A Search Model

The model is a generalized search model in the spirit of Mortensen and Pis- sarides (1994). Although this model is used as an example, any search model can be written to produce arrival and separation rates for each type of worker and produce these flows. To incorporate a participation margin, I use a search decision when a worker is not employed. Agents are heterogeneous in that they consist of two types, dictating inactivity or unemployment when not employed. In this case, type com­pletely dictates an agent’s search behavior, but any mechanism such as a search cost can be used to generate such a search decision.

Workers match with vacancies in a frictional labor market, with probabilities dependent on their type. Once employed, workers earn a wage and separate at a uni­form rate. Wages could be determined through any mechanism such as generalized Nash bargaining or directed search, so long as the separation rate remains exoge­nous in steady-state. An idiosyncratic shock process governs the transition of agents between types.

Environment

The economy is populated by a continuum of workers with measure one and a continuum of firms of positive measure. Both workers and firms are infinitely lived. Time is discrete, and both workers and firms discount the future at p G [0,1]. Workers have linear utility functions over discounted future consumption.

At the beginning of a period, an employed worker loses his job with probability ỏ G [0,1]. If an employed worker loses his job, he cannot apply to the labor market in that period.

Agents face idiosyncratic uncertainty in their type, determining the probabil­ity si, i G {n, u} that they will be able to reach the labor market in a given period. If unemployed, they have probability su of reaching the labor market, and if a non­participant, they can reach the labor market with probability sn, where su > sn. The labor market in the economy matches workers who reach the labor market with va­cancies randomly through a constant returns to scale matching function. If a worker reaches the labor market, they match with a vacancy with probability p(ớ), where 0 is the tightness ratio in the labor market. The probability that a worker of type i becomes employed is thus Ai = sip(ớ).

After matching, an agent of type i who is not employed receives b. Note that since all agents without a job get b, it can be thought of as home production, or that everyone receives an identical benefit from nonemployment. The classification of a non-employed worker as unemployed or inactive next period is completely dependent on an agent’s type. To keep the type and labor force participation status of an agent distinguishable, I will refer to the type of the worker as a search cost type. Those who choose nonemployment are ‘high search cost’ types, and types who choose unemployment when not employed will be referred to as ‘low search cost’ types. Employed workers produce y units of output and consume w as specified in the labor market. At the end of the period, nature draws the type i! of each agent from probability distribution x(iz|i). The expectation over the state tomorrow, E, is over types.