In this paper, we explore Bayesian inference in models with many instrumental variables that are potentially weakly correlated with the endogenous regressor. The prior distribution has a hierarchical (nested) structure. We apply the methods to the Angrist-Krueger (AK, 1991) analysis of returns...

The recent literature on instrumental variables (IV) features models in which agents sort into treatment status on the basis of gains from treatment as well as on baseline-pretreatment levels. Components of the gains known to the agents and acted on by them may not be known by the observing...

Econometric analyses of treatment response commonly use instrumental variable (IV) assumptions to identify treatment effects. Yet the credibility of IV assumptions is often a matter of considerable disagreement, with much debate about whether some covariate is or is not a "valid instrument" in...

This article introduces a new class of instrumental variable (IV) estimators of causal treatment effects for linear and nonlinear models with covariates. The rationale for focusing on nonlinear models is to improve the approximation to the causal response function of interest. For example, if...

This paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak, here modeled as local to zero. Asymptotic representations are provided for various instrumental variable...

This paper considers tests of the parameter on endogenous variables in an instrumental variables regression model. The focus is on determining tests that have certain optimal power properties. We start by considering a model with normally distributed errors and known error covariance matrix. We...

Weak instruments can produce biased IV estimators and hypothesis tests with large size distortions. But what, precisely, are weak instruments, and how does one detect them in practice? This paper proposes quantitative definitions of weak instruments based on the maximum IV estimator bias, or the...

This paper introduces an instrumental variables estimator for the effect of a binary treatment on the quantiles of potential outcomes. The quantile treatment effects (QTE) estimator accommodates exogenous covariates and reduces to quantile regression as a special case when treatment status is...