Directed Search for Equilibrium Wage–Tenure Contracts

I construct a theoretical framework in which firms offer wage–tenure contracts to direct the search by risk‐averse workers. All workers can search, on or off the job. I characterize an equilibrium and prove its existence. The equilibrium generates a nondegenerate, continuous distribution of employed workers over the values of contracts, despite that all matches are identical and workers observe all offers. A striking property is that the equilibrium is block recursive; that is, individuals' optimal decisions and optimal contracts are independent of the distribution of workers. This property makes the equilibrium analysis tractable. Consistent with stylized facts, the equilibrium predicts that (i) wages increase with tenure, (ii) job‐to‐job transitions decrease with tenure and wages, and (iii) wage mobility is limited in the sense that the lower the worker's wage, the lower the future wage a worker will move to in the next job transition. Moreover, block recursivity implies that changes in the unemployment benefit and the minimum wage have no effect on an employed worker's job‐to‐job transitions and contracts.     

Equilibrium Wage Dispersion with Worker and Employer Heterogeneity

We construct and estimate an equilibrium search model with on–the–job–search. Firms make take–it–or–leave–it wage offers to workers conditional on their characteristics and they can respond to the outside job offers received by their employees. Unobserved worker productive heterogeneity is introduced in the form of cross–worker differences in a “competence” parameter. On the other side of the market, firms also are heterogeneous with respect to their marginal productivity of labor. The model delivers a theory of steady–state wage dispersion driven by heterogenous worker abilities and firm productivities, as well as by matching frictions. The structural model is estimated using matched employer and employee French panel data. The exogenous distributions of worker and firm heterogeneity components are nonparametrically estimated. We use this structural estimation to provide a decomposition of cross–employee wage variance. We find that the share of the cross–sectional wage variance that is explained by person effects varies across skill groups. Specifically, this share lies close to 40% for high–skilled white collars, and quickly decreases to 0% as the observed skill level decreases. The contribution of market imperfections to wage dispersion is typically around 50%.     

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.     

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.     

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.     

DOWNSIZING AND JOB INSECURITY

This article offers an explanation of why firms' downsizing patterns may vary substantially in magnitude and timing, taking the form of one‐time massive cuts, waves of layoffs, or zero layoff policies. The key element of this theory is that workers' expectations about their job security affect their on‐the‐job performance. In a situation where firms face adverse shocks, the productivity effect of job insecurity forces firms to balance laying off redundant workers and maintaining survivors' commitment. The cost of ensuring commitment differs between firms with different characteristics and determines whether workers are laid off all at once or in stages. However, if firms have private information about their future profits, they may not lay off any workers in order to signal a bright future, boosting worker's confidence. (JEL: J21, J23, D21, D82)     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

PRICE DISPERSION WITH DIRECTED SEARCH

We present a model that generates empirically plausible price distributions in directed search equilibrium. There are many identical buyers and many identical capacity‐constrained sellers who post prices. These prices can be renegotiated to some degree and the outcome depends on the number of buyers who want to purchase the good. In equilibrium all sellers post the same price, demand is randomly distributed, and there is sale price dispersion. Prices and distributions depend on market tightness and on the properties of renegotiation outcomes. In a labor market context, the model generates a strong empirical prediction. If workers can renegotiate the posted wage, then the model predicts a positively skewed and realistic‐looking density function of realized wages when the mean number of job‐seekers per vacancy is large. (JEL: C780, D390, D490, E390)     

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)     

The Gender Wage Gap in the Turkish Labor Market

Abstract. This paper examines the sources of the gender wage gap in the Turkish labor market by using matched employer–employee data and the standard wage regression estimations as well as the Oaxaca decomposition method. The extensive number of variables in the data set enables a thorough quantitative analysis of the role of various individual‐ as well as firm‐related factors leading to wage differentials between men and women, namely human capital endowments including job tenure, occupational and industrial segregation, private/public sector location, coverage of the workplace under collective labor bargaining, and firm size. It also examines the extent of gender‐based industry and occupational segregation within the confines of data set and computes the Duncan & Duncan segregation index. We find that a large portion of the gender wage gap is attributable to women's considerably lower levels of work experience and job tenure. Other important variables that lead to pay differentials are women's lower concentration in jobs covered by collective labor bargaining and a substantial degree of occupational and industrial segregation. The differential rates of return to many of the wage determinant variables are also found to be significant in the formation of the gender wage gap.     

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.     

Job Tenure,Labour Mobility and Wage Profiles

Abstract. The features and the length of the attachment of workers to firms represent a central aspect of the labour relationship. The length of service is an important determinant of wages and of non-pecuniary benefits; it affects internal mobility in the firm, and insulates workers with long job tenure from unemployment. In this paper it is argued that the traditional “spot” labour market Characterization is difficult to reconcile with the existence of long term employment relationships. A number of alternative theories which predict the existence of an employer-worker attachment proposed, and their implications discussed. The relevance of long term employment relationships is then tested using micro-data for the Italian manufacturing industry. An appropriate methodology for the analysis of the duration of employment is developed. and separate “job tenure” equations for white and blue collar workers are estimated. A higher educational attainment - ceteris paribus- appears to increase the probability of a job separation; conversely, a higher working experience, previous to the current job, tends to reduce it. The effect of firm size is negative, as larger organizations seem to favour longer employment spells. Outside opportunities show a strong positive effect on the probability of separation. Finally, conditional on the current wage, the probability of leaving the job increases with the length of time worked. However, when the unconditional outcome is considered, separation decline with tenure; in this case. it is argued, the wage effect more than outweighs the conditional effect. This result is consistent with the predictions of both “specific” human capital and job matching theories.     

Unemployment and Business Cycles

We develop and estimate a general equilibrium search and matching model that accounts for key business cycle properties of macroeconomic aggregates, including labor market variables. In sharp contrast to leading New Keynesian models, we do not impose wage inertia. Instead we derive wage inertia from our specification of how firms and workers negotiate wages. Our model outperforms a variant of the standard New Keynesian Calvo sticky wage model. According to our estimated model, there is a critical interaction between the degree of price stickiness, monetary policy, and the duration of an increase in unemployment benefits.