Quantile regression for duration models with time-varying regressors

Since the seminal work of Koenker and Bassett (1978), quantile regression has become a widely used tool in duration analysis. The existing literature, however, has focused on time-invariant regressors, even though time-varying regressors are common in practice. In this paper, we introduce a quantile regression framework with time-varying regressors and develop quantile regression estimators. Our estimators are motivated by Manski's (1975, 1985) maximum score estimator and Chen's (2010) integrated maximum score estimator. Our estimators are consistent and asymptotically normal under some regularity conditions, and perform well in finite samples. Our method is illustrated with an unemployment duration data set.