Nonparametric Identification and Estimation of Bargaining Models

讨价还价理论在过去30年里蓬勃发展。最初的两个参与者之间的讨价还价模式已经扩展到多个方向，允许更一般的谈判协议和两个以上的参与者。理论文献的发展与讨价还价模型的广泛应用是齐头并进的，而且在很大程度上是由其推动的。这些谈判包括劳工、家庭、法律、住房、政治、国际和医疗谈判。关于这类谈判结果以及讨价还价过程细节的数据越来越多，这也刺激了经验工作的激增，在这些工作中，偶然的经验主义逐渐导致了将战略讨价还价模型用于数据的更系统的尝试。在理论和实证应用中得到广泛研究的两个讨价还价框架是随机序贯讨价还价模型和具有罕见先验的讨价还价。在随机序列讨价还价模型中，允许分配的盈余(或“蛋糕”)和讨价还价协议(即玩家提出要约和还价的顺序)根据一个随机过程随时间演变。这一功能使模型变得灵活(它为一大类讨价还价游戏提供了一个统一的框架)。它还使达成协议过程中经常出现的拖延现象合理化，这种情况在实际谈判中经常出现。随机讨价还价框架已被用于各种实证应用，从议会民主下的联合政府组建，到集体谈判协议，到企业破产重组，到产品市场的行业标准制定，再到主权债务重新谈判。具有罕见先例的讨价还价模型也使达成协议的拖延发生合理化，并代表着一个快速增长的理论和应用研究领域。在这些模型中，参与者对未能达成协议的后果有不同的预期，这在几种讨价还价的情况下都是一种看似合理的情景。例如，具有罕见先例的讨价还价模型被用于研究医疗事故诉讼中争议解决的过程或公司签署广泛的交叉许可协议的动机以及半导体行业广泛的交叉许可谈判的持续时间。尽管讨价还价模型在经济应用中非常重要，但对于这些模型的结构要素或反事实环境中的讨价还价结果是否能够在不施加参数假设的情况下被识别和估计，人们知之甚少。本文的研究将为讨价还价模型估计的文献提供积极的结果，为风险厌恶且具有异质折扣因素的随机讨价还价模型和具有非共同先验的讨价还价模型的非参数辨识和估计提供积极的结果。这项研究的统一主题是，这两类模型都可以解释达成协议延迟的发生，并且在经验上是相关的，因为在许多应用中，风险厌恶、时间偏好贴现率的异质性和过度乐观可能在决定谈判协议的时间和条款方面发挥重要作用。

Bargaining theory has flourished in the past thirty years. The original model of bargaining between two players who alternate in making offers and counteroffers has been extended in a number of directions allowing for more general negotiation protocols and more than two players. The development of the theoretical literature has gone hand in hand with, and for a large part has been motivated by, the broad range of applications of bargaining models. These include labor, family, legal, housing, political, international and medical negotiations. The increased availability of data on the outcomes of such negotiations, as well as on the details of the bargaining process, has also stimulated a surge in empirical work, where casual empiricism has progressively led the way to more systematic attempts to take strategic bargaining models to data.Two bargaining frameworks that have been extensively studied in theoretical and empirical applications are the stochastic sequential bargaining model, and bargaining with uncommon priors. In the model of stochastic sequential bargaining, the surplus to be allocated (or the "cake") and the bargaining protocol (i.e. the order in which players can make offers and counteroffers), are allowed to evolve over time according to a stochastic process. This feature makes the model flexible (it provides a unified framework for a large class of bargaining games). It also rationalizes the occurrence of delays in reaching an agreement, which are often observed in actual negotiations. The stochastic bargaining framework has been used in a variety of empirical applications that range from the formation of coalition governments in parliamentary democracy, to collective bargaining agreements, to corporate bankruptcy reorganizations, to the setting of industry standards in product markets, and to sovereign debt renegotiations.Models of bargaining with uncommon priors also rationalize the occurrence of delays in reaching an agreement, and represent a fast-growing area of both theoretical and applied research. In these models, players have different expectations regarding the consequences of failing to reach an agreement, which is a plausible scenario in several bargaining situations. For example, bargaining models with uncommon priors have been used to study the process of dispute resolution in medical malpractice litigation or the incentives of firms to sign broad cross-license agreements as well as the duration of broad cross-license negotiations in the semiconductor industry.In spite of the importance of bargaining models in economic applications, little is known about whether the structural elements of these models or the bargaining outcomes in counterfactual environments can be identified and estimated without imposing parametric assumptions. The proposed research will contribute to the literature on the estimation of bargaining models by providing positive results in the nonparametric identification and estimation of stochastic bargaining models where players are risk-averse and have heterogeneous discount factors, and of bargaining models where players have uncommon priors. The unifying theme of this research is that both classes of models may explain the occurrence of delays in reaching an agreement and are relevant empirically, as in many applications risk aversion, heterogeneity in the discount rate of time preference, and excessive optimism are likely to play an important role in determining the timing and terms of negotiation agreements.