Instrumental Variable Estimation for Duration Data

Abstract

In this article we develop an Instrumental Variable estimation procedure that corrects for possible endogeneity of a variable in a duration model. We assume a Generalized Accelerated Failure Time (GAFT) model. This model is based on transforming the durations and assuming a distribution for these transformed durations. The GAFT model encompasses two competing approaches to duration data; the (Mixed) Proportional Hazard (MPH) model and the Accelerated Failure Time (AFT) model. The basis of the Instrumental Variable Linear Rank estimator (IVLR) is that for the true GAFT model the instrument does not influence the hazard of the transformed duration. The inverse of an extended rank test provide the estimation equations the IVLR estimation procedure is based on. We discuss the large sample properties and the efficiency of this estimator. We discuss the practical issues of implementation of the estimator. We apply the IVLR estimation approach to the Illinois re-employment bonus experiment. In this experiment individuals who became unemployed were divided at random in three groups: two bonus groups and a control group. Those in the bonus groups could refuse to participate in the experiment. It is very likely that this decision is related to the unemployment duration. We use the IVLR estimator to obtain the effect of these endogenous claimant and employer bonuses on the re-employment hazard.

Keywords: Endogenous Variable, Duration model, Censoring, Instrumental Variable

JEL Classification: C21, C41, J64