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Article Excerpt
I. INTRODUCTION
How to design incentive schemes to motivate workers is an important topic in economics. The shirking models of efficiency wages, such as Shapiro and Stiglitz (1984), establish that firms need to pay a wage premium (efficiency wages) to motivate workers, with unemployment serving as a punishment device. However, one shortcoming of these models is that performance pay plays no role. One justification for their omission of performance pay is that individual performance may not be verifiable. Nevertheless, if workers' performance is observable and employment relationships are repeated, firms can use implicit bonuses or relational contracts based on workers' subjectively assessed performance to motivate workers. Since subjective performance pay cannot be legally enforced, it has to be self-enforcing.
Given that both efficiency wages and subjective performance pay motivate workers, what is the optimal wage contract from the firm's perspective? Will different labor markets (occupations) use different forms of wage contracts? What are the impacts of different forms of wage contracts on unemployment and social welfare? To answer these questions, this paper provides a theory of contract selection in a market setting.
In a seminal paper, MacLeod and Malcomson (1998, MM hereafter) provided a model of contract selection between efficiency wages and subjective performance pay. The driving force in their model is the market condition. In a market with more workers than jobs, a firm can always immediately and costlessly fill its vacancy after reneging on the promised bonus. Therefore, no subjective performance pay is credible, and firms have to use solely efficiency wages to motivate workers. On the other hand, in a market with more jobs than workers, efficiency wages are useless in providing incentives because a worker can find another job immediately after being fired. As a result, firms use solely subjective performance pay to motivate workers.
In MM, there are no exogenous turnover costs. Complementary to MM, this paper provides a model of contract selection driven by exogenous turnover costs in labor markets. We focus on the situation in which unemployment always exists in labor markets, thus ruling out market condition as a determinant of contract selection. It turns out that turnover costs affect the amount of efficiency wages and performance pay in optimal contracts. While in MM efficiency wages and subjective performance pay cannot be used together to motivate workers, in our model firms are able to use combinations of both methods of payments. By affecting optimal contracts, turnover costs also have impacts on the equilibrium employment level and social welfare. Finally, our model generates rich empirical implications about the relationships among turnover costs, forms of employment contracts, and levels of employment.
Our basic model studies how turnover costs borne by firms affect contract selection. From the firm's point of view, subjective performance pay is "cheaper" since efficiency wages entail a wage premium. Thus, the optimal wage contract uses the maximum amount of bonus to motivate workers. However, subjective performance pay may not be credible due to the firm's moral hazard problem: in labor markets with positive unemployment, a firm can immediately hire a new worker after reneging on the implicit bonus. The presence of turnover costs can alleviate this moral hazard problem. This is because a worker can punish a reneging firm by quitting and the firm has to incur turnover costs in hiring new workers. Therefore, in the optimal contract, the amount of bonus is increasing in turnover costs. Since subjective performance pay is cheaper, as the turnover costs increase, more subjective performance pay leads to a lower total wage payment.
After deriving the optimal contracts, we turn to study market equilibrium, which is determined by firms' free entry condition. In market equilibrium, the revenue product of labor equals the average labor cost (ALC), which consists of the wage payment each period and the average turnover costs incurred per period on the equilibrium path. Interestingly, up to some threshold (when the wage premium is positive), an increase in turnover costs reduces the ALC and leads to an increase in the equilibrium employment level. Moreover, when the revenue product of labor is elastic enough, an increase in turnover costs leads to higher social welfare. This is a surprising result: a little bit of(exogenous) friction in markets is beneficial for social welfare. The main reason behind this result is that friction in markets alleviates the firms' moral hazard problem and gives them commitment power, which in turn grants firms more flexibility to alleviate the workers' moral hazard problem. A general interpretation of this result is that exogenous friction might be more efficient than endogenously created friction (efficiency wages) in overcoming double moral hazard problems in markets.
In an extended model, we incorporate workers' search costs. Now, wage contracts should not only motivate workers to exert effort (IC condition) but also induce unemployed workers to search (IR condition). It turns out that inducing workers to search becomes more difficult as the unemployment rate increases. The main result in the extended model is that wages are increasing in the employment level only when employment is high and are completely rigid when employment is low. This implies that wage-unemployment relationship changes over the course of business cycles: wages are procyclical in booms and rigid during recessions.
Our model generates rich empirical implications. First, different labor markets (occupations) will adopt different forms of wage contracts. In particular, the efficiency wage component (wage premium) is negatively related to and the amount of bonuses is positively related to the turnover costs borne by firms in labor markets. Second, workers paid by bonuses on average earn less than workers paid fixed wages (efficiency wages). Third, occupations paid bonuses should have lower unemployment rates than occupations in which bonuses are seldom used. Fourth, wages are procyclical during booms and are either rigid or countercyclical in recessions. Finally, the wage-unemployment elasticity is decreasing in turnover costs in labor markets. All these predictions are consistent with some empirical evidence. (1)
Relational contracts have been studied by Bull (1987), MM (1989, 1998), Baker, Gibbons, and Murphy (1994), and Levin (2003). However, except for MM (1989, 1998), all the other papers study the one-firm-one-worker setting; hence, both the firm's and the worker's outside options are exogenously given. Moreover, these papers do not study contract selection between efficiency wages and subjective performance pay. MM (1989) offered a complete characterization of the set of relational contracts that can be implemented in a market setting, but it does not study the problem of contract selection.
Akerlof and Katz (1989) incorporated a performance bond into a shirking model of efficiency wages. They, however, assumed that firms are able to commit: firms never forfeit a worker's bond if he does not shirk. In contrast to their assumption, our model, following the literature of relational contracts, assumes that firms are not able to commit. The labor turnover models of efficiency wages, such as Salop (1979) and Stiglitz (1974), treat the turnover rate as endogenous. They derive the result that firms with higher turnover costs may pay higher wages in order to reduce total turnover costs. This result is in direct contrast to the prediction of our model.
The structure of the paper is as follows. Section II sets up the basic model. Section III studies the optimal wage contracts. In Section IV, first the stationary market equilibrium is derived and then comparative statics and welfare analysis are conducted. In Section V, we extend the basic model to incorporate search costs. Section VI presents some empirical evidence. Section VII concludes the paper.
II. THE BASIC MODEL
Consider a labor market over time, with time t being discrete. There are L workers and many firms which create J job vacancies in total. While L is exogenously given, there is free entry on the firms' side, thus J is endogenous. Both workers and firms are risk neutral and share the same discount factor [delta]. Each job has the same revenue product of labor p. Each firm takes p as given, but in the aggregate, p is a decreasing function of the total employment E. At the beginning of each period, unemployed workers and unfilled vacancies are randomly matched. Note that agents on the long side of the market may not get a match. At the end of each period, each existing match breaks up with probability 1--[rho] for exogenous reasons. In any existing match that survives this shock, the worker and the firm simultaneously decide whether to continue the relationship next period. If either party decides to leave, then the match is broken up endogenously. All the agents without a match enter into the unmatched pool at the beginning of the next period.
If employed, a worker gets utility [W.sub.t] - [ve.sub.t], where [W.sub.t] is the total wage payment, v > is the disutility of work, and [e.sub.t] is effort in period t. For simplicity, we assume that a worker can either work ([e.sub.t] = 1) or shirk ([e.sub.t] = 0). The profit of a filled job vacancy in period t is [pe.sub.t] - [W.sub.t]. Workers without a job receive an unemployment benefit u > per period, which is exogenously given. Consistent with employment at will, we assume that only spot contracts are legally enforceable. Following the incomplete contract literature, we assume that et is observable but not verifiable. (2) Therefore, spot contracts that are contingent on [e.sub.t] cannot be enforced by the court.
Nevertheless, since employment relationships have the potential to be long term, firms may use implicit bonuses. In particular, [W.sub.t] consists of a fixed wage [w.sub.t] [greater than or equal to] that the firm pays regardless of [e.sub.t] and a bonus [b.sub.t] [greater than or equal to] that the firm agrees to pay only if [e.sub.t] = 1. While [w.sub.t] is legally enforceable, [b.sub.t] cannot be enforced by the court; hence, it has to be self-enforcing.
Note that if an employed worker shirks, then his employer's period profit is negative. Thus, firms have to motivate workers to exert effort. To make sure there is positive employment, we assume that p(0) > u + v/([delta][rho]). In addition, we assume that p(L) [less than or equal to] u + v/([delta][rho]). This assumption ensures that J [less than or equal to] L; that is, there is always unemployment and workers are always on the long side of the market.
There are turnover costs in the labor market. Firms incur recruiting costs in finding job candidates. (3) Workers incur search costs in finding jobs. Moreover,...
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