Tests with correct size when instruments can be arbitrarily weak |
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Authors: | Marcelo J. Moreira |
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Affiliation: | aDepartment of Economics, Columbia University, New York, NY 10027, USA;bFGV/EPGE, Rio de Janeiro, RJ 22250, Brazil |
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Abstract: | This paper applies classical exponential-family statistical theory to develop a unifying framework for testing structural parameters in the simultaneous equations model under the assumption of normal errors with known reduced-form variance matrix. The results can be divided into the limited-information and full-information categories. In the limited-information model, it is possible to characterize the entire class of similar tests in a model with only one endogenous explanatory variable. In the full-information framework, this paper proposes a family of similar tests for subsets of endogenous variables’ coefficients. For both limited- and full-information models, there exist power upper bounds for unbiased tests. When the model is just-identified, the Anderson–Rubin, score, and (pseudo) conditional likelihood ratio tests are optimal. When the model is over-identified, the (pseudo) conditional likelihood ratio test has power close to the power envelope when identification is strong. |
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Keywords: | Instrumental variables regression Curved exponential family Weak instruments Pre-testing |
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