Status and incentives.

(6) This is true only to a certain extent. For instance, Lazear and Oyer (2004), exploiting Swedish data, show that in the long term, wages are determined externally, presumably reflecting centralized bargaining.

(7) This condition, along with some similar conditions on preferences in Assumption 2, ensures the convexity of the agent's optimal effort with respect to work incentives.

(8) See footnote 7.

(9) The interpretation of linearity with respect to status is provided in Section 3.

(l0) See, for instance, Day and Hamblin (1964) and Baum and Youngblood (1975).

(11) Many studies have shown that there is a positive correlation between job satisfaction and quality of services (see Varma, Beatty, Schneier, and Ulrich, 1999). A positive effect of status on productivity has been found by Greenberg (1988) in a study on office reallocation.

(12) For instance, children with high-income parents typically select high-status positions (see Treiman and Ganzeboom, 1990 and Lillard and Reville, 1997). On a more anecdotal note, Cornelius Vanderbilt Whitney earning a Ph.D. for the sheer pleasure of being referred to as Doctor Whitney illustrates this appetite for status among rich people (see Fussell, 1983).

(13) The linear functional form is a consequence of the convexity assumption. It is somewhat restrictive and is designed to facilitate the exposition of the results (especially in the optimization problem). Some discussion of the robustness of our results to more general functional forms is provided in Section 3.

(14) Here status can be adjusted continuously (preferences are defined for a continuous variable). In contrast, Dubey and Geanakoplos (2004) study the relative merits of absolute versus relative rewards in providing incentives when preferences are defined only over status rankings.

(15) The lottery divides the total wage bill by n relative to what it would have been were agents to have had identical status with probability 1. The individual probability of winning the lottery is 1/n The prize is [s.sup.win] = n and [w.sup.win] = [U.bar] + [psi] ([e.sup.*]), where [e.sup.*] is the first-best effort level (i.e., which solves [psi]' (e) [mu]' (e) [DELTA] q). With such a lottery, individual expected utility is [U.bar], each agent commits to effort level [e.sup.* s have identical status and all receive a wage with probability 1.

(16) A lottery is still optimal if utility is linear in one argument and either the agent is risk averse regarding income or utility is strictly concave in status. See Section 3 for related arguments.

(17) It is a priori less obvious whether the added constraints rule out lotteries altogether. Proposition 2 shows that they in fact do.

(18) This lower bound is obtained as follows. The status of the agent getting the worst treatment may not exceed 1. Because, from (i) in Proposition 1, monetary incentives may not exceed [DELTA]q, if (9) holds, her individual rationality constraint requires that she receive a strictly positive low performance wage. From our previous argument, all agents must therefore have status equal to 1. Then (ii) in Proposition 1 implies that all agents be rewarded [DELTA]q for high performance.

(19) For more on this, see Milgrom and Roberts (1992).

(20) Internal equity, which fulfills the requirement of status legitimacy, is often mandatory by law. For instance, in France, it is against the law to pay identical jobs differently. The rule is "a travail egal, salaire egal" (articles L.133-5, 4eme alinea and L.136-2, 8eme alinea in the Code du Travail). Firms have been prosecuted for violating this rule.

(21) In this specification, we do not allow income and consumption in a given period to differ. Our results below would not be affected by introducing a credit market as long as workers do not have better access to that market than the principal.

(22) As noted above, utility could easily be rewritten to allow for non-zero lower bounds (e.g., u(w, s, e) = (w + 1) (s + 1) - [psi](e)). The important point is that there are such lower bounds.

(23) They do not consider the problem of moral hazard. They obtain the nice result that starting from different distributions of wealth, society ends up with a unique unequal distribution.

(24) According to Doeringer and Piore (1971), the main features of internal labor markets are: long-term employment relationships, limited port of entry for hiring, career paths within the firm, and promotion from within.

(25) This does not mean that there is no internal labor market in the United States. Internal labor markets do exist and they are quite stable (see Groshen and Levine, 1998). However, they tend to begin late in the career (i.e., after age 35). As Farber (1999) shows, most new jobs in the United States end early, and the probability of a job ending falls with tenure.

(26) For updated data, see Brown, Nakata, Reich, and Ulman, 1997.

(27) From the age of 18 to 24, real hourly earnings grow on average by 6.6% per year. This growth rate falls to 4% between ages 25 and 29, and then to 2.4% between ages 30 and 34 (Department of Labor, 2000).

(28) University graduates can reach management in 10 years, typically by the time they are 35-40 years old. High school graduates can reach management in 22 years, and most have reached management by age 50.

(29) This is true up until age 55. After this age, companies encourage their workers to retire.

(30) Hofstede (1980) identified four dimensions along which dominant patterns of culture can be ordered: power distance, uncertainty avoidance, individualism, and masculinity. He later added long-term orientation. Japan scores higher than the United States on all of these dimensions except for individualism.

(31) He concludes that "the capital that accrues with tenure has a strong industry-specific rather than firm-specific component. To the extent that this is the case, it is harder to argue that the accrual of firm-specific capital is what drives the decline in the probability of job change with tenure."

(32) In Auriol and Renault (2001), we investigate the implications of Proposition 3 for the specific shape of the optimal incentive hierarchy, assuming that [micro](e) = min {e, 1} and [psi](e) = A[e.sup.2]/2. We find that the harder it is for an employee to improve performance through effort (i.e., the larger is A), the more pyramid-like is the incentive hierarchy. Indeed, when A is very large, success is rare; promotion is extremely prestigious and the associated pay raise is huge (it diverges to infinity in the limit). By contrast, if high performance is easy to achieve, a seniority-based promotion system may be optimal (i.e., everybody is successful and is promoted).

(33) Davis and Haltiwanger (1999) provide evidence that different job real location rates across firms induce different turnover rates, and that firms are very heterogeneous with respect to job reallocation.

(34) For instance, General Electric (chemical division) cut the number of pay grades from 22 to 5 (Gerhart and Milkovich, 1992).

Emmannelle Auriol, Toulouse School of Economics, Universit6 des Sciences Sociales de Toulouse, and Institut Universitaire de France; eanriol@cict.ff.

Regis Renault, Universite de Cergy-Pontoise, ThEMA, and Institut Universitaire de France; regis.renault@u-cergy.fr.