A Parametric Estimator for Multi-State Duration Models with an Application: The Yield Curve Slope as a Predictor of the US Recessions

Abstract

This paper proposes a new approach for the estimation of multi-state duration models with arbitrary number of transient and absorbing states. The approach is based on linking the multi-state duration models to the multi-state qualitative response models formally. The product integral in conjunction with the Jacobsen Construction Theorem is the main tool in establishing this formal link. The product integral is a convenient tool for expressing the transition probabilities in terms of the cumulative transition intensities. I demonstrate the convenience the product integral offers by obtaining formal asymptotic solutions connecting the asymptotic transition probabilities to the asymptotic cumulative transition intensities for the competing risks, two-state switching and three-state illness-death models, first. Then, taking a departure from the Jacobsen Construction Theorem, I establish the said formal link between the multi-state duration and multi-state qualitative response models in continuous time. The established formal link provides a flexible framework in which several important issues such as censoring, duration dependence, endogeneity and frailty can be addressed with ease. Finally, I compare and contrast some implications of the approach with those of several other approaches in a simple time-series problem with two transient states, the expansion and recession states of the US economy, and study the likelihood of recessions in the US as signaled by the slope of the US yield curve.