Assumption violations in instrumental variables regression: weak instruments in subvector testing under heteroskedasticity and assessing the exclusion restriction

Thesis

Instrumental variables (IV) is a commonly used regression technique to estimate treatment parameters when the treatment is not random, i.e., it is endogenous. It relies on key assumptions and this dissertation explores strategies to deploy when those assumptions may not hold. Chapter 1 deals with the case of testing a subset of non-random treatment parameters when both the assumptions of strong instrument relevance and homoskedasticity fail. We recommend bootstrapping the Kleibergen-Paap Test or a 2-step LIML-based J-test in this situation. Chapter 2 considers a different assumption of IV regression: the exclusion restriction. We prove that the test devised by Kiviet (2020) does not function as a true test of the exclusion restriction and recommend reformulating it as a test of the endogeneity of the treatment variable, a test that is only valid when the exclusion restriction holds. Thus while the problems considered in Chapter 1 - weak instruments and heteroskedasticity - can be addressed by using the tests we recommend in the subvector case, the exclusion restriction, considered in Chapter 2, is not easy to relax or test. It is a foundational assumption of IV regression without a simple workaround, although past work offers adjustments if a certain type of subsample is available (van Kippersluis and Rietveld, 2018) and our endogeneity test can provide limited information in assessing whether the exclusion restriction holds for a particular instrument, even though a true test of endogeneity remains impossible.

Authors: Esenther, A

• DOI: 10.5287/ora-gazzaxjre
• Type of award: MSc by Research
• Level of award: Masters
• Awarding institution: University of Oxford
• Language: English
• Keywords: Instrumental variables; Exclusion restriction; Weak instruments; Subvector testing; Heteroskedasticity; Endogeneity
• Subjects: Econometrics