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.     

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.     

The Role of Profit Sharing in Dual Labour Markets with Flexible Outsourcing

We combine profit sharing for high‐skilled workers and outsourcing of low‐skilled tasks in a partly imperfect dual domestic labour market, which means that only low‐skilled labour is represented by a labour union. In that framework we analyse how the implementation of profit sharing for high‐skilled workers influences the amount of outsourcing and the labour market outcome for low‐skilled worker. By doing this, we use some specific assumptions, e.g. exponentially increasing outsourcing costs or the wage for low‐skilled workers will be determined by a union whereas the wage for high‐skilled workers is given. Assuming that low‐skilled labour and outsourcing are interchangeable we show that profit sharing has a positive effect on the wage for low‐skilled workers and helps to decrease wage dispersion. However, under these circumstances, profit sharing enhances outsourcing. Concerning the employment effects for high‐ and low‐skilled workers, we show that there is an employment reducing effect due to higher wages for low‐skilled work, which can be offset by higher productivity of highly skilled workers, as the domestic labour inputs complement each other.     

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.     

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.     

Segmentation Opportunities for a Social Planner: Impact of Limited Resources

In this research note, we investigate segmentation opportunities for social planners such as government agencies, nonprofits, and public organizations. These opportunities arise when the potential products are vertically (quality) differentiated and the consumers are heterogeneous in their preferences toward quality. In these cases, whether to offer quality differentiated products and what quality level to choose are important decisions for a social planner. In this research note, we identify the conditions where it is socially optimal to offer either one homogenous or two quality differentiated products. We find that the resource limitations may result in a single product offering and that the quality of the product depends on the maximum surplus per unit resource consumed by the products. We also compare our findings to a profit‐maximizing firm. We find that the resource limitations may cause a profit‐maximizing firm to provide a better service to some consumers than the social planner. Contrary to common wisdom, we also show that the capacity limitations may force the social planner to act like a profit‐maximizing firm in terms of its pricing and product mix choice.     

Profit Sharing and the Firm‐Size Wage Premium

This study analyzes the relationships among wages, firm size, and profit sharing schemes. We develop a simple theoretical model and explore the relationship empirically using high‐quality panel data. The theoretical model shows that the firm‐size wage premium decreases in the presence of profit sharing. The empirical results based on rich matched employee‐employer data for private sector wage earners in Finland show that the firm‐size wage premium is modest, and it becomes negligible when we account for profit sharing and covariates describing assortative matching and monopsony behavior. The analysis suggests that profit sharing schemes embody effects of firm‐specific unobservables that raise productivity, support rent sharing, and boost wages.     

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.     

Quality Provision with Heterogeneous Consumer Reservation Utilities

This study examines a firm's quality and price decisions when consumers differ not only in their willingness‐to‐pay for quality but also in their reservation utility for the basic product. We find that while the firm offers lower‐quality products when consumers' valuations for quality deteriorate, the optimal quality may increase with a negative shift in consumers' reservation utilities. We also investigate the optimal price and quality of the products within a vertically differentiated product line when the number of products is exogenously given. The existing literature shows that when consumers differ only in their willingness‐to‐pay for quality, the firm sets the efficient quality for consumers with the highest valuation for quality, whereas the concern for cannibalization pushes down the quality of inferior products. We find that when consumers are heterogeneous in both their reservation utility and valuation for quality, the concern for cannibalization may distort the quality upwards, even for consumers with the highest willingness‐to‐pay for quality. In addition, a low‐quality product may enjoy a higher profit margin than a high‐quality product within the product line.     

JOB MARKET SIGNALING OF RELATIVE POSITION,OR BECKER MARRIED TO SPENCE

This paper considers a matching model of the labor market where workers, who have private information on their quality, signal to firms that also differ in quality. Signals allow assortative matching in which the highest‐quality workers send the highest signals and are hired by the best firms. Matching is considered both when wages are rigid (nontransferable utility) and when they are fully flexible (transferable utility). In both cases, equilibrium strategies and payoffs depend on the distributions of worker and firm types. This is in contrast to separating equilibria of the standard model, which do not respond to changes in supply or demand. With sticky wages, despite incomplete information, equilibrium investment in education by low‐ability workers can be inefficiently low, and this distortion can become worse in a more competitive environment. In contrast, with flexible wages, greater competition improves efficiency.     

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.     

Overeducated Workers as an Insurance Device

Empirical findings show that firms frequently employ overeducated workers. Since overeducated workers earn more than adequately educated ones working in similar jobs these findings seem to be puzzling. In this paper, we introduce an insurance approach to explain the employment of overeducated workers. Referring to this approach, overeducated workers are employed by a firm to avoid high losses in the case of a crisis (e.g. when the production process breaks down). Contrary to adequately educated workers, overeducated ones may be helpful in this situation by quickly offering improvisatorial solutions. First, we use a simple model to demonstrate the insurance argument. Second, we test the major implication of the model empirically by using industry panel data: if and only if high‐skilled workers are employed for insurance purposes, the average wage of high‐skilled workers in firms that need insurance will be lower compared with firms that do not need insurance. The data confirm this theoretical result.     

Intersectoral Labor Mobility and the Growth of the Service Sector

One of the most striking changes in the U.S. economy over the past 50 years has been the growth in the service sector. Between 1950 and 2000, service‐sector employment grew from 57 to 75 percent of total employment. However, over this time, the real hourly wage in the service sector grew only slightly faster than in the goods sector. In this paper, we assess whether or not the essential constancy of the relative wage implies that individuals face small costs of switching sectors, and we quantify the relative importance of labor supply and demand factors in the growth of the service sector. We specify and estimate a two‐sector labor market equilibrium model that allows us to address these empirical issues in a unified framework. Our estimates imply that there are large mobility costs: output in both sectors would have been double their current levels if these mobility costs had been zero. In addition, we find that demand‐side factors, that is, technological change and movements in product and capital prices, were responsible for the growth of the service sector.     

Combined Pricing and Portfolio Option Procurement

In this paper, we study a single‐product periodic‐review inventory system that faces random and price‐dependent demand. The firm can purchase the product either from option contracts or from the spot market. Different option contracts are offered by a set of suppliers with a two‐part fee structure: a unit reservation cost and a unit exercising cost. The spot market price is random and its realization may affect the subsequent option contract prices. The firm decides the reservation quantity from each supplier and the product selling price at the beginning of each period and the number of options to exercise (inventory replenishment) at the end of the period to maximize the total expected profit over its planning horizon. We show that the optimal inventory replenishment policy is order‐up‐to type with a sequence of decreasing thresholds. We also investigate the optimal option‐reservation policy and the optimal pricing strategy. The optimal reservation quantities and selling price are shown to be both decreasing in the starting inventory level when demand function is additive. Building upon the analytical results, we conduct a numerical study to unveil additional managerial insights. Among other things, we quantify the values of the option contracts and dynamic pricing to the firm and show that they are more significant when the market demand becomes more volatile.     

Quality‐Speed Competition in Customer‐Intensive Services with Boundedly Rational Customers

We consider a system in which two competing servers provide customer‐intensive services and the service reward is affected by the length of service time. The customers are boundedly rational and choose their service providers according to a logit model. We demonstrate that the service provider revenue function is unimodal in the service rate, its decision variable, and show that the service rate competition has a unique and stable equilibrium. We then study the price decision under three scenarios with the price determined by a revenue‐maximizing firm, a welfare‐maximizing social planner, or two servers in competition. We find that the socially optimal price, subject to the requirement that the customer actual utility must be non‐negative, is always lower than the competition equilibrium price which, in turn, is lower than the revenue‐maximizing monopoly price. However, if the customer actual utility is allowed to be negative in social optimization, the socially optimal price can be higher than the other two prices in a large market.     

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.     

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.     

Strategic Experimentation with Exponential Bandits

We analyze a game of strategic experimentation with two‐armed bandits whose risky arm might yield payoffs after exponentially distributed random times. Free‐riding causes an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with beliefs as the state variable. We construct the unique symmetric Markovian equilibrium of the game, followed by various asymmetric ones. There is no equilibrium where all players use simple cut‐off strategies. Equilibria where players switch finitely often between experimenting and free‐riding all yield a similar pattern of information acquisition, greater efficiency being achieved when the players share the burden of experimentation more equitably. When players switch roles infinitely often, they can acquire an approximately efficient amount of information, but still at an inefficient rate. In terms of aggregate payoffs, all these asymmetric equilibria dominate the symmetric one wherever the latter prescribes simultaneous use of both arms.     

The Male–Female Wage Gap and the Firm Effect: The Case of Young Italian Workers

Abstract. The idea that wages are determined by firm and individual characteristics suggests that there is a firm effect that influences wage differentials. This paper presents the results of an empirical analysis of gender wage differentials — based on INPS data for people between the ages of 20 and 25 employed in the private sector in 1996 — which takes into account the characteristics of workers and firms using a two‐level random‐effects model. Firm variables proved to be significant, and the proportion of females in the firm showed a negative effect on the wages of both men and women.