Status and incentives.

The initial conditions, [[gamma].sub.0], [c.sub.h0], and [c.sub.l0], are given exogenously. Finally, we define a steady state as a situation in which ([c.sub.lt], [c.sub.ht], [c.sub.lt]) is independent of time (i.e., all generations are offered the same intertemporal contract).

We now show that viewing promotions as an instance of status differentiation among workers yields valuable insights regarding their role in intertemporal incentive schemes.

* Incentives and promotions. In view of the various constraints pertaining to the dynamic profit optimization problem, we might expect that the exact nature of the solution will depend critically on which of these constraints are binding. Although this is to some extent true, the results in the next proposition are quite general.

Proposition 3 (Incentives through promotion). Under Assumptions 1, 2, and 3, in any steady state of a profit-maximizing solution, we have

[s.sub.l] = [[w.bar].sub.l] = [DELTA][w.sub.l] = 0, (13)

[s.sub.h] > [s.sub.t]. (14)

[[w.bar].sub.h] [greater than or equal to] [[w.bar].sub.l] and [DELTA][w.sub.h] [greater than or equal to] [DELTA][w.sub.l], (15)

where at least one of the inequalities in (15) is strict.

Proof See the Appendix.

The above proposition provides a crisp characterization of the optimal intertemporal incentive scheme. It is optimal to endow young agents with the lowest possible status level while providing them with no direct monetary incentives. (22) Junior workers earn the same salary independent of their performance. They are induced to exert effort by the prospect of a future promotion. That is, pay is attached to the job, and earnings profiles only become individual specific as careers unfold. When old, an agent's status and monetary incentive scheme depend on her past performance. As in the static context, it is optimal to combine higher wage and higher status. However, in contrast with the egalitarian solution of Proposition 2, it is optimal to introduce some differentiation between generations and among old agents. Better past performance brings about higher status as well as greater monetary compensation. This solution allows advantage to be taken of the complementarities between status and income by concentrating benefits in both dimensions on one state of nature. This is reminiscent of the first-best solution in the static problem where all of the status and wages are concentrated in one individual.

An important result in the literature on repeated moral hazard is that the optimal long-term incentive contract should involve some memory: the type of incentives currently given to an agent depends on her past performance (see, for instance, Rogerson, 1985; Chiappori et al., 1994). The idea is that, if agents are risk averse, it is optimal to spread the effect of income shocks resulting from good or bad performances over time; this is the preference for consumption smoothing emphasized by Malcomson and Spinnewyn (1988). This implies that it is not optimal to delay all rewards and penalties as prescribed by Proposition 3. One obvious difference between the model in this article and the standard repeated moral hazard framework relates to the agents' attitude toward income risk. We now briefly explore the robustness of our results to the introduction of risk aversion in agents' preferences.

Robustness. In our treatment of risk aversion, we will at the same time discuss the robustness of our results to changes in the status technology. In the model considered here, the status constraint is linear and utility is linear in status. This can loosely be interpreted as saying that there are constant returns to concentrating status in one group of individuals. It might be expected that, if those returns were sufficiently decreasing, the result that the young should have a minimal status would be overturned. There are two possible ways of making the returns to status concentration decreasing: either the left-hand side of the status feasibility constraint could be made strictly quasiconvex or utility could be written as strictly concave in status. The second route is followed in the argument below. Rewrite instantaneous utility as

u(w, s, e) = g(s)h(w) - [psi](e),s [greater than or equal to] 0, w [greater than or equal to] 0, e [greater than or equal to] 0, (16)

where h and g are concave and strictly increasing functions satisfying h (0) = g(0) = 0.

Proposition 4. Suppose that the agent's instantaneous utility is linear in income (h linear) or linear in status (g linear) and that there is sufficiently little discounting. Then, in any steady state of an optimal solution, we have [s.sub.l] = [w.bar].sub.l] = [DELTA][w.sub.l] = 0.

Proof. See the Appendix.

The result that young agents should receive minimal status holds when either income risk aversion is introduced or utility is strictly concave in status. Because earnings and status are complements, individuals are willing to take gambles in which winners receive both higher income and higher status. Becker, Murphy and Werning (2000) obtain related results in their examination of the evolution of inequalities when individuals care about income and status and the two are complements. (23) Here the principal exploits the complementarity to elicit effort at a lower wage cost.

4. Job tenure and career profiles

* Combining Propositions 2 and 3, our results suggest that an organization will resort to status differentiation for incentive purposes only when it can set up an internal labor market. (24) More specifically, in a long-term relationship, rewards for high performance are delayed over time and pay raises are associated with changes in status, which are usually achieved by a move up the hierarchy (i.e., promotion). Differences in productivity will then be reflected in wages for senior employees only. That is, earnings profiles are upward sloping and differences in earnings across individuals widen with seniority. By way of contrast, if commitment is not possible, no status differentiation occurs, and incentives are provided via direct monetary rewards. Employees with different productivity are paid different wages, so that individual earning profiles diverge early in the career. To assess the relevance of this theory, we now confront these predictions with a number of stylized facts.

The feasibility of an internal labor market hinges on employees' expected tenure within the organization. A comparison of work relations in the United States and Japan illustrates the two situations of strong and weak commitment. According to the U.S. Bureau of Labor Statistics, the average person in the United States holds 9.2 jobs from age 18 to age 34. More than half of these jobs are held between the ages of 18 and 24 (Department of Labor, 2000). (25) By contrast, in Japan, labor mobility is low for young core workers. For instance, three quarters of Japanese engineers will have only one employer during their entire career (Jacobs and Herbig, 1998). Hashimoto and Raisian (1985), using data from the 1960s and 1970s, indicate that in Japan, 65% of male workers with at least 5 years tenure in the job when aged 20-24 will be in the same job 15 years later, compared to an analogous figure of 30% in the United States. These differences have been remarkably stable since the early 1970s. (26)

The analysis presented here implies that, when young, Japanese core workers will be at the bottom of the hierarchy and receive relatively low wages, independent of their education level. Differentiation comes later in the career so that the earnings profile increases with seniority with increasing disparities between individuals. By contrast, in the United States, young workers, who are very mobile, do not accept delayed rewards. Their earnings profiles are relatively steeper when young (i.e., under 35). Earnings, which better reflect workers' productivity, are also more differentiated by education. This implies that earnings disparities are greater for young workers in the United States than in Japan.

According to the Bureau of Labor Statistics, individual real earnings in the United States increase more rapidly when young than when old. (27) Young American workers facing flat tenure-earnings profiles change jobs to increase their earnings. Topel and Ward (1992) found considerable returns to between-job mobility in a study of white male high school graduates. The reverse is true in Japan, where earnings profiles increase with age at an increasing rate. "White-collar and blue-collar pay tables are integrated into a single table that erases distinctions between the two categories. There is also no major gap between production workers and craft workers. New workers are placed at the bottom of the ability rank table and given simple assignments" (Brown et al., 1997). This implies that for young workers (i.e., under age 35), the level and variance of earnings are low. As predicted by our theory, differentiation appears with seniority, and pay raises are coupled with changes in status. "Much of the career-based pay increases take place only when, and if, workers are promoted to managerial positions that are not in the union, generally after age 35" (Brown et al., 1997). (28) Figures 1 and 2, which are borrowed from Brown et al. (1997), illustrate the results discussed above.

[FIGURE 1 OMITTED]