Simultaneous equations for hazards: Marriage duration and fertility timing

Abstract

The concept of simultaneous equations has been a fundamental contribution of econometrics. While the concepts have been extended quite fruitfully to limited and qualitative dependent variable models, they have been rarely applied to hazard or duration (failure time) models. This paper develops an approach to simultaneity among hazard equations which is similar in spirit to simultaneous Tobit models. It introduces a class of continuous time models which incorporates two forms of simultaneity across related processes - when the hazard rate of one process depends (1) on the hazard rate of another process or (2) on the actual current state of or prior outcomes of a related multi-episode process. This paper also develops an approach to modeling the notion of ‘multiple clocks’ in which one process may depend on the duration of a related process, in addition to its own. Maximum likelihood estimation is proposed based on specific parametric assumptions. The model is developed in the context of and empirically applied to the joint determination of marital duration and timing of marital conceptions.