Learning With Misspecified Models

这个项目调查的是估计一个模型的代理人，该模型很好地符合观察到的数据，尽管他可能永远不会学习“真正的”均衡，因为他的模型是“错误指定的”，因为它错过了环境的一个或多个关键参数。即使错误地指定了一个模型，决策者的信念也可以自我实现，他可能最终会使用该模型来选择一项政策。尽管自我实现信念的概念与在均衡范式下研究的理性预期密切相关，但它被称为自我确认均衡，以强调两种不同的模型相互作用以产生观察到的结果：被错误指定但用于选择行动的主体模型和产生实际数据的真实模型。真实模型和感知模型之间的相互作用是本研究的核心部分，它区别于现有的学习模型和经济均衡模型。在早些时候与托马斯·J·萨金特的合作中，首席研究员研究了基德兰和普雷斯科特的货币政策模型，在该模型中，政府根据估计的短期菲利普斯曲线选择目标通货膨胀率。实现了高通货膨胀率，并在各种条件下保持稳定。尽管在现实世界中广泛用于制定货币政策，但短期菲利普斯曲线是一个错误指定的经济模型，因为它没有认识到私人代理人的预期随着政府政策的反应而变化的事实。关键的发现是，政府对基础经济稳定性的任何轻微怀疑都可能导致目标通胀率突然大幅下降，现有文献已证明目标通胀率在各种条件下都是稳定的。这一明显自相矛盾的结果可以通过同一模型中两个根本不同的动态的内生切换机制来解释：即，决定自我确认均衡稳定性的“平均动态”，以及将经济推离均衡的“逃逸动态”。虽然现有的文献主要集中在“平均动力学”上，但拟议的研究项目研究的是“逃逸动力学”，它被忽视了，但可以显著地影响经济的动力学。该项目将内生转换机制推广到更广泛的一类学习模型，以便将这一想法应用于重要的经济问题。该项目考察了一类错误指定的学习模型，这些模型有一个稳定的自我确认均衡，而不是“真正的”均衡。这项研究首先建立了一个可以应用于不同类别模型的一般理论。其应用包括一项被称为泰勒规则的货币政策，该规则吸引了政策制定者和经济学家的相当大兴趣。有效的泰勒规则将名义利率改变为一比一以上，以控制通胀。尽管众所周知，活跃的泰勒规则是在一般情况下执行通胀目标的，但最近的一项研究表明，同样的政策可能会无意中导致“流动性陷阱”均衡，即政府不能再像最近的日本经济那样，通过降低名义利率来刺激经济。所提出的方法可以提供一个更简单但更现实的模型来解释活跃的泰勒规则的潜在极限。其核心思想是，即使政府完全致力于一项政策，但私营部门对政府承诺的轻微怀疑将促使代理人了解政府的政策规则，仅这一学习过程就可能将经济带入“流动性陷阱”。第二种应用利用逃逸动力学的思想，在保持经济稳定的同时，捕捉金融危机中突然出现的、可能反复出现的偏离正常汇率的情况。货币政策模型被用作基础，同时纳入了可能对政府政策规则有错误描述的外国投资者。

This project investigates the agent who estimates a model that fits the observed data well, although he may never learn the "true" equilibrium because his model is "misspecified" in the sense that it misses one or more key parameters of the environment. Even with a misspecified model, the decision-maker's belief can be self-fulfilled and he may end up using the model to choose a policy. Although the idea of self-fulfilling belief is closely related to rational expectations studied under equilibrium paradigm, it is called a self-confirming equilibrium to emphasize that the two different models interact to generate the observed outcomes: the agent's model, which is misspecified but used to select the action, and the true model that generates the actual data. The interaction between the true and the perceived models is the central part of this research that differentiates this project from the existing learning models and the equilibrium models of economy. In an earlier collaboration with Thomas J. Sargent, the principal investigator examined the monetary policy model of Kydland and Prescott in which the government chooses a target inflation rate based on theestimated short-term Phillips curve. A high inflation rate is realized and remains stable under various conditions. Although widely used in making monetary policy in real world, the short-term Phillips curve is a misspecified model of an economy, because it does not recognize the fact that the expectations of A private agent changes in response to the government's policy. The key finding is that any slight suspicion ofthe government about the stationarity of the underlying economy can generate an abrupt and significant drop of the target inflation rate, which the existing literature has proven stable under various conditions. Thisapparently paradoxical result can be explained through an endogenous switching mechanism of two fundamentally different dynamics within the same model: namely, the "mean dynamics" that dictates the stability of the self-confirming equilibrium, and the "escape dynamics" that pushes the economy away from the equilibrium. While the existing literature has concentrated mainly on the "mean dynamics," the proposed research project investigates the "escape dynamics," which has been overlooked but can influence the dynamics of an economy significantly. The project generalizes the endogenous switching mechanism to a wider class of learning models in order to apply this idea to important economic problems. The project examines a class of misspecified learning models that have a stable self-confirming equilibrium that is different from "true" equilibrium. This research starts by building a general theory that can be applied to a different class of models. Applications include a monetary policy known as the Taylor rule that has attracted considerable interest from policymakers as well as economists. An active Taylor rule changes the nominal interest rate more than one to one in order to control inflation. Although the active Taylor rule is known to implement the inflation target under general conditions, a recent study indicated that the same policy might unintentionally lead to a "liquidity trap" equilibrium, in which the government can no longer stimulate the economy by lowering the nominal interest rate as was the case in the recent episode of Japanese economy. The proposed approach can offer a simpler, yet more realistic, model to explain the potential limit of the active Taylor rule. The key idea is that even though the government is fully committed to a policy, a slight suspicion by the private sector about the government's commitment will prompt the agent to learn about the government's policy rule, and this learning process alone could lead the economy to the "liquidity trap."The second application uses the idea of escape dynamics to capture abrupt, and possibly recurrent departures from the normal exchange rate in financial crises while maintaining the stability of the economy. The monetary policy model is used as the foundation, while incorporating foreign investors who might have a misspecified model about the government's policy rule.