Search externalities in a Jackson queuing model for the labormarket

In this paper it is argued that unemployment is more related to waiting than to searching. In particular we focus on a congestion externality that employers and searchers place on the other searchers. This externality arises because the expected waiting time of unemployment increases with the amount of searchers relative to the amount of open jobs and the time employers need to screen the applicants. We have modeled the labor market as a Jackson queuing network which enabled us to make a distinction between the time a worker spends searching and the time he spends "waiting". Within this framework we were able to derxve analytical solutions for steady state unemployment and average waiting time. In the model, unemployed workers can only partly influence the duration of unemployment. Because of this, the resulting equilibrium is unlikely to be efficient. In equilibrium workers may decide not to participate although their reservation wage can be lower than the social marginal product. We also give a rational explanation for the discouraged worker effect. In severe recessions when many persons start searching, expected unemployment duration will increase and hence the expected benefits of entering the labor market will decrease. The author franks F.A. G. den Butter for useful comments and E. Brouwer for drawing the figures. Introduction In the Standard literature of job search theory, a representative worker samples wage offers sequentially and decides on the basis of the sample obtained whether or not to continue searching, see e.g Lucas and Prescott (1974). Those models often ignore externalities that arise when many persons search at the same time. One type of such an externality is described in Diamond (1982 b). Diamond shows that an increase in the number of potential trading partners increases the probability of a successful match. Other externalities are related to congestion effects in the search process, see for example Tobin (1972). The probability for an unemployed individual to find a job is likely to be lower, the larger the stock of unemployed, is the basic message. This type of externality does not differ in its origin significantly from the type of externality that the seller of any good imposes on other sellers. Other extensions of this idea can be found in Diamond (1981) where a worker can generate a negative externality if he reduces his reservation wage to fill a vacancy. This action reduces the stock of vacancies and hence the probability for other searches to find a job. This type of externality depends crucially on the assumption that the number of jobs is fixed. Another type of externality arises when productivity is match specific and revealed when a worker and a vacancy are matched. The meeting firm and worker are not likely to take into account the effect of their choices on other firms and workers still searching, this may lead to socially inefficient outcomes, see Diamond (1982:a), Mortenson (1982) and Pissarides (1990). If wages are determined by the outcome of a bilateral bargaining game, a match will only take place if the wage is within the interval determined by the reservation wage of the worker and the maximum wage the worker wants to pay. If there is a surplus, it is assumed that this surplus is shared between worker and employer. If the employer's share is high, this implies that the private return to a match is lower than the social return (marginal product) of a match. In the Standard stopping model of search unemployment there will be too few searchers. But if the worker share is high, unemployment may well be above the social optimum because the private return to search effort is lower than the marginal product of the match. A higher worker share of the match reduces the number of jobs and it raises the expected wages. Pissarides (1990) shows that if the surplus of a match is shared in a way that maximizes the expected returns of the unemployed, the outcome is socially efficient. This outcome can be reached under a centralized bargaining system. In this paper, we will focus on a different but related type of (congestion) externality. Given the fact that the application process takes some time, because for example application letters have to be read or interviews have to be taken, an increase in the number of searchers will influence the average waiting time of the other searchers and will indirectly lower the hazard rate out of unemployment. Moreover, 1 See Lucas and Prescott (1974) 1 employers who let applicants wait before inviting them for an interview do not intemalize the Costs of the waiting applicant. An increase in the expected "waiting time" and a decrease of the hazard rate will lower the expected returns on search, hence the number of searchers will be lower than the social optimum. In the model, three groups are distinguished; unemployed workers, employed workers and non participants. Every unit of time, people "flow", from one group to another. We will analyze those flows within a queuing framework. The advantage of this approach is that we can take a lot of factors into account that are important to explain the existence of unemployment for a relatively low price in terms of increasing complexity. The strategy that will be foliowed is not to derive all ideas from "first principles" but rather to refer to the existing literature in which those ideas have been derived rigorously. We will distinguish two obstacles that the unemployed have to take before they become employed. The first one is caused by the time the unemployed worker spends on searching for vacancies and waiting to get invited for an interview, the second one is determined by the application process (interviews and waiting till the employer has made his decision). The more people there are in the system, the longer the average waiting time will be. Thus the entrance of one worker will increase the waiting time of other workers. We will also take into account that people who are unemployed for a longer period of time loose human capital and become discouraged, because of that they face a lower probability of finding a successfiil match and devote fewer resources to search. This "persistence" of unemployment is what we observe in many European Countries. In addition we will assume, following Darby et al. (1985) that (older) workers with a lot of firm specific capital need to spend a longer time searching to find a successfiil. match, once they have become unemployed. Another stylized fact of labor markets is that, especially in the U.S., the search behavior of young workers is characterized by short employment spells (job hopping). This aspect is taken into account by assuming that alter a match has taken place, both employer and worker need to spend some time to learn about the real quality of the match. After that, a decision is made whether to continue the relationship or to separate. Separated workers have to start the search process again. The distinction between voluntary and involuntary unemployment is not very relevant here. In this model people can speed up their search process by accepting a lower wage. On the other hand, the duration of the application process is determined by the employers and there is also some time involved between the moment of application and the moment the worker knows whether he will be 2 If the supply of jobs would increase directly with the number of searchers, average waiting time can remain constant 2 invited for an interview or not. In this sense, the duration of unemployment is out of control of the unemployed worker. The outline of the paper is as follows: In section 1, the model with its assumptions will be presented. In section 2, the number of unemployed in the steady state will be derived as a function of the parameters of the model. We will show how expected unemployment duration infiuences wages in section 3. Finally in section 4 we will investigate whether the resulting search equilibrium is likely to be efficient.