Kitagawa, Toru; (2009) Three Essays on Instrumental Variables. Doctoral thesis (Ph.D), Brown University.

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Abstract

Can we refute the validity of an instrumental variable using data alone? The development of the instrumental variable method has been one of the most important innovations in econometrics and the method is now widely used in empirical work in economics. Although the validity of the conclusion relies crucially on the instrument validity assumptions made by the researcher, these assumptions have been considered untestable. In this dissertation I consider two models in which the instrumental variable method has been used; the sample selection model and the counterfactual causal model. For each of these models, I show that the assumption required for the validity of instrumental variable method can be tested. I focus on the identification region: the set of outcome distributions that are compatible with data and the instrument validity assumptions, and characterize the conditions under which the identification region is empty. Since the empty identification region implies a misspecification of the instrument validity assumptions, I can develop a nonparametric specification test for instrument validity that operates by inferring from data the emptiness of the identification region. The first chapter develops the identification region for the outcome distributions under the instrument exclusion restriction. I analyze the missing data model and the counterfactual causal model in the partial identification framework, and provide a closed-form expression of the tight identification region for the potential outcome distributions as well as the tight bounds for the causal effects under the instrument exclusion restriction. The second chapter develops a test for the independent instrument assumption in the sample selection model for missing data. The contributions of this chapter are to summarize the emptiness of the identification region by a scalar parameter and to develop an inferential procedure for this parameter. This chapter also develops a particular bootstrap algorithm that can be used to obtain the asymptotically valid critical values. The third chapter develops a test procedure for the instrument validity assumption in the heterogeneous treatment effect model, which is equivalent to the identifiability assumption for the causal effects of compliers.

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