In economics, contract theory studies
how economic actors can and do construct contractual arrangements, generally in
the presence of asymmetric
information. Because of its connections with both agency and incentives, contract theory is often
categorized within a field known as Law and economics. One prominent application of
it is the design of optimal schemes of managerial compensation. In the field of economics,
the first formal treatment of this topic was given by Kenneth Arrow in the 1960s. In 2016, Oliver Hart
(economist) and Bengt R. Holmström both received the Nobel Memorial Prize in Economic Sciences for their work on contract
theory, covering everything from CEO pay to privatisations.
A standard practice in the
microeconomics of contract theory is to represent the behaviour of a decision
maker under certain numerical utility structures, and then apply an optimization
algorithm to identify optimal decisions. Such a procedure has been used in the
contract theory framework to several typical situations, labeled moral hazard, adverse selection and signalling. The spirit of these models
lies in finding theoretical ways to motivate agents to take appropriate
actions, even under an insurance contract. The main results achieved through
this family of models involve: mathematical properties of the utility structure
of the principal and the agent, relaxation of assumptions, and variations of
the time structure of the contract relationship, among others.
It is customary to model people as maximizers of some von Neumann–Morgenstern utility functions, as stated by expected
utility theory.
Moral hazard
In moral hazard models, the information
asymmetry is the principal's inability to observe and/or verify
the agent's action. Performance-based contracts that depend on observable and
verifiable output can often be employed to create incentives for the agent to
act in the principal's interest. When agents are risk-averse, however, such
contracts are generally only second-best because incentivization precludes full insurance.
If the agent is risk-neutral and there are no bounds
on transfer payments, the fact that the agent's effort is unobservable (i.e.,
it is a "hidden action") does not pose a problem. In this case, the
same outcome can be achieved that would be attained with verifiable effort: The
agent chooses the so-called "first-best" effort level that maximizes
the expected total surplus of the two parties. Specifically, the principal can
give the realized output to the agent, but let the agent make a fixed up-front
payment. The agent is then a "residual claimant" and will maximize
the expected total surplus minus the fixed payment.
Hence, the first-best
effort level maximizes the agent's payoff, and the fixed payment can be chosen
such that in equilibrium the agent's expected payoff equals his or her
reservation utility (which is what the agent would get if no contract was
written). Yet, if the agent is risk-averse, there is a trade-off between
incentives and insurance. Moreover, if the agent is risk-neutral but wealth-constrained,
the agent cannot make the fixed up-front payment to the principal, so the
principal must leave a "limited liability rent" to the agent (i.e.,
the agent earns more than his or her reservation utility).
The moral hazard model
with risk aversion was pioneered by Steven Shavell, Sanford
J. Grossman, Oliver
D. Hart, and others in the
1970s and 1980s. It has been extended to the case of repeated moral hazard by
William P. Rogerson and to the case of multiple tasks by Bengt
Holmström and Paul Milgrom. The moral hazard model with risk-neutral but
wealth-constrained agents has also been extended to settings with repeated
interaction and multiple tasks. While it is difficult to test models with hidden
action empirically (since there is no field data on unobservable variables),
the premise of contract theory that incentives matter has been successfully
tested in the field.
Adverse
selection
In adverse selection models, the principal is not informed about a certain characteristic of the agent at the time the contract is written. The
characteristic is called the agent's "type". For example, health insurance is more likely to be purchased by people who are more
likely to get sick. In this case, the agent's type is his or her health status,
which is privately known by the agent. Another prominent example is public
procurement contracting: The government agency (the principal) does not know
the private firm's cost. In this case, the private firm is the agent and the
agent's type is the cost level.
In adverse
selection models, there is typically too little trade (i.e., there is a so-called
"downward distortion" of the trade level compared to a
"first-best" benchmark situation with complete information), except
when the agent is of the best possible type (which is known as the "no
distortion at the top" property). The principal offers a menu of contracts
to the agent; the menu is called "incentive-compatible" if the agent
picks the contract that was designed for his or her type. In order to make the
agent reveal the true type, the principal has to leave an information rent to
the agent (i.e., the agent earns more than his or her reservation utility,
which is what the agent would get if no contract was written).
Adverse
selection theory has been pioneered by Roger Myerson, Eric Maskin, and others in the 1980s. More recently, adverse selection theory has been
tested in laboratory experiments and in the field. Adverse selection theory has
been expanded in several directions, e.g. by endogenizing the information
structure (so the agent can decide whether or not to gather private
information) and by taking into consideration social
preferences and bounded
rationality.
Contract theory also utilizes the notion of a complete contract, which is thought of as a contract that specifies the
legal consequences of every possible state of the world. More recent
developments known as the theory of incomplete
contracts, pioneered by Oliver
Hart and his coauthors, study the incentive effects of
parties' inability to write complete contingent contracts, e.g. concerning
relationship-specific investments. A leading application of the incomplete
contracting paradigm is the Grossman-Hart-Moore property rights approach to the theory
of the firm (see Hart, 1995).
Because it would be
impossibly complex and costly for the parties to an agreement to make their
contract complete, the law provides default rules which fill in the gaps in the actual agreement of the
parties.
During the last 20
years, much effort has gone into the analysis of dynamic contracts. Important
early contributors to this literature include, among others, Edward J. Green, Stephen Spear, and Sanjay Srivastava.
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