This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
This project would contribute to the literature on identification and inference in incomplete econometric models. An econometric model may be incomplete when, for example, sample realizations are not fully observable, or when the model asserts that the relationship between the outcome variable of interest and the exogenous variables is a correspondence rather than a function. In these cases, the sampling process and the maintained assumptions are consistent with a set of values for the parameter vectors (or statistical functionals) characterizing the model. This set of values is the sharp identification region of the models parameters. When the sharp identification region is not a singleton, the model is partially identified. The investigators use the tools of random sets theory to study identification in incomplete econometric models. These tools are especially suited for partial identification analysis, because they provide conditional and unconditional .probability distributions and expectations for random sets, that allow researchers to characterize the identified features of a model in the space of sets, in a manner which is the exact analog of how this task is commonly performed for point identified models in the space of vectors. The methodology that the investigators aim to develop focuses on a specific class of incomplete models, for which it provides a computationally tractable characterization of the sharp identification region. An incomplete model belongs to the class treated in the proposed research, if it predicts a convex set of conditional probability distributions of outcomes given covariates, rather than a single conditional probability distribution. Examples of models in this class include: static, simultaneous move finite games of complete information in the presence of multiple mixed strategy Nash equilibria; and polychotomous choice models with interval regressor data. These examples are explicitly analyzed in the proposal. A computationally tractable characterization of the sharp identification region of the parameters of models in this class was considered unattainable in the related literature.
Partially identified models are ubiquitous in the recent theoretical and empirical literature in economics. Although it sometimes is easy to characterize their identification region explicitly, there exist many important problems in which a tractable characterization is difficult to obtain. It may be particularly difficult to establish sharpness, that is, to show that a conjectured region contains exactly the feasible parameter values and no others. Basing inference on a conjectured region which is not sharp may significantly weaken the ability of the researcher to make useful predictions, and to test for model misspecification. The intellectual merit of this proposal is twofold: (1) To provide a methodological framework to obtain a computationally tractable characterization of the sharp identification region of a model; (2) To provide practitioners with ready to use software to apply this methodology and conduct estimation and inference when point identification is not available.
Broader impacts: The proposed methodology for characterization and computation of the sharp identification region enables practitioners to evaluate the credibility of existing policy studies, and compare the results of different approaches to policy research, by addressing both the identification aspects, as well as the statistical inference aspects of the problem. This research program aims to integrate teaching and research through research experience for undergraduates, the use of graduate assistants, and the instruction of a graduate course on inference in partially identified models using random sets theory.
