Collaborative Research: Monotone Methods in Dynamic Screening Contracts

该项目的研究重点是在面临严重的同时流动性限制的情况下提供激励措施。因此，构建这个项目的一种方式是努力回答一个自然的经济问题：公司所有者(委托人)激励没有自己财富的员工经营者(代理人)的最佳方式是什么？假设的答案是，委托人应该使用“汗水股权契约”，通过增加代理人在公司的所有权股份来奖励代理人，奖励他取得好结果(即，低成本实现)，并通过减少持股来惩罚不良结果(即高成本实现)。因此，这些发现将对许多金融和合同环境产生影响，包括特许经营、风险投资和投资银行。此外，该项目的核心方法应该在这些环境中产生强有力的经验影响。例如，从工作到拥有的特许经营合同应该明确雇员经营者成为特许经营权的既得所有者或被解雇和取代的途径。同样，在风险投资契约的背景下，产出增长应该与控制权从风险资本家转移到创始企业家有关。此外，在该项目的支持下开发的方法将在许多动态机制设计的应用中产生溢出效应。例如，在多公司采购的背景下，在该项目下发展的理论可能有助于解释长期供应关系的内生出现。然而，在向现金有限的客户重复销售的背景下，该理论可能会揭示经常购买折扣计划等合同安排。最后，在私人财富冲击的背景下，该方法可以促进对最优相互保险机制的理解。从技术上讲，本项目的目的是研究最优动态筛选合同的结构和实施。具体地说，建议研究的模型是规范静态垄断筛选设置的无限水平版本，在该设置中，代理人被私下告知成本或收入流，并受到严重的流动性限制。由此产生的委托人面临的动态机制设计问题将被描述为递归的动态规划，其中相关的状态变量被承诺支付给代理人的未来租金。结果表明，在某些假设下，所有合同条款(产出、同期租金和未来租金)在状态变量中呈微弱增长，这提供了一种唯一的状态解释，即代理人在公司中的权益。较高的流汗股本水平与较低的产出扭曲和较宽松的流动性约束相关。此外，类型的单调性允许表征合同环境中的短期动态调整--高成本实现会导致较低的汗水公平和更多的扭曲，而低实现会产生相反的效果。根据最优动态保险文献，也可能建立长期契约动态，在这种动态下，代理人最终要么获得公司的既得所有权股份，要么被解雇和取代。

The research focus of this project is the provision of incentives in the face of severe contemporaneous liquidity constraints. Hence, one way of framing this project is as endeavoring to answer a natural economic question: what is the best way for the owner of a firm (the principal) to incentivize an employee operator (the agent) who has no wealth of his own? The posited answer is that the principal should use 'sweat equity contracts' that reward the agent for good outcomes (i.e., low cost realizations) by increasing his ownership stake in the firm and punish him for bad outcomes (i.e., high cost realizations) by reducing it. As such, the findings will have implications in numerous financial and contractual settings including: franchising, venture capital, and investment banking.Moreover, the methods at the heart of this project should give rise to robust empirical implications in such settings. For instance, work-to-own franchise contracts should specify the path by which an employee operator either becomes a vested owner of a franchise or is fired and replace. Similarly, in the context of venture capital covenants, output growth should be associated with the transfer of control rights from venture capitalists to the founding entrepreneurs.In addition, the methods developed under the auspices of this project will have spillovers in many applications of dynamic mechanism design. For example, in a setting of multi-firm procurement, the theory developed under this project may help to explain the endogenous emergence of long-term supply relationships. Whereas, in the context of repeated sales to cash constrained customers, the theory may shed light on such contractual arrangements as frequent-purchase discount plans. Finally, in a setting of private wealth shocks, the methodology may advance understanding of optimal mutual insurance mechanisms.Technically, the purpose of this project is to investigate the structure and implementation of optimal dynamic screening contracts. Specifically, the model proposed for study is an infinite-horizon version of the canonical static monopolistic screening setting in which the agent is privately informed about the stream of costs or revenues and is severely liquidity constrained. The resulting dynamic mechanism-design problem facing the principal will be formulated as a recursive dynamic program in which the relevant state variable is promised future rents paid to the agent. It will be shown that under certain assumptions all contractual terms (output, contemporaneous rents, and future rents) are weakly increasing in the state variable, affording a unique interpretation of the state as the agent's equity in the firm. Higher levels of sweat equity are associated with lower output distortions and less stringent liquidity constraints. Moreover, monotonicity in type permits characterization of short-run dynamic adjustments in the contractual environment -- high cost realizations result in lower sweat equity and more distortions while low realizations have the reverse effects. Following the optimal dynamic insurance literature, it may also be possible to establish long-run contractual dynamics under which the agent ultimately either achieves a vested ownership stake in the firm or is fired and replaced.