Tailored Randomized-block MCMC Methods for Analysis of DSGE Models∗
Tailored Randomized-block MCMC Methods for Analysis of DSGE Models∗
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用于 DSGE 模型分析的定制随机块 MCMC 方法*
DOI：
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发表时间：
2009
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通讯作者：
Srikanth Ramamurthy
中科院分区：
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作者：
S. Chib;Srikanth Ramamurthy
在本文中，我们开发了新的马尔可夫链蒙特卡罗方案的DSGE模型的贝叶斯估计。我们的工作的动机产生于一些缺点的单块随机游走大都会黑斯廷斯（M-H）算法（RW-MH），采样方法，已被用于在这方面的日期。在我们的基本定制随机块（TaRB-MH）算法中，模型的参数在每次迭代时随机聚类到任意数量的块中。然后通过M-H步骤顺序更新每个块。此外，根据Chib和Greenberg（1994，1995）以及Chib和Ergashev（2008）的模拟退火输出，每个块的建议密度都是根据目标密度的位置和曲率定制的。我们还提供了一个扩展的TaRB-MH算法采样多峰分布。在这个版本中，我们称之为TaRBMJ-MH算法，在预先指定的模式跳跃迭代中（比如每100次），使用混合建议密度从一个模态区域生成单块建议，然后根据M-H移动概率接受该建议。在非模式跳跃迭代时，通过应用TaRB-MH算法来获得绘制。方法的发展是通过展示Chib（1995年）和Chib和Jeliazkov（2001年）的方法如何适应这些抽样方案来估计模型的边际似然来完成的。我们说明我们的方法与援助的程式化问题和三个DSGE模型，已出现在文献中。第一个是爱尔兰（2004年）的模型，我们表明TaRB-MH算法比RW-MH算法更可靠和有效。我们的第二个例子是An and Schorfheide（2007）中的模型。该模型中的后验分布由于存在多个模式而更具挑战性。如这些作者所示，RW-MH算法不能从低模态区域跳到高模态区域，反之亦然。我们衷心感谢圣路易斯华盛顿大学奥林商学院经济与战略研究中心（克雷斯）的支持。[2] Chib：圣路易斯华盛顿大学奥林商学院，Campus Box 1133，1 Bookings Drive，St. Louis，MO 63130（电子邮件：chib@wustl.edu）; Ramamurthy：圣路易斯华盛顿大学经济系，Campus Box 1208，1 Bookings Drive，St. Louis，MO 63130（电子邮件：sramamur@artsci.wustl.edu）。
In this paper we develop new Markov chain Monte Carlo schemes for Bayesian estimation of DSGE models. The motivation for our work arises from some of the shortcomings of the single block random walk Metropolis Hastings (M-H) algorithm (RW-MH), the sampling method that has been used to date in this context. In our basic tailored randomized block (TaRB-MH) algorithm, the parameters of the model are randomly clustered at every iteration into an arbitrary number of blocks. Then each block is sequentially updated through an M-H step. Furthermore, the proposal density for each block is tailored to the location and curvature of the target density based on the output of simulated annealing, following Chib and Greenberg (1994, 1995) and Chib and Ergashev (2008). We also provide an extension of the TaRB-MH algorithm for sampling multi-modal distributions. In this version, which we refer to as the TaRBMJ-MH algorithm, at a pre-specified mode jumping iteration (say every 100th), a single-block proposal is generated from one of the modal regions using a mixture proposal density, and this proposal is then accepted according to an M-H probability of move. At the non-mode jumping iterations, the draws are obtained by applying the TaRB-MH algorithm. The methodological developments are completed by showing how the approach in Chib (1995) and Chib and Jeliazkov (2001) can be adapted to these sampling schemes for estimating the model marginal likelihood. We illustrate our methods with the aid of stylized problems and three DSGE models that have appeared in the literature. The first is the model in Ireland (2004) where we show that the TaRB-MH algorithm is more reliable and efficient than the RW-MH algorithm. Our second example is the model in An and Schorfheide (2007). The posterior distribution in this model is more challenging to simulate on account of multiple modes. As shown by these authors, the RW-MH algorithm is unable to jump from the low modal region to the high modal region, and vice-versa. The TaRBMJ-MH ∗We gratefully acknowledge the support from Center for Research in Economics and Strategy (CRES), in the Olin Business School, Washington University in St. Louis. †Chib: Olin Business School, Washington University in St. Louis, Campus Box 1133, 1 Bookings Drive, St. Louis, MO 63130 (e-mail: chib@wustl.edu); Ramamurthy: Department of Economics, Washington University in St. Louis, Campus Box 1208, 1 Bookings Drive, St. Louis, MO 63130 (e-mail: sramamur@artsci.wustl.edu).