​Economics Seminar | Robust Asymptotic Inference about Conditional Tail Properties: A Panel Data Approach 

I consider inference about conditional tail properties such as conditional tail index and conditional extremal quantile. Most existing suggestions with extremal quantile regression as the leading approach rely on the key assumption that the tail shape of the underlying conditional distribution remains unchanged given different conditional values, implying that the conditional extremal quantile can be approximated by a location-scale model. However, this assumption holds only in limited cases such as joint normal distribution. To construct robust interence with imposing only mild regularity conditions, I develop asymptotically valid confidence intervals for conditional tail properties based on panel data and extreme value theory. These intervals allow for unobserved heterogeneity and dynamic panel, and have excellent small sample coverage and length properties. To illustrate their empirical use, I study (i) tail risj of the U.S stock return given stock sie and (ii) the extremely low quantile of infant birthweight given mother’s net weight gain during pregnancy.