تعادل بیکاری جستجوگر با اصطکاک فضایی صریح

Assuming that job search efficiency decreases with distance to jobs, workers' location in a city depends on spatial elements such as commuting costs and land prices and on labour elements such as wages and the matching technology. In the absence of moving costs, we show that there exists a unique equilibrium in which employed and unemployed workers are perfectly segregated but move at each employment transition. We investigate the interactions between the land and the labour market equilibrium and show under which condition they are interdependent. When relocation costs become positive, a new zone appears in which both the employed and the unemployed co-exist and are not mobile. We demonstrate that the size of this area goes continuously to zero when moving costs vanish. Finally, we endogeneize search effort, show that it negatively depends on distance to jobs and that long and short-term unemployed workers coexist and locate in different areas of the city.

It has been recognized for a long time that distance interacts with the diffusion of information. In his seminal contribution to search, Stigler (1961) puts geographical dispersion as one of the four immediate determinants of price ignorance. The reason is simply that distance affects various costs associated with search. In most search models, say for example Diamond, 1981 and Diamond, 1982, distance between agents or units implies a fixed cost of making another draw in the distribution. In other words, a spatial dispersion of agents creates more frictions and thus more unemployment. Conventional labour economics faces difficulties in thinking about these spatial differences because it is biased towards the notion of a spaceless marketplace ruled by the walrasian auctioneer. This is a weakness of the analysis since empirical evidence supports the idea of a clear spatial dimension of labour markets (see for example the literature survey by Crampton, 1999). There are in fact several channels through which space affects the labour market. First, workers who live further away from jobs may have poorer labour market information and be less productive than those living closer to jobs ( Seater, 1979). This is particularly true for younger and/or less-skilled workers who rely heavily on informal search methods for obtaining employment ( Holzer, 1987). 1 The reliance on these informal methods of job search suggests that information on available job opportunities may decay rapidly with the distance from home ( Ihlanfeldt and Sjoquist, 1990). Second, distance also implies higher commuting costs for the unemployed, which directly affect the search process ( Van Ommeren et al., 1997). Third, workers residing too far away from jobs may quit their job more frequently because of too long commuting distances ( Zax and Kain, 1996). Finally, employers may discriminate against applicants living in remote areas because of lower productivity ( Zenou, 2002). As a result it is commonly observed that unemployment rates differ strongly across as well as within local labour markets (see e.g. Blanchflower and Oswald, 1994, Marston, 1985 and Topa, 2001). The interaction between space and labour markets is thus complex. We have divided our research questions into two parts. In a companion paper (Wasmer and Zenou, 2002), the focus was mainly urban and we have explicitly studied all possible urban configurations in a job-matching framework. We have in particular shown how a public transportation policy strongly depends on which type of urban equilibrium prevails. The aim of the present paper is to focus instead on the labour market aspects of urban equilibria. To this purpose, we focus on the most relevant urban equilibria of Wasmer and Zenou (2002), the one in which the unemployed reside far away from jobs. Within this urban equilibrium, we systematically explore the role of space, and notably the spatial dimension of search. We have more specifically three questions in mind: Does search equilibrium strongly depend on these spatial terms? Do relocation costs strongly affect the equilibrium? Is long term unemployment a phenomenon interacting with space? Our answers are yes to these three questions. In our approach, the matching of jobs and workers is a time-consuming process and the number of matches per unit of time between workers and open vacancies is represented by an aggregate matching function (à la Diamond-Mortensen-Pissarides). Even if firms pay workers their reservation wage, there is still some unemployment in the area (due to stochastic rationing not being eliminated by price adjustment). However, in this line of search models, the spatial dimension is often implicit. Here, we explicitly introduce it by considering that the distance between workers' residential locations and jobs plays an adverse role in the formation of matches. In this respect, our model can be viewed as a natural extension of the standard matching model. The land market will be kept rather simple in order to provide closed-form solutions. We consider a closed piece of land (that can be thought as an urban area, a city, an agglomeration or a region). This area is monocentric, i.e., firms are exogenously located in an employment center and workers consume inelastically one unit of space. In our analysis, local factors (rental price, distance to the employment center) and global factors (labour market tightness, wages) influence workers' location decisions, i.e. the land market equilibrium. Within this framework, we can have different land market equilibria. We only focus here on the equilibrium in which the unemployed reside far away from the employment center. We first study the case of zero-relocation costs so that workers change location as soon as they change employment status. We derive the labour market equilibrium in which spatial unemployment is due to frictions in the labour market. On the one hand, the land market equilibrium depends on aggregate variables (such as wages and labour market tightness) since these variables affect location choices of workers. On the other hand, the labour market equilibrium crucially depends on the land market equilibrium configuration. Indeed, the efficiency of aggregate matching depends on the average location of the unemployed. We first show that there exists a unique and stable market equilibrium in which both land and labour markets are solved for simultaneously. We then show that space has an important role on the interaction between land and labour markets. We notably decompose the equilibrium unemployment rate into two parts: a pure non-spatial one (which corresponds to the standard matching model) and a mixed of non-spatial and spatial elements, the first element amplifying the other one. In other words, space adds to search frictions in the labour market by making the access to jobs more difficult. We then investigate the case of positive moving costs paid when agents relocate within the city.2 Between the two perfectly segregated areas appears a zone where both the employed and the unemployed co-exist and are not mobile. We show that the size of this area goes continuously to zero when moving costs vanish. We finally study the endogeneity of job search effort. We show that long and short-term unemployed workers emerge and locate in different parts of the city. The remainder of the paper is organized as follows. The next section presents the model with no relocation costs and shows the different roles of space in the determination of equilibrium unemployment. Section 3 analyzes the role of positive relocation costs. Section 4 analyzes the case of endogenous search effort. Finally, Section 5 concludes.

In this paper, we have modelled the important interaction between the spatial dispersion of economic agents and the imperfection in information about economic opportunities. We have first demonstrated that there exists a unique and stable market equilibrium in which both land and labour markets are solved for simultaneously. We have investigated how space affects search by focusing on the interaction between land and labour markets. We have explored the mechanics of causality from the labour market to the land market and reciprocally, and further decomposed unemployment into a spatial part and a spaceless part. We have also shown the importance of relocation costs since it introduces a new area in the city where employed and unemployed workers are immobile. Finally, we have seen that when distance and search effort are complement in the cost function of individuals, long-term and short-term unemployed endogenously emerge and locate in very different location within a city.