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Contract Theory: Moral Hazard, Adverse Selection, and Incentive Design

契约理论：Moral Hazard、Adverse Selection与激励设计

Overview

概述

Contract theory studies how economic actors construct contractual arrangements in the presence of asymmetric information. The two canonical problems are moral hazard (hidden action — the agent's effort is unobservable) and adverse selection (hidden type — the agent's characteristics are private). The optimal contract balances the principal's desire for risk-sharing against the need to incentivize effort or truthful revelation. Hart and Holmstrom's contributions on incomplete contracts and incentive design form the modern foundation.
契约理论研究经济主体在信息不对称情况下如何构建契约安排。两类典型问题是moral hazard（隐藏行为——代理人的努力不可观测）和adverse selection（隐藏类型——代理人的特征为私有信息）。最优契约需在委托人的风险分担需求与激励代理人努力或真实披露信息的需求之间取得平衡。Hart和Holmstrom在不完全契约与激励设计方面的贡献构成了现代理论基础。

When to Use

适用场景

  • Designing compensation, bonus, or commission structures for employees or contractors
  • Evaluating insurance contracts for moral hazard (deductibles, copays) or adverse selection (screening)
  • Structuring partnerships, franchise agreements, or procurement contracts with unobservable quality
  • Analyzing incomplete contracts where not all states of the world can be specified
  • 为员工或承包商设计薪酬、奖金或佣金结构
  • 评估存在moral hazard（免赔额、共付额）或adverse selection（筛选机制）的保险合同
  • 构建存在不可观测质量的合伙协议、特许经营协议或采购合同
  • 分析无法明确所有现实状态的不完全契约问题

When NOT to Use

不适用场景

  • Both parties have symmetric information and trust is established (no incentive problem)
  • The relationship is a one-shot anonymous transaction with no contractual enforcement
  • Behavioral factors (reciprocity, intrinsic motivation) dominate monetary incentives
  • 双方信息对称且已建立信任（无激励问题）
  • 关系为一次性匿名交易，无契约执行力
  • 行为因素（互惠性、内在动机）主导货币激励

Assumptions

假设条件

IRON LAW: The optimal contract balances risk-sharing against incentive
provision — full insurance destroys incentives, full incentives impose
unbearable risk. There is no contract that achieves first-best when
information is asymmetric.
  • The principal is risk-neutral; the agent is risk-averse (standard setup)
  • The agent's action (effort) or type is private information
  • Output is a noisy signal of the agent's effort: x = f(e) + epsilon
  • Both parties are rational and can commit to the contract terms
  • Courts can verify output but not effort (contractibility constraint)
IRON LAW: 最优契约需在风险分担与激励提供之间取得平衡——完全保险会消解激励，完全激励则会带来难以承受的风险。当信息不对称时，不存在能实现最优结果的契约。
  • 委托人风险中性；代理人风险厌恶（标准设定）
  • 代理人的行为（努力）或类型为私有信息
  • 产出是代理人努力的带噪信号：x = f(e) + epsilon
  • 双方均为理性主体，且能承诺遵守契约条款
  • 法庭可验证产出但无法验证努力（契约可执行性约束）

Methodology

方法论

Step 1 — Classify the Information Problem Determine whether the core issue is moral hazard (hidden action after contracting), adverse selection (hidden type before contracting), or both. Identify who is the principal and who is the agent.
Step 2 — Specify Constraints Write down: (1) the Incentive Compatibility constraint (IC) — the agent prefers the intended action/type revelation; (2) the Participation Constraint (PC/IR) — the agent accepts the contract over the outside option; (3) Limited Liability (LL) if applicable — payments cannot go below zero.
Step 3 — Solve the Optimal Contract For moral hazard: maximize principal's expected profit subject to IC and PC. The optimal wage schedule w(x) satisfies the Holmstrom informativeness principle — pay should depend on output only insofar as it is informative about effort. For adverse selection: design a menu of contracts that induces self-selection (screening). Expect distortion at the bottom (inefficient allocation for low types) and efficiency at the top.
Step 4 — Assess Completeness and Renegotiation Check whether the contract is complete (covers all verifiable contingencies) or incomplete (residual rights matter). If incomplete, apply Hart's property rights approach: allocate residual control rights to the party whose investment is most important. Consider renegotiation-proofness.
步骤1——分类信息问题 确定核心问题是moral hazard（缔约后隐藏行为）、adverse selection（缔约前隐藏类型），或两者兼具。明确谁是委托人，谁是代理人。
步骤2——明确约束条件 列出：(1) 激励相容约束（IC）——代理人倾向于采取预期行为/披露真实类型；(2) 参与约束（PC/IR）——代理人接受契约的收益优于外部选项；(3) 若适用，有限责任约束（LL）——支付金额不得低于零。
步骤3——求解最优契约 针对moral hazard：在IC和PC约束下最大化委托人的期望利润。最优工资方案w(x)需满足Holmstrom信息性原则——薪酬仅应在产出能反映努力程度的范围内依赖产出。针对adverse selection：设计一套契约菜单以引导自我筛选（screening）。通常会出现底层扭曲（低类型主体的低效配置）和顶层高效的情况。
步骤4——评估契约完备性与再谈判 检查契约是完备的（涵盖所有可验证的可能情况）还是不完全的（剩余权利至关重要）。若为不完全契约，应用Hart的产权理论：将剩余控制权分配给投资最为重要的一方。同时需考虑契约的再谈判抗性。

Output Format

输出格式

markdown
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markdown
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Contract Design Analysis: [Context]

契约设计分析：[场景]

Information Problem

信息问题

  • Type: Moral hazard / Adverse selection / Both
  • Principal: [who]
  • Agent: [who]
  • Hidden variable: [effort level / agent type / quality]
  • 类型: Moral Hazard / Adverse Selection / 两者兼具
  • 委托人: [主体]
  • 代理人: [主体]
  • 隐藏变量: [努力水平 / 代理人类型 / 质量]

Constraints

约束条件

ConstraintExpressionBinding?
Incentive Compatibility
Participation (IR)
Limited Liability
约束类型表达式是否具有约束力?
激励相容约束
参与约束 (IR)
有限责任约束

Optimal Contract Structure

最优契约结构

  • Fixed component: [base salary / premium]
  • Variable component: [bonus / piece rate / deductible]
  • Informativeness: [which signals are used and why]
  • 固定部分: [基本工资 / 保费]
  • 可变部分: [奖金 / 计件工资 / 免赔额]
  • 信息性: [使用的信号及原因]

First-Best vs. Second-Best Gap

最优与次优差距

  • First-best outcome: [what would happen with full information]
  • Second-best distortion: [what is sacrificed]
  • Welfare loss: [qualitative or quantitative]
  • 最优结果: [完全信息下的情况]
  • 次优扭曲: [做出的牺牲]
  • 福利损失: [定性或定量描述]

Recommendation

建议

[Contract terms and implementation guidance]
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[契约条款与实施指导]
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Gotchas

注意事项

  • Multi-tasking (Holmstrom-Milgrom): incentivizing one measurable task crowds out effort on unmeasurable tasks — strong incentives can be counterproductive
  • Ratchet effect: if the principal updates expectations based on past performance, the agent strategically underperforms early
  • Career concerns (Holmstrom 1999) can substitute for explicit incentives — young agents work hard to build reputation even without bonuses
  • Limited liability constraints shift power to the agent and can require the principal to leave rents (efficiency wages)
  • In repeated relationships, relational contracts (self-enforcing, not court-enforced) often dominate formal contracts
  • Intrinsic motivation can be crowded out by extrinsic incentives (Benabou-Tirole) — paying volunteers may reduce their effort
  • 多任务问题（Holmstrom-Milgrom）：激励可衡量的任务会挤占代理人在不可衡量任务上的努力——过强的激励可能适得其反
  • 棘轮效应：若委托人根据过往表现更新预期，代理人会在前期战略性地低绩效
  • 职业关注（Holmstrom 1999）可替代显性激励——年轻代理人即使没有奖金也会努力工作以建立声誉
  • 有限责任约束会将权力转移给代理人，可能要求委托人保留租金（效率工资）
  • 在重复关系中，关系型契约（自我执行，非法庭执行）通常优于正式契约
  • 外在激励可能挤出内在动机（Benabou-Tirole）——为志愿者付费可能降低他们的努力程度

References

参考文献

  • Holmstrom, B. (1979). "Moral Hazard and Observability." Bell Journal of Economics.
  • Hart, O. & Moore, J. (1990). "Property Rights and the Nature of the Firm." Journal of Political Economy.
  • Laffont, J.-J. & Martimort, D. (2002). The Theory of Incentives: The Principal-Agent Model.
  • Bolton, P. & Dewatripont, M. (2005). Contract Theory. MIT Press.
  • Holmstrom, B. (1979). "Moral Hazard and Observability." Bell Journal of Economics.
  • Hart, O. & Moore, J. (1990). "Property Rights and the Nature of the Firm." Journal of Political Economy.
  • Laffont, J.-J. & Martimort, D. (2002). The Theory of Incentives: The Principal-Agent Model.
  • Bolton, P. & Dewatripont, M. (2005). Contract Theory. MIT Press.