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...principle is, any equilibrium with renegotiation can be implemented with a renegotiation-proof contract) in a dynamic LEN (linear contracts, exponential utility, normal distributions) model with renegotiation that generalizes Christensen et al. (2005). Second, it provides a general recursive solution for an N-period agency with renegotiation and (arbitrarily) correlated performance measures that generalizes Gibbons and Murphy (1992), Christensen et al. (2003a, 2005), and Dutta and Reichelstein (1999). Third, this paper characterizes optimal managerial tenure/turnover policies as a function of the time-series properties of performance measures.
Declining managerial performance prior to managerial turnover is usually interpreted in support of the theory that poor performance leads to forced turnover (see Murphy and Zimmerman 1993, Huson et al. 2001, Engel et al. 2003, Huson et al. 2004, and the references therein). This view of managerial tenure is based on the "common sense [...] that when an organization is performing poorly, replacement of the manager might be expected" (Salancick and Pfeffer 1980, p. 653). Others argue that CEO power determines the link between pay and performance, and tenure in office. For example, Hill and Phan (1991) present evidence that the pay/performance link for a CEO weakens with increased CEO tenure and attribute this to an increase in the CEO's power. Hermalin and Weisbach (1998) develop an analytical model of CEO performance, board of directors selection, and CEO turnover in which endogenous turnover is associated with poor performance--given that the CEO's power is based on perceived ability, which in turn is based on observed past performance.
Commenting on the existing empirical evidence on managerial turnover and firm performance, Brickley (2003, p. 232) writes: "[...] we have probably reached a point of diminishing returns in estimating logit models that focus on the relation between CEO turnover and firm performance measures." In the same discussion paper, Brickley points to the fact that age is a better explanatory variable for CEO turnover than firm performance. Moreover, Huson et al. (2004) find that firm performance declines prior to CEO turnover even for normal retirements, which are the majority of turnovers in their sample (almost three quarters). (2) These empirical facts raise the question of what may determine these nonforced turnovers.
This paper offers optimal managerial tenure as a possible alternative to performance-driven turnover. Thus, the proposed explanation to why age-related turnover dominates is that it is optimal in those cases to retain the manager until retirement age. But what is optimal for a manager's tenure, and what determines it? In a qualitative model of CEO tenure, Hambrick and Fukutomi (1991) raise the question of optimal managerial tenure, but do not pursue the issue other than discussing some trade-offs which are expected to determine optimal CEO tenure with a firm. In this paper, I use an N-period LEN moral hazard model in which the time-series properties of performance measures used in incentive contracts determine optimal managerial turnover policies. (3)
The LEN model is based on Dutta and Reichelstein (1999), and extends Christensen et al. (2003a, 2005) to N periods. Developing a multiperiod moral hazard model is necessary both for the analysis of managerial tenure and turnover, and for the analysis of the related question of incentives and performance dynamics. (4)
This paper contributes to the literature on multiperiod LEN models first by proving the renegotiation-proofness principle in the "standard" LEN model. This result is a generalization to multiple periods and time-additive agent utility of Christensen et al. (2005), who prove the renegotiation-proofness principle for a two-period LEN model with single consumption date multiplicative agent utility. (The renegotiation-proofness principle is well known for optimal contracts; see, for example, Fudenberg and Tirole 1990 and Brennan and Watson 2002: renegotiation-proof contracts are sufficient in characterizing equilibria with renegotiation.) Gibbons and Murphy (1992), Sliwka (2002), and Dutta and Reichelstein (2003) all use renegotiation-proof linear contracts, but do not provide a proof for their sufficiency given the linear contract restriction.
The second contribution is to provide a general solution to the agency problem under renegotiation, given performance measures with arbitrary time-series properties. The general solution to the agency problem allows for considering a variety of performance measurement systems, in particular, negatively auto-correlated accounting-based performance measures, and highlights the different implications of using different performance measurement systems. By contrast, Gibbons and Murphy (1992) and other related papers are restricted to a single performance measure structure corresponding to the career concerns model of Holmstrom (1999).
In addition to the managerial tenure questions considered in this paper, a multiperiod model allows for a separation between learning effects at the start of a manager's tenure and horizon effects at the end of the manager's tenure. These two main effects determining the dynamic of managerial incentives are due to: (a) observing the history of performance measures (the learning effect), which leads to changes in the posterior variances of the performance measures; and (b) the anticipation of future contractual terms (the horizon effect). Sabac (2006) further pursues the analysis of dynamic incentives when the performance measures are intertemporally correlated and the manager takes long-term actions.
Intertemporal correlation of the performance measures implies that the solution to the agency problem is not a simple repetition of the single-period contract, in particular, the sufficient conditions of Fudenberg et al. (1990) for short-term contracts to replicate long-term contracts are not satisfied. Institutional restrictions on contract form or duration, or the inability of parties to commit to not renegotiate, has been recognized as a key feature of a dynamic agency (see, for example, Hart and Tirole 1988, Dewatripont 1989, Fudenberg and Tirole 1990, Hermalin and Katz 1991, Ma 1994, Dewatripont and Maskin 1995). Demski and Frimor (2001) also examine the impact of repeated renegotiation in more than two periods and find that the negative effects of renegotiation are reduced by adding more periods. However, they are mainly concerned with "earnings management" and assume independent periods, while I exogenously assume that the agent has no control over the reporting of performance measures and focus on their inter-temporal correlation. (5)
To determine optimal managerial tenure, I consider three specific cases: an auto-regressive structure, a career concerns model with learning of a productivity parameter, and an accounting model that allows for reversible accruals. (6) The main findings on managerial tenure are as follows. First, the principal's welfare is increasing in managerial tenure if the performance measures are negatively correlated (in the accounting model). This finding suggests that normal retirement is optimal given negatively correlated performance measures, consistent with the view that negatively correlated performance measures are generally preferred in a dynamic agency (see Christensen et al. 2005), with the use of accounting-based performance measures, and with normal retirement as a dominant form of managerial turnover. Second, in all models with positive correlation, within a certain range of managerial switching costs, there exists interior optimal tenure. If the switching costs are high, the principal's preferences are for retaining the manager indefinitely, while if they are small enough, switching agents every period dominates.
The issue of optimal turnover has been addressed in two-period models. Dutta and Reichelstein (2003) compare contracting with a single agent over two periods under full commitment and contracting with two agents over the same two periods in a slightly different LEN model with long-term investments. They characterize conditions under which long-term/short-term contracts are preferred by the principal. In a two-period version of the setting considered in this paper, Christensen et al. (2003a, footnote 2) point out that the principal prefers agent turnover every period if and only if the performance measures are positively correlated. Christensen and Feltham (2005, Chapter 28) extend that analysis to include productivity information and quadratic contracts, and show how the principal's preferences for managerial turnover may be reversed for high positive correlation of the performance measures. Two-period models do not allow for interior tenure and we cannot infer from them how the principal's surplus changes with managerial tenure. Thus, the finding that switching costs are necessary, but not sufficient for interior tenure, and the examples of interior tenure, do require a dynamic agency model with multiple periods.
The remainder of this paper is organized as follows. Section 2 presents the model, and [section]3 presents the result on renegotiation-proof contracts, together with the optimal linear renegotiation-proof contract. Section 4 presents the analysis for managerial tenure. Section 5 concludes the paper. Appendix A gives a detailed analysis of the information structures used, Appendix B contains the proofs of Propositions 1 and 2, and the remaining proofs are in the online appendix (provided in the e-companion). (7)
2. The Principal-Agent Model
A risk-neutral principal owns a production technology that requires effort [a.sub.t] from an agent in each of N periods, t = 1,..., N. The agent's utility is time additive with multiplicatively separable effort cost [u.sub.t](q) = -[[summation].sub.k=t.sup.[infinity]] [[gamma].sup.k-t] exp(-[
.r]([q.sub.k] - [1/2][a.sub.k.sup.2])) for a consumption stream q = ([q.sub.t], [q.sub.t+1],...), where [q.sub.t] represents the agent's consumption at date t, the start of period t + 1, [1/2][a.sub.t.sup.2] is the agent's personal effort cost in period t, and [
.r] is the agent's risk aversion. The discount rate [gamma] = (1 + i)[.sup.-1] is the same for the principal and the agent and the agent can freely borrow or lend at rate i. The output [z.sub.t] from agent's effort [a.sub.t] [member of] R in period t has expected value E[[z.sub.t]] = [b.sub.t][a.sub.t]. Neither the outcomes [z.sub.t] nor the agent's actions [a.sub.t] are observable, hence neither is contractible. (8) A contractible performance measure [x.sub.t] is observed at the end of each period. The agent's effort in period t affects only the mean of the performance measure in that period, [x.sub.t] = [m.sub.t][a.sub.t] + [[epsilon].sub.t], where [[epsilon].sub.t] are mean zero noise terms that are joint normally distributed.
For each 1 [less than or equal to] t [less than or equal to] N, let [[a.bar].sub.t] = ([a.sub.1],..., [a.sub.t]), and [[x.bar].sub.t] = ([x.sub.1],..., [x.sub.t]) denote the histories of actions and performance for the first t periods. I use the notation [E.sub.t][dot] for the conditional expectation given history [[x.bar].sub.t] and co[v.sub.t]([dot], [dot]) for the conditional covariance given history [[x.bar].sub.t]. The conditional variance of [x.sub.t] given history [[x.bar].sub.t-1] is denoted [[sigma].sub.t.sup.2] = var([x.sub.t] | [[x.bar].sub.t-1]). (9)
Let [w.sub.t] denote the agent's compensation at date t (at the end of period t). After date N, the agent retires, provides no more productive effort, and receives no further compensation. Let [W.sub.t] represent the net present value (NPV) of future compensation discounted to date t for each employment date t = 1,..., N: [W.sub.t] = [[summation].sub.k=t.sup.N] [[gamma].sup.k-t] [w.sub.k]. Similarly, let [K.sub.t] represent the present value of future effort cost at date t: [K.sub.t] = [1/2][[summation].sub.k=t.sup.N] [[gamma].sup.k-t][a.sub.k.sup.2]. Because I assume that both the principal and the agent can borrow and lend at the same rate, the timing of the agent's compensation does not affect either the principal's or the agent's utility, provided the present value of total compensation at a fixed date is constant.
The agent's compensation is...
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