Binary Outcome Models with Extreme Covariates: Estimation and Prediction

TL;DR

This paper introduces a semiparametric approach using Bayes' theorem and regularly varying functions to model and predict binary outcomes influenced by extreme events, with applications in financial risk analysis.

Contribution

It develops a novel tail estimation method that handles unobserved tail properties and simplifies implementation by linking to panel Logit models.

Findings

The method accurately estimates tail effects in binary outcomes.

Application shows small banks' risk increases with housing price drops.

Establishes consistency and asymptotic normality of the estimator.

Abstract

This paper presents a novel semiparametric method to study the effects of extreme events on binary outcomes and subsequently forecast future outcomes. Our approach, based on Bayes' theorem and regularly varying (RV) functions, facilitates a Pareto approximation in the tail without imposing parametric assumptions beyond the tail. We analyze cross-sectional as well as static and dynamic panel data models, incorporate additional covariates, and accommodate the unobserved unit-specific tail thickness and RV functions in panel data. We establish consistency and asymptotic normality of our tail estimator, and show that our objective function converges to that of a panel Logit regression on tail observations with the log extreme covariate as a regressor, thereby simplifying implementation. The empirical application assesses whether small banks become riskier when local housing prices sharply decline, a crucial channel in the 2007--2008 financial crisis.