Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/241955 
Year of Publication: 
2021
Series/Report no.: 
cemmap working paper No. CWP19/21
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
Abstract: 
In many set identified models, it is difficult to obtain a tractable characterization of the identified set, therefore, empirical works often construct confidence region based on an outer set of the identified set. Because an outer set is always a superset of the identified set, this practice is often viewed as conservative yet valid. However, this paper shows that, when the model is refuted by the data, a nonempty outer set could deliver conflicting results with another outer set derived from the same underlying model structure, so that the results of outer sets could be misleading in the presence of misspecification. We provide a sufficient condition for the existence of discordant outer sets which covers models characterized by intersection bounds and the Artstein (1983) inequalities. Furthermore, we develop a method to salvage misspecified models. We consider all minimum relaxations of a refuted model which restore data-consistency. We find that the union of the identified sets of these minimum relaxations is misspecification-robust and it has a new and intuitive empirical interpretation. Although this paper primarily focuses on discrete relaxations, our new interpretation also applies to continuous relaxations.
Subjects: 
Partial Identification
Identified/outer set
misspecification
nonconflicting hypothesis
Robust Identified set
JEL: 
C12
C21
C26
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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