We estimate conditional quantiles of unemployment duration, using a method for interval-censored quantile regression. We apply a modeling approach in which the regression coefficients, \(\varvec{\beta }(p)\) , are described by parametric functions. Compared with standard quantile regression, in which quantiles are calculated one at a time, the proposed method drastically simplifies estimation and inference and makes it simpler to report and interpret the results. We discuss goodness-of-fit measures, present a simulation study, and describe the R package \(\texttt {qrcm}\) that provides the necessary functions for estimation, inference, and prediction. Our results show that age, education, and other individual and household-level covariates significantly affect unemployment duration. While the estimated effects generally align with the existing literature, most predictors exhibit heterogeneous effects across quantiles, suggesting a complexity that standard location-scale or proportional hazards models may fail to capture.
