Assessing the Proportionality Assumption in Default Rate Forecasting Using the Proportional Hazard Model

Abstract

The first generation quantitative bankruptcy prediction models are not designed to accommodate the time dimension. To overcome this limitation, various dynamic models based on survival analysis are developed recently. Among them, Cox (1972)’s proportional hazard model has been widely used in various fields because of the advantage of being free of distributional assumptions. The proportionality assumption, however, must be applied precisely when there is a potential structural change. In this paper, we assess the violation of proportionality assumption in the firm failure prediction model built around the Cox’s proportional hazard model and proposed non-proportional hazard model. We also examine the effect of macroeconomic variables to suggested non-proportional hazard model. We perform an investigation using the Korean stock market since the market, which has experienced two well-known structural changes caused by the Asian financial crisis and 2008 Global financial crisis, is well suited for analyzing the impact of the proportionality assumption on the appropriateness and predictability of the Cox’s proportional hazard model. It is shown that a non-proportional hazard model including a change point is a proper alternative, when the proportionality assumption is violated.

Keywords: Cox’s proportional hazard model, proportionality assumption, macroeconomic variable