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Estimating Economic Models with Testable Assumptions Theory and Applications

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Document pages: 171 pages

Abstract: This paper studies the identification, estimation, and hypothesis testingproblem in complete and incomplete economic models with testable assumptions.Testable assumptions ($A$) give strong and interpretable empirical content tothe models but they also carry the possibility that some distribution ofobserved outcomes may reject these assumptions. A natural way to avoid this isto find a set of relaxed assumptions ($ tilde{A}$) that cannot be rejected byany distribution of observed outcome and the identified set of the parameter ofinterest is not changed when the original assumption is not rejected. The maincontribution of this paper is to characterize the properties of such a relaxedassumption $ tilde{A}$ using a generalized definition of refutability andconfirmability. I also propose a general method to construct such $ tilde{A}$.A general estimation and inference procedure is proposed and can be applied tomost incomplete economic models. I apply my methodology to the instrumentmonotonicity assumption in Local Average Treatment Effect (LATE) estimation andto the sector selection assumption in a binary outcome Roy model of employmentsector choice. In the LATE application, I use my general method to construct aset of relaxed assumptions $ tilde{A}$ that can never be rejected, and theidentified set of LATE is the same as imposing $A$ when $A$ is not rejected.LATE is point identified under my extension $ tilde{A}$ in the LATEapplication. In the binary outcome Roy model, I use my method of incompletemodels to relax Roy s sector selection assumption and characterize theidentified set of the binary potential outcome as a polyhedron.

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