We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound...

In this paper, we propose a general method for testing inequality restrictions on nonparametric functions. Our framework includes many nonparametric testing problems in a uni ed framework, with a number of possible applications in auction models, game theoretic models, wage inequality, and...

This paper addresses the problem of estimation of a nonparametric regression function from selectively observed data when selection is endogenous. Our approach relies on independence between covariates and selection conditionally on potential outcomes. Endogeneity of regressors is also allowed...

We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound...

Consider the nonparametric regression model Y = m(X)+e, where the function m is smooth, but unknown. We construct tests for the independence of e and X, based on n independent copies of (X; Y). The testing procedures are based on differences of neighboring Y's. We establish asymptotic results...

We propose a new specification test for assessing the validity of fuzzy regression discontinuity designs (FRD‐validity). We derive a new set of testable implications, characterized by a set of inequality restrictions on the joint distribution of observed outcomes and treatment status at the...

Let i = 1, . . . , N index a simple random sample of units drawn from some large population. For each unit we observe the vector of regressors Xi and, for each of the N (N - 1) ordered pairs of units, an outcome Yij . The outcomes Yij and Ykl are independent if their indices are disjoint, but...

This paper proposes several tests of restricted specification in nonparametric instrumental regression. Based on series estimators, test statistics are established that allow for tests of the general model against a parametric or nonparametric specification as well as a test of exogeneity of the...

In a model with endogenous regressors, heteroskedastic and autocorrelated (HAC) errors and weak instruments, tests that depend on the data only through the Anderson-Rubin (AR) and Lagrange Multiplier (LM) statistics ignore important information on the regression coefficients. This is in contrast...

In a model with endogenous regressors, heteroskedastic and autocorrelated (HAC) errors and weak instruments, tests that depend on the data only through the Anderson-Rubin (AR) and Lagrange Multiplier (LM) statistics ignore important information on the regression coefficients. This is in contrast...