Abstract

1. STATEMENT OF THE PROBLEM

The purpose of this paper is to consider the use of various reward instruments in organizations where agents can be promoted to become principals in the future. An obvious example is partnerships such as law firms. We model such an organization using the principal-agent framework with overlapping generations. Landers, Rebitzer and Taylor (AER, 1996) considered partnerships with an overlapping generations structure, but focussed on the sorting by ability problem at the entry level. In their model each associate, once employed by the firm, had an equal probability of becoming a partner in the next period. Wages were central in compensating the employee's effort.

We focus on promotions, as well as wages, as reward instruments. There is empirical evidence that partners' monetary rewards are considerably higher than wages paid to the associates. This indicates that promotions prospects may be used as an instrument to exert extra effort from all associates, even though only a few get promoted at the end. There is some analogy with tournaments. A distinctive feature of rewarding with a probabilistic promotion is that, unlike wage, such a reward imposes no direct cost on the principal.

Here we investigate optimal contracts between the principal and the agents when monetary rewards may be combined with promotion possibilities. In this framework, we study implications of the principal's profit-maximizing behavior on firm's size, composition (if potential employees differ in their ability), and the structure of employment contracts. Which combination of reward instruments is optimal for the principal? Can promotion prospects completely substitute for monetary rewards? If agents differ in their abilities, how do the employment contracts vary depending on agents' types? In particular, do better workers get promoted more often?

These issues are being addressed in both complete and incomplete information framework.

2. FEATURES OF THE MODEL

We consider an overlapping generation model where each agent lives for two periods. An agent hired as an associate in the first period may be promoted to become a principal (a partner) in the second period. Without loss of generality, we assume that there is only one principal (partner) in the firm in each period.

The agents are involved in a productive activity which is costly for them. Each agent's effort necessary to produce a given output depends on their ability and, possibly, on the total number of workers hired by the firm, e.g., through congestion effects. For their efforts, the agents are compensated with wages and promotion probabilities.

For simplicity, we assume that the principal him- or her is not directly involved in production. Thus, the principal's objective is simply to maximize his or her profit, which is the firm's total output less the monetary compensations paid to the agents. The principal designs a contract which determines the output levels, wages, promotion probabilities for the agents depending on their types, and the number of agents of each type hired by the firm.

The distinctive feature of the model is the presence of promotion instruments that may help to achieve an alignment of the principal's and the agents' interests. Assuming risk-neutrality and no discounting between periods, the utility of an agent is his/her wage net of the disutility of effort, plus the expected payoff from becoming a principal in the next period. In a steady state, the agent's next period reward from becoming a principal is equal to the current principal's profit. Thus, by providing enough promotion prospects to the agents, the principal may be able to achieve high profits "for free," i.e., without using high monetary rewards.

The baseline case is the complete information model with homogeneous agents. This model is further extended to the case of heterogeneous population, where agents may differ in their ability. We then relax the complete information assumption and consider a model where the agents' abilities are unobservable to the principal.

3. PRELIMINARY RESULTS

3.1 Complete information, homogeneous agents.

Suppose all agents are of the same ability level. Then we can show that zero wages are always optimal, i.e., any employed agent is rewarded solely by a future prospect of becoming a principal. Moreover, if there are no congestion effects, i.e., if each agent's productivity does not decrease with the total number of people employed, then it is optimal for the principal to hire as many agents as possible (provided that production is technologically efficient). Thus, with no congestion (or other technological constraints on the size of the firm), the principal hires as many workers as there are, pays them nothing in monetary terms and rewards them with a very low probability of becoming a partner. This, effectively, demonstrates why associates can be kept at relatively low wages in partnerships, as long as the promotion probability is positive, and the value of being a partner is very high.

In a more realistic model, the size of the firm may be limited by at least two factors: (i) Agents' risk aversion, and/or (ii) Technological factors, or congestion effects. In this paper we focus on (ii) and ignore (i). We assume that each agent's effort function is increasing in the total number of agents hired by the firm. This assumption imposes a limit on the size of the firm. The optimal firm size then depends on the agents' productivities: agents of higher ability imply larger firms and higher profits for the principal.

Importantly, we find that the earlier zero wage result carries through: Any optimal employment contract involves zero wages.

3.2 Complete information, heterogeneous agents.

We next assume that agents may differ in their ability. We first show that if there are "enough" high ability agents in the economy, then the problem reduces to the homogeneous agent economy case: If the supply of the highest ability workers in the economy is above the optimal firm size in the corresponding homogeneous agent economy, then only the highest type agents are employed by the principal. Hence, every employed agent is offered a contract which involves a zero wage and a promotion probability which is equal across all employees.

In a more general case when the supply of top quality agents is limited, the firm structure is sequential. That is, a lower ability agent may be employed only if all agents of higher types are employed as well. In this case, we find that only agents who are promoted with certainly may be paid positive wages. Characterization of optimal employment contracts across types in such a firm is work in progress.

3.3 Incomplete information, heterogeneous agents.

We next suppose that the agents' types are not observable to the principal, and consider incentive compatible contracts where each agent has no incentive to misrepresent his or her type.

In general, the incomplete information complicates the problem considerably, and characterization of optimal incentive contracts is currently work in progress. However, we find that under certain conditions, the incomplete information does not present any difficulties to the principal: If the principal is informed that there are "enough" high ability agents in the economy, then we show that the first best (complete information) optimal contract is incentive compatible. In this special case, the compensation offered by the principal is just enough to ensure voluntary participation of high ability agents, but is not sufficient for lower ability agents. Thus the first best outcome is obtained.

In a more general case when the supply of high ability agents is limited, the principal will optimally employ agents of different abilities. We will characterize optimal employment contracts across types of agents, and compare these with the ones offered in the complete information case.