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 provides distribution free tests for detecting sample selection in conditional quantile functions. The first test is an omitted predictor test with the propensity score as the omitted variable. In the case of rejection we cannot distinguish between rejection due to genuine selection...

This paper considers regression-based tests for encompassing, when none of the models under consideration encompasses all the other models. For both in- and out-of-sample applications, I derive asymptotic distributions and propose feasible procedures to construct confidence intervals and test...