Urban unemployment and job search

Transcription

1 Urban unemployment and job search Yves Zenou Research Institute of Industrial Economics July 3, Introduction 2. A benchmark model There is a continuum of ex ante identical workers whose mass is N and a continuum of M identical firms. Among the N workers, there are L employed and U unemployed so that N = L + U. The workers are uniformly distributed along a linear, closed and monocentric city. Their density at each location is taken to be 1. All land is owned by absentee landlords and all firms are exogenously located in the Central Business District (CBD hereafter) and consume no space. Workers are assumed to be infinitely lived, risk neutral and decide their optimal place of residence between the CBD and the city fringe. There are no relocation costs, either in terms of time or money. This is a simplifying assumption, which is quite standard in urban economics. It implies that workers change location as soon as they change employment status. In the context of labor markets in which workers tend to experience long unemployment spells (for example black workers), it is a rather good approximation since, when workers become unemployed, they will be less able to pay land rents and, after some time, they will have to relocate in cheaper places. We will relax this assumption in chapter 4. Each individual is identified with one unit of labor. Each employed worker goes to the CBD to work and incurs a fixed monetary commuting cost τ per unit of distance. When living at a distance x from the CBD, he/she also pays alandrentr(x), consumesh L =1unity of land and z L unities of the non-

2 by: 1 W L (x) =w L τx R(x) (2.2) spatial composite good (which is taken as the numeraire so that its price is normalized to 1) andearnsawagew L (that will be determined at the labor market equilibrium). The budget constraints of employed workers are given by: R(x)+τx+ z L = w L (2.1) Because of risk neutrality, we assume that preferences of all workers (including the unemployed) are given by Ω(z L )=z L so that the instantaneous indirect utilities of an employed residing at a distance x from the CBD is given Concerning the unemployed, they commute less often to the CBD since they mainly go there to search for jobs. So, we assume that they incur a commuting cost sτ per unit of distance, where s 0 s 1 is a measure of search intensity or search efficiency and s 0 is the lowest possible level of search effort. It is assumed to be exogenous. Each unemployed worker earns a fixed unemployment benefit w U > 0, paysalandrentr(x), consumesh U =1unit of land and z U units of the non-spatial composite good. In this context, because the preferences are given by Ω(z U )=z U,theinstantaneous (indirect) utility of an unemployed worker is equal to: W U (x) =w U sτx R(x) (2.3) Let us describe the labor market. A firm is a unit of production that can either be filled by a worker whose production is y units of output or be unfilled and thus unproductive. In order to find a worker, a firm posts a vacancy. A vacancy can be filled according to a random Poisson process. Similarly, workers searching for a job will find one according to a random Poisson process. In aggregate, these processes imply that there is a number of contacts per unit of time between the two sides of the market that are determined by the following standard matching function: 2 d(su, V ) 1 The subscript L refers to the employed whereas the subscript U refers to the unemployed. 2 This matching function is written under the assumption that the city is monocentric, i.e. all firms are located in one fixed location. 2

3 where s is the average search efficiency of the unemployed workers, U and V the total number of unemployed and vacancies respectively. In this simple model, s = s. As in the standard search-matching model (see Appendix), we assume that d(.) is increasing both in its arguments, concave and homogeneous of degree 1 (or equivalently has constant return to scale). Thus, the rate at which vacancies are filled is d(su, V )/V. By constant return to scale, it can be rewritten as d(1/θ, 1) q(θ) where θ = V/(sU) is a measure of labor market tightness in efficiency units and q(θ) is a Poisson intensity. By using the properties of d(.), it is easily verified that q 0 (θ) 0: the greater the labor market tightness, the lower the probability for a firm of filling a vacancy. Similarly, the rate at which an unemployed worker with search intensity s leaves unemployment is s d(su, V ) sθq(θ) s U Finally, the rate at which jobs are destroyed is exogenous and denoted by δ. As stated in Part 1, a steady-state equilibrium requires solving simultaneously an urban land use equilibrium and a labor market equilibrium. It is convenient to present firsttheformerandthenthelatter Urban land use equilibrium Since there are no relocation costs, the urban equilibrium is such that all the employed enjoy the same level of utility W L while all the unemployed obtain W U. Bid rents are respectively given by: Ψ L (x, W L )=w L e τx W L (2.4) Ψ U (x, W U )=w U sτx W U (2.5) They are both linear and decreasing in x. We have the following straightforward result: Proposition 1. With workers risk neutrality and fixed housing consumption, the employed reside close to jobs whereas the unemployed live at the periphery of the city. 3

4 Let us now define the urban-land use equilibrium. We denote the agricultural land rent (the rent outside the city or opportunity rent) by R A and, without loss of generality, we normalize it to zero. We have: Definition 1. An urban-land use equilibrium with no relocation costs and fixed-housing consumption is a 5-tuple (WL,W U,x b,x f,r (x)) such that: Ψ L (x b,w L)=Ψ U (x b,w U) (2.6) Ψ U (x f,w U)=R A =0 (2.7) Z x f Z x b 0 1 h L dx = L (2.8) 1 dx = N L (2.9) x h b U R (x) =max{ψ L (x, WL), Ψ U (x, WU), 0} at each x (0,x f ] (2.10) By solving (2.6) and (2.7), we easily obtain the equilibrium values of the instantaneous utilities of the employed and the unemployed. There are given by: WL = w L e τx b sτ x f x b (2.11) = w L e τl sτ (N L) WU = w U sτ x f = w U sτn (2.12) The employment zone (i.e. the residential zone for the employed workers) is thus (0,L] and the unemployment zone (i.e. the residential zone for the unemployed workers) is thus [L, N] Steady-state equilibrium We are now able to solve the labor market equilibrium and thus the steadystate equilibrium. Definition 2. A (steady-state) labor market equilibrium (w, θ, U) is such that, given the matching technology d( ), all agents (workers and firms) maximize their respective objective function, i.e. this triple is determined by a steady-state condition, a free-entry condition for firms and a wage-setting mechanism. 4

5 In steady-state, the Bellman equations for the employed and unemployed are respectively given by: ri L = w L τl sτ (N L) δ (I L I U (s)) (2.13) ri U (s) =w U sτn + sθq(θ)(i L I U (s)) (2.14) where r is the exogenous discount rate. The interpretation of the Bellman equations are similar to those made in Part 1. This implies that I L I U (s) = w L w U (1 s) τl r + δ + sθq(θ) (2.15) We denote respectively by I F and I V the intertemporal profit ofajoband of a vacancy. If c is the search cost for the firmperunitoftimeandy is the product of the match, then, at the steady-state, I F and I V canbewrittenas: ri F = y w L δ(i F I V ) (2.16) ri V = c + q(θ)(i F I V ) (2.17) Following Pissarides (2000), we assume that firmspostvacancies uptoapoint where: I V =0 (2.18) which is a free entry condition. From (2.17) and using (2.18), the value of a job is now equal to: I F = c (2.19) q(θ) Finally, plugging (2.19) into (2.16), we obtain the following decreasing relation between labor market tightness and wages in equilibrium: c q(θ) = y w L r + δ (2.20) In words, the value of a job is equal to the expected search cost, i.e. the cost per unit of time multiplied by the average duration of search for the firm. Letusnowdeterminethewage. Ateachperiod,thetotalintertemporal surplus is shared through a generalized Nash-bargaining process between the firm and the worker. The total surplus is the sum of the surplus of the workers, I L I U, and the surplus of the firms I F I V. Ateachperiod,thewageis determined by: w = Arg max(i L I U ) β (I F I V ) 1 β (2.21) 5

6 where 0 β 1 is the bargaining power of workers. By solving (2.21), we obtain: w L =(1 β)[w U +(1 s) τl]+β (y + csθ) (2.22) Let us firstinterpretthewageequation(2.22). Thefirst part (1 β)[w U +(1 s) τl], is what firms must pay to induce workers to accept the job offer: firms must exactly compensate the transportation cost difference (between the employed and the unemployed) of the employed worker who is the furthest away from the CBD, i.e. located at x = L. This is referred to as the compensation effect This is exactly the same effect that we obtained with the efficiency wage (Part 1). The second part β (y + csθ) is the bargaining effect where workers obtain a part of the surplus. This is referred to as the outside option effect. The first effect is a pure spatial cost since (1 s) τl represents the space cost differential between employed and unemployed workers paying the same bid rent whereas the second effect is a mixed labor-spatial cost one. Finally, observe that θ has a positive impact on w L, implying in particular that unemployment negatively affects wages. Let us close the model. Since each job is destroyed according to a Poisson process with arrival rate δ, the number of workers who enter unemployment is δ(1 u) and the number who leave unemployment is θq(θ)su. The evolution oftheunemployment rateisthusgivenbythedifference between these two flows, u = δ(1 u) θq(θ)su (2.23) where u is the variation of unemployment with respect to time. In steady state, the rate of unemployment is constant and therefore these two flows are equal (flows out of unemployment equal flows into unemployment). We thus have: δ u = (2.24) δ + sθq(θ) By combining (2.20) and (2.22), the market solution that defines the equilibrium θ is given by: w L w U = c δ + r + sθq(θ)β +(1 s)tl (2.25) q(θ) 1 β The model can be solved recursively. It is easy to show that there exists a unique solution θ to (2.25). Plugging this value in (2.24) gives a unique u. 6

7 2.3. Welfare The welfare is given by the sum of the utilities of the employed and the unemployed, the production of the firms net of search costs, the land rents received by the (absentee) landlords. The wage w L as well as the land rent R(x), being pure transfers, are thus excluded in the social welfare function. The latter is therefore given by: Z + ½Z L Z N ¾ W = e rt (y τx)dx + (w U sτx)dx cθsu dt (2.26) 0 0 In the standard search-matching literature (Pissarides, 2000), market failures are caused by search externalities. Indeed, the job-acquisition rate is positively related to V and negatively related to U whereas the job-filling rate has exactly the opposite sign. For example, negative search externalities arise because of the congestion that firms and workers impose on each other during their search process. Therefore, two types of externalities must be considered: negative intra-group externalities (more searching workers reduces the job-acquisition rate) and positive inter-group externalities (more searching firms increases the job-acquisition rate). For a class of related search-matching models,hosios(1990)andpissarides(2000)haveestablishedthatthesetwo externalities just offset one another in the sense that search equilibrium is socially efficient if and only if the matching function is homogenous of degree oneandtheworker sshareofsurplusβ is equal to η(θ) the elasticity of the matching function with respect to unemployment (this is referred to as the Hosios-Pissarides condition). Of course, there is no reason for β to be equal to η(θ) since these two variables are not related at all and, therefore, the searchmatching equilibrium is in general inefficient. However, when β is larger than η(θ), there is too much unemployment, creating congestion in the matching process for the unemployed. When β is lower, there is too little unemployment, creating congestion for firms. In our present model, we have exactly the same externalities (intra- and inter-group externalities). The spatial dimension does not entail any inefficiency so that it is easily verified that the Hosios-Pissarides condition still holds, i.e. β = η(θ). Indeed, the social planner solves the following problem: he/she chooses θ L 7

8 and u that maximize (2.26) under the constraint (2.23). The solution of this problem is given by: y w U = c δ + r + θq(θ)sη(θ) +(1 s)tl (2.27) q(θ) 1 η(θ) In order to see if the private and social solutions coincide, we compare (2.25) and (2.27). It is easy to verify that the two solutions coincide if and only if β = η(θ) Endogenous search effort Each unemployed optimally choose s by maximizing (2.14) by taking as given θ and I L I U (s). We obtain: I U (s) s = τ N+ θq(θ)(i L I U (s)) Q 0 (2.28) Let us give the intuition of (2.28). When choosing s, there is a fundamental trade-off between short-run and long-run benefits for an unemployed worker. On the one hand, increasing search effort s is costly in the short run (more commuting costs) as it decreases instantaneous utility ( WL/ s < 0), but, on the other, it increases the long-run prospects of employment θq(θ)(i L I U (s)). In this particular case (s enters linearly in both the costs and benefits), we have a corner solution. If the long-run benefits are higher than the short run costs, i.e. θq(θ)(i L I U (s)) >τn,thens =1. Otherwise, s = s Endogenous search intensity and housing consumption 3 We assume that all workers have identical preferences among consumptions bundles (h, z) of land (housing), h, andcomposite good, z, representable by a log-linear utility U(q, z) =q α z ω (3.1) with α, ω > 0, where it is also assumed that α + β<1. However the budget constraints for employed and unemployed workers are different. Each employed 3 This is based on Smith and Zenou (2003). 8

9 worker living at location, x, has the standard budget constraint h L R(x)+τx+ z L = w L (3.2) where z is taken as the numeraire good with unit price. For an unemployed worker at x, we have the following budget constraint: h U R(x)+sτx + z U = w U (3.3) Maximizing utility (3.1) subject to (3.2) yields the following land demand for employed workers at x: h L (x) = α α + ω wl τx (3.4) R(x) Similarly, maximizing (3.1) subject to (3.3) yields the following land demand for unemployed workers at x: h U (x) = α α + ω wu s(x)τx (3.5) R(x) As one can see, s is now a function of x, distance to jobs. We can now derive the following indirect utility U L (x) =χ(w L τx) α+ω R(x) α (3.6) for each employed worker at x, whereχ =[α/(α + ω)] α [ω/(α + ω)] ω and the following indirect utility U U (s, x) =χ(w U sτx) α+ω R(x) α (3.7) for each unemployed worker at x, where in this case s is now included as a relevant choice variable. We can now write the different Bellman equations: ri L = χ(w L τx) α+ω R(x) α δ (I L I U ) (3.8) ri U = χ(w U sτx) α+ω R(x) α + sθq(θ)(i L I U ) (3.9) Unemployed workers optimally choose s by maximizing (3.9). We obtain: χτx (α + ω)(w U sτx) α+ω 1 R(x) α + sθq(θ)(i L I U )=0 Once again, there is a fundamental trade-off between short-run and long-run benefits for an unemployed worker. On the one hand, increasing search effort s 9

10 is costly in the short run (more commuting costs) but, on the other, it increases the long-run prospects of employment. However, contrary to the previous case, the solution can in fact be interior. Rearanging this expression, we obtain: " s = 1 θq(θ)(il I U ) R(x) α 1 # α+ω 1 w U τx χτx (α + ω) We have the following result: Proposition 2 (Optimal Search Intensities). At each location x, there is a unique search intensity s that maximizes (3.9). For any prevailing job acquisition rate, θq(θ), and constant lifetime values, I L,I U, the optimal search intensity function, s(x), for unemployed workersisgivenforeachlocation,x [0, w U ),by s 0 τ 1 for x x(1) h i α+ω w s(x) = U (1 r)i L 1 (α+ω) (α+ω)τx rθq(θ)(i L I U for x(1) <x<x(s ) 0 ) s 0 for x x(s 0 ) (3.10) where x(s) = w U sτ sr θq(θ) (I L I U ) (α + ω)(1 r)i U +[1 (α + ω)]sr θq(θ) (I L I U ) (3.11) The following figure describes s(x). There is a non-linear decreasing relationship between the residential distance to jobs of the unemployed and their search intensity s. In fact, individuals living sufficiently close to jobs search every day, s =1, whereas those residing far away provide a minimum search intensity, s = s 0. Workers living in between these two areas see a decrease in their search intensity from s =1to s = s 0. The intuition runs as follows. As stated above, there is in fact a fundamental trade-off between short-run and long-run benefits of various location choices for the unemployed. Indeed, locations near jobs are costly in the short run (both in terms of high rents and low housing consumption), but allow higher search intensities which in 10

11 turn increase the long-run prospects of reemployment. Conversely, locations far from jobs are more desirable in the short run (low rents and high housing consumption) but allow only infrequent trips to jobs and hence reduce the long-run prospects of reemployment. Therefore, for workers residing further away from the CBD, it is optimal to spend the minimal search effort whereas workers residing close to jobs provide high search effort. R(x), s(x) 1 Figure 1: Bid Rent for the Unemployed s (.) s 0 R (.) 0 0 x(1) x(s ) b/c b/s c 0 0 We can now focus on the urban-land use equilibria. However, the problem is very complex because the bid rents are not linear. Different urban structures can emerge. We would like now to present a simpler model that will help to understand how things work. 11

12 4. City structure Equilibrium We consider exactly the same model with two changes that greatly simplify the analysis. First, we impose rather than derive the negative relationship between s and x, thatisnowwehave:s(x), withs 0 (x) < 0, i.e. search effort decreases with distance to jobs. In order to have linear bid rents, we assume: s(x) =s 0 bx Second, the total commuting cost for the unemployed at a distance x from the CBD is now given by τ U x instead of s (x) τx. For the employed, it is as before τ L x. This implies that the Bellman equations of the employed and unemployed are now given by ri L = w L τ L x R(x) δ (I L I U ) ri U = w U τ U x R(x)+(s 0 bx) θq(θ)(i L I U ) where θ = V/(sU). The main difference is that the value of s will depend on the average location of the unemployed x U and thus on the prevailing urban equilibrium. Bidrentscanbewrittenas: Ψ u (x, I U,I L )=w U τ U x+[(s 0 bx) θq(θ)] I L [r +(s 0 bx) θq(θ)] I U (4.1) Ψ e (x, I U,I L )=w L τ L x + δi U (r + δ)i L (4.2) These bid rents are linear and decreasing in x andwehavethefollowing result: 4 This is based on Wasmer and Zenou (2002). 12

13 Proposition 3. (i) If τ L τ U <bθ 1 q(θ 1 )(I 1 L I 1 U) (4.3) we have Equilibrium 1 in which the unemployed live close to jobs. (ii) If τ L τ U >bθ 2 q(θ 2 )(I 2 L I 2 U) (4.4) Equilibrium 2 prevails and the employed live close to jobs. Equation (4.3) means that the differential in commuting costs per unit of distance between the employed and the unemployed is lower than the marginal expected return of search for the unemployed if he/she moves closer to the center by one unit of distance. Indeed, since bθ 1 q(θ 1 ) is the marginal increase in the probability of obtaining a job for an unemployed worker. Thus if (4.3) holds, the unemployed occupy the core of the city and the employed the outskirts of the city. In the other equilibrium (Equilibrium 2), we have the opposite inequality. If we define the two urban equilibria as in the previous chapters, then it is to obtain: IL k IU k = wk L w U (τ L τ U )x k b k =1, 2 (4.5) r + δ +(s 0 bx) θ k q(θ k ) where wl,u k k,θ k are determined at the labor market equilibrium k. Obviously, the border between the employed and the unemployed, x k b,issuchthatx1 b = U 1 and x 2 b = L1. The average search intensity in equilibrium k is equal to: s k = s 0 a x k k =1, 2 (4.6) where x k is the average location of the unemployed in equilibrium k. Itiseasy to verify that x 1 = U 1 /2 and x 2 = N U 2 /2. Since x 1 1 < x 2 (thisisalwaystruebecauseu 1 + U 2 < 2N), the average search efficiency in urban equilibrium 1 is higher than in urban equilibrium 2, i.e., s 1 > s 2. This result is quite intuitive. Indeed, in the integrated city, the unemployed reside closer to the CBD than in the segregated city and thus their probability of finding a job is higher. 13

14 We can now close the model as before. We first have a free-try condition that gives the following labor demand curve: c q(θ k ) = y wk L r + δ k =1, 2 (4.7) A wage determined by a bargaining between the firm and the worker: w k L =(1 β) w U +(τ L τ U )x k b + β y + s0 bx k b θ k c k =1, 2 (4.8) and a steady-state conditions on flows: u k = δ δ + θ k q(θ k )s k, k =1, 2 (4.9) By combining (4.7) and (4.8), we obtain the following market equilibrium: y b = γ δ + r + θk q(θ k )s(d k )β + d k (t e t u ) (4.10) q(θ k ) 1 β If we define then we have: b θ = 1 β β (t e t u ) aγ (4.11) Proposition 4. Thereexistsauniqueandstablemarketequilibrium(R k (x),wl k,θ k,u k ), k =1, 2, and only the two following cases are possible: If b θ<θ 1 <θ 2, urban equilibrium 1 prevails; If θ 2 <θ 1 < b θ, urban equilibrium 2 prevails Welfare Comparison of the two cities We firstinvestigatethewelfareofthecity,andstudyhowitvariesineach urban configuration. For each city, we use the welfare function defined by (2.26). 5 To see how this quantity varies and if it can be compared across cities, let us proceed to a simple numerical resolution of the model. We use the following Cobb-Douglas function for the matching function: x(s k u k,v k ) = 5 Of course we have to modify the welfare to take into account the different locations of the employed and the unemployed. 14

15 (s k u k ) 0.5 v k 0.5. This implies that q(θ k ) = θ k 0.5, s0 bxb k θ k q(θ k ) = θ k 0.5 and, whatever the prevailing urban equilibrium, the elasticity of the matching rate (defined as η(θ k )= q 0 (θ k )θ k /q(θ k ))isequalto0.5. Thevalues of the parameters (in yearly terms) are the following: the output y is normalized to unity, as is the scale parameter of the matching function. The relative bargaining power of workers is equal to η(θ), i.e. β = η(θ) = 0.5. Unemployment benefits have a value of 0.2 and the costs of maintaining a vacancy c are equal to 0.3 per unit of time. Commuting costs τ L are equal to 0.4 for the employed, and τ U =0.1 for the unemployed. The discount rate r =0.05, whereas the job destruction rate δ =0.1, which means that jobs last on average ten years. Finally, s 0 is normalized to 1, implyingthat0 b 1. Wealso normalize the total population N to 1. Inordertosingleoutthespatialeffects from the non-spatial ones, we have decomposed the total unemployment rate given by (4.9) by using a Taylor first-order expansion for small b/s 0 i.e. u k = δ δ + θ k q(θ k )[s 0 b(1 u k /2)] in two parts. The first one is the part of unemployment that is independent of spatial frictions, i.e. when b =0so that s = s 0. Thisunemploymentrateis thus given by: δ u 0 = δ + θ 0 q(θ 0 )s 0 (where θ 0 is the labor market tightness when b =0) and corresponds to the standard non-spatial unemployment rate in Pissarides (2000). The second one is the part of unemployment that is only due to additional spatial frictions, denoted by u s k, and defined by u k s = u k u 0 We obtain: 15

16 b City u k (%) u 0 (%) u k s (%) u k s /u k θ k x k b s k Welfare In this table, we have chosen to vary a key parameter b, the loss of information per unit of distance (remember that workers search intensity is defined by s(x) =s 0 bx). This parameter b varies from a very large value 1 (where city 1 is the prevailing equilibrium) to a very small value 0.1 (where city 2 is the prevailing equilibrium). The cut-off point is equal to b = Thesign indicates the limit to the left, whereas the sign + indicates the limit to the right. The first interesting result of this table is that, when we switch from an integrated city (equilibrium 1) to a segregated city (equilibrium 2), for values very close to the cut-off point b =0.522, the unemployment rate u k nearly doubles (from 6.85% to 12.4%). However, it is clear that this result is due to the spatial part of unemployment u k s since the non-spatial one u 0 isnotatall affected. Indeed, when we switch from equilibrium 1, where the unemployed are close to jobs and are very efficient in their job search (s = 0.982), to equilibrium 2, where the unemployed reside far away from jobs and are on average not very active in their search activity (s =0.511), the spatial part of unemployment changes values from 0.12 to Another way to see this is to consider column 6 ( u k s /u k ): the part of unemployment due to space varies from 2% to 46%. Sothemaineffect from switching from one equilibrium to another is that search frictions are amplified by space and consequently unemployment rates sharply increase. So here the spatial access to jobs is 16

17 crucial to understanding the formation of unemployment. The last column of the table shows the value of the welfare W k when b varies. The result is very striking: even though unemployment rates are higher in equilibrium 1 than in equilibrium 2, this does not imply that the general welfare of the economy is higher in the first equilibrium. Indeed, even though the unemployed are better off in equilibrium 1 (lower unemployment spells and lower commuting costs), the employed can in fact be worse off because of much higher commuting costs in equilibrium 1. In the above table, it is interesting to see that at the vicinity of b =0.522, switching from equilibrium 1 to equilibrium 2 does not involve much change in the welfare level (from to 0.712) Welfare within each city The shape of the city has thus little impact on welfare, since in the segregated city,what islostfromlower searchefficiency is gained through lower commuting costs. We now investigate the issue of the optimality of the decentralized equilibrium within each land market equilibrium. In our present model, we have exactly the same externalities (intra- and inter-group externalities). The spatial dimension does not entail any inefficiency so that it is easily verified that, for each equilibrium k = 1, 2, the Hosios-Pissarides condition still holds, i.e. β = η(θ k ). 5. Conclusion References [1] A. Hosios (1990), On the efficiency of matching and related models of search and unemployment, Review of Economic Studies, 57, [2] D.T. Mortensen and C.A. Pissarides (1999), New developments in models ofsearchinthelabormarket,inhandbook of Labor Economics, D.Card and O. Ashenfelter (Eds.), Amsterdam: Elsevier Science, ch.39, [3] C.A. Pissarides (2000), Equilibrium Unemployment Theory, Second edition, M.I.T. Press, Cambridge. 17

18 [4] Smith, T.E. and Y. Zenou (2003), Spatial mismatch, search effort and urban spatial structure, Journal of Urban Economics, 54, [5] Wasmer, E. and Y. Zenou (2002), Does city structure affect job search and welfare? Journal of Urban Economics, 51,