Novel Approaches to Nonlinear Panel Data Analysis and Model Selection

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This project will devise methods to handle the uncertainty that often is encountered in economic and statistical modeling. The project considers uncertainty taking the form of (i) unobserved variables and (ii) imperfect knowledge of the model itself. The first part of the project focuses on nonlinear panel data models, which currently are receiving considerable attention in economic and statistical modeling because they provide a natural way to describe the heterogeneity present in a population. These models share the feature of including various unobserved variables that represent factors that are constant over time but vary over individuals. The project will combine the ideas of entropy maximization and simulation-based estimation to handle, in a unified framework, the unobservable variables present in a wide range of nonlinear panel data models. The approach used aims to bypass the complex task of establishing identification of the model without sacrificing explanatory power. The second part of this project proposes a new, simple, approach to model selection that relies on method of moments estimation, adapted to deliver tests that are identically distributed whether or not the candidates models are overlapping. Model selection historically has received a lot of attention, but often involves the cumbersome step of "pre-testing" to first decide if the candidate models are overlapping or not. The key to avoiding pre-testing is to smoothly interpolate (rather than discontinuously switch) between a method valid for overlapping models and a method valid for non overlapping models.Given the large number of researchers focusing on nonlinear panel data models and model selection, any new development within these fields is likely to be of interest to a large community in virtually all fields of the social, medical, mathematical, and natural sciences. Ultimately, this project will enable more accurate statistical inference in these fields and permit the practical use of more general statistical models. Computer programs implementing the methods will be made publicly available.