We develop an equilibrium directed search model of the labor market where workers can simultaneously apply for multiple jobs. Our main theoretical contribution is to integrate the portfolio choice problem faced by workers into an equilibrium framework.All equilibria of our model exhibit wage dispersion. Consistent with stylized facts, the density of wages is decreasing and higher wage firms receive more applications per vacancy. Unlike most models of directed search, the equilibria are not constrained efficient.

We develop and analyze a labor search model in which heterogeneous firms operate under decreasing returns and compete for labor by publicly posting long-term contracts. Firms achieve faster growth by offering higher lifetime wages that attract more workers which allows to fill vacancies with higher probability, consistent with empirical regularities. The model also captures several other observations about firm size, job flows, and pay. In contrast to existing bargaining models, efficiency obtains on all margins of job creation and destruction, both with idiosyncratic and aggregate shocks. The planner solution allows a tractable characterization which is useful for computational applications.

Assortative Matching between workers and firms provides evidence of the complementarities or substitutes in production. The presence of complementarities is important for policies that aim to achieve the optimal allocation of resources, for example unemployment insurance. We argue that using wage data alone, it is virtually impossible to identify whether Assortative Matching is positive or negative. Even though we cannot identify the sign of the sorting, we can identify the strength, i.e., the magnitude of the cross-partial, and the associated welfare loss. We show first that the wage for a given worker is non-monotonic in the type of his employer. This is due to the fact that in a sorting model, wages reflect the opportunity cost of mismatch. We show analytically that this non-monotonicity prevents standard firm fixed effects to correlate with the true type of the firm. We then propose an alternative procedure that measures the strength of sorting in the presence of search frictions. Knowing the strength of sorting facilitates the measurement of the output loss due to mismatch.

Using administrative panel data on 100% of Danish population we document a new set of facts characterizing the patterns of occupational mobility. We find that a worker's probability of switching occupation is U-shaped in his position in the wage distribution in his occupation. It is the workers with the highest or lowest wages in their occupations who have the highest probability of leaving the occupation. Workers with higher (lower) relative wage within their occupation tend to switch to occupations with higher (lower) average wages. Higher (lower) paid workers within their occupation tend to leave it when relative productivity of that occupation declines (rises). These facts are not implied by existing theories of occupational mobility that mostly treat occupations as horizontally differentiated sets of tasks. We suggest that it might be productive to think of occupations as forming vertical hierarchies. Workers who are unsure of their abilities learn about them by observing their output realizations. Employment opportunities in each occupation are scarce inducing competition among workers for them. Complementarities in the production function between worker's ability and productivity of an occupation induce sorting of workers into occupations according to their expected ability. We present an equilibrium model of occupational choice with these features and show analytically that it is consistent with patterns of mobility described above.