The shocks which hit macroeconomic models such as Vector Autoregressions (VARs) have the potential to be non-Gaussian, exhibiting asymmetries and fat tails. This consideration motivates the VAR developed in this paper which uses a Dirichlet process mixture (DPM) to model the shocks. However, we do not follow the obvious strategy of simply modeling the VAR errors with a DPM since this would lead to computationally infeasible Bayesian inference in larger VARs and potentially a sensitivity to the way the variables are ordered in the VAR. Instead we develop a particular additive error structure inspired by Bayesian nonparametric treatments of random effects in panel data models. We show that this leads to a model which allows for computationally fast and order-invariant inference in large VARs with nonparametric shocks. Our empirical results with nonparametric VARs of various dimensions shows that nonparametric treatment of the VAR errors is particularly useful in periods such as the financial crisis and the pandemic.

翻译：冲击（如向量自回归模型中的冲击）可能呈现非高斯特征，表现出非对称性和厚尾现象。这一考虑促使本文开发了一种使用狄利克雷过程混合模型（DPM）对冲击进行建模的VAR模型。然而，我们并未采用简单的直接以DPM建模VAR误差的策略，因为这将导致较大规模VAR模型在贝叶斯推断中面临计算不可行性，并可能对变量在VAR中的排序方式存在敏感性。相反，我们借鉴面板数据模型中随机效应的贝叶斯非参数处理方法，开发了一种特定的加性误差结构。研究表明，该模型能够实现对具有非参数冲击的大规模VAR模型进行快速且排序不变的推断。针对不同维度的非参数VAR模型进行的实证分析表明，在金融危机和新冠疫情等时期，对VAR误差进行非参数处理尤为有效。