"Instrumental variable (IV) methods are widely used to identify causal effects in models with endogenous explanatory variables. Often the instrument exclusion restriction that underlies the validity of the usual IV inference is suspect; that is, instruments are only plausibly exogenous. We present practical methods for performing inference while relaxing the exclusion restriction. We illustrate the approaches with empirical examples that examine the effect of 401(k) participation on asset accumulation, price elasticity of demand for margarine, and returns to schooling. We find that inference is informative even with a substantial relaxation of the exclusion restriction in two of the three cases."

"We propose methods for inference on the average effect of a treatment on a scalar outcome in the presence of very many controls. Our setting is a partially linear regression model containing the treatment/policy variable and a large number $p$ of controls or series terms, with $p$ that is possibly much larger than the sample size $n$, but where only $s < n$ unknown controls or series terms are needed to approximate the regression function accurately. The latter sparsity condition makes it possible to estimate the entire regression function as well as the average treatment effect by selecting an approximately the right set of controls using Lasso and related methods. We develop estimation and inference methods for the average treatment effect in this setting, proposing a novel "post double selection" method that provides attractive inferential and estimation properties. In our analysis, in order to cover realistic applications, we expressly allow for imperfect selection of the controls and account for the impact of selection errors on estimation and inference. In order to cover typical applications in economics, we employ the selection methods designed to deal with non-Gaussian and heteroscedastic disturbances. We illustrate the use of new methods with numerical simulations and an application to the effect of abortion on crime rates."

"This article is about estimation and inference methods for high dimensional sparse (HDS) regression models in econometrics. High dimensional sparse models arise in situations where many regressors (or series terms) are available and the regression function is well-approximated by a parsimonious, yet unknown set of regressors. The latter condition makes it possible to estimate the entire regression function effectively by searching for approximately the right set of regressors. We discuss methods for identifying this set of regressors and estimating their coefficients based on $ell_1$-penalization and describe key theoretical results. In order to capture realistic practical situations, we expressly allow for imperfect selection of regressors and study the impact of this imperfect selection on estimation and inference results. We focus the main part of the article on the use of HDS models and methods in the instrumental variables model and the partially linear model. We present a set of novel inference results for these models and illustrate their use with applications to returns to schooling and growth regression."