This research studies identification and estimation problems that arise in parametric models with minimal plausible assumptions. Researchers commonly impose prior and sometimes untestable information (assumptions). If these assumptions are wrong, inference will be misleading. This research consists of four projects to study inference in incomplete models without making strong assumptions. It will provide empirical researchers with a richer menu of approaches to tackle a given problem using more robust methods. These robust methods shed light on the effects of the various, routinely made (point) identification assumptions.
Without making ad-hoc assumptions, oftentimes parametric models do not point identify the parameters of interest; rather, the identified feature of these partially identified models is a robust set of parameter values. This research shows that robust inference in partially identified models is practical, and of immediate relevance to empirical work. The first project examines the effect of ignoring measurement error in binary choice probit models. Without further assumptions, the binary choice model is not identified in the presence of covariate measurement error. This project will answer whether ignoring measurement error would lead to estimates that are "far away" from the "truth". This approach to inference can be used to answer similar questions in a wide variety of partially identified models.
The second project proposes a way to examine robustness in a classic panel data problem. A problem in this class of models is the need to make assumptions distribution of initial condition for point identification. This research relaxes these assumptions by providing methods to estimate the set of parameter values that is consistent with the econometric model and the data, a parameter set that is robust to ad-hoc and inconsistent assumptions on the initial conditions. The third project will provide a general framework for inference in discrete K-player games and apply it to study market structure in the airline industry. Inference is based on a class of models that is defined as the set of utility functions that obey necessary Nash equilibrium conditions. It will study the identified feature of this class of models and will apply the methods to examine an important empirical problem, thus showing the policy applicability of these models. The fourth project describes an econometric methodology to obtain asymptotically valid confidence regions that cover the identified set in a partially identified model with a pre-specified probability. This research integrates teaching and research through research experience for undergraduates as well the use of graduate assistants and the integration of a graduate course on robust inference.
