We propose a new econometric estimation method for analyzing the probability of leaving unemployment
using uncompleted spells from repeated cross-section data, which can be especially
useful when panel data are not available. The proposed method-of-moments-based estimator
has two important features: (1) it estimates the exit probability at the individual level and (2)
it does not rely on the stationarity assumption of the inflow composition. We illustrate and
gauge the performance of the proposed estimator using the Spanish Labor Force Survey data,
and analyze the changes in distribution of unemployment between the 1980s and 1990s during
a period of labor market reform. We find that the relative probability of leaving unemployment
of the short-term unemployed versus the long-term unemployed becomes significantly higher in
the 1990s.