Modeling the Evolution of Agents' Beliefs and Uncertainty in General Equilibrium Models

摘要提案题目：一般均衡模型中主体信念和不确定性的演化建模（提案号：SES - 1227397）首席研究员：Bianchi， Francesco本研究议程的目的是研究一般均衡模型中私营部门信念和不确定性的演化。核心观点是，可以通过定义一组机制来捕捉主体信念的演变，这些机制以主体的悲观、乐观和对未来均衡结果的不确定性程度为特征。一旦这种类型的结构被强加，就有可能在主体信念的进化和可观察的结果之间创建一个映射。所提出的方法超越了预期效用的假设，因为代理人知道他们不知道，并考虑到他们的信念将根据他们所观察到的而演变，从而形成期望。研究议程将提供解决、模拟和估计结构模型的方法，在这些模型中，前瞻性和完全理性的主体受到悲观、乐观和不确定性浪潮的影响，这些浪潮最终会严重影响宏观经济结果。这种悲观、乐观和不确定性的爆发可能突然发生，也可能在很长一段时间内逐渐展开，作为对其他主体行为、经济成果实现、公共信号或政策公告的反应。技术细节描述在第一个研究项目，公众期望和不确定性的演变建模。智能体信念的进化是在假设世界存在不同状态的情况下进行建模的，这些状态根据外生冲击的统计特性或模型中某些智能体的行为而不同。这样的制度遵循马尔科夫转换过程，这可能与模型的其他方面相关。人们假定代理人观察经济结果，而不是政权本身。相反，他们必须采用贝叶斯学习来推断当前的政权。这决定了代理人信念的渐进式演变，转化为经济结果的漂移、宏观经济波动和代理人的不确定性。在第二个项目“隐性冲击和财政美德”中，这些新方法被用来描述市场参与者试图评估公共债务可持续性的经济特征。私营部门不太可能确切地知道政策制定者未来将如何行动。不同的政府对公共部门的规模有不同的偏好，财政政策的制定是一个结果高度不可预测的过程。在该模型中，标准的政策组合包括一个良性的财政当局，它根据债务调整税收，以及一个完全控制通胀的央行。当政策制定者偏离这种良性政策组合时，智能体通过贝叶斯学习来推断偏离的可能持续时间。随着代理人观察到越来越多的偏差，他们对迅速回归良性制度越来越悲观，通货膨胀开始使债务保持在稳定的轨道上。在良性政策组合下蛰伏的冲击现在开始显现。这些变化最初是难以察觉的，可以在几十年内展开，并随着代理人确信财政当局不会增税而加速。新的建模框架允许代理人对政府偿还债务意愿的信念逐渐改变。因此，价格水平财政理论中典型的李嘉图和非李嘉图制度之间的标准区别就失效了。取而代之的是，一个反映主体对政策制定者未来行为信念的连续体系。代理有多快？信念的演变取决于一个国家的财政美德（Fiscal Virtue），体现在该国长期偏离维塔士政权的频率上。因此，该模型能够解释为什么财政纪律与宏观经济之间的关系在不同国家和时间内并不稳定。当一个良性政体盛行，或者代理人相信它将在未来盛行时，债务水平基本上是无关紧要的。然而，如果代理人确信经济进入了一个长期的偏差，那么利率和通货膨胀的差异就会出现。各国财政美德的差异越大，学习速度的差异也越大，这反过来又加速了通货膨胀和利率差异的开放。上述公众预期对政策行动的缓慢调整很难通过理性预期模型再现，在理性预期模型中，整个模型经济的运作是私人代理人的常识。例如，尽管美国联邦储备银行（Federal Reserve Bank）的资产负债表大幅扩大，但公众对长期通胀预期的预期在过去5年里几乎没有变化。在第三个项目中，通货膨胀情绪和货币政策沟通，表明这可能是中央银行多年来建立的声誉的结果。在该模型中，货币政策在积极稳定通胀（主动机制）和主要强调稳定产出（被动机制）的时期之间交替进行。当央行只是短暂地偏离“积极机制”时，通胀预期始终保持稳定，该模型捕捉到了美联储主席本•伯南克（Ben Bernanke）所描述的受约束的自由裁量权（constrained discretion）。然而，如果中央银行长时间偏离，通货膨胀情绪就会逐渐在经济主体中蔓延。该模型适合于美国的数据，表明增加美联储的透明度通过锚定通胀情绪来改善福利。对于那些央行未能在通胀稳定方面树立良好声誉的国家来说，透明度带来的好处甚至更大。

AbstractProposal Title: Modeling the Evolution of Agents' Beliefs and Uncertainty in General Equilibrium Models (Proposal Number: SES - 1227397)Principal Investigator: Bianchi, Francesco The objective of this research agenda is to study the evolution of private sector beliefs and uncertainty in general equilibrium models. The central insight is that the evolution of agents' beliefs can be captured by defining a set of regimes that are characterized by the degree of agents' pessimism, optimism, and uncertainty about future equilibrium outcomes. Once this type of structure is imposed, it is possible to create a mapping between the evolution of agents' beliefs and observable outcomes. The proposed approach goes beyond the assumption of anticipated utility, as agents know that they do not know and form expectations taking into account that their beliefs will evolve according to what they will observe. The research agenda will deliver methods to solve, simulate, and estimate structural models in which forward-looking and fully rational agents are subject to waves of pessimism, optimism, and uncertainty that turn out to critically affect macroeconomic outcomes. Such outbursts of pessimism, optimism, and uncertainty may happen abruptly or may gradually unfold over a long period of time in response to the behavior of other agents, the realizations of economic outcomes, public signals, or policy announcements. The technical details are described in the first research project, Modeling the Evolution of Public Expectations and Uncertainty. The evolution of agents' beliefs is modeled assuming the existence of different states of the world that differ according to the statistical properties of the exogenous shocks or based on the behavior of some of the agents in the model. Such regimes follow a Markov switching process, which may be correlated with other aspects of the model. Agents are assumed to observe economic outcomes, but not the regimes themselves. Instead, they have to adopt Bayesian learning to infer the regime in place. This determines a progressive evolution of agents' beliefs that translates into a drift of economic outcomes, macroeconomic volatility, and agents' uncertainty. In the second project, Dormant Shocks and Fiscal Virtue, these new methods are employed to characterize an economy in which market participants try to assess the sustainability of public debt. It is highly unlikely that the private sector knows with certainty how policy-makers will behave in the future. Different governments have different preferences about the size of the public sector and fiscal policy making is a process whose outcome is highly unpredictable. In the model, the standard policy mix consists of a virtuous fiscal authority that moves taxes in response to debt and a central bank that has full control over inflation. When policy-makers deviate from this virtuous policy mix, agents conduct Bayesian learning to infer the likely duration of the deviation. As agents observe more and more deviations, they become increasingly pessimistic about a prompt return to the Virtuous Regime and inflation starts moving to keep debt on a stable path. Shocks which were dormant under the virtuous policy mix now start manifesting themselves. These changes are initially imperceptible, can unfold over decades, and accelerate as agents become convinced that the fiscal authority will not raise taxes. The new modeling framework allows for gradual changes in agents' beliefs about government's willingness to repay its debt. Therefore, the standard distinction between Ricardian and non-Ricardian regimes typical of the Fiscal Theory of Price Level breaks down. In its stead, a continuum of regimes reflecting agents' beliefs about the future behavior of policy-makers arises. How quickly agents? beliefs evolve depends on the country's Fiscal Virtue, captured by the frequency with which the country engages in long lasting deviations from the Virtuos Regime. Thus, the model is able to explain why the relation between fiscal discipline and the macroeconomy is not stable across countries and over time. When a Virtuous regime prevails or agents are confident that it will prevail in the future, the level of debt is substantially irrelevant. However, if agents become convinced that the economy entered a long lasting deviation, then interest rate and inflation differentials open up. A larger difference in Fiscal Virtue across countries leads to a larger difference in the speed of learning, which in turn speeds up the opening of the inflation and interest rate differentials. The sluggish adjustment of public expectations to policy actions described above is hard to reproduce through rational expectations models in which the functioning of the whole model economy is common knowledge among private agents. For instance, despite the dramatic widening of the balance sheet of the Federal Reserve Bank, public expectations about long-run inflation expectations have hardly moved in the last five years. In the third project, Inflationary Sentiments and Monetary Policy Communication, it is shown that this can be the result of the central bank's reputation built up over the years. In the model, monetary policy alternates periods of active inflation stabilization (Active Regime) and periods during which the emphasis is mainly on output stabilization (Passive Regime). When the central bank engages in only short lasting deviations from the Active Regime, inflation expectations always remain anchored and the model captures the monetary approach described by the Fed Chairman Ben Bernanke as constrained discretion. However, if the central bank deviates for a prolonged period of time, inflationary sentiments progressively spread among agents. The model is fit to U.S. data to show that increasing the transparency of the Federal Reserve improves welfare by anchoring inflationary sentiments. Gains from transparency are even more sizeable for countries whose central bank has failed to establish a strong reputation for inflation stability.