Introduction

Economic data are rarely homogeneous; we seldom have observations that can be regarded as repeated drawings from the same probability distribution. We normally must allow for measured, and possibly for unmeasured, systematic differences between people, firms, or whatever is the unit of observation. In this chapter we shall introduce regressors or covariates explicitly into the hazard function and discuss the various types of covariate that econometricians seem likely to want to consider. We shall see that some of the relations of chapter 1 can fail to hold when covariates are present.

We shall suppose in this section that all covariates are fully observed by the econometrician. In chapter 4 and subsequently in many parts of the book we shall deal with models containing unobserved covariates.

Time-Invariant Covariates

The simplest covariates are those which do not change over time. Two examples might be the sex or the race of a person. More generally, the relevant characteristics of an agent at the time of entry to the state under study, that is, his relevant biography to that point in time, constitute a set of duration-invariant regressor variables. Other variables can and do change as the duration of stay changes, but at a sufficiently slow pace relative to typical durations of stay that, for practical purposes, they can be treated as if they were constants. Two examples might be the age of a person, or the state of the business cycle, in the context of studies of unemployment duration.