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Job Search Mechanism and Individual Behaviour Massimo Giannini Università del Molise∗ Preliminary Draft Abstract This paper is a first attempt at modelling job search mechanism at individual level by a determinstic-stochastic approach widely used in the analysis of epidemic models. Unlike standard literature on job search, each single unit, firm or worker, is take into consideration; aggregate dynamics comes directly from the micro-structure of the economy. We show that the unemployment as well as vacancy rate converge in the long run to an ergodic distribution whose average value lies on the Beverdige curve. ∗ Facoltà di Economia, Palazzo Orlando, Isernia. E-mail: [email protected] 1 1 Introduction Like most other aggregate functions in the macroeconomist’s tool kit, the matching function is a black box; we have good intuition about its existence and properties but only some tentative ideas about its microfoundations. Yet, those tentative ideas have not been rigorously tested....Further work needs to elaborate a number of issues. The search for microfoundations needs to continue and rigorous tests of plausible alternatives done..... The most popular microeconomic models, such as the urn-ball game, do not perform as well empirically.1 Job search is an intrinsically individual-level issue; it sums up the behaviour of two elementary units of an economy: firm and worker. What we observe in the job market data is the consequence of such elementary processes; unfortunately we have no a clear idea whether the aggregate level is just the mirror, on a larger scale, of the microcosm or only a fuzzy and distorted representation. In trying to challenge the question, we need to model the microcosm in a ”fair” way, i.e. sufficiently simple to be analytically tractable and, meanwhile, sufficiently complex to cope with the goal. The number of variables affecting the single match between firm and worker is high and well reviewed in the Petrongolo and Pissarides, 2000, survey. Under this point of view, our request of a ”fair” description of the microcosm could be frustrated; nevertheless it is worth the effort. This paper presents a first, and very preliminary, attempt at providing a simple but reasonably descriptive analytical body for modelling job search at the individual level which is coherent with a simple macroeconomic model. It relies heavily on recent developments of mathematical and statistical research applied to the investigation of the dynamics of epidemic processes. The simplest way of looking at the job search mechanism is the one described by the Pissarides Mortensen approach (PM hereafter): at every time a firm randomly ”contacts” a worker, the match is closed and the unemployed changes its status to employed (hence she is removed from the unemployment population), the firm fills the vacancy and it can be removed from the population of vacant firm. Meanwhile, new unemployed are born and new vacancy are opened as the result of an exogenous separation between an existing firmworker unit. The matching rate, as well as the separation one, can depend both on worker features, notably human capital, and firm characteristics as well as on local spillovers. The PM approach relies on an aggregation of the micro-economic behaviours and focusses on the steady state solution. By doing so, it does not allow to investigate indifferently the macro and the micro point of view of the question. Our goal is to provide an alternative approach to the problem based on a probabilistic law that allows us to analyze both sides of the problem in way that they are coherent to each other. The two-fold result allows us to investigate both on the variables relevant for the single unit history, as described by empirical analysis on microdata, and on the economy as a whole, undertaking in this case 1 Petrongolo and Pissarides, 2000. 2 empirical analysis based on aggregate data. Finally the analysis should not be limited to the steady state but on the transition path as well. The paper is organized in three logical steps: the first one is devoted to the individual analysis where ”optimal” tranistion rates are obtained according to a rational behaviour of firm and worker. The second one shows how obtaining macro-dynamical equations by averaging over these individual rates. Finally the probabilistic model shows how we can obtain the same aggregate laws by analyzing micro-dynamics. In the last part, we show how the micro-model allows to take into consideration some spillovers effect which can not be analyzed by the aggregate analysis; under this point of view, it stresses the greater explorative power of empirical analysis based on microdata rather than on a aggregate account. 2 The job search approach In this section we briefly recall the standard job search approach a la Pissarides and Mortensen; this helps us to stress where our approach overlaps with the former and where not. As it is well known, the crucial assumption of the job search mechanism is the ”matching function” which provides an average measure of the instantaneous rate at which an unemployed worker and a vacant firm match one each other. The matching rate is increasing in the number of unemployed workers U and vacant firms V ; by assuming CRS on the function, one can shift from U and V to the respective rate u and v and usually the matching function is described as m( uv , 1). The approach is basically a steady state analysis. It provides the number of jobs opened by rational, forward-looking, firms in equilibrium by taking into account the equilibrium conditions arising from the inflow and outflow of workers from the unemployment status. The main feature of the model is that, in equilibrium, the market does not clear, as both u and v are positive; more precisely, the equilibrium points lie on a downward sloping, convex-to-the-origin curve, in the u, v space, known as the ”Beveridge curve” since Lord Beveridge’s work on the empirical relationship between these two variables. The lack of full employment is due to the search mechanism and not to wage rigidity; the profit for a single firm is given by (terms have the usual meaning): f (k) − w − rk − (r + s)γ q( uv ) (1) A comparison with the profit in a walrasian context shows immediately that the extra term (r+s)γ v q( u ) matters; this is zero only if either the search cost γ is zero or the matching rate q( uv ) is very high , theoretically infinite; both conditions are true in a walrasian market. Since a competitive equilibrium implies the zero profit condition, it is straightforward to see that equation 1 can be solved with respect to ( uv ), leading to the result that, in equilibrium, u and v are not zero. This static framework can be analyzed in a dynamic setting (see Pissarides, 1990, ch.3); the adjustment dynamics towards the Beveridge curve is monotone; 3 off the equilibrium, both u and v are decreasing or increasing depending on the initial conditions. Anti-clock wise adjustments are also possible in response to productivity shocks. It is worth stressing that the long run equilibrium is characterized by a saddle dynamics; convergence to the unique stable branch requires a well specified initial condition on the market tightness v(0)/u(0). In general, empirical observations on the Beveridge curve over time show a rather complex dynamics, characterized by loops and shifts which are usually induced by structural changes as well as business cycle (Nickell et al. 2002, Wall and Zoega, 2002). Nevertheless, we can not exclude that a relevant part of this odd dynamics is induced by a more complex adjustment to the steady state that the standard job search model does not capture. However, our aim is to provide a theoretical framework which can describe the adjustment dynamics both in a macro and in a micro framework. Basically we derive the aggregate dynamics from the micro structure of the economy; under this point of view we can indifferently analyse the temporal evolution of the variables u and v either by the aggregate equations or by the more complex micro-structure. There are different gains in working at different levels; the macro-equations are simpler and can be account for a large range of dynamical behaviour, even including chaotic dynamics2 . From this point of view, suitable modifications of the macro equations modify heavily the dynamical paths; these modifications can span from a simple coefficient endogeneity to a more complex form for the matching function. If so, the wide range of observed dynamics for the UV curve could be induced not only by structural changes or business cycle but by different parameters, initial conditions and functional form for the matching function. Once the macro-equations successfully replicate the observed dynamics, the micro-structure can be fruitfully exploited to investigate individual behaviour at a finer level than the aggregate one. Concluding, we are going to use a dynamical framework where unemployed workers and vacant firms match at random; in this paper we use a highly stylized economy. Workers need work in order to gain income and firms need workers for producing and making profits. Under this point of view, both the single worker and the single firm behave as a two-state process switching from unemployed to employed at random times following a Poisson process. In this paper we investigate this type of simple dynamics both at the macro and micro level, showing that we can switch from the former to the latter without lack of coherency. 3 Single-Worker Analysis We start by considering the individual working life. In official statistics agency, the workforce is divided between unemployed and employed. Nevertheless this dicotomy does not represent the total supply of labour since we have to account for individuals temporary out of the workforce who would like to have a job. 2 We are going to show that such dynamical system involves three non linear differential equations and it is known that such systems can generate chaotic dynamics. 4 This share of labour supply is usually labelled as ”person not in the labor force who want a job now” according to the U.S. Bureau of Labor Statistics and in general is a form of hidden unemployment or labour reserve ( see Castillo 1998 for a detailed description). According to the US Current Population Survey, in September 2003 the number of workers who were out of workforce not looking for a job but that would like to work was about 4.6 million while the total official unemployment was about 16 million; it is worth stressing that the larger share of hidden unemployment lies between age 16 and 54, i.e. in the most productive part of the working life. Average duration of hidden unemployment is about 12 months in the CPS; one workerk recorded as ”person not in the labor force who want a job now” in the earler year becames a job seeker the following year (see Castillo 1998 again). The hidden uemployement is a sort of voluntary temporary retirement from the job market and this choice depends on a lot of individual characteristics not least the ”discouraged worker” effect; according to the US BLS: Discouraged workers are those persons who say that they want a job, were available to work, had searched for a job some time in the previous 12 months but had stopped looking for work because they believed that there were no jobs available for them. In this paper we are going to take into consideration hidden unemployment and, according, we are going to divide the total labour supply in unemployed, employed and temporary retired, L = U + E + R. A worker randomly drawn from the population occupies one of these three status; nevertheless the status will be ordered hierarchically since a worker is employed only after she was a job seeker, i.e. U −→ E. At same time, we assume that once the worker separates from the firm she does not became immediately a job seeker but stays in the state R before of entering again the state U ; if the transition rate from state R to U is very high, ideally infinite, then the temporal occupancy of R is close to zero and basically this means that a separation gives birth immediately to a job seeker. As will be clearer later, this assumption of stages hierarchically ordered allows us to characterize the steady state of the job market as a balancing of flows out and in the U, E and R states; in this way the model fits the official partition of the work force in unemployed, employed and labour reserve. Under a probabilistic point of view, the simplest way at modelling the single worker history over time is a ”three states process”. Worker life history is a continuos jump from three possible states: U, E and R. Under this point of view, each agent is characterized by an own string of U, E and R recording her history over time; the length of time the individual stays in a given state is a random variable and the Poisson distribution is a good aproximation of this occupancy time. This process can be easily described in a probabilistic way: if the worker is unemployed but actively engaged in search at time t, she can change her status to employed at the instantaneous rate α, and the probability that she will be effectively employed in the time interval t+∆t, is simply α∆t3 . Likewise, 3 More precisely is α∆t + o(∆t) where o(∆t) means a function which tend to zero more rapidly than ∆t. Intuitively this means that in a small time interval (ideally when ∆t tends 5 when the worker is employed, she has a probability β∆t to be separated during t+∆t,finally a temporary retired worker has a probability m∆t to be a job seeker during t+∆t. The coefficients α, β and m are the transition rates, i.e. the chance for a transition in a unit of time and they are not constrained in the unitary interval as they are not probabilities; they can depend both on individual and firm characteristic, although we are going to treat them as exogenous parameters along this section. When the worker changes her status, she stays in the new state for a random time τ ; as said, this waiting time is well modelled by a Poisson process. Under this point of view, our worker is a job seeker for a given time T1U after then she becomes employed for another random time T1E then changes again to nonseeker for a time T3R and finally come back to the status of job seeker and so on. The dynamic of the probability to be in a given state at time t follows the Kolmogorov forward equations (see Cox and Miller, page 172): dP E (t) dt dP U (t) dt dP R (t) dt = −βP E (t) + αP U (t) = −αP U (t) + mP R (t) (2) = −mP R (t) + βP E (t) with initial condition and P U (0) = 1 − P E (0)− P R (0) given. The above equations have a prompt interpretation; they describe the evolution of the probability over time according to a balancing of inflows and outflow. As an example, let us focus on the first one; the probability of finding a worker in the employed status increases with the inflows from unemployed to employed (αP U (t)) and decreases with the separation βP E (t). The steady state solution is : PE = PU = PR = mα βα + βm + αm βm βα + βm + αm βα βα + βm + αm The steady state is a stable node and so the long run distribution does not depend on initial conditions; this means that if we observe a single worker job history over a sufficient long horizon, then the percentage of time spent in a given state, E , U, or R is close to the theoretical distribution. The strong convergence and the independence of initial conditions are valuable properties for empirical analysis. to zero) the process can undertake only a single change of state (point process). 6 4 Single-firm Analysis In this section we are going to duplicate the previous point for the firm. For sake of simplicity,we are goint to assume that firms can occupy only two states: vacant and filled. In this case the system 2 reduces to two equations only dP F (t) dt dP V (t) dt = −βP F (t) + αF P V (t) = −αF P V (t) + βP F (t) where αF is the transition rate for vacant firms. The steady state solution of the system is: PF PV PF + PV 5 αF β + αF β = β + αF = 1 = (3) Individual Choice We start by analyzing firm behaviour. Any single firm knows the probability of being filled or vacant, according to 3. If we look at αF as the intensity of search, the higher αF the higher the probability of being a productive firm. But intensity is a resource wasting activity and so the single firm has to choose αF in order to maximize the expected discounted flow of profits net of the searching cost. Assuming that each single firm produces a fixed amount of the only commodity in the economy whose price is the numeraire, and it uses a simple one-to-one technology, the problem is quite simple: Z ∞ ¤γ £ M ax e−ρt (pF π − (1 − pF )C(α) dt α 0 where π = y − w is the profit when the firm is filled, C(α) the search cost that we assume quadratic, C(α) = α2 , and γ ≤ 1 is the risk aversion coefficient. The probability pF comes from 3 under the assumption that the firm life is sufficiently long, and that it can be approximated by the long run probability. This simple maximization scheme brings to α∗ = y−w β ; the higher the wage the lower the search intensity. This means that the demand curve is negatively sloped; in fact the average number of matches is α∗ V and for a given V the number of matches is decreasing in w. The worker faces a similar problem; let us suppose that the transition from unemployed to hired worker depends on the investment in human capital or 7 search intensity which is costly. By assuming that the worker earns w when employed, 0 when retired and −C(αe ) when seeker, the problem is then: Z ∞ e−ρt [(pe w − pu C(αe )]γ dt M ax αe 0 where the subfix e stands for ”employed”. The optimal human capital is α∗e = w β. In this case the average number of matches, from the side of unemployed workers, is increasing in w. Instantaneous equilibrium requires that same number of matches comes form both sides of the market, i.e. α∗ V = α∗e U or α∗ v = α∗e u and from this condition yv we obtain the equilibrium wage w = u+v < y hence: α∗ = α∗e = y u y 1 = β u+v β 1+θ y v y θ = β u+v β 1+θ (4a) It is worth stressing that: α∗e = α∗ θ, with θ = v/u and depends only on θ. Moreover the average instantaneous matching function m = α∗ v = α∗e u is increasing, concave and linearly homogenous of degree one in u and v, as in the spirit of the MP approach. 6 Macro-Dynamic Analysis The model is essentially dynamic in its nature and in this section we are going to obtain the differential equations characterizing the average dynamics; given an initial condition, the job market evolves towards the steady state represented by a point on the Beverdige Curve. Given the instantaneous transition rates 4a we derive the differential equations by averaging over firms and workers. For a job seeker, the average probability, per unit of time, of changing status from unemployed to hired (U → E) is α∗e times the probability of finding an individual in the unemployment status, PU , i.e. α∗e PU , where PU = U/L. In the time interval ∆t, corresponding to L elementary steps4 ,the average number of unemployed being employed is α∗e PU L∆t; hence, the number of unemployed decreases at the rate ∆U/∆t = − θ uv α∗e PU L = − βy 1+θ uL = −L βy u+v . The number of unemployed instead increases by mR. Likewise the number of vacancy decreases at the rate ∆V /∆t = − 1 uv uv vL = −L βy u+v . Clearly, the matching function βy u+v must α∗ PV L = − βy 1+θ be the same both for unemployed and vacant firm since that, once a match is closed, both variables decrease by one unit. Conversely the number of vacancies increases, in the unit of time, when a separation occurs, i.e. β(1 − v). Finally the number of workers out of labor force increases by β(1 − v) and decreases by mR. 4 For computational purposes we normalize the number of elementary units to the size of the economy. 8 Summing up, we obtain the following dynamical equations (we assume the normality condition y = 1): du dt dv dt dr dt 1 uv + mr β u+v 1 uv = − + β(1 − v) β u+v = − (5) = β(1 − v) − mr By imposing the steady state condition dv dt = 0 in the second equation we obtain the long run relationship between vacancy and unemployemnt, i.e. the Beveridge curve. v∗ = − ∗ ∗ 2 1 u − (1 − u )β − 2 q (u∗ − β 2 )2 + β 2 u∗ (2u∗ + 2β 2 + β 2 u∗ ) β2 It must be stressed that the determinant of the Jacobian matrix of eqs. 5 is zero and there are two complex roots with a negative real part while the third is zero. In such a situation, all solutions converge to a three-dimensional manifold with the consequence that the steady state, as well as the transition path, depends on initial conditions (see for example Kamien and Schwartz page 347). The Beveridge curve is the projection of such a manifold in the bidimensional plane u,v. Convergence to the steady state can be both clockwise and anticlockwise depending on parameters and initial conditions; finally the evolution of variables over time follows a stable oscillatory dynamics. Figure 1 shows both the Beveridge curve and some transitional paths for some initial conditions. Figure 2 shows the unemployment transition path: This sort of ”path-dependency” of the system is interesting in the comparison of the working of the job market and equilibrium unemployment across countries: long run differences are induced not only by a different institutional setting or search mechanism but by different initial conditions as well. In the above scheme the parameter m is exogenous; however the US Labour Statistics survey underlines that individual decisions about the staying in R on in U depends on individual expectations about the probability of being hired once the individuals becomes a seeker. Such a probability depends on job market conditions and in general on the tightness of the labour market. The ”discouraged worker” effect is expected to be as higher as unemployment is and vacancies are low. Even in absence of a clear microfoundation of such an effect, we have carried out the simulations of figure 1 when we allow m to depend on job market tightness, in the idea that workers comes out from R at a higher rate if unemployment is low and/or vacancies are high, i.e. m = g(θ). Figure 3 show results when g(θ) is driven by a concave function: The comparison of figure 3 with figure 1 does not show relevant changes in the results; there is still convergence to the Beverdige curve and tranistional 9 Figure 1: Figure 2: 10 Figure 3: dynamics are not dramatically different from the case when m is exogenous. We have performed other simulations, here not reported for brevity, involving more complex g(θ) but with similar results. In any case working with an exogenous m rate seems a reasonable assumption that does not modify remarkably the results. 7 Micro-Dynamic Analysis In the previous section we have obtained the dynamical equations describing the behaviour of the averages (macro-variables) over time. In this section we show the microeconomic behaviour driving the macro one. In other words, we are going to set-up a microeconomic world whose averages behave exactly as the equations obtained in the previous section; if both ways of obtaining the average dynamics produce same results then we conclude that the macro and micro are coherent to each other. In case of a positive result, we can indifferently investigate both the macro-world and the life history of a single agent, depending on our research goal. Probabilistic approach at modelling our problem involves, theoretically, the analysis of the Kolmogorov equation for the entire economy, as we did for a single agent. Unfortunately the dependence of the transition rates on u and v makes very hard or impossible managing it. This type of problems are common to other disciplines making use of a probabilistic approach to systems charac- 11 terized by a large number of states. Recently epidemiologists working on the spreading of diseas across individuals have used a dynamic Monte Carlo algorithm which can be fruitfully applied both to the numerical solutions of the probabilistic models used to forecast the evolution over time of diseases and to the estimation of individual transition rates; a good description of these methods is in Gilks et al., 1996. In particular we are going to follow the Monte Carlo algorithm presented by Aiello et al., 2000 and 2001. For a technical and detailed description of the algorithm and its probabilistic features the reader should refer to the original papers; here we present the main steps of the methodology applied to our problem of job search. The model we are investigating follows these steps: 1. There is an equal number of firms and workers, say L, .and the technology is 1:1, so full employment is theoretically possible. At the beginning, workers are divided in three sub-populations: employed M0 , unemployed looking for a job (seekers hereafter) U0 and unemployed not looking for a job, R0 . Firms are divided in vacant V0 and filled M0 . 2. Workers and entrepreneurs are completely separated and there is not flow from one to other; we can assume that this partition of the population is based on different abilities, managerial skills, business risk aversion and so on. The population is stationary. 3. When an unemployed worker meets successfully a vacant firm they become a productive unit labelled by the status M . Matched units can separate at the exogenous rate β. When separated, workers are temporary out of labor force and labelled R (retired); they come out from this state as a new seeker at the exogenous rate m. When separated, the firm becomes V . By doing so, workers have three possible stages hierarchically ordered, i.e. U → M → R whilst the firm has only two V → M. 4. As in MP, firms and workers do accept the match hence the latter comes indifferently either from the supply or demand side of the job market; we are interested in counting the number of matches and separations over time, and updating the set {U, M, R, V } consequently, and it does not matter who is ”driving” the match. There is a strict duality between workers and firms spaces. 5. Transition rates from U to M and from V to M are given by eqs 4a and from M to R and M to V by the exogenous separation rate β. Finally the exogenous parameter m is the transition rate from R to U. The DMC algorithm allows us to investigate the individual history over time. As stressed at point 4, it does not matter who is leading the matching process; what is important is that when a match occurs in the economy, the sub-populations are adequately updated. Since we are interested in analyzing the search mechanism on the side of the individual worker, we are going to focus on this population. Workers are divided into three sub-populations randomly 12 allocated in a one-dimensional vector; workers are hence represented as a random collection of indexed individuals U, U, M, R, M, U... and so on. The dual vector representing firms is V, M, M, V, V, M.... and so on. 1. At each elementary time step l one individual is randomly drawn from the population; let us suppose an unemployed worker. This agent could change her status from unemployed to matched according to α∗e but from a probabilistic point of view there can be other agents in the economy whose probability of changing the status is higher than the one characterizing our individual. So in deciding whether effectively the drawn individual will undertake a status change, we have to compare her transition rate with the higher one in the population, i.e. pU = α∗e /WMax where WMax = sup P, .P = {α∗e , β, m} The method suggested in Aiello et al., 2000, is to compare pU against a random number r in the closed unitary interval taken from a uniform distribution; the uniform assumption models a situation where every agent has the same a-priori probability of a jump; this means that when pU < r the real situation is less informative than the one characterized by a total ignorance about individual transition rates. Hence, if pU > r the drawn individual changes her status otherwise she stays in the original one. When the individual changes the status the sub-populations U, V, M, R are consequently updated. 2. The waiting time between two consecutive jumps follows a Poisson process at rate r = α∗e U + βM + mR. 3. After the delay time, a new draw is performed and the simulation restarts. The result of this Markov Chain5 is the convergence of the sub-populations to a long run probability measure whose first moment is given by the deterministic equations 5. In the following section we show some simulations. 8 Results We have performed 20 replications of the Monte Carlo method described in the previous section; we have chosen 20 runs because it is enough to obtain a smooth curve to be compared to the deterministic solution. Figure 2 shows the adjustment path obtained by the average equations, rotated in the v, u plane, and the average of 20 simulations obtained by the micro-model. As the reader can see, the fit is quite good. By doing so, we can describe the adjustment path to the Beveridge curve indifferently by the macro-equations and the microeconomic model; both analytical approach provides same results. Under this point of view, the macro model is well founded in the microstructure. The probabilistic law characterizeing the micro-behaviour is working properly: it does provide same dynamic path of the deterministic rules driving the first moment of the distributions. 5 The dual DMC is the one where we analyze firms instead of workers but the two chains lead obviously to same results. 13 Figure 4: 14 9 Local Effects and Individual Behaviour Once built a suitable analytical tool that allows us to obtain average dynamics from the micro-structure, it can be used in a very flexibile way to modify the individual behaviour. In this section we show how we can account for local interactions in the search mechanism. It is not hard to assume that matching can depends not only on macro-variables (the so-called field effect) such as total unemployment and vacancy in the economy but on ”local” variables as well. Local interactions, or neighborhood effects, are often invoked in the human capital literature for explaining ”club convergence” and inter-generational inequality persistence. We are going to assume a rather simple local effect; individual matching rates depends both on aggregate variables and on the number of workers individual in a neighbor of the unemployed individual. The higher the number of working agent in a surrounding of the unemployed worker, the higher the matching rate. We can think to a sort of positive spillover or complementarity effect. Let us define p as the probability that an unemployed worker becomes working due to the presence of a worker in the neighbor and so (1 −p)n is the probability, per unit of time, for a unemployed not to become working if she has n working neighbors hence (1 − (1 − p)n ) is the probability, per unit of time, for a unemployed to be hired if she has n working neighbors.;When n is large the local term tends to 1 whilst when n = 0 the local term is zero (no-spillover); an increase in n makes higher the transition rate from U to M . The individual transitions rates modify in: µ ¶ 1 θ U → M : WU = Γ + Λ(1 − (1 − p)n ) β 1+θ where Γ + Λ = 1 in order to balance macro and local effects (see again Aiello et al. 2000). The effect of this neighbor effect is summarized in figure 3; this shows the adjustment path without local variables and the one risulting from the introduction of the spillover term. The new path is righward shifted w.r.t. the baseline; this means that the Beveridge curve, representing the steady state of the path, can shift in the UV plane because of externalities effect in the individual behaviour, a novel result respect to the current literature. Moreover, for a given Γ and Λ, such a sifht is as higher as n is lower. By varying n, the beveridge curve undertake either shift in the plane according to the empirical findings. It is worth stressing that this type of local interaction can not be analyzed by the standard search model nor by the aggregate dynamical equations; under this point of view, this analytical tool represents an improvement over the standard tecnique. 15 Figure 5: 10 Conclusions This first attempt at modelling job search at individual level has interesting potentialities that the macro-dynamics can not capture. The debate on investment in human capital and the effects on job search and quitting probabilities can only be faced by analyzing the single worker; in particular, neighborhood effects can have important effects on the dynamics of the job market. The approach we are developing fits particularly well in coping with these spillover effects. Individual transition rates can depend on the social and economic neighbor of the individual and in general there is heterogeneity in such rates; this brings to multiple equilibria and to dynamical path which are quite different by the ones we can describe by the aggregate equations. In a more mature stage of our work we will exploit such interesting opportunity. 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