The primary concern of this article is the provision of definitions and tests for exogeneity appropriate for models defined through sets of conditional moment restrictions. These forms of exogeneity are expressed as additional conditional moment constraints and may be equivalently formulated as...

A common stochastic restriction in econometric models separable in the latent variables is the assumption of stochastic independence between the unobserved and observed exogenous variables. Both simple and composite tests of this assumption are derived from properties of independence empirical...

This paper studies a model widely used in the weak instruments literature and establishes admissibility of the weighted average power likelihood ratio tests recently derived by Andrews, Moreira, and Stock (2004). The class of tests covered by this admissibility result contains the Anderson and...

This paper proposes a test for missing at random (MAR). The MAR assumption is shown to be testable given instrumental variables which are independent of response given potential outcomes. A nonparametric testing procedure based on integrated squared distance is proposed. The statistic’s...

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...

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...

This paper proposes a test for missing at random (MAR). The MAR assumption is shown to be testable given instrumental variables which are independent of response given potential outcomes. A nonparametric testing procedure based on integrated squared distance is proposed. The statistic's...

We show that the Anderson-Rubin (AR) statistic is the sum of two independent piv-otal statistics. One statistic is a score statistic that tests location and the other statistictests misspecification. The chi-squared distribution of the location statistic has a degreesof freedom parameter that is...

Test statistics that are suitable for testing composite hypotheses are typically non-pivotal, and conservative bounds are commonly used to test composite hypotheses. In this paper, we propose a testing procedure for composite hypotheses that incorporates additional sample information. This...

We show that the Anderson-Rubin (AR) statistic is the sum of two independent piv-otal statistics. One statistic is a score statistic that tests location and the other statistictests misspecification. The chi-squared distribution of the location statistic has a degreesof freedom parameter that is...