We consider the nonparametric regression model with an additive error that is correlated with the explanatory variables. We suppose the existence of instrumental variables that are considered in this model for the identification and the estimation of the regression function. The nonparametric...

In nonparametric instrumental variables estimation, the mapping that identifies the function of interest, g say, is discontinuous and must be regularised (that is, modified) to make consistent estimation possible. The amount of modification is contolled by a regularisation parameter. The optimal...

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...

This note shows that adding monotonicity or convexity constraints on the regression function does not restore well-posedness in nonparametric instrumental variable regression. The minimum distance problem without regularisation is still locally ill-posed

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...

This article gives the asymptotic properties for nonparametric kernel based density and regression estimators when one of the variables, respectively regressors, had to be pre-estimated. Those variables are known as constructed variables or generatedregressors, and their impact on the -nal...

Partial derivatives have a special place in economics since the marginal revolution of the 1850s. We present results from multivariate partial derivative estimates using nonlinear non-parametric regressions in a finite difference method, accessible via the R-package NNS. Numerical partial...

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...