In countries with publicly financed health care systems, waiting time--rather than price--is the rationing mechanism for access to health care services. The normative statement underlying such a rationing device is that patients should wait according to need and irrespective of socioeconomic status or other non-need characteristics. The aim of this paper is to test empirically that waiting times for publicly funded specialist care do not depend on patients' socioeconomic status. Waiting times for specialist care can vary according to the type of medical specialty, type of consultation (review or diagnosis) and the region where patients' reside. In order to take into account such variability, we use Bayesian random parameter models to explain waiting times for specialist care in terms of need and non-need variables. We find that individuals with lower education and income levels wait significantly more time than their counterparts.