Mobility Costs and Localization of Labor Markets

Transcription

1 Mobility Costs and Localization of Labor Markets Andreas Kopp a,1 a Hamburg Institute of International Economics Neuer Jungfernstieg Hamburg Germany Abstract The paper seeks an explanation for the often observed clustering of workers in geographic space. Reluctance to leave such clusters may be due to perceptions of job uncertainty rather than inconsistent behavior or disincentives resulting from unemployment benefits. We show that uncertainty with respect to the employment duration coupled with market frictions in the form of search and relocation costs require a specific model of wage determination. The peculiar features of the spatial labor market induce the localization of the labor market. The agglomerative force demonstrated by showing that employers cannot break away from clusters of labor supply within distances determined by the number of vacancies and employment opportunities in the cluster as well as search and relocation costs. Key Words: labor market uncertainty, bargaining and search equilibrium, localization 1 Andreas.Kopp@hwwa.de, Andreas.Kopp@mailbox.tu-dresden.de 1

2 1 Introduction The most immediate reason for localized production is the fact that resources are only available at certain points in geographic space and that the use of these inputs is associated with transportation costs which are large relative to returns from selling the produce. This provides a natural explanation for industries which rely heavily on natural resources and/or specific environmental production conditions. It is less obvious why resources which are mobile in principle are only locally available and lead to the location of certain industries at c points in geographic space. Most of the theoretical literature on the localization of industries which are input dependent takes localized factor markets for granted and studies the consequences for local, regional or national economies. If the immobility of resources is not just treated as a physical phenomenon, it is traced back to factor market externalities, the externalities being defined as pecuniary externalities that tend to reduce the prices at which primary inputs can be purchased as more and more of those inputs come to be assembled at the locale in question. [2] More specifically, we focus here on the localization of labor markets (on an analysis related to ours here of the geographic segmentation of capital markets cf. [5]). A first approach to study the localization of labor markets proceeds from the assumptions of decreasing average costs in production and firm specific demand shocks. Given these conditions, localized labor markets provide an insurance against unemployment on the supply side of the market and against the unavailability of labor supply on the part of the employers who face positive demand shocks. Models following this line of argument differ in the way how wage determination is incorporated. In Krugman s model [7] wages are exogenously given while Rothemberg and Saloner [10] consider a positive feedback from localization of the labor market to the local level to the local level of nominal wages as central to the localization process. Closer to what we present here is the previous work trying to derive an agglomerative force from the workers behavior to cope with the uncertainty with respect to employment opportunities and to the terms of labor contracts. David [1] assumes that workers consider labor market conditions as being subject to different stochastic processes at different points in geographic space, depending on the size of the local labor markets. Workers are attracted to agglomerations by the fact that search requires residential location at these places and values of employment opportunities having identical means but a greater variance the larger the number of employers at certain locations. Other models based on the assumption that costs of (re-) location are part of search costs are those of 2

3 Maier [8], emphasizing the importance of information channels by which labor market information is obtained, and Helsley and Strange [4] focussing on the heterogeneity of the labor force and a greater expected match quality in larger local labor markets. In our model we derive a microeconomic basis for the localization of labor markets without being bound to decreasing average costs in production. The argument does neither depend on localized search or the heterogeneity of workers. The localization rests upon the perceived uncertainty with respect to employment duration, the search costs of employers and workers as well as the relocation costs which are associated with switching jobs. As we will argue, the spatial frictions of labor markets require a peculiar analysis of wage determination. We start by presenting the analytics of wage determination in uncertain labor markets before we turn to its geographical dimension. 2 The model 2.1 Motivation of a search and bargaining model The basic assumption of our model is that the workers information regarding job opportunities and the duration of a job is imperfect. Job-related information has to be acquired and evaluated before a worker can be or is willing to become employed. In accordance with the literature on job search, this process is considered to be costly and sequential (for a review see [9]). As in standard models of optimal stopping of statistical decision theory ([3]) the worker is regarded as sampling offers one at a time and deciding on the basis of the sample obtained to that date whether or not to stop the search process. Time requirements for search are random variable depending on job availability, i.e. on the speed of the Poisson process with which job offers arrive. The speed is controlled by the workers search intensity,with search costs being an exponential function of the search intensity. Future costs and returns of the search process in the form of wage payments are discounted. In most of the literature on job search it is assumed that wage offers and demands are made as take-it-or-leave-it proposals. The assumptions that workers and employers are able to commit to such offers is in contrast with the basic behavioral assumptions of the model: If the announced wage rate is higher than the subsistence wage and a worker accepts such an offer the employer could reduce the wage by slightly less than the search costs without risking to be deserted by the worker. If only the employers could commit to wage offers the equilibrium 3

4 wage would therefore be equal to the subsistence wage. Any search process would be obsolete as this equilibrium wage would hold for all employment relations. If on the other hand the workers could commit to a wage demand and this were accepted by the employer the worker could increase the wage demand by slightly less than the search costs of the employer. The equilibrium wage would then be equal to the productivity. With competitive product markets marginal productivity were identical for all workers and again there is no basis for search. As both parties cannot commit to their proposals the compensation for work must be the result of a bargaining agreement between the worker and the employer on the division of the surplus which is generated by establishing the employment relationship (on search and bargaining in matching markets cf. [12]). The agreement on the division of the surplus is obtained by a non-cooperative bargaining process. (cf. [11]) Outline of the search and bargaining process Assuming that there are many employers and many workers such that we can exclude coalition formation on either side of the labor market, the bargaining game is played bilaterally between a potential employer and a potential worker. Workers and employers search for bargaining opportunities over discrete time periods of length. The probability of having a bargaining opportunity in a certain period depends on the search intensity s i. Search costs are given by a search cost function c i (s i ) which is continuous and twice differentiable. As both employers and workers search, the probability of finding a bargaining opportunity also depends on the search activities of agents on the other side of the market as well as the relative numbers of job seekers and vacancies. The probability of an agent i of finding a match without own activities, given activities of potential bargaining partners j is given by: s i 0 = N j N i s j (1) Workers and employers know the probability distribution function of bargaining opportunities F(x). If partners agree to bargain a chance move determines who is the first proposer. If the first proposal is accepted the agreement is immediately implemented. If the bargaining partner rejects the proposal both partners search for other bargaining opportunities, for outside options. Decisions on the search activities are taken in the same way as search for bargaining opportunities is optimized when searching from an unmatched position. If anyone of the partners 4

5 finds a superior bargaining opportunity she or he switches to another bargaining process. If the alternative is inferior both continue the ongoing bargaining process. 2.2 Equilibrium analysis Optimal search After each draw from the distribution function F(.) the researcher has to decide whether to accept the job opportunity or not. A job opportunity is defined by the surplus of an employment relationship m and a layoff rate γ > 0. The layoff rate indicates the probability that the employment ends at the end of the current period. The optimal search rule of an agent maximizes the expected net return of the searcher. Let Ω denote the information set of an agent i. W i (m, γ) be the present value of stopping the search process, accepting the best bargaining opportunity m to that date. W (m, γ) is a continuous, strictly increasing function of m. Let V i denote the expected value of participating in the search and bargaining process in case of an optimal search strategy. This value is given by [ (si ) M V i = c i (s i ) + δ i + s i 0 0 ] max[v i, W i (x, γ)]df (x) (2) The equation has a unique solution provided that the mean of the distribution function and its higher moments are finite [6]. Given these conditions the agent s optimal search strategy satisfies the reservation property saying that the wealth maximizing search strategy has the characteristic that it is optimal to accept an opportunity when its value in any period is equal to or in excess of a critical number called the reservation value m. Therefore, searching optimally the reservation value m is implicitly determined from equating the value of search and the value of accepting a job: V i (m i, γ) = W i (m i, γ). (3) The optimal search intensity s i follows from (2) by calculating first order conditions. δ i M m i [W i (x, γ) W i (m i, γ)] df (x) = c (s i ), (4) 5

6 with c denoting the first derivative of the search cost function. Turning to the bargaining process we first note that the employer and the worker learn immediately upon being matched about the value of the match The bargaining process Let V 1 denote the worker s value of searching optimally from an unmatched position, and V 2 the corresponding value for the employer. Let m be the surplus that is generated by establishing a certain employment relationship. It is then clear that the bargaining will not start if the sum of the values of the bargaining partners of searching from an unmatched position exceeds the bargaining surplus m. If V 1 + V 2 > m there is no solution to the bargaining process that gives both partners at least V i. Searching from within the bargaining process for outside options the only difference to the search from the unmatched position is that the reservation value is equal to m which must be at least as high as the reservation value m. The worker s value of searching for outside options is then V 1 = c 1(s 1 ) + δ 1 (s 1 + s 1 0) M W m 1 (x, γ)df (x), (5) 1 (1 (1 F (m ))(s 1 + s 1 0) )δ 1 and the employer s value of search for outside options V 2 = c 2(s 2 ) + δ 2 (s 2 + s 2 0) M W m 2 (x, γ)df (x). (6) 1 (1 (1 F (m ))(s 2 + s 2 0) )δ 2 Given the stationarity of the Markov decision problem equilibrium demands and offers are determined from the equality of the values of accepting and rejecting the bargaining partner s offer or demand. Given the surplus m the values of accepting the equilibrium offer of the partner is denoted by Wi, i=1,2. The value of rejecting an offer is determined by the value of search from a matched position and the risk of loosing the bargaining opportunity because the bargaining partner has found a superior match. The basic equations of the bargaining solution are then m W 2 = RO 1 (7) m W 1 = RO 2, (8) 6

7 with RO i denoting the value of rejecting an offer to agent i. These values are given by RO i =(1 (1 F (m ))(s j + s j 0) )(1 (1 F (m ))(s i + s i 0) )δ i W c i (s i ) + (s i + s i 0) M m W i (x, γ)df (x) + (1 (1 F (m ))(s i + s i 0) )(1 F (m ))s j + s j 0) V i. i (9) Switching to a continuous time version of the basic bargaining equations and letting recede to a small but positive number we obtain as the solutions to the search and bargaining problem W1 = r 1 + (a + b)a r 1 + r 2 + 2(a + b)a m + (r 1 + aa)v1 + bav 1 r 1 + r 2 2(a + b)a (r 2 + ba)v 2 + aav 2 r 1 + r 2 2(a + b)a (10) W2 = r 2 + (a + b)a r 2 + r 1 + 2(a + b)a m + (r 2 + aa)v2 + bav 2 r 2 + r 1 2(a + b)a (r 1 + ba)v 1 + aav 1 r 2 + r 1 2(a + b)a (11) The implied optimal search intensities while searching for outside options follow from δ i M m [W i (x, γ) W i (m, γ)] df (x) = c (s ) (12) The bargaining equations equally split the difference between the surplus of the employment relation and the disagreement payoffs of the individuals, the disagreement payoffs being the values of search from a matched or an unmatched position respectively, weighting these values with relative probabilities depending on the distribution function, the discount rates, the search intensities and the relative numbers of job seekers and vacancies. 7

8 2.3 Localization So far we have only looked at a one-point market. In this subsection we shall demonstrate that the existence of a positive layoff rate alone, without the assumption of a residential relocation being required for the search process, may lead to the localization of the labor market. We do, however, assume that the distance between the residential location of the job seeker and potential work places is such that the acceptance of a job requires residential relocation. These costs are assumed to be substantial relative to the wages earned and distance dependent. The relocation costs R are given by R = τd, (13) with R denoting the relocation costs, τ the transportation cost rate per distance unit and D the distance between the residential location of the worker and a prospective workplace. To keep things simple and without loss of generality we assume that there are only two prospective workplaces H 2 with N 2 vacancies and H 3 with only one prospective employer. The distance between H 2 and H 3 is denoted by d, between H 1 and H 2 D 2 and between H 1 and H 2 D 1. Let H 1 denote the residential location of the worker. Whether there will be a localization of the labor market depends on whether, and under which conditions, the worker who is searching for employment, benefits from turning down a job offer at the single firm location H 3. In other words, we have to find out under which conditions the value of searching for a job only at location H 2 exceeds the value of accepting a job offer at H 3. There are three potential reasons why to turn down a job offer at an isolated place may be a superior policy: - Due to an assumed triangle configuration (D 2 + d > D 1 ) the total relocation costs may be higher if the worker is laid off at H 3 and has to move to H 2 afterwards. - The reservation value when searching for outside options at location H 3 is lower than the corresponding reservation value when searching for an outside option at location H 2. As both search values, when searching from an unmatched position as well as when searching from a matched position at H 3, the share of the surplus of the worker who accepts a job at H 3 is reflected in a lower wage. - If the bargaining process at H 3 fails the opportunity to find a match at location H 2 with a potentially higher wage is delayed by one period. The costs of turning down the job offer at location H 3 are the following: 8

9 - The rejection of the job offer forces the worker to wait for one period to have the opportunity to search for a job at location H 2, and therefore foregoes at least one period of wage income. - If a job opportunity comes up at H 2 the worker has higher initial relocation costs due to D 1 being greater than D 2. Let w 3 be the per period wage, W 3 the value of continued employment and V 3 2 the value of searching from an unmatched position at H 3. The value of accepting a job offer at H 3 is then given by W 13 = τd 2 + w 3 + δγv 32 + δ(1 γ)w 3. (14) The value of searching from an unmatched position at H 1 while restricting the search to location H 2 is defined by V 12 = c 1 (s 1 ) + δ(1 (s 1 + s 2 0) + (s 1 + s 2 0)F (m 1 ))V 12 + δ(s 1 + s 2 0) M m 1 [W 2 (x, γ) τd 1 ] df (x), (15) Both V 12 and V 32 are positive functions of the number of employment opportunities at location H 2. Therefore with δ(s 1 + s 2 0) δ(1 (s 1 + s 2 0) + (s 1 + s 2 0)F (m 1 )) δ(s 3 + s 2 > 0) δ(1 (s 3 + s 2 0) + (s 3 + s 2 0)F (m 3 )) (16) the difference between the value V 12 and W 13 will become positive for values of N 2 being greater than some threshold value N 2. Given these conditions no employer outside H 2 can expect positive labor supply. In other words, if a localized labor market exists due to the uncertainty of being laid off employers may not be able to break away from an existing cluster. 3 Conclusions It has been argued that uncertainty with respect to the job duration may lead to the segmentation of labor markets. Our analysis is based on the assumption that workers who search for a job are confronted with uncertainty with respect to the job productivity and the duration of an employment relationship once it 9

10 is established. Wage payments are to be agreed upon by bargaining as both the workers and the employers cannot commit to wage demands or wage offers ex ante due to the frictions resulting from the labor market uncertainty. Even without any dependence of the reservation value determining the search behavior on the layoff rate and without any dependence of the search costs on the geographic structure of the labor market there is a tendency for the labor market to localize depending on the unevenness of the geographic distribution of job opportunities. The workers economies from searching in a cluster prevent firms to locate outside that cluster. 10

11 References [1] David, P., 1973, Fortune, risk and the microeconomics of migration, in Nations and Households in Economic Growth. Essays in Honour of Moses Abramowitz, ed. by P. David & M.W. Reder (New York). [2] David, P. & J.I. Rosenbloom, 1990, Marshallian factor market externalities and the dynamics of industry location, Journal of urban economics 28, [3] DeGroot, M.H, 1970, Optimal Statistical Decisions (New York). [4] Helsley, R.W. & W.C. Strange, 1990, Matching and agglomeration economies in a system of cities Regional Science and Urban Economics 20, [5] Helsley, R.W. & W.C. Strange, 1991, Agglomeration economies and urban capital markets, Journal of Urban Economics 29, [6] Kohn, M.G. & S. Shavell, 1974, The theory of search Journal of Economic Theory 9, [7] Krugman, P., 1991, Geography and Trade (MIT Press Cambridge, Mass.). [8] Maier, G., 1987, Job search and migration, in Regional Labour Markets, ed. by M. Fischer & P. Nijkamp (North Holland Amsterdam). [9] Mortensen, D.T., 1986, Job search and labor market analysis, in Handbook of Labour Economics, Vol. II, ed. by O. Ashenfelter & R. Layard (North- Holland Amsterdam). [10] Rothemberg, J. & G. Saloner, 2000, Competition and human capital accumulation: a theory of interregional specialization and trade Regional Science and Urban Economics 30, [11] Rubinstein, A., 1982, Perfect equilibrium in a bargaining model, Econometrica50, [12] Wolinsky, A., 1987, Matching, search and bargaining, Journal of Economic Theory 42,