Estimating Macroeconomic Models of Financial Crises: An Endogenous Regime Switching Approach

本基金的研究为金融危机的宏观经济模型的实证分析开发了一种新的方法。这种新方法将提供一种方法来衡量哪些经济冲击正在将一个经济体推向危机。它还将为分析避免和减轻危机影响的政策有效性提供一个框架。该模型基于金融危机是罕见但大事件的想法，这意味着任何分析危机的合理模型都必须是非线性的。该研究将金融危机的模型写成两种制度模型。新模型的一个关键创新特征是，进入危机机制的可能性是当前经济状况的函数；例如，当债务相对于GDP上升时，债务危机的可能性就会增加。最近的全球金融危机清楚地表明，有必要制定政策，既防止此类事件的发生，又在此类事件发生时更有效地应对。该项目通过开发对重要宏观经济模型进行实证检验的新方法，促进了科学的进步。加深对如何避免和减轻金融危机的理解显然有助于国家繁荣。本项目开发了一种内生机制转换方法来模拟金融危机。在模型中有两种制度，一种是危机制度，另一种是正常经济时期的制度。制度之间的转换是基于由经济中的经济变量决定的概率。经济中的主体知道经济基本面如何影响进入或走出危机状态的可能性。也就是说，它是模型的理性预期解。然后，解决方案确保在正常状态下做出的决策充分考虑了这些决策如何影响进入危机状态的可能性，以及经济在危机中如何运行。所开发的模型捕捉到了人们希望在金融危机的经验模型中看到的所有显著特征。首先，它抓住了危机的非线性本质。其次，利用微扰法和二阶解求解了状态切换模型。这使得解决方案能够捕捉在危机发生时和危机结束时风险对决策规则的影响。第三，由于求解方法是基于摄动的，它可以处理许多状态变量和许多冲击。也就是说，在模型的大小方面，我们比当前的非线性方法受到的约束更少。第四，求解方法的速度意味着可以使用非线性滤波器（例如粒子滤波器）来计算模型的似然函数，以便对相关冲击和摩擦进行完整的贝叶斯估计，这些冲击和摩擦是金融危机模型的基础。第五，解决方案的完全理性预期性质允许人们提出关键的反事实政策问题。例如，什么政策（如果有的话）可以减轻或消除大衰退？

The research in this grant develops a new approach for empirical analysis of macroeconomic models of financial crises. This new approach will provide a way to measure which economic shocks are driving an economy towards a crisis. It will also provide a framework for analyzing the effectiveness of policies to avoid and mitigate the impact of crises. The model developed is based on the idea that financial crises are rare but large events, implying that any reasonable model for analyzing crises must be non-linear. The research writes models of financial crises as a two-regime model. A key innovative feature of the new model is that the probability of moving to the crisis regime is a function of the current state of the economy; for example when debt rises relative to GDP the probability of a debt crisis increases. The recent global financial crisis has clearly shown the need to develop policies to both prevent such events from occurring as well as more effectively dealing with such events when they do occur. The project contributes to the progress of science by developing new methods for empirical testing of important macroeconomic models. Developing a deeper understanding of how to avoid and mitigate financial crises clearly contributes to the national prosperity. This project develops an endogenous regime switching approach to modeling financial crises. In the model there are two regimes, one a crisis regime, the second a regime for normal economic times. The switch between regimes is based on a probability determined by economic variables in the economy. Agents in the economy know how economic fundamentals affect the probability of moving in or out of the crisis state. That is, it is a rational expectations solution of the model. The solution then ensures that decisions made in the normal state fully incorporate how those decision affect the probability of moving into the crisis state as well as how the economy will operate in a crisis. The model developed captures all of the salient features one would want in an empirical model of financial crises. First, it captures the non-linear nature of a crisis. Second, the regime switching model is solved using perturbation methods and a second order solution. This allows the solution to capture the impact of risk on decision rules due both in an out of the crisis. Third, since the solution method is perturbation based it can handle a number of state variables and many shocks. That is, we are less constrained than current non-linear methods in terms of the size of the model. Fourth, the speed of the solution method means that non-linear filters (e.g. particle filter) can be used to calculate the likelihood function of the model for a full Bayesian estimation of the relevant shocks and frictions that are fundamental to models of financial crises. Fifth, the fully rational expectations nature of the solution allows one to ask key counterfactual policy questions. For example, what policies, if any, would have mitigated or eliminated the Great Recession?