown in applications. This...

We propose a quasi-Bayesian nonparametric approach to estimating the structural relationship φ among endogenous variables when instruments are available. We show that the posterior distribution of φ is inconsistent in the frequentist sense. We interpret this fact as the ill-posedness of the...

We study a Tikhonov Regularized (TiR) estimator of a functional parameter identified by conditional moment restrictions in a linear model with both exogenous and endogenous regressors. The nonparametric instrumental variable estimator is based on a minimum distance principle with penalization by...

This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and the parameters diverge along with the sample size. The...

This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence rate results. A particular emphasis is on instrumental...

This paper develops a framework for the analysis of semiparametric conditional moment models with endogenous and mismeasured causes, which is of empirical importance. We show that one set of valid instruments is sufficient to control for both endogeneity and measurement errors of the causes of...

In nonparametric instrumental variable estimation, the function being estimated is the solution to an integral equation. A solution may not exist if, for example, the instrument is not valid. This paper discusses the problem of testing the null hypothesis that a solution exists against the...

Frontier estimation appears in productivity analysis. Firm’s performance is measured by the distance between its output and an optimal production frontier. Frontier estimation becomes difficult if outputs are measured with noise and most approaches rely on restrictive parametric assumptions....

In this paper, we investigate the problem of estimating nonparametric and semiparametric panel data models with fixed effects. We focus on establishing the asymptotic results for estimators using smooth backfitting methods. We consider two estimators for the smooth unknown function in...

We propose a consistent test for a linear functional form against a nonparametric alternative in a fixed effects panel data model. We show that the test has a limiting standard normal distribution under the null hypothesis, and show that the test is a consistent test. We also establish the...