Equilibrium Wage‐Tenure Contracts

In this study we consider a labor market matching model where firms post wage‐tenure contracts and workers, both employed and unemployed, search for new job opportunities. Given workers are risk averse, we establish there is a unique equilibrium in the environment considered. Although firms in the market make different offers in equilibrium, all post a wage‐tenure contract that implies a worker's wage increases smoothly with tenure at the firm. As firms make different offers, there is job turnover, as employed workers move jobs as the opportunity arises. This implies the increase in a worker's wage can be due to job‐to‐job movements as well as wage‐tenure effects. Further, there is a nondegenerate equilibrium distribution of initial wage offers that is differentiable on its support except for a mass point at the lowest initial wage. We also show that relevant characteristics of the equilibrium can be written as explicit functions of preferences and the other market parameters.     

Residential Location,Job Location,and Wages: Theory and Empirics

I develop a stylized partial on‐the‐job equilibrium search model that incorporates a spatial dimension. Workers reside on a circle and can move at a cost. Each point on the circle has a wage distribution. Implications about wages and job mobility are drawn from the model and tested on Danish matched employer–employee data. The model predictions hold true. I find that workers working farther away from their residence earn higher wages. When a worker is making a job‐to‐job transition where he/she changes workplace location he/she experiences a higher wage change than a worker making a job‐to‐job transition without changing workplace location. However, workers making a job‐to‐job transition that makes the workplace location closer to the residence experience a wage drop. Furthermore, low‐wage workers and workers with high transportation costs are more likely to make job‐to‐job transitions, but also residential moves.     

An Equilibrium Theory of Learning,Search, and Wages

We examine the labor market effects of incomplete information about the workers' own job‐finding process. Search outcomes convey valuable information, and learning from search generates endogenous heterogeneity in workers' beliefs about their job‐finding probability. We characterize this process and analyze its interactions with job creation and wage determination. Our theory sheds new light on how unemployment can affect workers' labor market outcomes and wage determination, providing a rational explanation for discouragement as the consequence of negative search outcomes. In particular, longer unemployment durations are likely to be followed by lower reemployment wages because a worker's beliefs about his job‐finding process deteriorate with unemployment duration. Moreover, our analysis provides a set of useful results on dynamic programming with optimal learning.     

SEARCH INTENSITY,DIRECTED SEARCH,AND THE WAGE DISTRIBUTION

We propose a search equilibrium model in which homogeneous firms post wages along with a vacancy to attract job seekers while homogeneous unemployed workers invest in costly job seeking. The key innovation relies on the organization of the search market and the search behavior of the job seekers. The search market is continuously segmented by wage level, individuals can spread their search investment over the different submarkets, and search intensity has marginal decreasing returns in each submarket. We demonstrate the existence of a nondegenerate equilibrium wage distribution. The density of this wage distribution is increasing at low wages and decreasing at high wages. The distribution can be right‐tailed, and, under additional restrictions, is hump‐shaped. Our results are illustrated by an example generating a Beta wage distribution.     

Wage Bargaining with On‐the‐Job Search: Theory and Evidence

Most applications of Nash bargaining over wages ignore between‐employer competition for labor services and attribute all of the workers' rent to their bargaining power. In this paper, we write and estimate an equilibrium model with strategic wage bargaining and on‐the‐job search and use it to take another look at the determinants of wages in France. There are three essential determinants of wages in our model: productivity, competition between employers resulting from on‐the‐job search, and the workers' bargaining power. We find that between‐firm competition matters a lot in the determination of wages, because it is quantitatively more important than wage bargaining à la Nash in raising wages above the workers' “reservation wages,” defined as out‐of‐work income. In particular, we detect no significant bargaining power for intermediate‐ and low‐skilled workers, and a modestly positive bargaining power for high‐skilled workers.     

Returns to Tenure or Seniority?

This study documents two empirical facts using matched employer–employee data for Denmark and Portugal. First, workers who are hired last, are the first to leave the firm. Second, workers' wages rise with seniority, where seniority is defined as a worker's tenure relative to the tenure of his colleagues. Controlling for tenure, the probability of a worker leaving the firm decreases with seniority. The increase in expected seniority with tenure explains a large part of the negative duration dependence of the separation hazard. Conditional on ten years of tenure, the wage differential between the 10th and the 90th percentiles of the seniority distribution is 1.1–1.4 percentage points in Denmark and 2.3–3.4 in Portugal.     

Wage Dispersion and Equilibrium Search Models: Some Evidence from Italy

This paper provides a structural estimation of an equilibrium search model with on‐the‐job search and heterogeneity in firms' productivities using a sample of Italian male workers. Results indicate that arrival rates of offers for workers are higher when unemployed than when employed and firms exploit their monopsony power when setting wages. As a result, workers earn far less than their marginal product. The model is then used to study regional labour market differentials in Italy. Wide variation in frictional transition parameters across areas helps to explain persistent unemployment and wage differentials.     

ON‐THE‐JOB SEARCH AND MORAL HAZARD

We analyze the interaction between intertemporal incentive contracts and search frictions associated with on‐the‐job search. In our model, agency problems call for wage contracts with deferred compensation. At the same time workers do on‐the‐job search. Deferred compensation improves workers' incentives to exert effort but distorts their on‐the‐job search decisions. We show that deferred compensation is less attractive when the value to the worker–firm pair of on‐the‐job search is high. Moreover, the interplay between search frictions and wage contracts creates feedback effects. If firms in equilibrium use contracts with deferred compensation, fewer firms with vacancies enter the on‐the‐job search market, and this in turn reduces the distortions created by deferred compensation. These feedback effects between the incentive contracts used and the activity level in the search markets can lead to multiple equilibria: a low‐turnover equilibrium where firms use deferred compensation, and a high‐turnover equilibrium where they do not. Furthermore, the model predicts that firms are more likely to use deferred compensation when search frictions are high and when the gains from on‐the‐job search are small.     

A Note on Job Tenure and Collective Contracts

Abstract. This paper analyses the relationship between individual tenure and the application of collective contracts at the firm level under the specific institutional settings in Germany. The empirical approach is based on a multilevel model and a linked employer–employee data set for the years 1990, 1995, and 2001. The main result is that elapsed tenure is longer in firms applying collective contracts than in companies with individual wage setting: workers in firms with collective contracts benefit not only from higher wages, but also from higher job stability. Furthermore, we find no significant changes in mean tenure during the 1990s as well as stable differences across wage‐setting regimes.     

Wage Cuts as Investment in Future Wage Growth

Abstract. Wage cuts are often presumed to reflect an adverse change in economic constraints. However, several theoretical models have shown they can be a form of investment in future wage growth. This paper provides empirical evidence of the latter by explicitly modeling the worker's job choice when the job offer consists of both a starting wage and expected future wage growth. We use our analytical model to estimate the distribution of job offers faced by workers who are searching across jobs differing in both initial wage and expected wage growth. For females, roughly one‐third of job changes that result in immediate wage cuts are transitions to jobs that have a higher value function than the existing job. For males, the corresponding value is one‐fifth.     

On the Dynamics of Unemployment and Wage Distributions

Postel‐Vinay and Robin's (2002) sequential auction model is extended to allow for aggregate productivity shocks. Workers exhibit permanent differences in ability while firms are identical. Negative aggregate productivity shocks induce job destruction by driving the surplus of matches with low ability workers to negative values. Endogenous job destruction coupled with worker heterogeneity thus provides a mechanism for amplifying productivity shocks that offers an original solution to the unemployment volatility puzzle (Shimer (2005)). Moreover, positive or negative shocks may lead employers and employees to renegotiate low wages up and high wages down when agents' individual surpluses become negative. The model delivers rich business cycle dynamics of wage distributions and explains why both low wages and high wages are more procyclical than wages in the middle of the distribution.     

EQUILIBRIUM INCENTIVE CONTRACTS AND EFFICIENCY WAGES

We analyze the optimal (efficiency) wage contract when output is contractible but firms neither observe the workers' effort nor their match‐specific productivity. Firms offer wage contracts that optimally trade off effort and wage costs. As a result, employed workers enjoy rents, which in turn creates unemployment. Nonetheless, the incentive power of the equilibrium wage contract is constrained efficient in the absence of taxes and unemployment benefits. We also show that more high‐powered incentive contracts tend to be associated with higher equilibrium unemployment rates. (JEL: E24, J30, J41)     

A Theory of the Firm with Non‐binding Employment Contracts

This paper examines an employment relation in which individual workers enjoy some bargaining power vis‐a‐vis the firm although they are not unionized. The main elements of the situations studied here are that the employment contracts are non‐binding across periods of production and that the firm has opportunities to replace workers. The paper analyzes a dynamic model in which the processes of contracting and recontracting between the firm and its workers are intertwined with the dynamic evolution of the firm's workforce. The analysis of the model is somewhat complicated because the employment level is a nondegenerate state variable that evolves over time and is affected by past decisions. The main analytical results characterize certain important equilibria: the profit maximizing and stationary equilibria. The unique stationary equilibrium is markedly inefficient: it exhibits inefficient over‐employment and the steady state wages coincide with the workers' reservation wage. It confirms earlier results derived by Stole and Zwiebel (1996a, b) in the context of a static model and shows that they are very robust even when the firm has nearly frictionless hiring opportunities. In contrast, in the profit maximizing equilibrium the outcome is nearly efficient and the wage exhibits a mark‐up over the reservation wage.     

Noncontractible Heterogeneity in Directed Search

This paper provides a directed search model designed to explain the residual part of wage variation left over after the impact of education and other observable worker characteristics have been removed. Workers have private information about their characteristics at the time they apply for jobs. Firms value these characteristics differently and can observe them once workers apply. They hire the worker they most prefer. However, the characteristics are not contractible, so firms cannot condition their wages on them. This paper shows how to extend arguments from directed search to handle this, allowing for arbitrary distributions of worker and firm types. The model is used to provide a functional relationship that ties together the wage distribution and the wage–duration function. This relationship provides a testable implication of the model. This relationship suggests a common property of wage distributions that guarantees that workers who leave unemployment at the highest wages also have the shortest unemployment duration. This is in strict contrast to the usual (and somewhat implausible) directed search story in which high wages are always accompanied by higher probability of unemployment.     

Contract Length as Risk Management When Labor is not Homogeneous

This paper examines the choice of contract length for workers who possess unique skills. Uncertainty, facing both the worker and the firm, creates an incentive to reallocate risk. The uncertainty arises from two sources: variation in the market value of the worker's human capital and fluctuation in the worker's physical production. Long‐term contracts are typically modeled as compensating wage differentials, or as a solution to the problem of asymmetric information. This paper develops a model proposing more complex behavior in the reallocation of risk between the contracting parties. The model shows that long‐term labor contracts are most likely to be observed when price uncertainty in the labor market exceeds the worker's productive uncertainty.     

Education,Mobility and Employers’ Monopsony Power: A Search‐theoretic Analysis

Abstract. We analyse the efficiency of schooling choices in a wage‐posting search equilibrium model with on‐the‐job search. The workers have multidimensional skills and the search market is segmented by technology. Education determines the scope — or adaptability— of individual skills. Individuals obtain schooling to leave unemployment more quickly and to climb the wage ladder rapidly through job‐to‐job mobility — that is, to speed up job shopping. Education reduces firms’ monopsony power in the wage determination by improving workers’ mobility. As a result, the wage distribution shifts rightward with aggregate schooling. However, the ratio of vacant jobs to job seekers also falls in each sector. Either one or the other externality may dominate, implying, respectively, under‐ or over‐education. A combination of minimum wage and schooling fee can decentralize the efficient allocation.     

Job Matching and the Wage Distribution

This paper brings together the microeconomic‐labor and the macroeconomic‐equilibrium views of matching in labor markets. We nest a job matching model à la Jovanovic (1984) into a Mortensen and Pissarides (1994)‐type equilibrium search environment. The resulting framework preserves the implications of job matching theory for worker turnover and wage dynamics, and it also allows for aggregation and general equilibrium analysis. We obtain two new equilibrium implications of job matching and search frictions for wage inequality. First, learning about match quality and worker turnover map Gaussian output noise into an ergodic wage distribution of empirically accurate shape: unimodal, skewed, with a Paretian right tail. Second, high idiosyncratic productivity risk hinders learning and sorting, and reduces wage inequality. The equilibrium solutions for the wage distribution and for the aggregate worker flows—quits to unemployment and to other jobs, displacements, hires—provide the likelihood function of the model in closed form.     

Does Industrial Composition Matter for Wages? A Test of Search and Bargaining Theory

Does switching the composition of jobs between low‐paying and high‐paying industries have important effects on wages in other sectors? In this paper, we build on search and bargaining theory to clarify a key general equilibrium channel through which changes in industrial composition could have substantial effects on wages in all sectors. In this class of models, wage determination takes the form of a social interaction problem and we illustrate how the implied sectoral linkages can be empirically explored using U.S. Census data. We find that sector‐level wages interact as implied by the model and that the predicted general equilibrium effects are present and substantial. We interpret our results as highlighting the relevance of search and bargaining theory for understanding the determination of wages, and we argue that the results provide support for the view that industrial composition is important for understanding wage outcomes.     

Endogenous Contracts in Unionized Oligopoly

We study the endogenous determination of contracts in a unionized oligopoly and the welfare implications thereof. Alternative contracts specify the sequencing in the selection of R&D and wages. They can be classified as ‘fixed’ when the unions set wages before the firms make their R&D decisions or ‘floating’ when the sequencing of these choices is reversed. If the unions are highly employment‐oriented, we find that either all firm–union pairs choose floating‐wage contracts or both contract types may coexist depending on the degree of technological spillovers. However, when the unions have stronger preference over attaining a good wage deal, then it becomes very likely that fixed‐wage contracts will endogenously emerge because they can serve as an insurance device against oppor tunistic wage increases. Our welfare analysis suggests that welfare‐improving contracts may nevertheless not always arise in equilibrium.     

The Unemployment Volatility Puzzle: Is Wage Stickiness the Answer?

I discuss the failure of the canonical search and matching model to match the cyclical volatility in the job finding rate. I show that job creation in the model is influenced by wages in new matches. I summarize microeconometric evidence and find that wages in new matches are volatile and consistent with the model's key predictions. Therefore, explanations of the unemployment volatility puzzle have to preserve the cyclical volatility of wages. I discuss a modification of the model, based on fixed matching costs, that can increase cyclical unemployment volatility and is consistent with wage flexibility in new matches.