外文翻译原文：Differentiation of Skills, Firms’ Recruitment Strategy andUnemployment Benefits in an Efficiency Wage ModelFrédéric GavrelSummary:It is well known that the recruitment strategy of firms depends on the state of the labour market. In order to account for this fact, we build a matching model where the differentiation of skills is explicit. Along the line of Salop 1979b workers and firms are distributed on the same circle and the distance between two points on this circle measures the mismatch between a firm and a worker. Another feature of this model concerns wage setting. In a natural way, wages are subject to the constraint that ‘good’ workers (i.e. workers who are not ‘too’ far on the circle prefer to keep their job. In addition, on a suggestion by Phelps 1992, we assume that workers who quit their job are not eligible to unemployment insurance. Two main results are established. First, the lower the tightness of the labour market the more stringent the requirements of firms are. Second, as a consequence of the incentive constraint, unemployment benefits appear to raise employment.Key words: differentiation of skills, matching, recruitment strategy, efficiency wage, unemployment benefits1 INTRODUCTIONSince the early 1990s, many analyses of the labour market rest on a matching model. According to this approach, the heterogeneity of the workforce and the jobs and the imperfect information of agents explain why unemployment and vacancies can permanently coexist and why the so-called Beveridge curve does not coincide with one of the axes of the diagram.For the sake of simplicity, standard matching models Pissarides 1990 formalize the frictions of the labour market by assuming that the hiring flow per period rises continuously with the stock of unemployed people and vacancies. However, though a simple and useful tool, this hiringfunction is subject to serious limits.First, it is a shortcut and, from a theoretical point of view, such an ‘adhocery’is quite unsatisfactory. Overall, this tool of analysis occults some important aspects of the hiring process. In particular, the hiring flow depends on the behavior of firms whose recruitment strategy reflects the tightness of the labour market.One aim of this article is to account for this fact. To that purpose, we build a matching model where the differentiation of workers and jobs as well as the searching behaviour of the unemployed are explicit. The hiring process is then based on microeconomic grounds. Considering the differentiation of agents, we adopt the approach of Salop( 1979b).Workers and firms are distributed on the same circle and the distance between two points on this circle measures the mismatch between the requirements of a firm and the skill of a worker. Regarding job search, we assume that workers issue one application in each period until they find an acceptable job. Another feature of this model concerns wage setting. Usually, in matching models, wages are negotiated :the surplus created by the formation of an employer-employee pair is divided between both parties according to their bargaining power. Here,in a natural way, we assume that firms decide on wages so that ‘good’ workers( i.e. workers who are not ‘too’ far on the circle )prefer to keep their job. In other terms, as in Phelps (1970) and Salop (1979a), wages are subject to an incentive constraint, the ‘no quitting’constraint. Taking their wage decision, firms then face a trade-off between their labour costs and the probability of filling their vacancies which rises with the number of workers who are ready to accept their wage offer.In addition, on a suggestion by Phelps (1992), we assume that workers who quit their job are not eligible to unemployment insurance. In other terms, only workers whose jobs are destroyed can receive unemployment benefits.Two main results are established. First, the lower the tightness of the labour market the stronger the requirements of firms are. Second, as a consequence of the incentive constraint, unemployment benefits appear to raise employment.The paper is organized as follows. Section 2 presents the model. In section 3, we study the behaviour of firms and their recruitment strategy. In section 4, we study the equilibrium and the comparative statics of the model. The last section collects some final comments.2 THE MODELThe economy includes two sets of numerous risk-nautral agents: the workers and the firms. The workers, in number N, are heterogenous. The jobs which the firms offer them are heterogenous too.All the workers are infinitely lived. On the contrary ,the firms, which produce the same good, can die. We assume that, at each period, the firms face a constant risk of destruction; its probability is denoted by s. The firms are then eternally young like the households in Blanchard and Fisher(1989).By the law of large numbers, a share, s, of the firms disappears at each period. However, the free entry of new firms on the market stabilizes their number. All the agents have the same discount rate, r. Let R denote the sum (1+r).In order to describe the differentiation of workers and jobs, we use the tool of analysis of Salop (1979b).2.1 The cirle of skillsWe assume that the set of the workers is uniformly distributed on a circle which circumference is equal to two(see Figure 1).This distribution is exogenous. The position of a worker on this circle does not represent his spatial localization or the level of his ability but the ‘type’ of his skill. The distribution of the firms on the circle, which is endogenous, is uniform too.1 Likewise, the position of a firm on the circle represents its ‘type,’ that is the skill which perfectly suits its needs. When differentiation is modelled with a circle, each job and each worker face the same situation. Indeed, each job, whatever its requirements, faces the same distribution of more or less suitable workers. The model makes the heterogeneity of jobs and workers compatible with the symmetry of their situation. So, workers have the same hiring opportunities and employers adopt the same recruitment strategy. In short, the circle symmetry allows me to base the usual matching model (Pissarides( 1990)) on microeconomic grounds.Let’s consider two points A and B on the circle of skills. Let l be the distance between A and B ( 0≤l≤1). This distance measures the match between the type of a worker located in A or a firm, respectively and the type of a firm located in B or a worker, respectively. Thus, the match is perfect when the distance l equals zero. On the opposite, the mismatch is maximum when l reaches unity.Each active firm employs only one worker. The production of an active firm is a constant denoted by y. In other words, we assume that production y does not depend on mismatch l. Conversely, the mismatch affects the effort which workers have to perform in order to reach production y. Consequently, the disutility of a worker is an increasing function in distance l between his skill and the needs of the firm which employs him.2.2 Hiring process and flow equilibriumFollowing the job search theory of Mc Kenna (1985), we assume for simplicity that each unemployed issues just one application per period. Because they have no priori information about job offers, the hiring firm they meet is drawn at random. One important assumption is that when a meeting occurs, information is asymmetric. Only firms know the type of their applicants. But, this asymmetry lasts for just one period the hiring period and the new employees learn the type of their job when they start working. Although unusual, this assumption aboutthe information available to both parties is quite natural in this context. Specifically, we assume that the examination of applicants is accurate enough to predict the firms with the perfect knowledge of their characteristics. They can then measure the extent of the mismatch. Conversely, workers do not learn about jobs before work begins. Indeed, for wage setting to be derived from the no quitting condition, the information of workers must be postponed until the beginning of the production process. Then, jo bs’ attributes can be experienced. As a consequence, firms decide on the mismatch limit, that is, the distance to their own type, denoted by, above which an applicant will be rejected. At this stage of the analysis, the limit is exogenous.2.2.1 The hiring functionLet U be the number of unemployed and V the number of vacancies. The tightness of thelabour market is then given by the ratio Hence, one can show see Appendix A that the probability of filling a vacancy, denoted by q, is determined by:Indeed, to fill its vacancy, a hiring firm only needs to meet just one employable worker, that is a worker whose type is not further than the limit. For obvious reasons, more selectivity (i.e.a decrease in λ) and either more vacancies or less unemployment (i.e.an increase in θ) reduce the probability of filling a job. Total hiring of workers, denoted by H, derives then from the following function:One can easily verify that this hiring function exhibits constant returns to scale with respect to variables U and V. The hiring probability p obtains by dividing total hiring H by unemployment U:Clearly, probability p is an increasing function in mismatch limit. In Appendix B, we establish that p is also an increasing function in labour market tightness. Therefore, an increase in mismatch limit less selectivity raises both probabilities p and q.2.2.2 Flow equilibriumIn stationary equilibrium, the flow of the workers who get a job equals the flow of those who loose their job:where (N-U) then represents the level, L, of employment, the number of active firms.2.3 Intertemporal utilities and profitsThe mismatch limit, which is the distance above which firms reject an applicant, stays exogenous. It will be determined when we study the behaviour of firms section 3.To this aim, we first need to state the expression of the expected intertemporal utilities of workers and the intertemporal profits of firms.2.3.1 Intertemporal utilitiesFirst consider the intertemporal utility of an employee. It is a function of the mismatch:.In the current period, this worker receives the net wage: w-E(l). In the next period, either the firm where he holds his job is destroyed and he is laid off for ‘economic reasons’ event of probability s or the firm is still alive and the employee keeps his job. Let W uf denote the intertemporal utility of an eligible unemployment, that is a worker who receives unemployment benefits because he lost his job for economic reasons. In stationary equilibrium, utility w l then satisfies:Consider now the intertemporal utility of an eligible unemployed. In the current period, this worker receives benefit b. Next period, either he remains unemployed (event of probability (1-p)) or he finds a job (event of probability p). In this second case, his intertemporal utility will depend on the effort, E (l), he will have to perform. We then obtain:where denotes the expected intertemporal utility of a worker who finds a job (that is, knowing that he found a job). Since the mismatch degree, l, is uniformly distributed on the interval,conditional expectation is determined by:Let denote the average disutility of effort:We then have:Similarly, the intertemporal utility of an eligible unemployed ,that is an unemployed who does not receive benefit b because he left his job voluntarily, writes:2.3.2 Intertemporal profitsEach firm offers a single job which is either vacant of filled. Firms maximise the intertemporal profit of vacancies with respect to. They then decide on the set of workers who are eligible for their jobs. From, we directly deduce the value of w, because both variables are linked together by the ‘no quitting’condition. Firms then have an optimal hiring behaviour. However, because of the assumption of no barriers to entry, new firms are created as long as profits remain positive. Consequently, the intertemporal profit of a vacant job necessarily equals zero. When production begins, the firm’s decision process is closed.One worker has been selected and the wage he will earn is already set. The same goes for the value of the occupied job,J F.3.wage setting and firms selectivity3.1 wage settingThe wags must be high enough to discourage employees whose mismatch is below iimitto quit their job. Hence, wage w must ensure that:Because firms maximize their profit, this incentive constraint holds as an equality. We thenobtain the no quitting condition:Given this latter condition, equations 5,6,9,and 10 allow to exhibit the wage setting equation. To that aim, consider the average intertemporal utility W. Combining equations 9 and 6 gives:Hence, the intertemporal utilities W u f and W uqFinally, imposing the no quitting condition (equation 17), we get the wage setting equation:According to it, the wage is an increasing function in the hiring probability p. This is because, for obvious reasons, an increase in probability p raises the intertemporal utility of the ineligible unemployed more than it raises the intertemporal utility of a marginal employee. Others things equal,expected utility W uq would turn out higher than expected utility W(λ).Since the wage effect on W(λ) is stronger than on W uq, the no quitting constraint leads to an increase in w.译文：在一个高效工资模式中，企业在人才招聘策略和失业救济金之间的技术区别Frédéric Gavrel摘要：众所周知，公司的招聘策略依赖于国家的劳动力市场。
