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.     

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.     

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.     

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.     

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.     

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.     

SORTING AND THE OUTPUT LOSS DUE TO SEARCH FRICTIONS

We analyze a general search model with on‐the‐job search (OJS) and sorting of heterogeneous workers into heterogeneous jobs. For given values of nonmarket time, the relative efficiency of OJS, and the amount of search frictions, we derive a simple relationship between the unemployment rate, mismatch, and wage dispersion. We estimate the latter two from standard micro data. Our methodology accounts for measurement error, which is crucial to distinguish true from spurious mismatch and wage dispersion. We find that without frictions, output would be about 9.5% higher if firms can commit to pay wages as a function of match quality and 15.5% higher if they cannot. Noncommitment leads to a business‐stealing externality which causes a 5.5% drop in output.     

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.     

The Effect of Temporary Agency Workers on Wage of Permanent Employees: Evidence From Linked Employer‐Employee Data

The effect of flexibility at‐the‐margin on wage of permanent employees is evaluated using Italian Linked Employer‐Employee Data for the period 1991–2004. Temporary Agency Workers (TAW) introduced in Italy in 1997 in some specific industries represents a form of flexible job providing a quasi‐experimental setup that can be used to obtain identification by applying difference‐in‐differences. Concerns related to confounding trends are addressed through several robustness and falsification tests. Norms introducing TAW in all sectors in 2000 are also exploited. Results show an increase in permanent employees’ wage in industries involved in the reform. This evidence is consistent with insider‐outsider theories wherein — in a dual labor market — a rise in the share of unprotected employees may spill over upon insiders’ wage.     

The Impact of Worker and Establishment‐level Characteristics on Male–Female Wage Differentials: Evidence from Danish Matched Employee–Employer Data

Abstract. This paper uses matched employer–employee data from Denmark to examine how gender segregation at the level of occupation, industry, establishment, and job‐cell impacts the gender wage differential of full‐time, private‐sector salaried and manual workers. Wage effects of gender segregation at the above four levels are estimated through fixed effects or through controls for the proportion females within these structures. We find that occupation has a much larger role than industry or establishment in accounting for the gender gap for salaried but not manual workers, and that for both groups there is a significant within‐job‐cell gender wage differential.     

Why Do People from Southern Italy Seek Jobs in the Public Sector?

This paper analyses the choice open to a worker seeking a job in the public and private sectors of the labour market. The private sector is identified by a steeper wage profile and by lower job security than the public sector. The reservation wage for the two sectors is calculated in the first part of the paper. The results reveal that the reservation wage for the public sector is higher than that for the private sector. The effect of career prospects, job riskiness and labour demand on optimal time allocation between the search in the two sectors is then analysed. Finally, an empirical analysis is made in order to study Italian workers’ search strategies. It highlights relevant geographical differences which can be interpreted through the theoretical results obtained in the paper.     

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.     

The Employment–Hours Trade‐off: Theory and an Application to the Portuguese Case

Abstract. Using traditional production theory, it is possible to estimate production functions in which hours per worker and number of workers hired are treated as endogenous and chosen by the firm, priced respectively by the variable hourly wage and the so‐called quasi‐fixed unit cost. The available data suggested the use of Cobb–Douglas or CES specifications or the use of two‐stage separable technologies, with a second‐level Cobb–Douglas being possible. Quasi‐fixed costs were associated with legal social security payments, which were also conditioned by the data. The estimates for the Portuguese metal products and engineering industries — using cross‐section evidence for 1987 — showed that disaggregation of the labor input is empirically justifiable, and total man‐hours employed and the numbers of workers hired are complements in production. Hours per worker respond negatively to the variable hourly wage and positively to the quasi‐fixed unit cost. Nevertheless, in our framework, this would be so by construction. Total labor costs increase with both the hourly wage and the quasi‐fixed unit costs.     

Non‐linear Effects of Comparison Income in Quit Decisions: Status versus Signal!

This research note utilizes German matched employer–employee data to investigate the relationship between mobility and relative wage positions within establishments for workers without university degrees. The main innovation involves the examination of non‐linear effects, because previous literature mainly analyses mean linear effects. Our random‐effects probit estimates of mobility suggest a non‐linear U‐shaped effect with respect to relative standing. This is plausible because workers in low relative wage positions might quit because of their low status and those in high relative wage positions because of their low career advancement opportunities. Consideration of non‐linearities, thus, is a major improvement for the analysis of the effects of relative wage positions.     

THE POLITICAL ECONOMY OF FLEXICURITY

We document the presence of a trade‐off in the labor market between the protection of jobs and the support offered to unemployed people. Different countries’ locations along this trade‐off represent stable political‐economic equilibria. We develop a model in which individuals determine the mix of job protection and support for the unemployed in a political environment. Agents are heterogeneous along two dimensions: employment status (insiders and outsiders) and skills (low and high). Unlike previous work on the political economy of labor market institutions, we emphasize the role of job protection and unemployment benefits in the wage‐setting process. A key implication of the model is that flexicurity configurations with low levels of job protection and high levels of support to the unemployed should emerge in the presence of a highly educated workforce. Panel regressions of countries’ locations along this institutional trade‐off are consistent with the implications of our model.     

An Equilibrium Model of Health Insurance Provision and Wage Determination

We investigate the effect of employer‐provided health insurance on job mobility rates and economic welfare using a search, matching, and bargaining framework. In our model, health insurance coverage decisions are made in a cooperative manner that recognizes the productivity effects of health insurance as well as its nonpecuniary value to the employee. The resulting equilibrium is one in which not all employment matches are covered by health insurance, wages at jobs providing health insurance are larger (in a stochastic sense) than those at jobs without health insurance, and workers at jobs with health insurance are less likely to leave those jobs, even after conditioning on the wage rate. We estimate the model using the 1996 panel of the Survey of Income and Program Participation, and find that the employer‐provided health insurance system does not lead to any serious inefficiencies in mobility decisions.     

Urban Versus Rural Return to Human Capital in Portugal: A Cookbook Recipe for Applying Assignment Models

Abstract. The Portuguese economy has been characterized by modernization since the post‐war period, and Lisbon is a centre of this process. This paper analyses rates of return on human capital in Lisbon versus the rest of the country in the period 1982–92. An assignment model of heterogeneous workers to heterogeneous jobs is applied. We introduce the concept of the complexity dispersion parameter, which measures job heterogeneity and the ease of substitution between worker types. It is free dimension and can be compared across countries. We also develop a cookbook recipe for the estimation of this parameter. The main implication of the model — a high return to human capital is associated with similar workers being assigned to more complex jobs — is confirmed by the data. The complexity dispersion parameter suggests that paying half of the optimal wage level at least doubles the cost per efficiency unit of labour.     

The Impact on Inequality of Raising the Minimum Wage: Gap‐narrowing and Reranking Effects

Raising the minimum wage may reduce inequality by increasing the wages of low‐skill workers, but it may also increase inequality due to negative impacts on employment that produce wage losses. Using previous estimates of the elasticities of wages and employment to changes in the minimum wage in Colombia and Brazil, we show that the net impact on inequality of increasing the minimum wage may depend on the distributional weights used for inequality measurement. The results are obtained by decomposing the Gini index into reranking and gap‐narrowing effects. Inequality‐increasing reranking effects, which are associated with job losses, may dominate inequality‐decreasing gap‐narrowing effects, which are associated with wage gains, when high weights are placed on workers with low earnings. For standard distributional weights, however, the likely net impact is a reduction in wage inequality.     

Employer Changes and Wage Changes: Estimation with Measurement Error in a Binary Variable

Self‐reported tenure is often used to determine job changes. We show there are substantial inconsistencies in these responses; consequently, we risk misclassifying job changes as stays and vice versa. An estimator from Hausman et al. is applied to a job change model for Ireland, and we find that ignoring misclassification may substantially underestimate the true number of changes and lead to diminished covariate effects. The main contribution of the paper is to control for misclassification when estimating the wage effects of job mobility. A two‐step approach is adopted. We find ignoring misclassification leads to a significant downwards bias in the wage impact, and we provide an estimate that corrects for measurement error.