انگیزه پویا و بازنشستگی

This paper examines multi-period compensation contracts when retirement is anticipated. Short-term contracts in long-term employment relationships are equivalent to a long-term renegotiation-proof contract. The dynamic of incentive rates is determined by (i) how and in which periods managerial effort affects the contractible performance measures; and by (ii) the time-series correlation of error terms in performance reports. The model explains why long-term investments can decrease while incentive rates increase as managers approach retirement. Earnings persistence is negatively associated to earnings-based incentive rates but, towards retirement, high earnings persistence implies increasing earnings-based incentive rates.

This paper presents a LEN (linear contracts, exponential utility, normal distributions) model of multi-period compensation contracts subject to renegotiation when the manager's retirement date is fixed. The incentives are characterized by either a long-term renegotiation-proof contract or by an equivalent sequence of short-term contracts subject to interim participation constraints. The optimal incentives are subject to a renegotiation-proofness constraint and are determined by two key characteristics of the performance measures used in contracting: (i) how and in which periods managerial effort affects the performance measures; and (ii) the time-series correlation of error terms in the performance measures. The impact of performance measures’ characteristics on multi-period compensation arrangements with a fixed retirement date reflects institutional features not properly considered in the existing compensation literature. First, managerial effort in one period may affect cash flows and performance measures in the current and future periods. This is explicitly modelled as long-term effort, defined as effort in one period that affects performance measures in subsequent periods. For example, managers seek and decide on new capital investments, new directions for research and product development, strategies for developing brands and customer relations, and employee training programs. The manager's effort leads then to the corresponding investment in capital assets, R&D, etc. Stock prices are more timely than earnings in recognizing the impact of these investments on firm value. Furthermore, under U.S. GAAP, accounting asset recognition rules determine how investments are treated for financial reporting purposes: investments in property, plant, and equipment are capitalized and expensed over time, investments in R&D, advertising, and human capital development are immediately expensed. 1 Modelling long-term effort allows exploration of the dependence of compensation arrangements on the effects of current effort on future cash flows, the timeliness of the performance measure, and the time until the agent retires. Second, the persistence in performance measures of random factors outside the manager's control is modelled as autocorrelation of error terms in the performance measures. For example, earnings can be highly persistent, with error terms following a random walk, but can also have low persistence due to reversing accrual estimation errors (such as underestimates of the allowance for bad debts, or conservative biases in estimating future gains/losses, which are later corrected). Modelling the autocorrelation of error terms in performance measures allows exploration of the dependence of compensation arrangements on earnings persistence and the time until the agent retires. Third, while CEO contracts are renewed after an interval of one to five years, employment relationships extend over multiple periods, and a majority of turnovers are retirements.2 Finally, compensation committees set salary and bonus payments every year, while long-term compensation such as stock option grants are subject to renegotiation. Even when long-term contracts are used, their three to five year terms are generally shorter than a CEO's tenure with the firm; while the CEO can, in principle, leave, he rarely does so, and the board ensures retention by benchmarking of salary and other compensation.3 These various compensation arrangements are explicitly modelled as either a sequence of short-term contracts or as a long-term contract subject to renegotiation, with a fixed retirement date for the manager. This allows exploration of explicit and effective incentives in multi-period compensation arrangements as a function of the performance measures characteristics discussed above and the time until the agent retires. The key results are as follows. First, short-term contracts and implicit commitment to long-term employment provide the same effective incentives and induce the same managerial effort as a renegotiation-proof contract. As a result, renegotiation-proof incentive rates are independent of how compensation is paid over time through short-term contracts. Second, limited commitment arising from institutional restrictions on contract form or duration, or from the inability of contracting parties to commit ex ante not to renegotiate ex-post to an efficient contract has three key consequences for incentives: learning, effort externalities, and compensation risk externalities. I discuss these consequences of renegotiation next. Performance measures can be used to update beliefs, or learn, about persistent uncertain components of performance (such as managerial ability). Renegotiation offers are therefore based on more precise updated beliefs about the contractible performance measures; decreasing posterior variances then allow the principal to set increasing incentive rates without increasing compensation risk. Effort and risk externalities arise because the principal is unable to commit to future incentive rates and cannot “cooperate with himself” in setting incentive rates at different points in time (“An externality is […][…] defined as the effect of one person's decision on someone who is not a party to that decision.”, Coase, 1988, p. 24). Effort externalities arise, for example, when managerial effort positively influences reported performance in the current and subsequent periods, anticipated positive incentive rates on future performance provide motivation and allow the principal to set a lower incentive rate, and thus a lower risk premium, to motivate the same or higher level of effort in the current period. Risk externalities arise, for example, when positive covariance between current and future performance measures requires the principal to lower current incentive rates to avoid imposing too much compensation risk on the agent, thus reducing the level of induced effort.4 The model has several empirical implications. First, effective incentive rates, defined as the sensitivities of aggregate compensation over a manager's tenure to performance, are a better estimate of incentives than the commonly estimated explicit incentive rates, defined as the sensitivity of compensation in one period to performance in the same period, because the latter are affected by implicit incentives. The effective and explicit incentives generally differ, if the performance measures are correlated over time; in this case, performance in one period may impact future performance benchmarks, thus generating implicit incentives (for example, the “ratchet effect” in Indjejikian and Nanda, 1999). 5 Second, if the manager's long-term effort positively affects performance over multiple periods, towards the manager's retirement, positive effort externalities decrease, the principal partially compensates by increasing effective incentives, but managerial effort still decreases. Thus long-term effort, and the associated long-term investment, are negatively related to the effective incentive rates. For example, managerial effort on capital investments, and thus capital expenditures, are predicted to decrease, while effective incentive rates increase when compensation is based on either earnings or stock prices. Similarly, managerial effort on investments that result in internally generated intangible assets (R&D, advertising, employee training), and the associated expenditures, are predicted to decrease, while the effective incentive rates increase, when compensation is based relatively more on stock prices.6 Third, effort and effective incentive rates based on positively correlated performance measures (such as earnings with high persistence, or quality) increase towards retirement, while effort and effective incentive rates based on negatively correlated performance measures (such as earnings with low persistence, or quality) decrease towards retirement. The paper makes two contributions to the literature on dynamic agency. First, it proves that short-term contracts with implicit commitment to long-term employment are equivalent to a long-term renegotiation-proof contract. This generalizes Meyer and Vickers (1997) to multiple periods, long-term effort, and general performance measures. Second, the paper derives the optimal structure of incentives over a manager's tenure or career as a function of the sensitivities of performance measures to effort over multiple periods and the time-series correlations of error terms in the performance measures. This generalizes Şabac (2007) to include long-term effort. The paper fills a gap in the compensation literature by providing a theory which explains optimal incentives when the manager commits to work until retirement at the firm, does not leave for another firm, and cannot be dismissed before retirement. A fixed, rationally anticipated, retirement date is consistent both with executive compensation contracts and the majority of observed turnovers. After an initial three to five year term, contracts are automatically extended for another term and retirement ages are commonly specified in CEO contracts. While there are 158 sudden deaths and departures in which the CEO or another senior executive was raided by another firm in Hayes and Schaefer (1999) (6% of turnovers between 1979 and 1994), there are 1035 (77% of 1344 total CEO turnovers in the comparable period 1971–1994) voluntary turnovers in Huson et al. (2004).7 A fixed retirement date can be the result of many factors: deferred compensation and benchmarking of compensation ensure managerial retention; “golden parachutes” commit the employer not to dismiss the manager early; an equilibrium retirement date that is rationally anticipated by all parties, is renegotiation-proof, and no different from a fixed retirement date. For example, the retirement date could be determined by an optimal tenure/turnover policy as described in Şabac (2007), where in many cases it is optimal to retain the manager as long as possible, that is until age-related retirement. Research on CEO incentives and performance has primarily focused on the association between declining performance and forced CEO turnovers, despite the fact that most CEO turnovers are retirements, see Brickley (2003) and the references therein. Gibbons and Murphy (1992) use a career concerns model to predict increasing incentives and performance towards retirement, but their empirical evidence provides only weak support for the model. Furthermore, Huson et al. (2004) find evidence of declining performance prior to voluntary CEO turnovers. A related issue to which the findings of this paper apply is the horizon problem: CEOs reduce long-term investments in anticipation of retirement when the benefits of such investments (and the associated compensation) are realized after retirement. The empirical evidence is contradictory: Dechow and Sloan (1991) find evidence in support of the horizon problem prior to retirement, while Cheng (2004) does not. Murphy and Zimmerman (1993) argue that both CEO turnover and declines in long-term investments are determined by exogenous poor firm performance. Thus, while the majority of CEO turnovers are retirements, the empirical evidence on performance and incentives around turnover is contradictory and inconsistent with the one theoretical model by Gibbons and Murphy (1992). The paper is closest to and extends the model in Şabac (2007) to include long-term managerial effort. The paper is also related to and generalizes Christensen et al., 2003b and Christensen et al., 2005 to multiple periods and long-term effort. The relation between explicit incentive rates over time for short-term contracts generalizes the analysis of the “ratchet effect” in Indjejikian and Nanda (1999) to multiple periods and general time-series correlation of performance measures. The analysis of how the time-series correlation of performance measures impacts incentive rates extends Christensen et al. (2005) to multiple periods, and the career concerns model of Gibbons and Murphy (1992) to include general time-series correlations and performance measures. The LEN model in the paper is based on Dutta and Reichelstein (1999) and uses the renegotiation-proofness principle for LEN models proved by Şabac (2007).8 The paper provides guidance for empirical research on the link between executive performance and turnover for those cases when turnover is retirement and the retirement date is fixed and publicly known. The paper also provides insights on the inter-temporal effects that have to be considered in the design of multi-period compensation, and should be of interest to both academic researchers and compensation committees and consultants.

In this paper I examine how the multi-period sensitivity of performance measures to managerial effort and the time-series correlation of error terms in performance measures determine the structure of multi-period compensation in an agency model that incorporates two key features: (i) the CEO's retirement date is fixed and rationally anticipated; and (ii) compensation is either set annually (such as salary and bonus) or provided through long-term incentive plans subject to renegotiation (such as long-term cash incentives or options). The analysis is based on a multi-period LEN agency model with renegotiation and a fixed retirement date for the agent. The main findings are that (i) short-term contracts with implicit commitment to multi-period employment are equivalent to a long-term renegotiation-proof contract; (ii) contract renegotiation impacts incentive rates through three dynamic effects: learning, effort externalities, and risk externalities. I illustrate these dynamic effects separately through a series of examples. The equivalence of short-term contracts to a long-term renegotiation-proof contract implies that the renegotiation-proof incentive rates are independent of how compensation may be paid through short-term contracts over multiple periods. As a result, effective incentive rates can be estimated empirically without having to control for implicit incentives in a regression of aggregate compensation over time on performance. Learning is the reduction in the performance measures’ variance resulting from observing the history of realized performance. Renegotiation allows the principal to incorporate learning into contracts, lower risk is imposed on the agent for the same level of incentive rates, which allows the principal to increase both the incentive rates and the induced effort. Effort externalities arise whenever the agent's actions in one period impact the performance measures over subsequent periods, so that current agent effort is determined both by current incentives, and by future incentives that will be set ignoring current effort as sunk. If the incentives for long-term investment effort are based on performance measures that gradually incorporate the net benefit of the investment effort over time, future periods provide positive effort externalities for the current period and allow a lower incentive rate to induce a higher level of effort. Such is the case generally when the incentives are primarily based on stock prices; when incentives are primarily based on earnings, the implication holds only for capital investments. A reduction in positive effort externalities leads to increasing incentive rates and decreasing investment towards retirement. As a result, incentive rates and the level of investment are negatively related when the CEO nears retirement. If the incentives are based on performance measures that are reduced by managerial effort in the current period, with the benefits recognized only in subsequent periods, the incentive rates are negative, future periods provide negative effort externalities for the current period, and the principal is forced to use a lower (negative) incentive rate to induce lower effort in the current period. This case corresponds to using only reported earnings to motivate investments in internally generated intangible assets (such as R&D, advertising, or employee training), because the costs of such investments is immediately expensed in earnings. A reduction in negative effort externalities leads to increasing incentive rates and investment towards retirement. Risk externalities arise when the performance measures are correlated over time, so there is covariance compensation risk. Positive correlation of performance measures increases compensation risk through the covariance of compensation across multiple periods; as a result, with fewer periods until retirement, the covariance component of compensation risk decreases and allows for higher incentive rates and induced effort. Negative correlation of performance measures has the opposite effect: it decreases the covariance component of compensation risk across multiple periods; as a result, with fewer periods until retirement the covariance component of compensation risk increases and leads to lower incentive rates and induced effort. The error terms in earnings with high persistence follow a random walk and imply increasing incentive rates towards retirement. The error terms in earnings with low persistence—due to reversible accrual estimation errors—are negatively correlated and imply decreasing incentive rates towards retirement. Risk externalities also determine implicit and explicit incentive rates through a “ratchet effect” as described by Indjejikian and Nanda (1999). If performance benchmarks in short-term contracts are set equal to expected performance and the performance measures are positively correlated over time, higher current effort increases future performance benchmarks. As a result, a lower level of effort is induced with a higher incentive rate, and effort increases while explicit incentive rates decrease towards retirement. With negatively correlated performance measures, the ratchet effect works in reverse, and effort decreases while explicit incentive rates increase towards retirement. To examine the link between performance measure characteristics and the dynamic of incentive rates, I have excluded multiple managerial tasks and multiple performance measures. A natural extension of the model would include both multiple tasks and performance measures and could provide further insights on relative incentive weights in a dynamic setting. The model could also be extended to include either implicit contracts on performance measures observed only by firm insiders as in Hayes and Schaefer (2000) or earnings management driven by changes in incentive rates over time as in Liang (2004).