Estimating the density of unemployment duration based on contaminated samples or small samples

In estimating a density function for the duration of unemployment, we consider two departures from what would be ideal conditions. If the so-called digit preference effect produces local distortion in observed samples, we can apply a maximum entropy density estimation method. To establish the functional form of the density, we maximize entropy subject to moment restrictions. The global shape of the density is determined by the lower ordered sample moments which are not affected much by the digit preference effect. As a by-product of this method, we can establish the local transition structure of the digit preference effect. As a second case of departure from an ideal condition, we consider coarse sample observations where unemployment duration was observed only for 4, 10, 14, 26, and 52 weeks. Once the unemployment duration density is derived, quintile behavior over time, the Lorenz curve, and the Gini coefficient for the distribution of unemployment duration can be obtained. Finally, we discuss the ramifications of only focusing on the headcount ratio of unemployment when other information is available.