Directed search with multiple job applications

We develop an equilibrium directed search model of the labor market where workers can simultaneously apply for multiple jobs. Our main theoretical contribution is to integrate the portfolio choice problem faced by workers into an equilibrium framework. All equilibria of our model exhibit wage dispersion. Consistent with stylized facts, the density of wages is decreasing and higher wage firms receive more applications per vacancy. Unlike most models of directed search, the equilibria are not constrained efficient.     

Excess supply equilibria

This paper addresses a fundamental problem in economic theory: How can there be equilibria of the economic system where some commodity is in excess supply, yet that commodity's relative price shows no tendency to fall? Of course, the principal example of such a phenomenon is an economy experiencing a prolonged period of involuntary unemployment of the labor force during which there is no significant change in the real wage.In the following pages, I shall describe a two-commodity, general equilibrium model that has a continuum of unemployment equilibria, one for any given unemployment rate. The important feature of this model is that workers establish their wage rates in an attempt to maximize expected utility. The information upon which these wage setting decisions are based is provided by actual labor market transactions.Despite the voluntary nature of the wage setting decision, I shall argue that each equilibrium of this economy exhibits involuntary unemployment in the Keynesian sense. For there will always be another equilibrium with a lower real wage, a higher level of employment, and at which (at least when workers are risk neutral) each worker achieves a higher level of expected utility.     

On-the-job search and strategic bargaining

This paper studies wage bargaining in a simple economy in which both employed and unemployed workers search for better jobs. The axiomatic Nash bargaining solution and standard strategic bargaining solutions are inapplicable because the set of feasible payoffs is nonconvex. I instead develop a strategic model of wage bargaining between a single worker and firm that is applicable to such an environment. I show that if workers and firms are homogeneous, there are market equilibria with a continuous wage distribution in which identical firms bargain to different wages, each of which is a subgame perfect equilibrium of the bargaining game. If firms are heterogeneous, I characterize market equilibria in which more productive firms pay higher wages. I compare the quantitative predictions of this model with Burdett and Mortensen's [1998. Wage differentials, employer size and unemployment. International Economic Review 39, 257-273.] wage posting model and argue that the bargaining model is theoretically more appealing along important dimensions.     

SEARCH DIRECTION AND WAGE DISPERSION*

In a directed search model, we allow the unemployed and the vacancies to choose whether to send or receive wage offers. This determines the market structure. There are several equilibria but a unique evolutionary stable one. Wage offers are made under incomplete information about the number of offers, and the equilibrium strategies involve mixing. This results in wage dispersion. We show that if the unemployment–vacancy ratio is close to unity, the stable equilibrium consists of two submarkets with opposite search directions. Otherwise, the long side of the market sends offers. The stable equilibrium is efficient, given the frictions.     

A Model of Spillovers Through Labor Recruitment

This paper develops a model where spillovers can be generated through domestic firm recruitment of employees at a multinational corporation (MNC) where more advanced technologies are employed. It is shown that both spillover and no-spilover equilibria are possible in the model, depending on the marginal costs and benefits of recruitment. Spillover benefits depend on demand parameters and the technological capabilities of the domestic firm, and spillover costs are determined by the MNC's internal wage. Compared with the no-spillover equilibrium, spillovers lead to fewer technology transfers by the MNC and higher market prices. [031, F23]     

Wage–vacancy contracts and multiplicity of equilibria in a directed search model of the labour market

This paper studies a directed search model of the labour market, which is standard in all aspects except two. First, we allow firms to post wage–vacancy contracts advertising the number of workers they would pay as well as the payment all will receive. Second, we consider two cases: one where workers are risk neutral and one where workers are risk averse, both in finite and large economies. Our paper shows that when firms post wage–vacancy contracts, whether workers are modelled as risk neutral or risk averse matters: the types of symmetric equilibria and the nature of multiplicity of equilibria are different. Somewhat surprisingly, when there are finite numbers of risk‐neutral workers and firms, we obtain a finite number of symmetric equilibria, but when workers are risk averse, we obtain a continuum of equilibria. Furthermore, our paper sounds a cautionary note on using large economies as an approximation of finite economies: when workers are risk neutral, the nature of equilibrium is preserved going from a finite to a large economy, but the nature of equilibrium is different when workers are risk averse.     

Microeconomic uncertainty and macroeconomic indeterminacy

We propose a stylized intertemporal macroeconomic model wherein the combination of decentralized trading and microeconomic uncertainty (taking the form of privately observed and uninsured idiosyncratic shocks) creates an information problem between agents and generates indeterminacy of the macroeconomic equilibrium. For a given value of the economic fundamentals, the economy admits a continuum of equilibria that can be indexed by the sales expectations of firms at the time of investment. The Walrasian equilibrium is one of these possible equilibria but it is reached only if firms are optimistic enough. With a weaker degree of optimism, equilibrium output, employment and real wages will be lower than in the Walrasian equilibrium. Moreover, the range of possible equilibria will depend positively on the wage elasticity of the labour supply and on the magnitude of the information problem between buyers and sellers (in our case, the variance of the idiosyncratic shocks).Stochastic simulations performed on a calibrated version of the model show that pure demand expectation shocks may generate business cycle statistics that are not inconsistent with the observed ones.     

INDUSTRIAL RELATIONS AND ECONOMIC GROWTH IN KOREA

The wage rate, labour productivity, and labour share are examined as they relate to changing industrial relations over the last four decades in the Korea. The results imply that the labour share is greater than that of Korea's competitive equilibrium in the 1990s. We analyse the effect of industrial relations on economic growth through a theoretical model comparing the growth rate of the competitive equilibrium with that of the bargaining equilibrium. The bargaining growth rate is lower than that of the competitive equilibrium. Among bargaining equilibria, the growth rate decreases as the labour share increases.     

A new model of equilibrium involuntary unemployment

Summary. We show that equilibrium involuntary unemployment emerges in a multi-stage game model where all market power resides with firms, on both the labour and the output market. Firms decide wages, employment, output and prices, and under constant returns there exists a continuum of subgame perfect Nash equilibria involving unemployment and positive profits. A firm does not undercut the equilibrium wage since then high wage firms would attract its workers, thus forcing the undercutting firm out of both markets. Full employment equilibria are payoff dominated by unemployment equilibria, and the arguments are robust to decreasing returns.Received: 21 May 2001, Revised: 15 April 2003, JEL Classification Numbers: D43, E24.Correspondence to: Leo KaasWe thank an anonymous referee, Woojin Lee, Klaus Ritzberger and seminar participants in Konstanz, Manchester, Milan, Prague, Vienna, and Warwick for helpful comments. Financial support from the Economic and Social Research Council (UK) under grant L138251030 and from the Manchester School Visiting Fellowship Scheme is gratefully acknowledged.     

Overseas Employment and Remittances to a Dual Economy

Overseas employment has become more commonplace, and remittances have increased in similar proportions. For poor countries, remittances often substantially influence domestic expenditures and real exchange rates. We study overseas employment, remittances and domestic underemployment in a simple general equilibrium model with a non-traded good and minimum wage. The influence of population growth, rural productivity, and family altruism are examined. If remittances per migrant exceed domestic productivity then multiple equilibria may occur exhibiting high or low overseas employment. We discuss how the equilibrium with highest overseas employment conditionally Pareto dominates the other equilibria, and analyse policy co-ordination.     

Cycle and Trend in Models of the Range of Equilibria

This paper investigates the potential of models of the range of equilibria to yield a pattern of equilibrium rates of unemployment that is consistent with the observed mix of cycle with no trend in the rate of unemployment. To do this the paper considers a model in which wages are determined by a group of unionised insiders bargaining with an employer. In the model the supply of labour is endogenous. Specifications of the utility function are found which are consistent with the mix of cycle and no trend in the rate of unemployment. Of these it is concluded that loss aversion in the evaluation of wage relativities is a crucial ingredient for models of the range of equilibria.     

Equilibrium Search with Continuous Productivity Dispersion: Theory and Nonparametric Estimation

In this article we develop an equilibrium search model with a continuous distribution of firm productivity types within a given labor market. We characterize equilibrium, derive expressions for the endogenous equilibrium wage distributions, and characterize the set of wage distributions that can be generated by the model. We develop a structural nonparametric estimation method for the productivity distribution. We estimate the model using French longitudinal survey data on labor supply, and we compare the results with those from a French panel data set of firms. The results are informative on the degree to which firms exploit search frictions.     

Real wages,quantity constraints and equilibrium unemployment: Belgium, 1955–1988

This paper examines the determinants of equilibrium wage and unemployment rates in Belgium within the framework of a quantity rationing, right-to-manage model with decentralised wage-setting. Empirical results are obtained by first using the Johansen maximum-likelihood procedure for the analysis of cointegration among the variables of interest. The information from this stage is then used to estimate a three equation econometric model explaining the wage share, the unemployment rate and the capital gap. The slowdown in world trade is depicted as the most important factor explaining the rise in unemployment in Belgium, with dampening effects due to wage control policies imposed in the eighties. Because we obtain only two cointegrating relations, for three endogenous variables, our results are compatible with the hypothesis of path dependency and multiple equilibria.     

On the role of network externalities in strategic delegation contracts with an industry-wide union

This article analyses the role of network externalities in managerial delegation contracts for differentiated products when the marginal product costs (the wage) are set by an industry-wide union. The results show that, in both Bertrand and Cournot equilibria, each owner offers a profit-oriented incentive scheme to his or her managers by penalizing sales maximization, irrespective of the strength of the network externalities. In the presence of weak network externalities and low product differentiation, firms can obtain higher profits in the equilibrium under Cournot-type quantity competition compared with that under Bertrand-type price competition. Furthermore, the wage chosen by the union is higher in the Cournot than in the Bertrand equilibrium. In the Cournot equilibrium, the wage increases with the strength of the network externalities. However, in the Bertrand equilibrium, there exists a threshold level of the degree of product differentiation.     

TRAINING,TURNOVER, AND SEARCH*

This article explores a model of firm‐specific training in a job search environment with labor turnover. The main substantive finding is a positive association between training and wages (when dispersed). The article then precisely characterizes how both wage dispersion and firm profitability depend on the flow value b≥ 0 of workers' unmatched time. It is shown that: (i) for all high values b, no equilibrium exists; (ii) for intermediate values b, multiple equilibria arise, where firms earn zero profits, and choose from a general wage distribution; (iii) for all lower values b, there is a unique equilibrium, with firms earning positive profits, and choosing from an atomless set of wages.     

Wage/tenure contracts with heterogeneous firms

This paper investigates equilibria where firms post wage/tenure contracts and risk averse workers search for new job opportunities whether employed or unemployed. We generalize previous work by assuming firms have different productivities. Equilibrium implies more productive firms always offer more desirable contracts. Thus workers never quit from more productive firms for less productive firms. Nevertheless turnover is inefficient as employees with long tenures at low productivity firms may reject outside job offers from more productive firms. A worker who quits to a more productive firm may accept a wage cut. Such wage cuts are compensated by faster “promotion” rates to higher wage levels in the future. We also generalize previous arguments by showing equilibria exist where the distribution of offers contains interior mass points and find equilibrium wage/tenure contracts need not be smooth.     

Profit sharing as entry deterrence mechanism

In a right-to-manage framework, this paper analyzes the optimal choice of the pay scheme (profit sharing vs. fixed wage) in a unionized duopoly with potential market entry and decentralized bargaining. The paper shows that, depending on the institutional features, both pay systems can arise as equilibria in Nash strategies. Under duopoly with committed bargaining, the fixed wage is the Nash equilibrium; with flexible bargaining, an agreement between the incumbent firm and its union about profit sharing arises as Nash equilibrium, if the union is not too strong. A monopoly with threat of entry reinforces the selection of profit sharing as a deterrent mechanism.     

Multiple Equilibria and Minimum Wages in Labor Markets with Informational Frictions and Heterogeneous Production Technologies*

It is often argued that a mandatory minimum wage is binding only if the wage density displays a spike at it. In this article, we analyze a model with search frictions and heterogeneous production technologies, in which imposition of a minimum wage affects wages even though, after imposition, the lowest wage in the market exceeds the minimum wage. The model has multiple equilibria as a result of the fact that the reservation wage of the unemployed and the lowest production technology in use affect each other. Imposition of a minimum wage may improve social welfare.     

Imperfectly competitive factor markets and price normalization

A two-sector general equilibrium model with imperfectly competitive labor markets is set up. Noncooperative equilibria with wage setting at the sectoral level are shown to depend on the choice of price-normalization rule even though all agents behave fully rationally. Hence, imposing rationality is not sufficient to deprive the choice of price-normalization rule of its importance. It is argued that the importance of the choice of price-normalization rule may follow from the strategic interaction of agents and not from imperfectness of competition per se, and some examples are provided.     

WAGES,PROFITS AND CAPITAL FLIGHT*

We model capital flight as the outcome of a non-cooperative differential game between workers (who control the wage share) and capitalists (who control investment at home and abroad). There are three equilibria for such a game. Along the interior equilibrium, the domestic economy becomes “decapitalized” as investors build up their holdings of foreign assets, in a situation reminiscent of the experience of several developing countries.