Collaborative Research: Monotone Methods in Dynamic Screening Contracts

本项目的研究重点是在面对严重的同期流动性约束时提供激励。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：企业所有者（委托人）激励自己没有财富的雇员经营者（代理人）的最佳方式是什么？假设的答案是，委托人应该使用“血汗股权合同”，通过增加代理人在公司的所有权股份来奖励好的结果（即低成本实现），并通过减少坏结果（即高成本实现）来惩罚他。因此，研究结果将对许多金融和合同环境产生影响，包括：特许经营、风险资本和投资银行业务。此外，这个项目的核心方法应该在这种情况下产生强有力的实证意义。例如，从工作到拥有的特许经营合同应该明确规定员工经营者成为特许经营的既定所有者或被解雇和替换的途径。同样，就风险资本契约而言，产出增长应与从风险资本家向创始企业家转让控制权联系起来。此外，在本项目主持下开发的方法将在动态机制设计的许多应用中产生溢出效应。例如，在多公司采购的背景下，本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，在向现金紧张的客户重复销售的背景下，该理论可能会揭示诸如频繁购买折扣计划之类的合同安排。最后，在私人财富冲击的背景下，该方法可以促进对最佳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契约的结构和实现。具体来说，所提出的研究模型是一个经典静态垄断筛选设置的无限视界版本，在该模型中，代理被私下告知成本或收入流，并且受到严重的流动性约束。委托人面临的动态机制设计问题将被表述为递归动态规划，其中相关状态变量被承诺未来支付给代理人的租金。在一定的假设下，所有的合同条款（产量、同期租金和未来租金）在状态变量中都是弱增长的，这提供了一种独特的解释，即作为代理在公司中的权益。较高水平的血汗权益与较低的产出扭曲和较不严格的流动性约束有关。此外，类型的单调性允许表征合同环境中的短期动态调整——高成本实现导致更低的血汗权益和更多的扭曲，而低实现具有相反的效果。根据最优动态保险文献，也有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，要么被解雇和替换。

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.