Aggregation and linearity in the provision of intertemporal incentives
01 Mar 1987-Econometrica (Institute for Mathematical Studies in the Social Sciences, Stanford Univ.)-Vol. 55, Iss: 2, pp 303-328
TL;DR: In this paper, the authors consider the problem of providing incentives over time for an agent with constant absolute risk aversion, and find that the optimal compensation scheme is a linear function of a vector of accounts which count the number of times that each of the N kinds of observable events occurs.
Abstract: We consider the problem of providing incentives over time for an agent with constant absolute risk aversion. The optimal compensation scheme is found to be a linear function of a vector of N accounts which count the number of times that each of the N kinds of observable events occurs. The number N is independent of the number of time periods, so the accounts may entail substantial aggregation. In a continuous time version of the problem, the agent controls the drift rate of a vector of accounts that is subject to frequent, small random fluctuations. The solution is as if the problem were the static one in which the agent controls only the mean of a multivariate normal distribution and the principal is constrained to use a linear compensation rule. If the principal can observe only coarser linear aggregates, such as revenues, costs, or profits, the optimal compensation scheme is then a linear function of those aggregates. The combination of exponential utility, normal distributions, and linear compensation schemes makes computations and comparative statics easy to do, as we illustrate. We interpret our linearity results as deriving in part from the richness of the agent's strategy space, which makes it possible for the agent to undermine and exploit complicated, nonlinear functions of the accounting aggregates.
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TL;DR: In this article, a principal-agent model that can explain why employment is sometimes superior to independent contracting even when there are no productive advantages to specific physical or human capital and no financial market imperfections to limit the agent's borrowings is presented.
Abstract: Introduction In the standard economic treatment of the principal–agent problem, compensation systems serve the dual function of allocating risks and rewarding productive work. A tension between these two functions arises when the agent is risk averse, for providing the agent with effective work incentives often forces him to bear unwanted risk. Existing formal models that have analyzed this tension, however, have produced only limited results. It remains a puzzle for this theory that employment contracts so often specify fixed wages and more generally that incentives within firms appear to be so muted, especially compared to those of the market. Also, the models have remained too intractable to effectively address broader organizational issues such as asset ownership, job design, and allocation of authority. In this article, we will analyze a principal–agent model that (i) can account for paying fixed wages even when good, objective output measures are available and agents are highly responsive to incentive pay; (ii) can make recommendations and predictions about ownership patterns even when contracts can take full account of all observable variables and court enforcement is perfect; (iii) can explain why employment is sometimes superior to independent contracting even when there are no productive advantages to specific physical or human capital and no financial market imperfections to limit the agent's borrowings; (iv) can explain bureaucratic constraints; and (v) can shed light on how tasks get allocated to different jobs.
5,678 citations
Cites background from "Aggregation and linearity in the pr..."
...A special case of this, discussed in Holmstrom and Milgrom (1987),occurs when the agent acts on private information (to avoid adverse selection, one assumes that the information is observed after contracting)....
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...A remarkable fact, which we established in Holmstrom and Milgrom (1987), is that these trvo simplifiing assumptions are exactly offsetting in this model....
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TL;DR: This paper found that higher sensitivity of CEO wealth to stock volatility (vega) implements riskier policy choices, including relatively more investment in R&D, less investment in PPE, more focus, and higher leverage.
2,476 citations
Additional excerpts
...Along these lines, prior studies that use vega as the 1See Holmstrom (1979), Mirrlees (1976), Holmstrom and Milgrom (1987), as well as the survey of Murphy (1999), for various interpretations of the principal-agent problem....
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Book•
26 Dec 2001
TL;DR: Laffont and Martimort as mentioned in this paper focus on the principal-agent model, the "simple" situation where a principal, or company, delegates a task to a single agent through a contract, the essence of management and contract theory.
Abstract: Economics has much to do with incentives--not least, incentives to work hard, to produce quality products, to study, to invest, and to save. Although Adam Smith amply confirmed this more than two hundred years ago in his analysis of sharecropping contracts, only in recent decades has a theory begun to emerge to place the topic at the heart of economic thinking. In this book, Jean-Jacques Laffont and David Martimort present the most thorough yet accessible introduction to incentives theory to date. Central to this theory is a simple question as pivotal to modern-day management as it is to economics research: What makes people act in a particular way in an economic or business situation? In seeking an answer, the authors provide the methodological tools to design institutions that can ensure good incentives for economic agents. This book focuses on the principal-agent model, the "simple" situation where a principal, or company, delegates a task to a single agent through a contract--the essence of management and contract theory. How does the owner or manager of a firm align the objectives of its various members to maximize profits? Following a brief historical overview showing how the problem of incentives has come to the fore in the past two centuries, the authors devote the bulk of their work to exploring principal-agent models and various extensions thereof in light of three types of information problems: adverse selection, moral hazard, and non-verifiability. Offering an unprecedented look at a subject vital to industrial organization, labor economics, and behavioral economics, this book is set to become the definitive resource for students, researchers, and others who might find themselves pondering what contracts, and the incentives they embody, are really all about.
2,454 citations
TL;DR: In this paper, the authors developed a simple equilibrium model of CEO pay and found that a CEO's pay changes one for one with aggregate firm size, while changing much less with the size of his own firm.
Abstract: This paper develops a simple equilibrium model of CEO pay. CEOs have different talents and are matched to firms in a competitive assignment model. In market equilibrium, a CEO’s pay changes one for one with aggregate firm size, while changing much less with the size of his own firm. The model determines the level of CEO pay across firms and over time, offering a benchmark for calibratable corporate finance. The sixfold increase of CEO pay between 1980 and 2003 can be fully attributed to the six-fold increase in market capitalization of large US companies during that period. We find a very small dispersion in CEO talent, which nonetheless justifies large pay differences. The data broadly support the model. The size of large fi rms explains many of the patterns in CEO pay, across firms, over time, and between countries. (JEL D2, D3, G34, J3)
1,959 citations
Cites background from "Aggregation and linearity in the pr..."
...Jensen and Murphy (1998) and Hall and Liebman (2000), estimate empirical pay-performance measures....
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TL;DR: In this paper, the authors examine a potential agency conflict between mutual fund investors and mutual fund companies, where investors would like the fund company to use its judgment to maximize risk-adjusted fund retraction.
Abstract: This paper examines a potential agency conflict between mutual fund investors and mutual fund companies. Investors would like the fund company to use its judgment to maximize risk‐adjusted fund ret...
1,752 citations
References
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Book•
01 Jan 1968
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Abstract: Weak Convergence in Metric Spaces. The Space C. The Space D. Dependent Variables. Other Modes of Convergence. Appendix. Some Notes on the Problems. Bibliographical Notes. Bibliography. Index.
13,153 citations
TL;DR: In this article, the role of imperfect information in a principal-agent relationship subject to moral hazard is considered, and a necessary and sufficient condition for imperfect information to improve on contracts based on the payoff alone is derived.
Abstract: The role of imperfect information in a principal-agent relationship subject to moral hazard is considered. A necessary and sufficient condition for imperfect information to improve on contracts based on the payoff alone is derived, and a characterization of the optimal use of such information is given.
7,964 citations
TL;DR: In this paper, the authors make the following simplifying assumptions: (1) Intertemporal problems are ignored; (2) the tax system that would bring about that result would completely discourage unpleasant work; and (3) what such a tax schedule would look like; and what degree of inequality would remain once it was established.
Abstract: you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We enable the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org. 1. INTRODUCTION One would suppose that in any economic system where equality is valued, progressive income taxation would be an important instrument of policy. Even in a highly socialist economy, where all who work are employed by the State, the shadow price of highly skilled labour should surely be considerably greater than the disposable income actually available to the labourer. In Western Europe and America, tax rates on both high and low incomes are widely and lengthily discussed3: but there is virtually no relevant economic theory to appeal to, despite the importance of the tax. Redistributive progressive taxation is usually related to a man's income (or, rather, his estimated income). One might obtain information about a man's income-earning potential from his apparent I.Q., the number of his degrees, his address, age or colour: but the natural, and one would suppose the most reliable, indicator of his income-earning potential is his income. As a result of using men's economic performance as evidence of their economic potentialities, complete equality of social marginal utilities of income ceases to be desirable, for the tax system that would bring about that result would completely discourage unpleasant work. The questions therefore arise what principles should govern an optimum income tax; what such a tax schedule would look like; and what degree of inequality would remain once it was established. The problem seems to be a rather difficult one even in the simplest cases. In this paper, I make the following simplifying assumptions: (1) Intertemporal problems are ignored. It is usual to levy income tax upon each year's income, with only limited possibilities of transferring one year's income to another for tax purposes. In an optimum system, one would no doubt wish …
4,157 citations
Posted Content•
TL;DR: In this paper, the authors study moral hazard with many agents and focus on two features that are novel in a multiagent setting: free riding and competition, and show that competition among agents (due to relative evaluations) has merit solely as a device to extract information optimally.
Abstract: This article studies moral hazard with many agents. The focus is on two features that are novel in a multiagent setting: free riding and competition. The free-rider problem implies a new role for the principal: administering incentive schemes that do not balance the budget. This new role is essential for controlling incentives and suggests that firms in which ownership and labor are partly separated will have an advantage over partnerships in which output is distributed among agents. A new characterization of informative (hence valuable) monitoring is derived and applied to analyze the value of relative performance evaluation. It is shown that competition among agents (due to relative evaluations) has merit solely as a device to extract information optimally. Competition per se is worthless. The role of aggregate measures in relative performance evaluation is also explored, and the implications for investment rules are discussed.(This abstract was borrowed from another version of this item.)
4,125 citations
"Aggregation and linearity in the pr..." refers result in this paper
...In general, y is used to reduce risk in accordance with earlier results on relative performance evaluation (see Holmstrom, 1982)....
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TL;DR: In this article, a notion of "favorableness" of news is introduced, characterized, and applied to four simple models: the arrival of good news about a firm's prospects always causes its share price to rise, more favorable evidence about an agent's effort leads the principal to pay a larger bonus, buyers expect that any product information withheld by a salesman is unfavorable to his product, and bidders figure that low bids by their competitors signal a low value for the object being sold.
Abstract: This is an article about modeling methods in information economics. A notion of "favorableness" of news is introduced, characterized, and applied to four simple models. In the equilibria of these models, (1) the arrival of good news about a firm's prospects always causes its share price to rise, (2) more favorable evidence about an agent's effort leads the principal to pay a larger bonus, (3) buyers expect that any product information withheld by a salesman is unfavorable to his product, and (4) bidders figure that low bids by their competitors signal a low value for the object being sold.
3,092 citations