Unobserved Individual and Firm Heterogeneity in Wage and Job‐Duration Functions: Evidence from German Linked Employer–Employee Data

Abstract. We analyse the correlations between individual and firm fixed effects, and wage and job‐duration functions. Our results for large firms suggest that low‐wage firms tend to be stable firms, suggesting that lower wages can buy job stability. Furthermore, high‐wage workers sort into the stable low‐wage firms. Our interpretation is that high‐wage workers have a higher wage to insure against job loss and can afford more easily to forgo wages in favour of job stability. This may provide an explanation of the puzzle identified in previous literature that high‐wage workers are matched to low‐wage firms.     

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.     

Monitoring Job Offer Decisions,Punishments, Exit to Work,and Job Quality

Unemployment insurance systems include the monitoring of unemployed workers and punitive sanctions if job search requirements are violated. We analyze the causal effect of sanctions on the ensuing job quality, notably on wages and occupational level. We use Swedish data and estimate duration models dealing with selection on unobservables. We also develop a theoretical job search model that monitors job offer rejection versus job search effort. The empirical results show that, after a sanction, the wage rate is lower and individuals move more often to a part‐time job and a lower occupational level, incurring human capital losses.     

LABOR MARKET EQUILIBRIUM WITH REHIRING

Consistent with the empirical evidence, this article analyzes a labor market in which separations are not permanent and reactivated firms prefer to rehire former employees instead of seek new ones. Workers engage in job search due to the uncertain prospects of rehiring. If firms can commit to wages contingent on rehiring, they backload wages to provide incentives for workers to reduce their unobservable search effort. Under risk aversion and incomplete markets, if productivity at reactivation is sufficiently high, the tension between wage backloading and consumption smoothing leads to excessive search in equilibrium.     

DYNAMIC CONTRACTS WITH WORKER MOBILITY VIA DIRECTED ON‐THE‐JOB SEARCH

This article proposes a model with dynamic incentive contracts and on‐the‐job search in a frictional labor market. The optimal long‐term contract exhibits an increasing wage–tenure profile. With increasing wages, worker effort also increases with tenure. These two features imply that the probabilities of both voluntary and involuntary job separation decrease with both job tenure and the duration of employment. Given these results, workers experience differing labor market transitions—between employment, unemployment, and across different employers—and the equilibrium generates endogenous heterogeneity among ex ante homogeneous workers.     

Worker flows, job flows and firm wage policies

Like many transition economies, Slovenia is undergoing profound changes in the workings of the labour market with potentially greater flexibility in terms of both wage and employment adjustment. To investigate the impact of these changes, we use unique longitudinal matched employer‐employee data that permits measurement of employment transitions and wages for workers and enables links of the workers to the firms in which they are employed. We can thus measure worker flows and job flows in a comprehensive and integrated manner. We find a high pace of job flows in Slovenia especially for young, small, private and foreign‐owned firms and for young, less educated workers. While job flows have approached the rates observed in developed market economies, the excess of worker flows above job flows is lower than that observed in market economies. A key factor in the patterns of the worker and job flows is the determination of wages in Slovenia. A base wage schedule provides strict guidelines for minimum wages for different skill categories. However, firms are permitted to offer higher wages to an individual based upon the success of the worker and/or the firm. Our analysis shows that firms deviate from the base wage schedule significantly and that the idiosyncratic wage policies of firms are closely related to the observed pattern of worker and job flows at the firm. Firms with more flexible wages (measured as less compression of wages within the firm) have less employment instability and are also able to improve the match quality of their workers. JEL Classifications: J23, J31, J41, J61, P23, P31.     

AN EQUILIBRIUM SEARCH MODEL WHEN FIRMS OBSERVE WORKERS' EMPLOYMENT STATUS*

This article considers an equilibrium search model, where firms post wages using information on workers' employment status. Earnings differentials between workers of different employment statuses are driven by firms' ability to discriminate workers' reservation wages. I study how these wage policies depend on firms' and workers' characteristics, and how these policies affect the wage distribution. The model delivers new predictions for the amount of wage dispersion that can be generated with search models and provides a better representation of the left tail of the wage distribution in the presence of a legal minimum wage than standard equilibrium search models.     

Egalitarian Wage Policies and Long-Term Unemployment

How does a centrally imposed egalitarian wage policy affect unemployment, when workers differ with respect to productivity? The effect on total unemployment is found to be ambiguous. Egalitarian wages encourage job creation because increased profits derived from the most productive workers more than outweigh reduced profits derived from the least productive workers. Short-term unemployment is reduced. On the other hand, firms respond by raising their reservation productivity. Some workers are left almost completely unemployable. Long-term unemployment rises. Less inequality in the wage distribution is obtained at the expense of more inequality in the distribution of unemployment.     

Wage and Technology Dispersion

This paper explains why firms with identical opportunities may use different technologies and offer different wages. Our key assumption is that workers must engage in costly search in order to gather information about jobs (Stigler (1961)). In equilibrium, some firms adopt high fixed cost, high productivity technologies, offer high wages, and fill job openings quickly. Other firms adopt less capital-intensive technologies and offer low wages, hiring mostly uninformed workers. In equilibrium, the amount of wage dispersion leaves workers indifferent about whether to gather information, and the fraction of informed workers leaves firms indifferent about their wage and technology choice. We show that worker search, which would appear to be a rent-seeking activity in partial equilibrium, may be efficiency-enhancing in general equilibrium.     

Wage posting without full commitment

Wage posting models of job search typically assume that firms can commit to paying workers exactly the posted wage. We relax this assumption and impose “downward” commitment; firms can commit only to paying at least their advertised wage. As each firm can only commit to pay at least their advertised wage, workers may demand that the firm pay more than the advertised wage. In labor markets with a finite number of workers and firms, the strategic interaction between firms makes it costly for firms to provide applicants the incentive not to demand wages in excess of the advertised wage. In equilibrium, firms may settle for running job auctions at the cost of losing control of the number of applicants that they can attract. When this strategic interaction between firms vanishes, workers never choose to demand more than the advertised wage.     

STRUCTURAL EMPIRICAL EVALUATION OF JOB SEARCH MONITORING

To evaluate search effort monitoring of unemployed workers, it is important to take account of post‐unemployment wages and job‐to‐job mobility. We structurally estimate a model with search channels, using a controlled trial in which monitoring is randomized. The data include registers and survey data on search behavior. We find that the opportunity to move to better‐paid jobs in employment reduces the extent to which monitoring induces substitution toward formal search channels in unemployment. Job mobility compensates for adverse long‐run effects of monitoring on wages. We examine counterfactual policies against moral hazard, like reemployment bonuses and changes of the benefits path.     

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.     

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.     

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.     

A MATCHING MODEL WITH ENDOGENOUS SKILL REQUIREMENTS>*

We consider a labor market in which workers differ in their abilities and jobs differ in their skill requirements. The distribution of worker abilities is exogenous, but we model the choice of skill requirements by firms. High‐skill jobs produce more output than low‐skill jobs, but high‐skill jobs require high‐skill workers and thus are more difficult to fill. We use a matching model together with a Nash bargaining approach to wage setting to determine the equilibrium mix of job types, along with the equilibrium relationship between worker and job characteristics, wages, and unemployment.     

The Distribution of Earnings in an Equilibrium Search Model with State‐Dependent Offers and Counteroffers*

We construct an equilibrium job search model with on‐the‐job search in which firms implement optimal‐wage strategies under full information in the sense that they leave no rent to their employees and counter the offers received by their employees from competing firms. Productivity dispersion across firms results in wage mobility both within and across firms. Workers may accept wage cuts to move to firms offering higher future wage prospects. Equilibrium productivity dispersion across ex ante homogeneous firms can be endogenously generated. Productivity dispersion then generates a nontrivial wage distribution which is generically thin‐tailed, as typically observed in the data.     

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.     

Unobserved Heterogeneity,Job Training and the Employer Size–Wage Effect in Australia

This study attempts to clarify the nature of the employer size–wage effect in Australia by determining the extent to which it can be explained by observed and unobserved quality differences of workers. Our empirical results show that, for men, quality‐adjusted employer size–wage effects are quite small and are mostly driven by lower wages for workers in the smallest firms (fewer than 20 workers). For women, size–wage effects disappear when unobserved quality differences are accounted for. We also find that accounting for differences in the incidence of job training has no effect on the structure of wage differences by employer size.     

Directed search with heterogeneous firms: an experimental study

Directed search models labor markets where workers observe wages before deciding where they will apply. This paper tests this model for the case of heterogeneous firms in a laboratory experiment. The theory predicts that more productive firms offer higher wages and workers apply more often to these higher wages. In consequence, more productive firms are more likely to match and the market is more efficient than the prediction of an alternative model where search is random. The main results of the experiment are that average firms offer wages that are close to or a little lower than the theoretical predictions but highly variable and workers apply more often to high offers but not to the extent predicted. The markets are no more efficient than random search predicts, because of the variation in wage offers.     

Participation,Recruitment Selection,and the Minimum Wage

In this paper, we re‐examine the efficiency of participation with heterogeneous workers in a search‐matching model with bargained wages and free entry. Assuming that firms hire their best applicants, we show that participation is always too low. The reason for this is a hold‐up phenomenon: to be active, a worker must pay the entire search cost whereas part of the gain from this investment goes to the firm. As a consequence, introducing a (small) minimum wage raises participation, job creation, and employment. Therefore, net aggregate income of the economy is increased.