True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model

Abstract

Lancaster and Nickell (1980) have argued that in the proportional hazard model the effects of time dependence (true duration dependence) and unobserved sample heterogeneity (spurious duration dependence) cannot be distinguished. We show that both effects can be distinguished if the model allows for observed explanatory variables in the hazard. We also discuss the application of our result to practical situations.

Temporary layoffs and the duration of unemployment

“…Identification is also aided by the existence of repeated unemployment spells, since v i is assumed constant at the individual level across different spells. As proved by Elbers and Ridder (1982), the Mixed Proportional Hazards model that we use in the present paper is ident ified even without variation in lagged covariates and without multiple spells; variation in current covariates is sufficient. However, in that case the identification rests heavily on the proportionality assumption, for which we have no theoretical justification.…”

An empirical analysis of the importance of controlling for unobserved heterogeneity when estimating the income-mortality gradient

“…Elbers and Ridder (1982) prove the nonparametric identification of both a hazard rate's duration dependence and the unobserved heterogeneity distribution when assuming the multiplicative specification formalized in equation (1). 5 Such identification is, however, impossible using a left-truncated sample and an assumption is needed concerning the distribution of unobserved heterogeneity.…”

“…survival up to the age of sample entry (see Online Supplementary Appendix A). 7 This modeling is based on predicted mortality risks at 5 Elbers and Ridder (1982) prove that, in this case, the densities of duration (conditional on unobserved heterogeneity) and unobserved heterogeneity are separately and non-parametrically identified from observed individuals' (incomplete) durations when the risk model contains at least one continuous covariate and an assumption concerning either the first moment (needs to be finite) or the tail behavior of the mixing distribution. A semi-parametric estimator is provided in Horowitz (1999).…”

The effect of temporary in-work support on employment retention: Evidence from a field experiment

“…Elbers and Ridder (1982) prove identification of both the unobserved heterogeneity (or, 'mixing') distribution and the baseline hazard in single-spell models under assumptions about the mixing distribution, so long as there is variation in regressors. Honoré (1993) shows that identification is achieved without the need for regressor variation or an assumption about the mixing distribution when multiple spells are observed.…”