This paper studies the identification and estimationproblem in incomplete economic models with testable assumptions. Testable assumptions  give strong and interpretable empirical content to the models but they also carry the possibility that our distribution of observed outcome may reject these assumptions. A natural way  is to find a set of relaxed assumptions  A  that cannot be rejected by any reasonable distribution of observed outcome and preserves identified set of  parameter of interest  . The main contribution of this paper is to characterize the property of such relaxed assumption \tilde{A} using a generalized definition of refutability and confirmability. \tilde{A} A general estimation and inference procedure is proposed , and can be applied to most incomplete economic models. As the key application, I study the Imbens and Angrist Monotonicity assumption in potential outcome framework. I give a set of relaxed assumptions \tilde{A} that can never be rejected and always preserve the identified set of local average treatment effect (LATE ). The LATE  is point identified and easy to estimate under \tilde{A} 
This paper studies the identification , estimation, and hypothesis testing problem in complete and incomplete economic models with testable assumptions. Testable assumptions (A) give strong and interpretable empirical content to the models but they also carry the possibility that some distribution of observed outcomes may reject these assumptions. A natural way to avoid this is to find a set of relaxed assumptions ( A ) that cannot be rejected by any distribution of observed outcome and the identified set of the parameter of interest is not changed when the original assumption is not rejected . The main contribution of this paper is to characterize the properties of such a relaxed assumption \tilde{A} using a generalized definition of refutability and confirmability. I also propose a general method to construct such\tilde{A}. A general estimation and inference procedure is proposed and can be applied to most incomplete economic models. I apply my methodology to the instrument monotonicity assumption in Local Average Treatment Effect (LATE) estimation and to the sector selection assumption in a binary outcome Roy model of employment sector choice. In the LATE application, I use my general method to construct a set of relaxed assumptions \tilde{A} that can never be rejected , and the identified 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 LATE application. In the binary outcome Roy model, I use my method of incomplete models to relax Roy's sector selection assumption and characterize the identified set of the binary potential outcome as a polyhedron.
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