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.     

Wage-vacancy contracts and coordination frictions

We consider a directed search model with risk-averse workers and risk-neutral entrepreneurs who can set up firms that post wage-vacancy contracts, i.e., contracts where firms can make payments to more than one applicant, and where the payments can be different for each applicant and be contingent on the number of applicants. We establish that the type of contracts the literature focuses on are not offered if firms can post wage-vacancy contracts. We show that there exists an equilibrium satisfying a Monotonic Expected Utility property which is efficient. Furthermore, we investigate the role of wage-vacancy contracts on welfare and competition.     

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.     

An equilibrium search model with optimal wage-experience contracts

The objective of this paper is to study equilibrium in a labour market, in which workers search on the job and firms offer wage contracts conditional upon workers' experience and employment status. In this environment, the optimal contract can be described by a promotion contract. The distribution of contract offers is dispersed within and across experience levels. As workers stay longer in the market and promotion dates get closer, the option value of holding a job increases. Firms offer early promotions to attract more experienced workers. A positive relation between experience and earnings can arise purely from firms' optimal response to labour market competition brought about by workers' on-the-job search. We characterise the offer distribution for each experience level and show how these change with labour market conditions.     

Holdups and Efficiency with Search Frictions

A natural holdup problem arises in a market with search frictions: Firms have to make a range of investments before finding their employees, and larger investments translate into higher wages. In particular, when wages are determined by ex post bargaining, the equilibrium is always inefficient: Recognizing that capital-intensive production relations have to pay higher wages, firms reduce their investments. This can only be prevented by removing all the bargaining power from the workers, but this, in turn, depresses wages below their social product and creates excessive entry of firms. In contrast to this benchmark, we show that efficiency is achieved when firms post wages and workers can direct their search toward more attractive offers. This efficiency result generalizes to an environment with imperfect information where workers only observe a few of the equilibrium wage offers. We show that the underlying reason for efficiency is not wage posting per se, but the ability of workers to direct their search toward more capital-intensive jobs.     

Contractual distortions in a market with frictions

This paper analyses contract design in a decentralized market environment with frictions. While principals (e.g., firms) have all contractual power, their market power is constrained as agents (e.g., workers) can choose to wait and search for better offers. We find that results depend crucially on how market frictions affect agents’ utilities. With type-independent costs of search and waiting, equilibrium contracts are always first-best. If agents are impatient and discount future payoffs, however, distortions vanish only gradually. In the latter case, we also characterize equilibrium offers and show that the market exhibits two types of externalities, both of which are absent in the case of type-independent costs of search.     

Wage-Tenure Contracts in a Frictional Labour Market: Firms' Strategies for Recruitment and Retention

A common assumption in equilibrium search and matching models of the labour market is that each firm posts a wage, to be paid to any worker hired. This paper considers the implications of firms posting contracts , in a random matching model with on-the-job search. More complex contracts enable firms to address both recruitment and retention problems by, for example, increasing the wage with tenure. The effect on the labour market is to reduce turnover, below the level required for efficient matching of workers to firms.     

Equilibrium Wage Dispersion,Firm Size,and Growth

This paper analyzes a model of equilibrium wage dynamics and wage dispersion across firms. It considers a labor market where firms set wages and workers use on-the-job search to look for better paid work. It analyzes a perfect equilibrium where each firm can change its wage paid at any time, and workers use optimal quit strategies. Firms trade off higher wages against a lower quit rate, and large firms (those with more employees) always pay higher wages than small firms. Non-steady-state dispersed price equilibria are also analyzed, which describe how wages vary as each firm and the industry as a whole grow over time. Journal of Economic Literature Classification Numbers: D43, J41.     

The composition of wage differentials between migrants and natives

We consider the role of unobservables, such as differences in search frictions, reservation wages, and productivities for the explanation of wage differentials between migrants and natives. We disentangle these by estimating an empirical general equilibrium search model with on-the-job search due to Bontemps et al. (1999) on segments of the labour market defined by occupation, age, and nationality using a large scale German administrative dataset.The native-migrant wage differential is then decomposed into several parts, and we focus especially on the component that we label “migrant effect”, being the difference in wage offers between natives and migrants in the same occupation-age segment in firms of the same productivity. Counterfactual decompositions of wage differentials allow us to identify and quantify their drivers, thus explaining within a common framework what is often labelled the unexplained wage gap.     

Unionization,information asymmetry and the de‐location of firms

We analyze the effects of unionization on the decision of a firm to de‐locate internationally. In a model in which home and foreign workers are perfect substitutes and firms have an informational advantage concerning their productivity, the union offers a menu of wage–employment contracts. Because firms' outside options (producing abroad) depend on productivity, the problem is characterized by countervailing incentives. With the foreign profit sufficiently increasing in productivity, the overstating incentive dominates in equilibrium. Contracts are then characterized by overemployment. The union also affects the extensive margin. High‐productivity firms are excluded because this narrows the possibility to overstate productivity, which saves on information rent. Using a numerical simulation, we show that these effects are quantitatively sizable.     

Upstream mergers,downstream mergers,and secret vertical contracts

In an industry characterized by secret vertical contracts, we consider a benchmark case where two vertical chains exist, with two upstream manufacturers selling to two downstream retailers, and show that the equilibrium prices are independent of whether upstream or downstream firms have all the bargaining power. We then analyse two alternative mergers, and show that a downstream merger (which gives the downstream monopolist all the bargaining power) is more welfare detrimental than an upstream merger (which gives the bargaining power to the upstream monopolist). We also show that downstream and upstream mergers have the same effects when contracts are observable.     

EFFICIENCY OF WAGE BARGAINING WITH ON-THE-JOB SEARCH

This article studies efficiency in a general class of search models where both unemployed and employed workers search for better jobs and can meet multiple firms simultaneously. Employers can respond to outside offers and wages are a weighted average of the productivities of the current employer and a credible poaching firm. I derive a condition that balances firms' bargaining power and their meeting externality. This condition ensures efficiency of both worker turnover and firm entry. Finally, the efficiency condition unifies and extends many of the results on the efficiency of equilibrium search models.     

RESIDUAL WAGE DISPARITY AND COORDINATION UNEMPLOYMENT*

How much of residual wage dispersion can be explained by an absence of coordination among firms? To answer, we construct a dynamic directed search model with identical workers where firms can create high‐ or low‐productivity jobs and are uncoordinated in their offers to workers, calibrated to the U.S. economy. Workers can exploit ex post opportunities once approached by firms, and can conduct on‐the‐job search. The stationary equilibrium wage distribution is hump‐shaped, skewed significantly to the right, and, with baseline parameters, generates residual dispersion statistics 75–90% of those found empirically. However, the model underestimates the average duration of unemployment.     

Sorting by search intensity

In this paper, I characterize matching in an on-the-job search model with endogenous search intensity, heterogeneous workers and firms, and match surplus is shared between workers and firms through bargaining. I provide proof of existence and uniqueness of steady state equilibrium. Given equally efficient matched and unmatched search, the worker skill conditional distribution of firm productivity over matches is stochastically increasing (decreasing) in worker skill if the production function is supermodular (submodular). I also show that this strong notion of sorting does not obtain everywhere for the firm productivity conditional match distribution.     

Capacity constrained firms in (labor) markets with adverse selection

Summary. We discuss a competitive (labor) market where firms face capacity constraints and individuals differ according to their productivity. Firms offer two-dimensional contracts like wage and task level. Then workers choose firms and contracts. Workers might be rationed if the number of applicants exceeds the capacity of the firm. We show that under reasonable assumptions on the distribution of capacity an equilibrium in pure strategies (by the firms) exists. This result stands in contrast to the case of unlimited capacity. The utility level is uniquely determined in equilibrium. No rationing occurs in equilibrium, but it does off the equilibrium path. Received: December 29, 1999; revised version: November 30, 2000     

Informality,public employment and employment protection in developing countries

This paper proposes an equilibrium matching model for developing countries’ labor markets where the interaction between public, formal private and informal private sectors are taken into account. Theoretical analysis shows that gains from reforms aiming at liberalizing formal labor markets can be annulled by shifts in the public sector employment and wage policies. Since the public sector accounts for a substantial share of employment in developing countries, this approach is crucial to understand the main labor market outcomes of such economies. Wages offered by the public sector increase the outside option value of the workers during the bargaining processes in the formal and informal sectors. It becomes more profitable for workers to search on-the-job, in order to move to these more attractive and more stable types of jobs. The public sector therefore acts as an additional tax for the formal private firms. Using data on workers’ flows from Egypt, we show empirically and theoretically that the liberalization of labor markets plays against informal employment by increasing the profitability, and hence job creations, of formal jobs. The latter effect is however dampened or even sometimes nullified by the increase of the offered wages in the public sector observed at the same time.     

COMPETITIVE SEARCH,EFFICIENCY, AND MULTIWORKER FIRMS*

I study competitive search equilibrium in an environment where firms operate a decreasing‐returns production technology and hire multiple workers simultaneously. Firms post wages, possibly several of them. The equilibrium can feature wage dispersion even though all firms and workers are ex ante identical. Unlike the benchmark where firms hire a single worker, hiring is constrained inefficient. Efficiency requires that firms commit to the number of hires, pay all applicants, or pay wages that depend on the number of applicants. Under wage‐posting, the inefficiency is highest at intermediate levels of labor market tightness.     

DIRECTED SEARCH ON THE JOB AND THE WAGE LADDER*

We model a labor market where employed workers search on the job and firms direct workers' search using wage offers and employment probabilities. Applicants observe all offers and face a trade‐off between wage and employment probability. There is wage dispersion among workers, even though all workers and jobs are homogeneous. Equilibrium wages form a ladder, as workers optimally choose to climb the ladder one rung at a time. This is because low‐wage applicants are relatively more sensitive to employment probability than to wage and thus forgo the opportunity to apply for a high wage, with a lower chance of success.     

Quality distortions in vertical relations

This paper examines how delivery tariffs and private quality standards are determined in vertical relations that are subject to asymmetric information. We consider an infinitely repeated game where an upstream firm sells a product to a downstream firm. In each period, the firms negotiate a delivery contract comprising the quality of the good as well as a non-linear tariff. Assuming asymmetric information about the actual quality of the product and focusing on incentive compatible contracts, we show that from the firms’ perspective delivery contracts lead to more efficient contracts and thus higher overall profits the lower the firms’ outside options, i.e. the higher their mutual dependency. Buyer power driven by a reduced outside option of the upstream firm enhances the efficiency of vertical relations, while buyer power due to an improved outside option of the downstream firm implies less efficient outcomes.     

Performance Pay and Adverse Selection*

It is well known in personnel economics that firms may improve the quality of their workforce by offering performance pay. We analyze an equilibrium model where worker productivity is private information and show that the firms’ gain from worker self‐selection may not be matched by a corresponding social gain. In particular, the equilibrium incentive contracts are excessively high‐powered, thereby inducing the more productive workers to exert too much effort and increasing agency costs stemming from the misallocation of effort.