Testing Instrument Validity with Covariates
|Speaker:||Toru Kitawaga, University College London|
|Date:||Friday 22 October 2021|
We develop a test for instrument validity in the heterogeneous treatment effect model that can accommodate conditioning covariates. Building on a common empirical setting of local average treatment effect or marginal treatment effect analysis, we assume semiparametric dependence between the potential outcomes and conditioning covariates, and show that this allows us to express the testable implication of the instrument validity in terms of equality and inequality restrictions among the subdensities of estimable partial residuals. To develop a powerful test for these testable implications, we propose a use of a distilled instrument. The distilled instrument is a transformation of the instrument and propensity scores designed to distil the sample down to the information useful for detecting violation of instrument validity. Our proposed test procedure assesses validity of the distilled instrument, and rejecting its validity allows us to reject the validity of the original instrument also. We perform Monte Carlo exercises to demonstrate the gain in power from using a distilled instrument and the importance of controlling for conditioning covariates when testing for instrument validity. We apply our test procedure to the college proximity instrument of Card (1993), the same-sex instrument of Angrist and Evans(1998), the school leaving age instrument of Oreopoulos (2006), and the mean land gradient instrument of Dinkelman (2011). We find that the null of instrument validity conditional on covariates cannot be rejected for Card (1993) and Angrist and Evans (1998), but it is rejected at conventional levels of significance in the case of Oreopoulos (2006).