A class of binary response models for grouped duration data

Abstract

This paper explores the relationship between conventional models for binary response such as the probit and logit, and the proportional hazard (PH) and related specifications for grouped duration data. I outline a general class of hazard models for grouped duration data based upon the choice of period‐specific distribution functions, facilitating a thorough analysis of the implications of various specifications and consideration of various issues of model identification. This class of models nests, among others, the proportional hazard, probit, and logit specifications for interval survival. I consider the implications of various specifications for hazard behaviour, focusing on familiar specifications. While the specifications will generally yield results that are quite similar along a number of dimensions, there are significant differences. The probit model generates non‐proportional effects of variables on the discrete hazard, while the logit and PH tend to show only slight non‐proportionality. Furthermore, while the effects of variables on the derivatives are considerably larger for the probit specification, the time‐pattern of the probit effects is relatively insensitive to changes in explanatory variables. I illustrate these issues by providing an example taken from Katz's (1986) unemployment data from the Panel Study of Income Dynamics.