Robust Inference and Specification Analysis in Incomplete Models

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Empirical researchers in social science often face situations in which their models or data are in- complete. Such incompleteness arises when researchers do not want to impose strong assumptions on parts of their model or some of the data are missing for reasons not known to the researcher. Incomplete models occur in many empirical studies, such as strategic voting, product choice, school choice, and network formation. Incomplete observations of data are common in studies that evaluates public or business policies. This research will develop new statistical methods that allow researchers to estimate incomplete models and conduct hypothesis testing in a way that does not depend on how the model is written. The research will develop a theoretical framework for understanding the best statistical procedures to judge the costs of incorrect models. The project will also develop computer programs for implementing the proposed estimation and hypothesis testing procedures that will be freely distributed to the public through an online repository. The results of this research will improve policy evaluation, hence establish the US as the global leader in policy evaluation.This research will develop a likelihood-based framework for robust inference and specification analysis in incomplete models. It will study a class of models that have one of the following structures: i) given a structural parameter and observable and unboservable variables, the model predicts a set of values for an outcome; or ii) given a structural parameter and observable and unboservable variables, the model predicts a unique value of outcome, but the researcher only observes a set-valued outcome. Such models are nonstandard because they may admit multiple likelihood functions. Identification and inference methods based on moment inequalities have been extensively studied recently, but an alternative likelihood-based approach is less explored. The research aims at developing a novel framework for constructing robust estimation and inference procedures based on the least favorable pair of likelihoods and its associated scores. Furthermore, it will provide a framework for understanding the consequences of model misspecification in the presence of model or data incompleteness and introducing the notion of pseudo-true identified sets. The methods developed in this research will be useful for policy evaluation, hence contribute to effective policy formulation and implementation of efficient policies in the U.S. and elsewhere.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.