Two-step estimation of censored quantile regression for duration models with time-varying regressors

Common duration models are characterized by strong homogeneity and thus are highly restrictive in allowing for how regressors affect the conditional duration distribution. In particular, the implied sign and relative marginal quantile effects remain the same over the entire range of the conditional duration distribution, which rules out general heterogeneous effects in duration data. Quantile regression, which offers a flexible and unified framework that allows for general heterogeneous effects, is particularly well suited to duration analysis. Based on the insights behind the accelerated failure time model (AFT) with time-varying regressors (Cox and Oakes, 1984) and the standard quantile regression model (Koenker and Bassett, 1978), Chen (2019) recently developed a quantile regression framework with time-varying regressors. However, Chen’s (2019) estimator is very difficult to compute because the estimation procedure involves a non-convex and nonlinear high dimensional optimization problem due to censoring and the nonlinearity of the quantile function. In this paper I propose an easy-to-implement two-step quantile regression estimator, which significantly reduces the computational burden. The estimator is shown to be consistent and asymptotically normal. Monte Carlo experiments indicate that our estimator perform well in finite samples.