Collaborative Research: Perturbation Methods for Markov-Switching Models

协作研究：马尔可夫切换模型的扰动方法

• 批准号: 1223271
• 负责人: Jesus Fernandez-Villaverde
• 金额: $ 19.98万
• 依托单位: National Bureau of Economic Research Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1223271&HistoricalAwards=false
• 关键词: Collaborative; Research; Perturbation; Methods; Markov

AbstractProposal Title: Collaborative Research: Perturbation Methods for Markov-Switching ModelsProposal Number: SES - 1223198 This proposal aims to develop new tools for the computation and estimation of dynamic models in macroeconomics and for the application of those tools to relevant policy questions. Dynamic models have become a standard instrument in modern macroeconomics. Because they are built to analyze how the economy evolves over time, they are used to study growth and business cycles, to design monetary and fiscal policy, or to investigate the aggregate aspects of financial and labor markets, among many other tasks. However, many instruments are still missing in the toolbox of the applied macroeconomic researcher. For instance, economists do not have a good understanding of the effects of changes in policy regimes ?that is, variations in the way in which economic policy is systematically conducted in opposition to changes within one regime- or how the beliefs about future policies affect current behavior by households and firms.The goal of this proposal is to provide some of the required tools for these tasks and show how they can be used to address important questions in the design and evaluation of public policy. Consequently, much of this new research may have positive externalities for other economists within macro and, more generally, for researchers in other fields where dynamic models are also employed. In particular, this proposal focuses on how to use perturbation methods to solve Markov switching rational expectations (MSRE) models starting from first principles, that is, from the set of non-linearized optimality conditions that describe the behavior of the economic agents, rather than from the set of linearized ones, as the literature has previously done. Perturbation methods, commonly used in natural sciences and economics, built approximated solution to models that are analytically intractable. MSRE models allow for different possible policy regimes (for instance, a hawkish central banker and a dovish central banker) that evolve and switch over time (hawkish central bankers are followed, with some probability, by dovish central bankers and so on).The proposal derives the set of algebraic equations to be solved to find the first-order Taylor expansion to the policy functions using a perturbation. Next, it shows how the traditional approach, based on singular value decomposition (SVD) algorithms and used in the constant parameter case, does not work in the case of MSRE models. Instead, the proposal uses a Gröbner basis method. Then, it studies how to check for determinacy and, as an example, it solves a business cycle model with nominal rigidities. Finally, the proposal points out how the perturbation approach also allows us to find higher-order approximations to the solution of MSRE models. Policy-making institutions in the U.S. and abroad can apply the methods presented in this proposal. For instance, the Federal Reserve Board and several regional Federal Reserve Banks, the International Monetary Fund, the European Central Bank, the Bank of England, and the central banks of Austria, Canada, Germany, Italy, Japan, Spain, and Sweden (just to name a few) are actively formulating and estimating dynamic macroeconomic models for policy analysis and forecasting that can benefit from the type of extensions presented in the proposal. Moreover, the economics profession is accumulating evidence of the good forecasting performance of this class of models, even when compared with judgmental predictions from staff economists. The newer and better tools that this proposal outlines are designed explicitly for the purpose of helping the Federal Reserve Board and other policy-making institutions to develop more flexible models that will contribute to the implementation of an effective public policy in the U.S. Finally, the development of new computation techniques has potential applications in other fields of economics (such as international economics, industrial organization, or labor economics), and other social sciences where researchers want to solve and estimate dynamic models using flexible, yet powerful tools.

摘要提案标题：协作研究：马尔可夫切换模型的扰动方法提案编号：SES - 1223198 该提案旨在开发用于计算和估计宏观经济学动态模型的新工具，并将这些工具应用于相关政策问题。动态模型已成为现代宏观经济学的标准工具。因为它们是为了分析经济如何随时间演变而建立的，所以它们被用来研究增长和商业周期，设计货币和财政政策，或调查金融和劳动力市场的总体方面，以及许多其他任务。然而，应用宏观经济研究者的工具箱中仍然缺少许多工具。例如，经济学家并没有很好地理解政策体制变化的影响，即系统地执行经济政策的方式与一个体制内的变化相对应的变化，或者对未来政策的信念如何影响家庭和企业当前的行为。本提案的目标是为这些任务提供一些所需的工具，并展示如何使用它们来解决公共政策设计和评估中的重要问题。因此，这些新研究中的大部分可能对宏观范围内的其他经济学家，更广泛地说，对也采用动态模型的其他领域的研究人员产生积极的外部性。特别是，该提案侧重于如何使用扰动方法从第一原理开始解决马尔可夫切换理性预期（MSRE）模型，即从描述经济主体行为的非线性最优条件集开始，而不是像文献之前所做的那样从线性化条件集开始。自然科学和经济学中常用的扰动方法为分析上难以处理的模型建立了近似解。 MSRE 模型允许不同的可能政策制度（例如，鹰派央行行长和鸽派央行行长）随着时间的推移而演变和切换（鹰派央行行长之后有一定概率是鸽派央行行长等）。该提案导出了一组需要求解的代数方程，以使用扰动找到政策函数的一阶泰勒展开式。接下来，它展示了基于奇异值分解 (SVD) 算法并在常数参数情况下使用的传统方法如何不适用于 MSRE 模型。相反，该提案使用 Gröbner 基础方法。然后，它研究如何检查确定性，例如，它求解具有名义刚性的经济周期模型。最后，该提案指出扰动方法如何让我们能够找到 MSRE 模型解的高阶近似。美国和国外的政策制定机构可以应用本提案中提出的方法。例如，联邦储备委员会和几个地区联邦储备银行、国际货币基金组织、欧洲中央银行、英格兰银行以及奥地利、加拿大、德国、意大利、日本、西班牙和瑞典（仅举几例）的中央银行正在积极制定和估计用于政策分析和预测的动态宏观经济模型，这些模型可以从提案中提出的扩展类型中受益。此外，经济学界正在积累证据，证明此类模型具有良好的预测性能，即使与经济学家的判断性预测相比也是如此。该提案概述的更新更好的工具的明确目的是帮助美联储和其他决策机构开发更灵活的模型，这将有助于在美国实施有效的公共政策。最后，新计算技术的开发在其他经济学领域（例如国际经济学、产业组织或劳动经济学）以及其他社会科学领域具有潜在的应用，在这些领域，研究人员希望使用动态模型来求解和估计 灵活而强大的工具。