Rohit KUMAR will defend his thesis on " Essays in Partial Identification " on Thursday 30 August 2018, at 2.30pm, room MQ 212 (Manufacture des Tabacs).
Supervisor : Christian BONTEMPS
Jury :
- Professeur Marc HENRY, Penn State University
- Professeur Aureo de PAULA, University College London
- Professeur Thierry MAGNAC, Professeur TSE
- Professeur Christian BONTEMPS, Professeur TSE
Abstract:
In the first paper (joint with C. Bontemps), we provide a general methodology to sharply characterize the game theoretical models with complete information. The set of choice probabilities, implied by the model, is a convex set. However, the number of inequalities required to sharply characterize the convex set is growing exponentially with the number of players. We reduce this complexity first by eliminating the redundant inequalities or finding the core determining class. Secondly, we characterize the local geometry of the convex set which provides the set of inequalities sufficient to check whether a point belongs to the convex set or not. For any point, the local geometry is exponentially smaller than the core determining class, but this local geometry depends on the point being tested. Finally, we propose a procedure which selects the appropriate local geometry for any point. We also apply our methodology to entry game, ordered response game and social interaction game.
In the second paper (joint with C. Bontemps), we provide inference procedures for game theoretical models with complete information. The identified set can be characterized by the support function of the set of choice probabilities implied by the model. The support function based characterization of these models is particularly useful as the distribution of the test statistic depends on the parameters only through the set of binding inequalities. Using the geometry of these games, we upper bound the test statistics by a quantity whose distribution doesn’t depend on the parameters. We provide simple upper bounds for inference for points in the identified set as well as for inference on the identified set itself. The finite-sample properties of the procedure, via simulation studies, remain competitive with existing procedures while being computationally more attractive.
The third paper provides feasible methods for inference in a very general class of partially identified econometric models defined by unconditional or conditional moment inequalities with discrete regressors. The goal is to draw inference about points in the identified set. In the first stage, we test multiple hypotheses for the binding inequalities using a simple step-down procedure and then use this information in the second stage to provide a testing procedure that controls size pointwise. Bonferroni, as well as alternate correction, is used to account for the fact that, with some probability, the first stage test may result in the error. The procedure is subsequently extended to models with discrete conditional moment inequalities. Simulations demonstrate the better finite sample properties of our procedure compare to the existing methods.
