Identification and Inference With Many Invalid Instruments
نویسندگان
چکیده
We study estimation and inference in settings where the interest is in the effect of a potentially endogenous regressor on some outcome. To address the endogeneity we exploit the presence of additional variables. Like conventional instrumental variables, these variables are correlated with the endogenous regressor. However, unlike conventional instrumental variables, they also have direct effects on the outcome, and thus are “invalid” instruments. Our novel identifying assumption is that the direct effects of these invalid instruments are uncorrelated with the effects of the instruments on the endogenous regressor. We show that in this case the limited-information-maximum-likelihood (liml) estimator is no longer consistent, but that a modification of the bias-corrected two-stage-least-squares (tsls) estimator is consistent. We also show that conventional tests for over-identifying restrictions, adapted to the many instruments setting, can be used to test for the presence of these direct effects. We recommend that empirical researchers carry out such tests and compare estimates based on liml and the modified version of bias-corrected tsls. We illustrate in the context of two applications that such practice can be illuminating, and that our novel identifying assumption has substantive empirical content.
منابع مشابه
Confidence Intervals for Causal Effects with Invalid In- struments using Two-Stage Hard Thresholding
The instrumental variable (IV) method is commonly used to estimate the causal effect of a treatment on an outcome by using IVs that satisfy the assumptions of association with treatment, no direct effect on the outcome and ignorability. A major challenge in IV analysis is to find said IVs, but typically one is unsure of whether all of the putative IVs are in fact valid (i.e. satisfy the assumpt...
متن کاملConfidence Intervals for Causal Effects with Invalid In- struments using Two-Stage Hard Thresholding with Vot- ing
A major challenge in instrumental variables (IV) analysis is to find instruments that are valid, or have no direct effect on the outcome and are ignorable. Typically one is unsure whether all of the putative IVs are in fact valid. We propose a general inference procedure in the presence of invalid IVs, called Two-Stage Hard Thresholding (TSHT) with voting. TSHT uses two hard thresholding steps ...
متن کاملTesting Endogeneity with Possibly Invalid Instruments and High Dimensional Covariates
The Durbin-Wu-Hausman (DWH) test is a commonly used test for endogeneity in instrumental variables (IV) regression. Unfortunately, the DWH test depends, among other things, on assuming all the instruments are valid, a rarity in practice. In this paper, we show that the DWH test often has distorted size even if one IV is invalid. Also, the DWH test may have low power when many, possibly high dim...
متن کاملConditional Moment Models under Weak Identification
We consider models defined by a set of conditional moment restrictions where weak identification may arise. Weak identification is directly defined through the conditional moments that are allowed to flatten as the sample size increases. We propose a minimum distance estimator of the structural parameters that is robust to potential weak identification and that uses neither instrumental variabl...
متن کامل