A major issue in the analysis of unemployment durations concerns distinguishing genuine duration dependence of the exit rate out of unemployment from unobserved heterogeneity. We present a method for the nonparametric estimation of both phenomena, designed to be applicable to time-series data on aggregate outflows from different duration classes. The model explicitly takes into account that individual exit rates are affected by the business cycle and by seasonal effects. The method is applied to U.S. data. We find diverging duration effects among black and white individuals. However, except for white males, duration dependence is dominated by unobserved heterogeneity.