Economics External Seminar: Joachim Freyberger (U. Madison)
Joachim Freyberger (U. Madison)
1B6 Priory Road Complex
Title: Inference under shape restrictions
Abstract: We propose a uniformly valid inference method for an unknown function or parameter vector satisfying certain shape restrictions. The method applies very generally, namely to a wide range of finite dimensional and nonparametric problems, such as regressions or instrumental variable estimation, to both kernel or series estimators, and to many different shape restrictions. One application of our inference method is to construct uniform confidence bands for an unknown function of interest. These bands are build around a shape restricted estimator and the upper and lower bound functions are consistent with the shape restrictions. Moreover, the bands are asymptotically equivalent to standard unrestricted confidence bands if the true function strictly satisfies all shape restrictions, but they can be much smaller if some of the shape restrictions are binding or close to binding. We illustrate these sizable width gains as well as the wide applicability of our method in Monte Carlo simulations and in an empirical application.