Incentives, Wages, and Promotions: Theory and Evidence

Transcription

1 Incentives, Wages, and Promotions: Theory and Evidence Illoong Kwon University of Michigan Department of Economics Ann Arbor, MI June 2001 Abstract Human capital theory and agency theory are two of the most important building blocks of labor economics. However, the connection between these two building blocks has never been explicitly analyzed. This paper demonstrates that a simple moral hazard model, based on the premise that an agent s e ort has a persistent e ect on future productivity through human capital accumulation, generates rich implications that solve numerous puzzling aspects of the observed internal wage and incentive structures within rms. This paper also presents an empirical analysis using new personnel records. JEL CLASSIFICATION: D82, J41, J31 This paper is based on the rst part of my Ph.D. dissertation. Special thanks to Eric Maskin and Zvi Griliches for guidance and encouragement. Zvi Griliches also kindly shared the dataset with me. I would like to thank Lawrence Katz and Catherine Wolfram for many invaluable comments and suggestions. I am grateful to Phillippe Aghion, Richard Caves, Drew Fudenberg, Seki Obata, John Sutton, and participants of numerous seminars for useful comments and discussions. I also wish to thank Michael Whinston for helpful comments at early stages of this project. Financial support from the Korean Foundation for Advanced Studies is gratefully acknowledged. All remaining errors are my own. 1

2 1 Introduction Recent empirical studies have produced several stylized facts on the wage and incentive structure in large organizations; (i) wages are closely linked to job-levels, (ii) wages increase signi cantly with promotions, (iii) wages vary signi cantly within a job-level despite (i), and wage distributions overlap between adjacent job-levels 1, and (iv) there are signi cant wage cohort e ects (Lazear [1992], Baker, Gibbs and Holmstrom [1994a,b] (hereinafter BGH), Seltzer and Merrett [2000]). Despite many theoretical models of internal labor markets (see Baker and Holmstrom [1995]) and recent attempts to integrate di erent models (e.g. Gibbons and Waldman [1999]), each of these models explains only a few of these stylized facts. This paper demonstrates that a simple moral hazard model, based on the premise that a worker s e ort has a persistent e ect on the future productivity (e.g. through human capital investment or learning-by-doing), provides rich implications encompassing all of these stylized facts. Furthermore, using new personnel data, this paper shows that various other aspects of the data are consistent with the predictions of the model presented. It has been di cult to explain all of the stylized facts for the following reasons: the rst two stylized facts imply that most incentives are given by infrequent promotions. However, in a typical principal-agent model, the optimal contract often resembles a frequent bonus scheme. Then, as Baker et. al. [1988] noted 2, the puzzles are: (a) why wages are closely linked to job-levels, but not to individual performances, and (b) why most incentives are given with infrequent promotions. Models with incomplete contracts (including tournament models) avoid these puzzles by assuming away the performance-based bonus scheme using the assumption of unveri able perfor- 1 That is, some workers in a certain job-level receive lower wages than those in a lower job-level. 2 Baker, Jensen, and Murphy [1988, p601] We don t understand why rms systematically choose promotion-based incentive systems instead of bonus-based system, and solving this mystery is an exciting direction for future research. 2

3 mance, which essentially leaves the promotion as the only possible incentive device. (e.g. Prendergast [1993], Fairburn and Malcomson [1996]) However, since wages can be contingent only on the job-levels in these models, there is a single wage attached to each job-level. Then, these models cannot explain the third stylized fact. Therefore, another puzzle arises: (c) the signi cant wage variations within a job-level, and especially overlapping wage distributions between adjacent job-levels. There are also models that try to explain these stylized facts without considering the incentive problem (e.g. Demougin and Siow [1994], Bernhardt [1995], and Gibbons and Waldman [1999]). Even though these models can explain many of the stylized facts, they can not explain all of them, and they exclude consideration of the incentive problem. For example, in Gibbons and Waldman [1999], wages are determined in the spot market. Therefore, they cannot explain the fourth stylized fact - the cohort e ect. Also in their model, both promotions and wages are determined by a worker s expected ability. Therefore, no workers in a lower job-level can receive higher wages than other workers in a higher job-level. That is, they cannot explain the overlapping wage distributions between adjacent job-levels. This paper allows a performance-based incentive contract, but assumes that unobservable e ort by an agent improves both his current and future performance. Such e ort can be interpreted as either explicit human capital investment or as ordinary learning-by-doing. Despite the importance of human capital investment in labor economics, there has been little analysis in the agency literature of the optimal incentive scheme for such an investment. 3 The paper shows that the optimal contract has the following salient features : (i) the wage is constant for each individual within a job-level, (ii) explicit incentives are given mainly by wage increases at the time 3 Gaudet et. al. [1996, p322] situations where current opportunities depend on past, as well current actions,..., is considered standard in all areas of economics other than the information literature. 3

4 of promotions, (iii) there is wage variation across individuals within a job-level, and (iv) there are overlapping wage distributions between adjacent job-levels. The intuition behind these ndings is simple. In a simple two-outcome moral hazard model, an incentive payment can be de ned as the additional compensation paid when the outcome is high rather than low. In an equilibrium, the principal needs to provide an incentive payment only in the last period of the contract. The reason is as follows: in the last period, the principal has to provide an explicit incentive payment to motivate the agent, since there are no implicit incentives from the future. Given this last period incentive payment, if the agent has failed to invest in some previous period(s), his (human) capital level will be correspondingly lower in the last period, so that he will receive an incentive payment with lower probability. To avoid this probability reduction in the last period, the agent will invest in previous periods even if they do not entail incentive payments. Therefore, the principal need not provide incentive payments throughout the contract as standard agency theory predicts, but only in the last period. Indeed, to have any signi cant variability in the wage before the last period would impose unnecessary riskontheagent.thisexplainswhywagesareconstantwithinajob-level. To explain why wages change with promotions, note that the principal will need to provide incentives before the last period of a contract if investments made in previous periods do not change future productivity. When a promotion occurs, some of the skills and knowledge acquired from the previous job may not be useful in the new job. Thus, the model predicts that we will see wage increases at the time of promotion; these increases are rewards for investments that do not carry over to the new jobs. These features can explain all the stylized facts, thereby resolving all the puzzles mentioned above. First, since each individual worker receives a constant wage within a job-level, wages are closely linked to the job-levels, but not to individual performances. Second, since the explicit incentive payments are given with promotions, wages will increase signi cantly with promotions. 4

5 Third, since the wage increases from promotions (i.e. promotion premiums) di er among workers due to their performance, di erent individuals will receive di erent wages within job-levels and some workers may receive smaller wages than those in a lower job-level. Fourth, since the contract is a long-term one, the overall wage level is decided by the reservation wage at the time of rm entry. Therefore, if reservation wages change over time, the overall wage level also changes with the entry year, generating the wage cohort e ect. While the main focus of the paper is on the incentive and wage structure within a rm, due to its simplicity, the model can be easily extended to explain the various promotion dynamics such as fast-track by introducing heterogenous agents as Gibbons and Waldman [1999] do. For the empirical analysis, this paper uses new personnel records of health insurance claims processors in a large US insurance company. These processors are white-collar, female, nonmanagerial, service industry workers, a rapidly growing group that has been rarely studied. This dataset is also unique in that it has an objective and consistent measure of performances across di erent job-levels, while Lazear [1992] or BGH use subjective performance rating. This objective and consistent measure of performance allows to measure and compare the sizes of the incentive payments across di erent job-levels. For example, the data show that a signi cant portion of incentives are given by promotions and that both promotion-based incentives and bonus-based incentives are increasing in job-levels, which are consistent with the predictions of the model. The data also show that a large portion of wage variation is explained by job-levels alone, but that there are signi cant wage variations within a job-level and wage overlaps between joblevels. Furthermore, most within-job wage variations are due to cross-individual variations even after controlling for performance. These ndings are again consistent with the predictions of the model. These ndings are also similar to Lazear [1992] and BGH. This similarity is interesting since the workers in the Lazear and BGH studies are managers with an average (annual) wage of $59,000, while workers in this study are non-managerial workers with an average wage of $21,900. 5

6 This suggests that the empirical ndings of this paper are not con ned to a single company or to a single class of workers. The following patterns are also found in the data: (i) There exist long-term employment relationships, limited ports of entry for hiring, career paths within the rm, and promotion from within, all of which are key features of an internal labor market. 4 (ii) Nominal wage cuts are rare, but real wage declines are common. (iii) Wage variations increase with job-levels. (iv) Promotions come from and go to all quantiles of the wage distributions of the lower and higher job-levels. (v) Promotion depends primarily on recent performance. The optimal contract characterized in this paper can explain all of these patterns. Thus, this paper contributes to an emerging literature that attempts to explain broad patterns of wage dynamics in rms rather than one pattern in isolation. The paper is organized as follows. Section 2 presents the theoretical analysis. Section 2.1 sets up the basic model. Section 2.2. derives the optimal contract and shows its robustness to various commitment assumptions. Section 2.3 introduces a job-ladder and promotions, then shows that the optimal contract explains all the stylized facts. Section 2.4 discusses an extension of the model with heterogenous agents. Section 3 provides the empirical analysis. Section 3.1 describes the dataset and shows that various underlying aspects of the dataset satisfy the assumptions of the theoretical model. Section 3.2 to 3.5 analyzes wages, incentives, and promotions, respectively, and shows that the ndings are consistent with the prediction of the model. Section 3.6 discusses the alternative explanations. Section 4 discusses the other possible applications of the model and concludes the paper. 4 Milgrom and Roberts [1992, p359] 6

7 2 Theoretical Analysis This section analyzes the optimal incentive scheme in a dynamic moral hazard model. The agent s e orts in the model improve both current and future performance; so the agent s unobservable e orts are the repeated investment e orts. 2.1 Basic Model In each period t (t =1; ::; N), the agent can make one unit of investment i t : i t =1if the agent invests and i t =0if the agent does not invest: For simplicity, assume that the agent does not make any other non-investment e ort. 5 The investments are not observable to the principal. In each period, there are two possible outcomes, y 1 and y 2 (y 2 >y 1 ): The outcomes are publicly observable. The probability distribution of the outcome depends on the sum of investments the agent has made, i:e: the capital level K t = P t j=1 i j. For simplicity, I assume no depreciation of capital. 6 Denote the probability of high outcome (y 2 ) when the capital level is k by p k : The higher the capital level, the larger the probability of the high outcome. That is, p 0 <p 1 <:::<p N : Assume that there are non-increasing marginal returns to investment. That is: (A.1) p k+1 p k p k p k 1 ; n =1; 2; ::; N 1 The principal is risk-neutral and the agent is risk-averse. The agent has an additive and separable utility function: P T t=1 [V (x t) G(i t )] where x t is his income in period t: V (:) is a Von Neumann-Morgenstern utility function of income with V 0 > 0 and V 00 < 0: G(:) is the disutility from investment e ort. I will normalize G(0) = 0 and denote G(1) by H: For simplicity, I assume 5 Alternatively, I can assume that the agent s e ort has a learning-by-doing e ect. 6 Even with depreciation, the qualitative results of this analysis do not change. In fact, the optimal contract with depreciation becomes closer to the observed internal wage structures. 7

8 no discounting. 7 It is often more convenient to think that the principal pays the agent in utils. Therefore, de ne h V 1 : Note that h 0 > 0 and h 00 > 0 since the agent is risk-averse. In a long-term contract, the commitment level of each party is an important factor. For the moment, I will assume that both the principal and the agent can make a binding long-term contract (full-commitment). Later, the full-commitment assumption will be relaxed to the case with possible renegotiations and also to the case where the agent can not make a binding long-term commitment (unilateral commitment). The timing is the following: at the beginning of the rst period, the principal o ers a binding long-term contract to the agent. The agent either accepts or rejects it. If the agent accepts, he decides (possibly randomly) whether he will invest at the beginning of each period. At the end of each period, the outcome is realized, and the agent gets paid according to the contract. For a benchmark and also to introduce notation, let us consider the one-period model. In the one-period case, the problem is the same as in the standard agency model. Suppose that the agent s capital level is k 1 at the beginning of the period. In the one-period case, the contract will take the following form: C =(u 1 ;u 2 ); where u j is the utility payment when the outcome is y j (j =1; 2): For simplicity, assume that the reservation utility is zero. If the principal wants to induce an investment, the principal will solve the following cost minimization problem: subject to min u 1 ;u 2 (1 p k )h(u 1 )+p k h(u 2 ) (1) (1 p k )u 1 + p k u 2 H 0 (2) (1 p k )u 1 + p k u 2 H (1 p k 1 )u 1 + p k 1 u 2 (3) 7 The qualitative results of this analysis do not change with discounting. 8

9 The rst constraint is the participation constraint when reservation utility is zero: The second constraint is the incentive constraint. It is easy to show that these two constraints are both binding. Therefore, the solution is (u 1;u 2)=(w k 1;w k 2) (H p k H; H + 1 p k H) (4) p k p k 1 p k p k 1 If the principal wants to induce no investment, then the principal will give full insurance which just guarantees the reservation utility That is, (u 1 ;u 2 )=(0; 0): However, since I am interested in inducing investment e orts, I will assume that the principal wants to induce an investment for any reservation utility U and for any capital level k: That is, (A.2) For all U and k, (1 p k )(y 1 h(u+w k 1 ))+p k(y 2 h(u+w k 2 )) > (1 p k 1)y 1 +p k 1 y 2 h(u). Then the optimal contract in the one-period case will be given by (4). 2.2 Optimal Contract with A Single Job-Level Suppose there are N ( 2) periods. The problem is now di erent from the standard repeated moral hazard problem, since the agent s e ort changes the probability distribution of the future outcome. Given the assumption (A.2), it is optimal for the principal to induce investments in every period with probability one. Then the contract has to specify in each period t; given the history of the outcomes h, the (utility) payment u t h1 for the low outcome and ut h2 for the high outcome 8. As in the one-period model, the optimal contract will be the solution to the cost minimization problem with the participation and incentive constraints. I will characterize the incentive constraints rst, then solve for the optimal contract. 8 To be precise, h should be denoted as h t: However, I will drop the subscript t as long as it does not cause confusion. 9

10 Suppose that the agent has zero capital at the beginning of the rst period. If the agent invests in all the periods as the principal intends, the agent s capital level will be N 1 at the beginning of period N. Then, for a history of outcome h; the Nth period incentive constraint is (1 p N )u N h1 + p Nu N h2 H (1 p N 1)u N h1 + p N 1u N h2 8h (5) The following lemma provides the key result in characterizing the optimal contract. Lemma 1 If the Nth-period incentive constraint, (5); is satis ed, then the incentive constraints in any period, regardless of the agent s capital level, are not strictly binding. Proof Suppose that the lemma is true. Given that the agent is risk-averse and has an additive and separable utility function, the principal will optimally provide a constant (utility) payment, say V; for all the periods except for the last where the incentive payments has to be given from (5). Therefore, it is su cient to show that under such contract, the agent will invest in all the periods regardless of his capital level. Step 1 : Consider the last period. In the beginning of the last period N; suppose that the agent s capital level is K 1( N 1): The agent will invest i (1 p K )u N h1 + p Ku N h2 H (1 p K 1 )u N h1 + p K 1u N h2 ; or un h2 un h1 H p K p K 1 : Note that from (5), u N h2 un h1 and from (A.1), regardless of his capital level. H p N p N 1 ; H H p N p N 1 p K p K 1 : Therefore, given (5), the agent will invest in the last period Step 2 : Now consider the period N 1: Suppose that the agent capital level is K 0 2( N 2). If the agent invests in period N 1; the agent s utility in period N 1 is V H; regardless of the outcome; and his capital level becomes K 0 1: In period N; from Step 1, the agent will invest again, and receive expected utility (1 p K 0)u N h1 + p K 0uN h2 H. If the agent does not invest in period N 1; the agent s utility in period N 1 is V; and his capital level stays at K 0 2: In period N; from Step 1, the agent will invest, and receive the expected utility (1 p K 0 1)u N h1 + p K 0 1u N h2 H. 10

11 Therefore, the agent will invest in period N 1 i V H +[(1 p K 0)u N h1 + p K 0uN h2 H] V +[(1 p K 0 1)u N h1 + p K 0 1u N h2 H] (6) That is, i (1 p K 0)u N h1 + p K 0uN h2 H (1 p K 0 1)u N h1 + p K 0 1u N h2 (7). However, from (5) and (A.1), (7) is satis ed for all K 0 ( N) and h: Therefore, the agent will invest in period N 1; even though the N 1 period payment does not depend on the outcomes. Step 3: The same logic can be applied for all the previous periods to show that the agent will invest in all the previous periods, even though the payment does not depend on the outcome except for the last period. The intuition of the lemma suggests the following: To induce an investment in the last period, the principal must provide incentive payments. Given this last period incentive payments, if the agent does not invest in a previous period, the his capital level in the last period is lower, and the probability of getting a high incentive payment becomes smaller: To avoid this reduction of expected utility in the last period, the agent will invest in previous periods even without any direct incentive payments. 9 Furthermore, the utility payments in the rst N 1 periods are a constant V. Therefore, the last period incentive payment does not depend on the history of previous outcomes, since it imposes unnecessary variations of income to the risk-averse agent. Now, the principal s optimization problem can be stated as follows: min V;u N 1 ;un 2 (N 1)h(V )+(1 p N )h(u N 1 )+p N h(u N 2 ) (8) 9 Note that the investment dynamics relaxes the incentive constraints in this model. In usual multi-period agency models, however, the information dynamics provide more constraints (e.g. the ratchet e ect). See footnote 27 for an empirical comparison. 11

12 subject to (N 1)(V H)+(1 p N )u N 1 + p Nu N 2 H 0 (9) (1 p N )u N 1 + p N u N 2 H (1 p N 1 )u N 1 + p N 1 u N 2 (5 0 ) It is easy to see that both constraints must be binding. From solving the binding constraints, u N p N 1 = (N 1)(H V )+H H (N 1)(H V )+w1 N (10) p N p N 1 u N 2 = (N 1)(H V )+H + 1 p N H (N 1)(H V )+w2 N (11) p N p N 1. Substituting these into the objective function and solving for V fully characterizes the optimal contract. V will be determined by the following FOC: (V ) h 0 (V ) (1 p N )h 0 ((N 1)(H V )+w N 1 ) p N h 0 ((N 1)(H V )+w N 2 )=0 (12) For the future reference, denote this FOC as a function of V by (V ): The following proposition summarizes the results. Proposition 1 In the N period optimal contract, wages remain constant until the last period regardless of the outcomes. In the last period, there are incentive payments which depend on the last period s outcome only. The properties of the optimal contract are noteworthy. First, wages are constant until the last period. In other words, the principal does not need to provide direct incentives to induce an agent s investment, except in the last period. As shown in lemma 1, this property is entirely driven by the fact that the e ort today a ects the productivity in the future. Indeed, this property continues to hold even if the agent is risk-neutral If the agent is risk-neutral, the optimal contract is not unique. However, if there is even a slight cost of monitoring output, Proposition 1 will hold as the unique optimal contract. 12

13 Second, the principal does not backload the incentive payments to the last period. The last period s incentive payments are just enough to induce a last period investment. Therefore, the overall size of the incentive payments are far less than the overall size of the incentive payments that the standard agency model predicts. Another interesting feature is that the last period s payments do not depend on the previous periods outcomes. This property follows immediately from the constant wages in all previous periods, as there is no need for utility smoothing. In a standard repeated moral hazard model, this property does not hold. For example, Rogerson [1985] shows that the optimal contract always exhibits memory (i.e. the last period s incentive scheme always depends on the previous periods realized outcomes). These properties of the optimal contract are robust to various assumptions of commitment level. For example, the optimal contract characterized above is renegotiation-proof. Suppose that the principal and the agent can renegotiate the contract at the beginning of each period. Since the explicit incentive payments are given only in the last period, from the logic of lemma 1, the constant payment scheme until the last period remains optimal. Since the principal would not agree to increase V; and the agent would not agree to decrease V; the original constant payment V would not change either. Therefore, the original contract cannot be improved upon through renegotiation. 11 Corollary 1 Proposition 1 holds even if renegotiation is possible. 11 One could directly solve the optimal renegotiation-proof contract from the beginning. However, the advantage of starting with full-commitment assumptions is that it allows me to show that the renegotiation-proof constraint is not binding. This rules out the possibility of randomization, which will generate adverse selection problem as well as moral hazard problem (see Ma [1991]). If the renegotiation-proofness constraint is binding, it has been shown that the randomization of the agent s e ort can relax this renegotiaton-proofness constraint (see Fudenberg and Tirole [1991] and Ma [1991]). 13

14 All the qualitative results of Proposition 1 also hold even if the agent can quit. However, this result is not trivial since the agent who does not invest may want to quit before the last period. Then, the right-hand sides of the incentive constraints must be modi ed. First, I will make the following assumption 12 : (A.3) The agent can quit at anytime, especially after the performance is realized but before the payment is made. Note that under (A.3), overall payment levels will be backloaded. Since the principal can not use negative incentive payments in the last period, the principal must provide positive rewards for the high outcome. Then, for those who have invested in all the previous periods, the last period s expected utility will be larger than the reservation utility. However, from the binding participation constraint, the expected utility in the previous periods will be less than the reservation utility. This backloaded payment has been observed in various studies. If the backloaded payments are large enough, the agent who does not invest in a previous period will still remain in the last period. Then, none of the results in Proposition 1 will change. If the backloaded payments are not large enough, the agent who does not invest in a previous period will be better o by quitting before the last period to avoid the utility reduction in the last period. However, since the last period s expected utility would be larger than the reservation utility if the agent invests and stays, this loss of positive expected utility provides implicit incentives for the investments. Proposition 2 Under (A.3), (i) If p N 1 p N p N 1 or ( N 2 N 1H) 0; proposition 1 holds, where (:) is de ned in (12). 12 One can also assume that the agent can quit only at the end of each period (i.e. after the compensations (or pentalies) are made). In the earlier version of this paper, I showed that, provided h 000 < 0; all the qualitative results of Proposition 1 still hold even in this case. 14

15 (ii) If p N 1 <p N p N 1 and ( N 2 N 1H) < 0; there will be explicit incentive payments in each period, which are increasing over time. The explicit incentive in each period is smaller than that in the one period model. Proof See Appendix. In the remainder of this paper I will focus on case (i) for a simpler exposition, even though case (ii) in Proposition 2 allows the model to explain an additional stylized fact that the incentive payments (e.g. bonus) as well as the overall salary increase in tenure. Since the principal needs to provide incentives only in the last period, I can now explain why infrequent incentive schemes can optimally motivate high e ort in every period. In addition, since wages are constant except in the last period, I can also explain why wages are attached to job-levels. However, incentives are often provided by promotions even before the last period of contracts. To explain why the principal needs to provide (direct) incentives with promotions in the middle of the contract period, I need to consider promotions explicitly. 2.3 Optimal Contract with Two Job-Levels Incentive payments are needed before the last period of the contract if the investments made do not change the future productivity. This situation can occur when the job changes, since some skills and know-how acquired in a job may not be useful in the subsequent jobs. Suppose that an agent is promoted from one job to another. If the two jobs are very di erent, a large portion of the human capital accumulated at the old job will not be useful in the new job. For example, learning typing as a secretary will increase performance in a secretarial job, but it may not increase performance when in a managerial job. If the two jobs are similar, however, the degree of the skill s obsoleteness will not be large. I will make the following assumption: (A.4) µ of an investment is job-speci c and 1 µ of an investment is general (0 µ 1): 15

16 (A.4) means that when a worker gets promoted, only (1 µ) of investments or learning at the old job will be useful at the new job. If both jobs are same, then µ =0and if both jobs are completely di erent, then µ =1: For simplicity, let us consider a two period model. Suppose the agent works at job A in period 1 and gets promoted to job B at the end of the period. If µ =0; then the optimization problem is exactly the same as before since the two jobs are exactly the same. Therefore, there will be no incentive payment at the end of period 1. In other words, there will be no incentive payment associated with a promotion. If µ>0; however, the principal will need an incentive payment at the end of period 1, i.e. with a promotion; this incentive is for investments that do not carry over to job B. Therefore, the larger the di erences between two jobs, the larger the incentive payment accompanying a promotion. Lemma 2 If µ>0; then there is an incentive payment accompanying a promotion. The size of the incentive payment accompanying a promotion is an increasing function of µ: Proof If the agent invests in the rst period, his capital level at the beginning of period 2 will be 1 µ since a µ portionofaninvestmentinjobaisnotusefulinjobb.iftheagentinvestsin the second period again, then his capital level at the end of period 2 will be 2 µ: Let us denote the probability of high-outcome (say z 2 ) in job B as q k when the capital level is k µ and assume q 2 q 1 <p 1 p 0 : Then, given the rst period outcome y j (j =1; 2); thesecondperiodincentive constraints are: (1 q 2 )u j1 + q 2 u j2 H (1 q 1 )u j1 + q 2 u j2 (13) Suppose that the rst period incentive constraint is not strictly binding. Then, there will be no incentive payment in the rst period, and the second period incentive constraints will be binding. 16

17 If the agent does not invest in the rst period, his human capital level will be 0 at the beginning of the second period and 1 at the end of the second period (recall that from Lemma 1, the agent will invest in the second period regardless of whether he has invested in the rst period or not). Let us denote the probability of a high outcome in job B when K =1as q1 0 : Note that q 2 q1 0 since 2 µ 1: Therefore, if the agent invests in the rst period, he receives (1 q 2 )u j1 + q 2 u j2 : If the agent does not invest in the rst period, he receives (1 q1 0 )u j1 + q1 0 u j2. From the binding second period incentive constraint (13), the indirect incentive from the second period is less than H; i.e., [(1 q 2 )u j1 + q 2 u j2 ] [(1 q 0 1 )u j1 + q 0 1 u j2] <H (14) since q 2 >q1 0 and u j2 >u j1: Then, without an incentive payment in the rst period, the rst period incentive constraint will be violated since the indirect incentive from the second period is not large enough. Therefore, the rst period incentive constraint will be strictly binding, and there will be an explicit incentive payment at the end of the rst period. In other words, there will be an incentive payment alongside a promotion. Recall that q1 0 and q 2 are the probabilities of a high outcome in job B when K = 1 and K =2 µ; respectively. Therefore, as µ gets close to 1; the di erence between q 2 and q1 0 gets smaller: Then the indirect incentives in (14) will decrease. Therefore, the direct incentive payment at the end of the rst period increases as µ increases. Now consider a case where an agent stays in the same job level for more than one period. Suppose that there are two job-levels A and B, and job B values human capital more than job A. Let us consider the N-period model. Assume that job B requires N 1 (<N) periods of investments in job A. Therefore, if the agent invests in every period, he will get promoted after N 1 periods Note that I am taking the promotion schedule as given and analyzing the optimal incentive scheme given this exogenous promotion schedule. Section 2.4 will discuss how one can endogenize the promotion schedule. 17

18 Suppose that µ =1: In other words, none of the investments made in job A change the agent s productivity in job B. Then, the incentive payments in job B have no e ect on the incentives in joba.inthetwo-periodmodel,ifµ =1; then q1 0 = q 2 and, from (14), there will be no indirect incentive from the second period. Therefore, the incentive payments in job A and in job B will take the same form as the single job-level case analyzed in section 2.2. This implies that from Proposition 1, the wages will remain constant within a job-level until the last period of the joblevel. In the last period of the job-level, there will be incentive payments that do not depend on the past outcomes in the same job-level. It is straightforward to extend these results to more than two job-levels. Therefore, if all the investments are job-speci c (µ =1), then the (direct) incentive payments are provided only in the last period of each job-level. That is, it is optimal for the principal to provide direct incentive payments only with job-changes, i.e. with promotions, and in the last period of the contract. Note that the incentive payments with promotions are not one-time bonuses. Since the agent s utility function is the sum of the concave functions, the principal wants to smooth the agent s income path (utility-smoothing e ect). If the agent gets high (low) incentive payment in the last period of job A, then the subsequent utility from job B has to be equally high (low). In other words, if the agents receives an incentive payment u l (l =1; 2) inthelastperiodofjoba,then the constant utility payments in job B until the last period will be u l ; too. Therefore, the last period incentive payment in each job-level can be interpreted as a salary change. If 0 <µ<1; then some portion of the investments in job A will change the agent s productivity in job B. Therefore, the incentives in job B will provide indirect incentives for job A. Hence, the size of optimal incentives in the last period of job A will be reduced, but will be still positive since µ>0: Note that now there are incentive payments in job B even before the last period, if 0 <µ<1. 18

19 The reason is the following: Suppose that there are no incentive payments in some periods of job B. If the principal introduces a small amount of incentive payments in those periods, it will not change the cost for the principal in those periods (the second-order e ect), but it will reduce the incentives in the last period of job A and reduce costs (the rst-order e ect). It is easy to see that these within-job-level incentive payments will get larger in higher job-levels. These within-job-level incentive payments can be interpreted as bonuses or merit salary increases. By continuity, if µ is close to 1, then the optimal contract will be close to the optimal contract with µ =1: Therefore, under the full-commitment assumption, the following proposition will hold. Proposition 3 If µ is close to 1, then within a job-level, wages remain almost constant with small bonuses that are increasing in job-levels. Most incentives are provided by salary changes with promotions. Proof The proof follows from the discussion above. For 8µ 2 (0; 1]; Proposition 1 still holds in the optimal renegotiation-proof contract with a reasonable assumption. Note that when 0 <µ<1; the principal would provide the incentive payments in job B even before the last period in order to reduce the size of incentive payments in the last period of job A. However, providing incentive payments in job B before the last period is not renegotiation-proof. As shown in section 2.2, if the incentive constraints in the last period of job B are satis ed, then no direct incentives are required to induce investments in job B. Thus, once an agent gets promoted to job B, it is not optimal to provide incentives before the last period. Therefore, assuming that there is no randomization 14, it is not renegotiation-proof to provide incentives within a job-level before the last period of the job-level. 14 If an agent randomizes the investment in the last period of job A, it is renegotiation-proof for the principal to provide incentives in job B even before the last period. The reason is the following: if an agent randomizes investment in the last period of job A, it creates the adverse selection problem for the principal. Then, to separate two di erent types (one who invested and one who did not), the truth-telling conditions must be satis ed. It can 19

20 Proposition 4 In the optimal renegotiation-proof contract (without randomization), wages remain constant within a job-level and all the incentives are provided by salary changes with promotions, 8µ 2 (0; 1]: Proof The proof follows from the discussion above. Figure 1 describes these properties of the optimal contract. 15 [Figure 1 here] I can now explain the puzzles raised in the introduction. The rst puzzle asks why individual wages are attached to job-levels, not to individual performances. I have shown that for each individual, it is optimal to give a single constant wage in each job-level regardless of the realized outcomes, if the incentives for human capital investments are considered. The second puzzle asks why organizations use promotions as main incentive devices rather than using bonuses. Proposition 3 or 4 shows that if learning-by-doing or human capital investments are important, it is optimal to provide incentives using salary changes associated with promotions. be shown that the truth-telling conditions require the incentive payments in job B. Therefore, it is now optimal for the principal using incentive payments in job B to separate the two di erent types. The bene t of randomization is to reduce the size of the incentives in the last period of job A by introducing incentives in job B. The cost of the randomization is the no-investment by the agent with positive probability in the last period of job A. Since the principal will not promote the agent who did not invest, the loss from the ine cient job-assignment is another cost of the randomization. Therefore, the randomization will not be optimal if (i) the pro t loss from not investing in the last period of job A is large, (ii) the e ciency gain from promotion is large, and (iii) there are many remaining periods. 15 Note that the agent s utility payment can actually decrease with promotions if the outcomes are bad. The reason is the following: since the agent s utility function is the sum of a concave function, the principal wants to provide roughly the same expected utility in each period. Then, if the agent s utility increases due to high outcome, the agent s utility must decrease with bad outcomes. 20

21 Furthermore, in this model, the promotion decision is independent of the incentive decision. Therefore, the dual role of promotions as both assignment mechanisms and incentive mechanisms no longer remains a puzzle. I can also resolve the third puzzle: the large wage variations within a job-level, and especially overlapping wage distributions between adjacent job-levels.. Proposition 3 or 4 shows that even if each individual receives a single constant wage in each job-level, di erent individuals can receive di erent wages depending on the performances in their previous job-levels. This explains the wage variations within a particular job-level. Since an agent can receive smaller or even negative incentive payments with promotions if the outcomes are bad, there are wage-overlaps between joblevels and the real wage decline are not unusual. Therefore, individual wage dynamics resemble the stylized description of the wage structure with a single wage attached to each job-level. However, aggregated wage dynamics are consistent with the recent empirical ndings. This optimal contract also explains low-powered incentives. Many empirical studies nd that the size of actual incentives is much smaller than the standard agency model predicts (e.g. Medo and Abraham [1980]). Propositions 3 and 4 show that when learning-by-doing or investments are important, the optimal incentive scheme does not need large or frequent incentive payments (recall that the incentives given with promotions in the model are not the sum of delayed incentive payments). 2.4 Heterogeneous Agents The previous sections have demonstrated how the optimal incentive for (human capital) investment and the task assignment through promotions can explain the puzzles raised in the introduction. However, due to the homogeneity of the agents along the equilibrium path, all the agents get promoted at the same time regardless of their realized performance. The amount of salary increase with promotions provides the incentives, not the probability of promotion. However, in 21

22 reality, whether one gets promoted or not depends on one s performance. Furthermore, it is often observed that there is serial correlation between promotions (i.e. fast track). A simple way of explaining these aspects involves introducing heterogeneous agents, like Gibbons and Waldman [1999]. Suppose that there are two types of agents, one who accumulates the human capital quickly (i.e. fast learner) and the other who accumulates the human capital slowly (i.e. slow learner). Assume that the types are known both to the principal and to the agent (but not to the econometrician). Denote the probability of high outcome in time t by P t : Suppose that there are J jobs where an agent with P t 2 [P j ;P j+1 ) getting assigned to job j is the optimal (P j+1 >P j ): Then, as Gibbons and Waldman [1999] show, the fast learners will get, on average, higher outcomes than the slow learners, and the fast learners will get promoted consistently faster than the slow learners. Therefore, the agents with higher outcomes get promoted faster, and the promotions are serially correlated. Note that these promotion dynamics do not change any of the properties of the optimal contract presented in the previous sections. Since the principal can o er separate contracts to di erent types, the optimal contract design problem for each type is exactly the same as before. If the types are not known either to the principal nor to the agent, both will update the probability of high outcome, P t ; based on the history of the realized outcomes. Now assume that for the agent with E[P t jh t ] 2 [P j ;P j+1 ); getting assigned to job j is optimal (P j+1 >P j ): Then, high performance will raise the posterior expectation of P and lead to a promotion. Furthermore, a high type agent will, on average, continue to perform better than a low type agent, and will get promoted consistently faster. Therefore, performance based promotions and fast-tracks can be explained again. Since the wages are still determined by the incentive concerns analyzed previously, all the 22

23 qualitative results of Proposition 1-4 still hold even with heterogenous agents and learning. The previous propositions may not hold exactly due to the fact that an agent who did not invest will update his belief on type di erently from an agent who did invest. A di erence from Gibbons and Waldman [1999] is how wages are determined. In their model, human capital is general and wages are determined in the spot market. In our model, human capital is rm-speci c, and wages are determined by a long-term contract o ered by a principal. Which model is more appropriate in a speci c case is empirically testable as the two models provide di erent predictions on wage dynamics, as we will discuss in section 3.5 and Empirical Implications This section summarizes the empirical implications of the optimal contract, which provide the hypotheses for an empirical analysis. Two hypotheses immediately follow from Figure 1 and the discussion above. Hypothesis 1 (Incentives): Most incentives are given with promotions. The incentives associated with promotions increase with job-levels, hence the variance of the promotion premium also increases with job-levels. There are small within-job-level incentive payments that are increasing in tenure. Hypothesis 2 (Wages): Wages are closely related to job-levels, but there are cross-individual wage variations within job-levels. Wages overlap between adjacent job-levels, and real wage decline is common. The wage variations increase with higher job-levels. Since wages are constant within a job-level, the incentives in the end of each job-period will not depend on the past realized outcomes in the same job-level for utility-smoothing (memoryless property). As noted above, promotion is independent of incentives. Incentives are designed with 23

24 a given promotion schedule. With homogeneous workers in every period, the incentive payments depend only on the random component. Therefore, the promotees are uniformly distributed across the wage distribution in the lower job-level. However, if the agents are heterogenous, then from section 2.4, the agent with high innate ability will, on average, perform well consistently, which will result in higher wages and faster promotions through Bayesian update. Therefore, the promotees will come from the upper portion of the wage distribution in the lower job-level, and there will be serial correlations between promotions and also between wages. Hypothesis 3 (Promotions): Controlling for job-levels, promotion-based incentives depend only on recent performance. With homogenous workers, promotees come uniformly from all the quantiles of the wage distribution in the lower job-level. With heterogenous workers, promotees come from upper quantiles of the wage distribution in the lower job-level, and there are serial correlations between promotions and between wages. If the human capital in the model is rm-speci c, then this model can explain the key features of an internal labor market. Milgrom and Roberts (1992) characterize the internal labor market by the following key features: long-term employment relationships, limited ports of entry for hiring, career paths within the rm, and promotion from within. Another indication of an internal labor market is a cohort e ect ; if the labor market within a rm is shielded from external labor market conditions, then external labor market conditions will have an e ect only through new hiring. Then, the year of the worker s entry will have a signi cant e ect on wages. In the theoretical model, since a worker s human capital increases through learning (or through rm-speci c human capital investments), new workers cannot enter high job-levels directly. Therefore, all newcomers will enter the company through the lowest level and all the promotions will come from within. All these features are consistent with the key features of an internal labor market. The binding long-term contract also explains the cohort e ect. Since the reservation 24

25 wage at the time of signing the contract determines the overall wage level, if the reservation wages are di erent from year to year, the year of the entry creates wage di erentials. Such cohort e ects follow the movement of reservation wages, which can be approximated by industry average wages. Hypothesis 4 (Internal Labor Market) : Workers enter the rm at the lowest job-level (limited port-of-entry). The industry average wage at the time of entry determines the overall wage level (cohort e ect). Higher job-levels are lled by own workers from the lower level (promotions from within). The average employment duration is long (long-term employment relationships). 3 Empirical Analysis This section tests the hypotheses raised in the last section, using personnel records of health insurance claim processors in a large US insurance company operating in more than 42 states. The task individuals perform is computer data entry of the information on health insurance claims. The initial dataset comprises 5,888 processors over 910 day period (01/01/93-06/30/95). Of this group, I restrict the focus to 3,373 full-time employees working only on indemnity claims. 16 This dataset is ideal for the test since human capital accumulation is very important in this job and workers are relatively homogenous. The data mainly consist of productivity, compensation, demographic and organization datasets. The productivity dataset contains the (weighted) number of claims processed for each day. The compensation dataset has salary, salary change date, salary change reason, bonus, bonus date, overtime payment and overtime payment date information. The demographic dataset includes date of birth, date of hire, date of termination, termination reason, education, gender, marital 16 The rest of the processors work on HMO claims. From a workplace perspective, the nature of HMO claims processed at this company appears to be su ciently di erent from that of indemnity claims. Less than 0.5% of processors work on both indemnity and HMO claims. These processors are excluded. 25

26 status and residence zipcode. The organization dataset contains the job-code and the job-code change date. 17 In the next sub-section, I will describe the dataset in more detail, and then in the following sub-sections, analyze wages, incentives, promotions and the internal labor market. 3.1 Data A. Employees The employees in this study are health insurance claim processors. The average age of these 3,373 processors is just over 31 years. Almost 90% of them are female and 56% of them are married. The average annual compensation, including salary, bonus and overtime payment, is $22,003 (nominal). The average education level is 13.4 years. Almost 70% of these workers are high school graduates, and most in the remaining 30% have attained some education beyond high school. Therefore, these employees can be characterized as female, white-collar, non-managerial, service industry, full-time workers. Even though this group of employees is growing fast in the economy, few studies have been done on this group. See Table 1(a) for more details. B. Wages The compensation consists of salary, bonus and overtime payment. Even though these workers are all non-exempt, all are contracted for 37.5 weekly work-hours. The company sets and pays the compensation in terms of a salary instead of an hourly rate. 18 The average annual salary is $20, On average, the salary changes every 6 months either by merit or by promotion. 17 We also have data on health insurance claims by these processors. It opens up a possibility to look at the relationship between health and productivity in a micro-level. This avenue of research is being pursued by Berndt, et.al. 18 The precise number of hours spent at work is not clocked by this company on a daily basis. However, the timing and amount of overtime pay per bi-weekly period are recorded. 19 Note that these employees are quite di erent from those studied in BGH(Baker, Gibbs and Holmstrom 1994a,b) 26