Bayesian Analysis of DSGE Models by S. An and F. Schorfheide

The paper that An and Schorfheide have written is an excellent piece of work and will become a useful reference for teaching and consultation purposes. The paper discusses in an articulate and convincing manner almost everything that one could think of covering in such a review. This makes the task of the commentator difficult. Nevertheless, I will attempt to add few insights on three issues which, in my opinion, play an important role in applied work and in the interpretation of the estimation result. In particular, I will discuss a) the sensitivity of posterior distributions to prior spreads; b) the effects of model misspecification and an approach to model respecification; c) parameter identification and its consequences for posterior inference.     

Bayesian Analysis of DSGE Models by S. An and F. Schorfheide

The paper that An and Schorfheide have written is an excellent piece of work and will become a useful reference for teaching and consultation purposes. The paper discusses in an articulate and convincing manner almost everything that one could think of covering in such a review. This makes the task of the commentator difficult. Nevertheless, I will attempt to add few insights on three issues which, in my opinion, play an important role in applied work and in the interpretation of the estimation result. In particular, I will discuss a) the sensitivity of posterior distributions to prior spreads; b) the effects of model misspecification and an approach to model respecification; c) parameter identification and its consequences for posterior inference.     

Bayesian Analysis of DSGE Models—Rejoinder

We would like to thank all the discussants for their stimulating comments. While our article to a large extent reviews current practice of Bayesian analysis of Dynamic Stochastic General Equilibrium (DSGE) models the discussants provide many ideas to improve upon the current practice, thereby outlining a research agenda for the years to come. In our rejoinder we will briefly revisit some of the issues that were raised.     

Bayesian Analysis of DSGE Models—Some Comments

Sungbae An and Frank Schorfheide have provided an excellent review of the main elements of Bayesian inference in Dynamic Stochastic General Equilibrium (DSGE) models. Bayesian methods have, for reasons clearly outlined in the paper, a very natural role to play in DSGE analysis, and the appeal of the Bayesian paradigm is indeed strongly evidenced by the flood of empirical applications in the area over the last couple of years. We expect their paper to be the natural starting point for applied economists interested in learning about Bayesian techniques for analyzing DSGE models, and as such the paper is likely to have a strong influence on what will be considered best practice for estimating DSGE models.

The authors have, for good reasons, chosen a stylized six-equation model to present the methodology. We shall use here the large-scale model in Adolfson et al. (2005), henceforth ALLV, to illustrate a few econometric problems which we have found to be especially important as the size of the model increases. The model in ALLV is an open economy extension of the closed economy model in Christiano et al. (2005). It consists of 25 log-linearized equations, which can be written as a state space representation with 60 state variables, many of them unobserved. Fifteen observed unfiltered time series are used to estimate 51 structural parameters. An additional complication compared to the model in An and Schorfheide's paper is that some of the coefficients in the measurement equation are non-linear functions of the structural parameters. The model is currently the main vehicle for policy analysis at Sveriges Riksbank (Central Bank of Sweden) and similar models are being developed in many other policy institutions, which testifies to the model's practical relevance. The version considered here is estimated on Euro area data over the period 1980Q1-2002Q4. We refer to ALLV for details.     

Forecasting Performance of an Open Economy DSGE Model

This paper analyzes the forecasting performance of an open economy dynamic stochastic general equilibrium (DSGE) model, estimated with Bayesian methods, for the Euro area during 1994Q1-2002Q4. We compare the DSGE model and a few variants of this model to various reduced-form forecasting models such as vector autoregressions (VARs) and vector error correction models (VECM), estimated both by maximum likelihood and two different Bayesian approaches, and traditional benchmark models, e.g., the random walk. The accuracy of point forecasts, interval forecasts and the predictive distribution as a whole are assessed in an out-of-sample rolling event evaluation using several univariate and multivariate measures. The results show that the open economy DSGE model compares well with more empirical models and thus that the tension between rigor and fit in older generations of DSGE models is no longer present. We also critically examine the role of Bayesian model probabilities and other frequently used low-dimensional summaries, e.g., the log determinant statistic, as measures of overall forecasting performance.     

Forecasting Performance of an Open Economy DSGE Model

This paper analyzes the forecasting performance of an open economy dynamic stochastic general equilibrium (DSGE) model, estimated with Bayesian methods, for the Euro area during 1994Q1–2002Q4. We compare the DSGE model and a few variants of this model to various reduced-form forecasting models such as vector autoregressions (VARs) and vector error correction models (VECM), estimated both by maximum likelihood and two different Bayesian approaches, and traditional benchmark models, e.g., the random walk. The accuracy of point forecasts, interval forecasts and the predictive distribution as a whole are assessed in an out-of-sample rolling event evaluation using several univariate and multivariate measures. The results show that the open economy DSGE model compares well with more empirical models and thus that the tension between rigor and fit in older generations of DSGE models is no longer present. We also critically examine the role of Bayesian model probabilities and other frequently used low-dimensional summaries, e.g., the log determinant statistic, as measures of overall forecasting performance.     

情绪冲击、资产泡沫与经济波动:基于贝叶斯DSGE的分析

本文在Smets和Wouters(2003)、Christiano等(2005)模型基础上,引入驱动股价泡沫的情绪冲击,构建了情绪冲击通过资产价格渠道影响经济波动的动态随机一般均衡模型,并采用我国2000-2016年的季度数据对模型进行贝叶斯估计。研究表明,由于企业面临融资约束,正向情绪冲击带来股价泡沫的上升起到了放松信贷约束的作用,因而企业投资增加,进而触发一系列经济变量的顺周期波动。情绪冲击能够解释我国股票价格波动的552%以及顺周期性;劳动供给冲击、技术冲击、投资专有冲击、金融冲击都是我国经济波动的来源,尽管其对产出、消费、投资、劳动时间和股票价格波动的贡献存在异质性。     

财政政策DSGE模型中国化构建及其应用

事前模拟经济对财政政策变化的反应是检验政策效果的重要手段。本文通过国外经典模型中国化改进,并引入系统财政规则,构建财政政策DSGE模型。在有效税率估算校准与参数贝叶斯估计基础上,给出政策模拟检验应用示例。发现税率冲击效应模拟是税制改革实验的有效方法,资本税率可作为经济结构调整的政策工具,以及当前增加政府支出拉动增长作用微弱等结论。该研究也可为我国DSGE模型研究提供参考。     

Comment on An and Schorfheide's Bayesian Analysis of DSGE Models

An and Schorfheide's article provides an excellent review of Bayesian estimation of DSGE models. Rather than recapitulating the points already made in this article, my comment focuses on three aspects. It proposes a convergence measure to take account of serial correlation of MCMC draws, explains why the DSGE-VAR framework for policy analysis can be improved by avoiding the ad hoc identification assumption, and discusses an alternative structural approach to model misspecification.     

贝叶斯非线性混合效应模型及其应用研究

由于常用的线性混合效应模型对具有非线性关系的纵向数据建模具有一定的局限性,因此对线性混合效应模型进行扩展,根据变量间的非线性关系建立不同的非线性混合效应模型,并根据因变量的分布特征建立混合分布模型。基于一组实际的保险损失数据,建立多项式混合效应模型、截断多项式混合效应模型和B样条混合效应模型。研究结果表明,非线性混合效应模型能够显著改进对保险损失数据的建模效果,对非寿险费率厘定具有重要参考价值。     

基于多重尝试Metropolis算法的非线性DSGE模型贝叶斯推断

本文提出一种改进的多重尝试Metropolis算法,用于非线性动态随机一般均衡模型的贝叶斯参数估计和模型选择。多重尝试策略通过每次迭代抽取多个尝试点的方法来提高算法的混合速率,新方法中提出使用近似的方法提高计算速度,并通过接收概率调整偏差。数值实验表明新方法在相同的计算时间内具有更高的估计效率。最后,本文比较了具有不同货币政策设定的模型对中国经济数据的拟合效果,发现中国数据更加支持具有时变通胀目标的模型。     

A Bayesian Approach to Model Interdependent Event Histories by Graphical Models

In event history analysis, the problem of modeling two interdependent processes is still not completely solved. In a frequentist framework, there are two most general approaches: the causal approach and the system approach. The recent growing interest in Bayesian statistics suggests some interesting works on survival models and event history analysis in a Bayesian perspective. In this work we present a possible solution for the analysis of dynamic interdependence by a Bayesian perspective in a graphical duration model framework, using marked point processes. Main results from the Bayesian approach and the comparison with the frequentist one are illustrated on a real example: the analysis of the dynamic relationship between fertility and female employment.     

Comment

The article provides detailed and accurate illustrations of Bayesian analysis of DSGE models that are likely to be used increasingly in support of central bank policy making. These comments identify a dozen aspects of these methods, discussing how their application and improvement can contribute to effective support of policy.     

DSGE Models with Student-t Errors

This paper deals with Dynamic Stochastic General Equilibrium (DSGE) models under a multivariate student-t distribution for the structural shocks. Based on the solution algorithm of Klein (2000) and the gamma-normal representation of the t-distribution, the TaRB-MH algorithm of Chib and Ramamurthy (2010 Chib , S. , Ramamurthy , S. ( 2010 ). Tailored randomized block MCMC methods with application to DSGE models . Journal of Econometrics 108 : 19 – 38 .[Crossref], [Web of Science ®] , [Google Scholar]) is used to estimate the model. A technique for estimating the marginal likelihood of the DSGE student-t model is also provided. The methodologies are illustrated first with simulated data and then with the DSGE model of Ireland (2004 Ireland , P. N. ( 2004 ). Technology shocks in the new keynesian model . Review of Economics and Statistics 86 ( 4 ): 923 – 936 .[Crossref], [Web of Science ®] , [Google Scholar]) where the results support the t-error model in relation to the Gaussian model.     

Heteroscedastic Weibull-Normal Mixture Models: A Bayesian Approach

In this article, we propose Bayesian methodology to obtain parameter estimates of the mixture of distributions belonging to the normal and biparametric Weibull families, modeling the mean and the variance parameters. Simulated studies and applications show the performance of the proposed models.     

Bayesian Longitudinal Data Analysis with Mixed Models and Thick-tailed Distributions using MCMC

Linear mixed effects models are frequently used to analyse longitudinal data, due to their flexibility in modelling the covariance structure between and within observations. Further, it is easy to deal with unbalanced data, either with respect to the number of observations per subject or per time period, and with varying time intervals between observations. In most applications of mixed models to biological sciences, a normal distribution is assumed both for the random effects and for the residuals. This, however, makes inferences vulnerable to the presence of outliers. Here, linear mixed models employing thick-tailed distributions for robust inferences in longitudinal data analysis are described. Specific distributions discussed include the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted, and the Gibbs sampler and the Metropolis-Hastings algorithms are used to carry out the posterior analyses. An example with data on orthodontic distance growth in children is discussed to illustrate the methodology. Analyses based on either the Student-t distribution or on the usual Gaussian assumption are contrasted. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process for modelling distributions of the random effects and of residuals in linear mixed models, and the MCMC implementation allows the computations to be performed in a flexible manner.     

Two-Stage Bayesian Model Averaging in Endogenous Variable Models

Economic modeling in the presence of endogeneity is subject to model uncertainty at both the instrument and covariate level. We propose a Two-Stage Bayesian Model Averaging (2SBMA) methodology that extends the Two-Stage Least Squares (2SLS) estimator. By constructing a Two-Stage Unit Information Prior in the endogenous variable model, we are able to efficiently combine established methods for addressing model uncertainty in regression models with the classic technique of 2SLS. To assess the validity of instruments in the 2SBMA context, we develop Bayesian tests of the identification restriction that are based on model averaged posterior predictive p-values. A simulation study showed that 2SBMA has the ability to recover structure in both the instrument and covariate set, and substantially improves the sharpness of resulting coefficient estimates in comparison to 2SLS using the full specification in an automatic fashion. Due to the increased parsimony of the 2SBMA estimate, the Bayesian Sargan test had a power of 50% in detecting a violation of the exogeneity assumption, while the method based on 2SLS using the full specification had negligible power. We apply our approach to the problem of development accounting, and find support not only for institutions, but also for geography and integration as development determinants, once both model uncertainty and endogeneity have been jointly addressed.     

Bayesian Estimation and Prediction of Stochastic Volatility Models via INLA

In this article, we assess Bayesian estimation and prediction using integrated Laplace approximation (INLA) on a stochastic volatility (SV) model. This was performed through a Monte Carlo study with 1,000 simulated time series. To evaluate the estimation method, two criteria were considered: the bias and square root of the mean square error (smse). The criteria used for prediction are the one step ahead forecast of volatility and the one day Value at Risk (VaR). The main findings are that the INLA approximations are fairly accurate and relatively robust to the choice of prior distribution on the persistence parameter. Additionally, VaR estimates are computed and compared for three financial time series returns indexes.