A New Posterior Simulation Toolkit for Estimation of a Multitude of Economic Models

在这个项目中，研究人员提供了一个新的贝叶斯模拟工具包，允许经济学家研究各种经济模型，这些模型由于计算复杂而难以量化。主要的技术困难包括充满多个峰值的难以处理的可能性和由宽的零概率区域隔开的细小的曲折脊线。提供一套全新的模拟工具的一个重要原因与本文提出的两个体制转换一般均衡模型的估计有关。在估计这些模型的过程中，研究者发现了几个令人费解的结果。人们很容易推断，这种令人不快的结果反映了文献中研究的那种宏观经济模型的一些根本缺陷。事实证明，这个推论是不正确的。研究人员发现，似然函数和后验分布远比现有的蒙特卡洛马尔可夫链(MCMC)技术所能处理的复杂得多。令人费解的估计并不是模型本身的反映，而主要是宏观经济学家目前可用的计算技术不足的结果。为了迎接这一挑战，研究人员开发了一种更全面的估计技术。拟议的研究旨在避免经济模型中固有的上述问题。具体地说，它由三个主要部分组成。(1)调查者开发了两个结构模型，明确地阐述了最近住房和金融市场动荡对宏观经济的影响以及随后政策干预的影响。(2)为了获得这些模型的准确估计技术，调查者开发了一套新的MCMC技术，解决了多个局部峰值、细小的曲折脊线、以及高维参数空间，这使得利用现有的MCMC算法变得非常困难，而且往往是不可行的。(3)为了使新方法能够为公众所接受，研究人员开发了一个工具包，该工具包包括一个动态调度器，允许开发许多现代定量经济应用所需的并行计算。这一通用工具包可以应用于除本提案讨论的新模型之外的广泛的经济问题。可以用来解决当前经济问题的宏观经济模型和相关的政策配方不可避免地是复杂的。众所周知，对这类模型的准确估计是一项极具挑战性的任务，因为当模型变得几乎难以处理时，宏观经济文献中使用的标准方法可能会失效。为了避免模型本身对经济影响的扭曲，需要提出新的计算技术。这将允许研究人员实现高水平的推理精度，从而使计算不准确不会污染或损害模型的经济意义和后续的政策建议。该提案的最终目标是使该工具包可供学术和政府研究人员以及研究生使用，并允许研究人员评估各种结构模型，以相对简单的资源解决相关和紧迫的政策问题。即使对于经验丰富的程序员来说，为每个经济应用程序编写并行化计算机程序也是一项具有挑战性和耗时的任务；许多经济学家根本没有时间或计算机技能来编写利用并行计算和通用网格可用性的源代码。建议的工具包将不再需要花费时间为每个经济应用程序编写复杂的程序。建议的工具包的架构设计得足够通用，可以产生重大的更广泛的影响。最终产品一旦完成，研究人员就可以在提案中研究的两个模型以及当前线性模型之外估计多种宏观经济模型，目前线性模型的广度和深度往往受到计算困难的影响。在当前经济环境下，可用于政策分析的更具挑战性的经济模型的例子有：非线性结构经济模型、大型非线性计量经济学模型、动态学习模型以及允许模型错误指定的稳健性分析。

In this project, the investigator provides a new Bayesian simulation toolkit that allows economists to study a variety of economic models which are difficult to quantify due to their computational complexity. Major technical difficulties include intractable likelihoods full of multiple peaks and thin winding ridges, separated by wide zero-probability regions.An important reason for providing a completely new set of simulation tools relates to the estimation of the two regime-switching general equilibrium models proposed here. In the process of estimating these models the investigator identifies several puzzling results. It is tempting to infer that such undesirable results are a reflection of some fundamental defects of the kind of macroeconomic models studied in the literature. This inference turns out to be incorrect. The investigator's discovery is that the likelihood functions and the posterior distributions are far more complicated than what existing Monte Carlo Markov Chain (MCMC) techniques can handle. The puzzling estimates are not a reflection of the model's property itself, but rather are predominantly a consequence of the inadequacy of the current computational techniques available to macroeconomists.To meet this challenge the investigator develops a more complete treatment of estimation techniques. The proposed research is designed to avoid the aforementioned problems inherent in economic models. In particular, it consists of three main components.(1) The investigator develops two structural models that explicitly address the impact of the recent turmoil in housing and financial markets on the macroeconomy and the effect of subsequent policy interventions.(2) To obtain accurate estimation techniques for these models the investigator develops a new set of MCMC techniques, addressing a combination of multiple local peaks, thin winding ridges, and a high-dimensional parameter pace which often makes it very difficult and frequently infeasible to utilize existing MCMC algorithms.(3) To make the new methods accessible to the general public the investigator develops a toolkit that comprises a dynamic scheduler that allows exploitation of parallel computation required by many modern quantitative economic applications. This general toolkit can be applied to a wide range of economic problems beyond the new models discussed in this proposal.Macroeconomic models that can be utilized to address the current economic problems and the relevant policy recipes are, inevitably, complicated. It is well-known that the accurate estimation of such models poses an extraordinarily challenging task since the standard methods used in the macroeconomic literature can fail when the model becomes almost intractable. To avoid distortion of the economic implications from the model itself, the proposed new computational techniques are needed. This will permit researchers to achieve a high level of inferential accuracy so that computational inaccuracy does not contaminate or compromise the model's economic meaning and subsequent policy recommendations.The ultimate goal of the proposal is to make the toolkit available to academic and government researchers, as well as graduate students, and to allow researchers to estimate various structural models to address pertinent and pressing policy questions with relatively simple resources. Writing a parallelized computer program for each economic application is a challenging and time-consuming task even to a seasoned programmer; many economists simply do not have the time or the computer skills to write the source code that takes advantage of parallel computing and general grid usability. The proposed toolkit will eliminate the need to invest time on writing a sophisticated program for each and every economic application.The architecture of the proposed toolkit is designed to be general enough to have a significant broader impact. The final product, once completed, allows researchers to estimate a multitude of macroeconomic models beyond the two models studied in the proposal and beyond current linear models whose breadth and depth are often comprised by computational difficulties. Examples of more challenging economic models usable for policy analysis in the current economic environment are nonlinear structural economic models, large nonlinear econometric models, dynamic learning models, and robustness analysis that allows for model misspecification.