标题： 基于归一化流神经网络的异质性和代表性代理模型的快速模拟贝叶斯估计 显示英文标题

标题： Fast Simulation-Based Bayesian Estimation of Heterogeneous and Representative Agent Models using Normalizing Flow Neural Networks

摘要： 本文提出了一种基于仿真的深度学习贝叶斯方法，用于宏观经济模型的估计。 该方法即使在似然函数不可处理的情况下也能推导后验分布。 由于贝叶斯估计不需要似然函数，因此也不需要过滤。 这使得能够对具有多达800个潜在状态的HANK模型进行贝叶斯估计，以及对通过不产生似然的方法（例如投影和值函数迭代方法）求解的代表性代理人模型进行估计。 我通过估计一个通过Reiter方法求解的10参数HANK模型来验证该方法的有效性，该模型每时间步生成812个协变量，其中810个是潜在变量，表明这种方法可以在不进行模型简化的情况下处理大规模潜在空间。 我还用通过值函数迭代求解的11参数模型对该算法进行了估计，这种模型无法用Metropolis-Hastings甚至传统的最大似然估计器进行估计。 此外，我展示了使用基于仿真的推断方法相比Metropolis-Hastings，在Smets-Wouters 2007模型上得到的后验分布质量更高且速度更快。 这种方法有助于解决Metropolis-Hastings的计算成本问题，并允许对不产生可处理似然的求解方法进行估计。 显示英文摘要

摘要： This paper proposes a simulation-based deep learning Bayesian procedure for the estimation of macroeconomic models. This approach is able to derive posteriors even when the likelihood function is not tractable. Because the likelihood is not needed for Bayesian estimation, filtering is also not needed. This allows Bayesian estimation of HANK models with upwards of 800 latent states as well as estimation of representative agent models that are solved with methods that don't yield a likelihood--for example, projection and value function iteration approaches. I demonstrate the validity of the approach by estimating a 10 parameter HANK model solved via the Reiter method that generates 812 covariates per time step, where 810 are latent variables, showing this can handle a large latent space without model reduction. I also estimate the algorithm with an 11-parameter model solved via value function iteration, which cannot be estimated with Metropolis-Hastings or even conventional maximum likelihood estimators. In addition, I show the posteriors estimated on Smets-Wouters 2007 are higher quality and faster using simulation-based inference compared to Metropolis-Hastings. This approach helps address the computational expense of Metropolis-Hastings and allows solution methods which don't yield a tractable likelihood to be estimated.