No abstract

When instruments are weakly correlated with endogenous regressors, conventional methods for instrumental variables (IV) estimation and inference become unreliable. A large literature in econometrics has developed procedures for detecting weak instruments and constructing robust confidence sets, but many of the results in this literature are limited to settings with independent and homoskedastic data, while data encountered in practice frequently violate these assumptions. We review the literature on weak instruments in linear IV regression with an emphasis on results for nonhomoskedastic (heteroskedastic, serially correlated, or clustered) data. To assess the practical importance of weak instruments, we also report tabulations and simulations based on a survey of papers published in the American Economic Review from 2014 to 2018 that use IV. These results suggest that weak instruments remain an important issue for empirical practice, and that there are simple steps that researchers can take to better handle weak instruments in applications.

Event studies are frequently used to estimate average treatment effects on the treated (ATT). In estimating the ATT, researchers commonly use fixed effects models that implicitly assume constant treatment effects across cohorts. We show that this is not an innocuous assumption. In fixed effect models where the sole regressor is treatment status, the OLS coefficient is a non-convex average of the heterogeneous cohort-specific ATTs. When regressors containing lags and leads of treatment are added, the OLS coefficient corresponding to a given lead or lag picks up spurious terms consisting of treatment effects from other periods. Therefore, estimates from these commonly used models are not causally interpretable. We propose alternative estimators that identify certain convex averages of the cohortspecific ATTs, hence allowing for causal interpretation even under heterogeneous treatment effects. To illustrate the empirical content of our results, we show that the fixed effects estimators and our proposed estimators differ substantially in an application to the economic consequences of hospitalization.

We develop a concept of weak identification in linear IV models in which the number of instruments can grow at the same rate or slower than the sample size. We propose a jackknifed version of the classical weak identification-robust Anderson-Rubin (AR) test statistic. Large-sample inference based on the jackknifed AR is valid under heteroscedasticity and weak identification. The feasible version of this statistic uses a novel variance estimator. The test has uniformly correct size and good power properties. We also develop a pre-test for weak identification that is related to the size property of a Wald test based on the Jackknife Instrumental Variable Estimator. This new pre-test is valid under heteroscedasticity and with many instruments.