Status and incentives.

In order to introduce benefits from differentiation, we adopt a long-term perspective and consider an organization composed of overlapping generations of agents. We find that it is optimal to give young agents as low a status as possible along with no monetary incentives. Their work motivation stems solely from promotion prospects. For incentive purposes, promotions bring more substantial rewards for those who have been more successful in the past: they end up with prestigious positions and are paid above their marginal productivity. Because individual preferences exhibit complementarities between status and money, symbolic and material rewards reinforce each other. By concentrating both types of compensation in the same time period and in the same state of nature, the organization exploits their complementarity so as to reduce the total wage bill. Although this differential treatment of older employees reduces instantaneous profits, this loss is more than compensated by the benefits associated with sharper incentives for junior employees. In other words, an employer who is able to commit organizes an internal labor market where pay is attached to jobs, rewards are delayed in time, and higher incomes are associated with greater recognition (e.g., a higher rank in the hierarchy). Whereas wage differences are small early on in the career, they become substantially larger than productivity differences as tenure rises. We show that these results are robust to the introduction of income risk aversion, a case for which a standard repeated moral hazard model would prescribe smoothed consumption over time (see, for instance, Rogerson, 1985; Chiappori, Macho, Rey, and Salanir, 1994).

More complicated issues would arise were we to take into account equilibrium status allocations with multiple organizations. For instance, Fershtman, Hvide, and Weiss (2005) consider a model with competitive firms, each comprising one principal and two agents, where workers have the same productivity but different status concerns. They analyze the impact of cultural diversity in the workplace on labor market equilibrium. (5) Performing a similar equilibrium analysis for large corporations is challenging because large firms use their market power to shield their employees from market pressures. (6) As a first step, the present article focuses on internal labor markets.

We present the static setting in Section 2 where we describe the organization, agents' preferences, and the allocation of status among agents; we also establish that optimal short-term incentives involve no differentiation in status among agents. The overlapping generations framework is introduced in Section 3, where we show that promotions are optimal if long-term commitment is feasible. Section 4 illustrates the empirical relevance of our theoretical findings through a comparison of work relations in the United States and Japan, and Section 5 compares our approach to some related literature on work incentives. We finally provide concluding remarks in Section 6.

2. The cost of status manipulation

We consider the provision of work incentives to agents whose effort level is unobservable. If, as is usually assumed, an agent's preferences are fully characterized by a taste for money and a distaste for effort, incentives can be provided through monetary rewards and penalties. As we argued in the Introduction, actual incentive procedures typically involve many nonmonetary attributes that are valued mostly as signs of a greater workplace recognition. We use the concept of status to summarize the overall access to the psychological or social benefits that an employee can secure through her position in the organization. In this section, we describe the static framework and show that it is costly to differentiate status between organization members when the work relationship is short term.

The organization. The organization (bureau, subdivision, firm) is supervised by a risk-neutral principal. There are n [greater than or equal to] 2 workers indexed by i = 1, ..., n. These are ex ante identical individuals, hired to do the same type of work, so that there is no a priori legitimate motive for treating them differently. The principal aims to maximize expected profit, with profit [pi] being defined by

[pi] (Q, [w.sub.1], ..., [w.sub.n]) = Q - [n.summation over (i=1)] [w.sub.i], (1)

where Q = [[summation].sup.n.sub.i=l] [q.sub.i] is total output (with a price normalized to 1) and w.sub.i] is agent i's wage.

Each worker contributes to the collective outcome by exerting effort [e.sub.i] [greater than or equal to] 0. The harder agent i works (the higher [e.sub.i] is), the greater is the probability of high output. Formally, individual i's output [q.sub.i] can be either high, [q.sub.i] = [[bar].q], with probability [mu] ([e.sub.i]), or low, [q.sub.i] = [q.[bar]], with probability 1 -[mu]([e.sub.i]) ([bar] q > q [bar] > 0). Individual output, and thus absolute performance, is verifiable. This is a case where direct individual monetary incentives are particularly appropriate. The probability of high performance for agent i increases with [e.sub.i] at a decreasing rate. The function [mu] (*) is also assumed to be three times continuously differentiable with a strictly negative third derivative. (7)

Assumption 1. [mu]' (e) > 0, [mu]" (e) < 0, [mu]'" (e) < 0 for e [greater than or equal to] 0, [lim.sub.e [right arrow] + [infinity]][mu]' (e) = 0.

We next discuss in some detail the two novel ingredients of our framework: employee preferences and the allocation of status in the organization.

Employees' preferences. A key feature of our approach is the specification of agents' preferences, which assumes some complementarity between status and income. We posit the following utility function:

u(w, s, e) = sw - [psi](e), s [greater than or equal to] 0, w [greater than or equal to] 0, e [greater than or equal to] 0, (2)

where s is status, w is wage income, and e is effort. The disutility of work, [psi], is taken to be a strictly increasing, strictly convex, and twice continuously differentiable function, with a strictly positive third derivative. (8)

Assumption 2. [psi]' (e) > 0 [psi]" (e) > 0 [psi]'" (e) > 0 for e [greater than or equal to] 0.

This specification reflects in a simple manner agents' taste for money and status and their distaste for effort. Setting status equal to 1 yields, as a special case, the standard quasilinear utility, so that our results can be readily compared with the predictions in the standard moral hazard framework. Linearity with respect to wage indicates that agents are risk neutral regarding income. In subsequent sections, we discuss how our results can be affected if this assumption is relaxed. (9) The requirement that status and wages be positive is a normalization. Utility could easily be rewritten to allow for non-zero lower bounds. The important point is that there are such lower bounds.

Because income and status are both positively valued, the indifference curves relating these two variables for a given effort level are strictly decreasing. This reflects substitution between status and income. However, preferences over status and income are strictly convex, so that there is not perfect substitution between these two variables: a prestigious title does not compensate for the absence of wages, nor does a good wage make up for the contempt of others. Utility also has important implications for the income-effort and status-effort tradeoffs. Formally, the marginal rate of substitution between effort and income is decreasing in status whereas the marginal rate of substitution between effort and status is decreasing in income. These cross effects can be best interpreted by relating them to the psychological analysis of work motivation and the conventional wisdom prevailing among management practitioners.

We first consider the impact of a change in status on the income-effort tradeoff. Our specification of preferences implies that, for a given level of monetary incentives, an agent should be all the more willing to exert effort when she has higher status. The literature on job satisfaction suggests that a higher status enhances work commitment. On the one hand, status is closely related to the need for recognition, which has been found to be a key factor in job satisfaction (e.g., Dunette, Campbell, and Hakel, 1967). On the other hand, many studies have shown that low job satisfaction results in high turnover and absenteeism rates. (10) Tahlin (1999) found in a study on job mobility in Sweden that, all else equal, people with low status (i.e., a low prestige score according to Treiman, 1977) are more likely to make voluntary job shifts than people with high status. It should be expected that low satisfaction also results in shirking which, contrary to absence and resignation, is not readily observable. (11)