We present a new method for estimating Bayesian vector auto-regression (VAR) models using priors from a dynamic stochastic general equilibrium (DSGE) model. We use the DSGE model priors to determine the moments of an independent Normal-Wishart prior for the VAR parameters. Two hyper-parameters control the tightness of the DSGE-implied priors on the autoregressive coefficients and the residual covariance matrix respectively. Determining these hyper-parameters by selecting the values that maximize the marginal likelihood of the Bayesian VAR provides a method for isolating subsets of DSGE parameter priors that are at odds with the data. We illustrate the ability of our approach to correctly detect incorrect DSGE priors for the variance of structural shocks using a Monte Carlo experiment. We also demonstrate how posterior estimates of the DSGE parameter vector can be recovered from the BVAR posterior estimates: a new ‘quasi-Bayesian’ DSGE estimation. An empirical application on US data reveals economically meaningful differences in posterior parameter estimates when comparing our quasi-Bayesian estimator with Bayesian maximum likelihood. Our method also indicates that the DSGE prior implications for the residual covariance matrix are at odds with the data.

中文翻译：

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BVAR和准贝叶斯DSGE估计的基于DSGE的先验

我们提出了一种使用动态随机一般均衡（DSGE）模型中的先验估计贝叶斯矢量自回归（VAR）模型的新方法。我们使用DSGE模型先验来确定VAR参数的独立Normal-Wishart先验矩。两个超参数分别控制自回归系数和残差协方差矩阵的DSGE隐含先验的紧度。通过选择使贝叶斯VAR的边际可能性最大化的值来确定这些超参数，提供了一种隔离与数据不一致的DSGE参数先验子集的方法。我们使用蒙特卡洛实验说明了我们的方法能够针对结构冲击的变化正确检测不正确的DSGE先验的能力。我们还演示了如何从BVAR后验估计中恢复DSGE参数向量的后验估计：一种新的“准贝叶斯” DSGE估计。在将我们的准贝叶斯估计量与贝叶斯最大似然值进行比较时，对美国数据的经验应用揭示了后参数估计在经济上有意义的差异。我们的方法还表明，残差协方差矩阵的DSGE先验含义与数据不一致。