Abstract. This paper provides a model of directed search in which workers have private information about type at the point where they make their applications to firms. Firms are able to observe these types once workers apply. The paper shows that for any smooth wage distribution there is a continuation equilibrium in which unemployed workers choose a reservation wage which is a strictly increasing function of their type, then apply with equal probability to all positions that offer more than that wage. We consider a case where matching occurs 'quickly', and show two main results. First, the wages at which workers are employed throughout their lives are correlated, but very imperfectly because of the fact that equilibrium involves a lot of mismatch. Second, the variance of future income of workers must be a decreasing function of the wage at which they are currently employed. In other words, high wage workers will enjoy more stable lifetime income.

Abstract. These results make it possible to distinguish between the three main models of directed search empirically. The imperfect correlation - declining variance results in this paper contrast sharply with the classic directed search, where wages are uncorrelated over time, and models with assortative matching, in which wages are perfectly correlated over time.

Abstract. The paper concludes with an analysis of data from the executive labor market from 1993 to 2009.