Optimal Invariant Tests in an Instrumental Variables Regression With Heteroskedastic and Autocorrelated Errors
Conference
64th ISI World Statistics Congress
Format: IPS Abstract
Keywords: causal inference, instrumental variable
Session: IPS 66 - Recent Advances in High-Dimensional Machine Learning and Inference
Tuesday 18 July 10 a.m. - noon (Canada/Eastern)
Abstract
This paper uses model symmetries in the instrumental variable (IV) regression to derive an invariant test for the causal structural parameter. Contrary to popular belief, we show that there exist model symmetries when equation errors are heteroskedastic and autocorrelated (HAC). Our theory is consistent with existing results for the homoskedastic model (Andrews, Moreira, and Stock (2006) and Chamberlain (2007)). We use these symmetries to propose the conditional integrated likelihood (CIL) test for the causality parameter in the over-identified model. Theoretical and numerical findings show that the CIL test performs well compared to other tests in terms of power and implementation. We recommend that practitioners use the Anderson-Rubin (AR) test in the just-identified model, and the CIL test in the over-identified model.