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.     

Bayesian Analysis of DSGE Models

This paper reviews Bayesian methods that have been developed in recent years to estimate and evaluate dynamic stochastic general equilibrium (DSGE) models. We consider the estimation of linearized DSGE models, the evaluation of models based on Bayesian model checking, posterior odds comparisons, and comparisons to vector autoregressions, as well as the non-linear estimation based on a second-order accurate model solution. These methods are applied to data generated from correctly specified and misspecified linearized DSGE models and a DSGE model that was solved with a second-order perturbation method.     

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.     

货币政策转型背景下汇率调整对宏观经济的影响——基于开放经济DSGE模型的研究

在货币政策转型背景下研究人民币汇率调整对宏观经济波动的影响,通过构建一个符合中国实际情况的开放经济DSGE模型,对比分析数量型和价格型的货币政策规则对烫平人民币汇率调整导致的宏观经济波动的效果。研究结果表明:当人民币汇率冲击导致经济波动时,数量型规则比价格型规则对烫平经济波动的作用更有效,且能够更好地减小社会福利损失。因此,在货币政策逐渐从数量型向价格型转变的过程中,仍然不能放弃数量型工具的使用,综合运用数量和价格两种调控手段对于转型中的中国而言是比较合适的选择。     

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.     

An Application of Vector Time Series Techniques to Macroeconomic Forecasting

A wide variety of time series techniques are now used for generating forecasts of economic variables, with each technique attempting to summarize and exploit whatever regularities exist in a given data set. It appears that many researchers arbitrarily choose one of these techniques. The purpose of this article is to provide an example for which the choice of time series technique appears important; merely choosing arbitrarily among available techniques may lead to suboptimal results.     

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。     

Forecasting composite indicators with anticipated information: an application to the industrial production index

Summary. Many economic and social phenomena are measured by composite indicators computed as weighted averages of a set of elementary time series. Often data are collected by means of large sample surveys, and processing takes a long time, whereas the values of some elementary component series may be available a considerable time before the others and may be used for forecasting the composite index. This problem is addressed within the framework of prediction theory for stochastic processes. A method is proposed for exploiting anticipated information to minimize the mean-square forecast error, and for selecting the most useful elementary series. An application to the Italian general industrial production index is illustrated, which demonstrates that knowledge of anticipated values of some, or even just one, component series may reduce the forecast error considerably.     

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.     

Bayesian analysis of spatial data using different variance and neighbourhood structures

In disease mapping, the overall goal is to study the incidence or mortality risk caused by a specific disease in a number of geographical regions. It is common to assume that the response variable follows a Poisson distribution, whose average rate can be explained by a group of covariates and a random effect. For this random effect, it is considered conditional autoregressive (CAR) models, which carry information about the neighbourhood relationship between the regions. The focus of this paper was to explore and compare some CAR models proposed in the literature. An application with epidemiological data was conducted to model the risk of death due to Crohn's Disease and Ulcerative Colitis in the State of São Paulo – Brazil. Finally, a simulation study was done to strengthen the results and assess the performance of the models in the presence of various levels of spatial dependence.     

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.     

A NOTE ON ASYMPTOTIC POSTERIOR NORMALITY FOR STOCHASTIC PROCESSES

In a recent paper, Sweeting & Adekola (1987) presented a fairly general set of conditions for asymptotic posterior normality which covers a wide class of problems. In this paper we present an example of an explosive autoregressive model where our condition A4 does not hold.     

An Interest-rate Model Analysis Based on Data Augmentation Bayesian Forecasting

In this paper, the author presents an efficient method of analyzing an interest-rate model using a new approach called 'data augmentation Bayesian forecasting.' First, a dynamic linear model estimation was constructed with a hierarchically-incorporated model. Next, an observational replication was generated based on the one-step forecast distribution derived from the model. A Markov-chain Monte Carlo sampling method was conducted on it as a new observation and unknown parameters were estimated. At that time, the EM algorithm was applied to establish initial values of unknown parameters while the 'quasi Bayes factor' was used to appreciate parameter candidates. 'Data augmentation Bayesian forecasting' is a method of evaluating the transition and history of 'future,' 'present' and 'past' of an arbitrary stochastic process by which an appropriate evaluation is conducted based on the probability measure that has been sequentially modified with additional information. It would be possible to use future prediction results for modifying the model to grasp the present state or re-evaluate the past state. It would be also possible to raise the degree of precision in predicting the future through the modification of the present and the past. Thus, 'data augmentation Bayesian forecasting' is applicable not only in the field of financial data analysis but also in forecasting and controlling the stochastic process.     

Forecasting for some stochastic process models related to sow farm management

Sow farm management requires appropriate methods to forecast the sow population structure evolution. We describe two models for such purpose. The first is a semi-Markov process model, used for long-term predictions and strategic management. The second is a state-space model for continuous proportions, used for short-term predictions and operational management.     

A comparison of Bayesian model selection based on MCMC with an application to GARCH-type models

This paper presents a comprehensive review and comparison of five computational methods for Bayesian model selection, based on MCMC simulations from posterior model parameter distributions. We apply these methods to a well-known and important class of models in financial time series analysis, namely GARCH and GARCH-t models for conditional return distributions (assuming normal and t-distributions). We compare their performance with the more common maximum likelihood-based model selection for simulated and real market data. All five MCMC methods proved reliable in the simulation study, although differing in their computational demands. Results on simulated data also show that for large degrees of freedom (where the t-distribution becomes more similar to a normal one), Bayesian model selection results in better decisions in favor of the true model than maximum likelihood. Results on market data show the instability of the harmonic mean estimator and reliability of the advanced model selection methods.     

Exact Bayesian Inference and Model Selection for Stochastic Models of Epidemics Among a Community of Households

Abstract.  Much recent methodological progress in the analysis of infectious disease data has been due to Markov chain Monte Carlo (MCMC) methodology. In this paper, it is illustrated that rejection sampling can also be applied to a family of inference problems in the context of epidemic models, avoiding the issues of convergence associated with MCMC methods. Specifically, we consider models for epidemic data arising from a population divided into households. The models allow individuals to be potentially infected both from outside and from within the household. We develop methodology for selection between competing models via the computation of Bayes factors. We also demonstrate how an initial sample can be used to adjust the algorithm and improve efficiency. The data are assumed to consist of the final numbers ultimately infected within a sample of households in some community. The methods are applied to data taken from outbreaks of influenza.     

Spectral representation and autocovariance structure of Markov switching DSGE models

Abstract

We investigate the L²-structure of Markov switching Dynamic Stochastic General Equilibrium (MS DSGE) models and derive conditions for strict and second-order stationarity. Then we determine the autocovariance function of the process driven by a stationary MS DSGE model and give a stable VARMA representation of it. It turns out that the autocovariance structure of the process coincides with that of a standard VARMA. Finally, we propose a method to derive the spectral density in a matrix closed-form of MS DSGE models. Our results relate with the works of Francq and Zakoian, Krolzig, Zhang and Stine. Numerical and empirical illustrations complete the article.     

Model Selection for Vector Autoregressive Processes via Adaptive Lasso

Determination of the best subset is an important step in vector autoregressive (VAR) modeling. Traditional methods either conduct subset selection and parameter estimation separately or compute expensively. In this article, we propose a VAR model selection procedure using adaptive Lasso, for it is computational efficient and can select subset and estimate parameters simultaneously. By proper choice of tuning parameters, we can choose the correct subset and obtain the asymptotic normality of the non zero parameters. Simulation studies and real data analysis show that adaptive Lasso performs better than existing methods in VAR model fitting and prediction.