Replication data for: Designing Optimal Macroeconomic Policy Rules under Parameter Uncertainty: A Stochastic Dominance Approach

Research data associated with the manuscript: [1] Górajski, M., Kuchta, Z., 2022, Designing Optimal Macroeconomic Policy Rules under Parameter Uncertainty: A Stochastic Dominance Approach. This work is supported by the National Science Centre in Poland under Grant No. 2017/26/D/HS4/00942. It contains all user-defined MATLAB and R functions that implement our algorithms and replicate all results. We group them into seven folders: 1. main_data It performs the data preparation process. 2. main_estimation It estimates 25 versions of the Erceg, Henderson, and Levine (2000) small-scale DSGE model (EHL model). They differ by the monetary policy rule. We consider eight Taylor-type rules (see Table 1) and one nominal GDP targeting rule (H.2) (see Appendix H). 3. main_measuring_uncertainty It evaluates the MWL and OPFC distributions for all versions of the EHL model. 4. main_compare_losses It contains the novel EP Bayesian tests for the SDk relations from Section 4.2. We use these tests to compare the MWLs. 5. main_robust_simple_rules It replicates all Bayesian and min-max robust strategies. 6. main_simulations It collects all codes that perform the simulations of the EHL model with SDk-optimal and estimated policy rules. 7. main_performance_BayesEP_SDk_tests It assesses the performance of the EP Bayesian tests for SDk relations. Abstract In this paper, we offer a Bayesian decision-theoretic approach to policy evaluation in rational expectation models. First, we show how to correctly assess and rank simple policy rules under the welfare loss minimization criterion in the presence of uncertainty about the model's structural parameters. We consider a Bayesian policymaker that assesses the effectiveness of policy actions, by comparing the distributions of welfare losses using stochastic dominance orderings. Second, we propose a new Bayesian testing procedure to verify higher and infinite degrees of stochastic dominance. Third, we demonstrate a potential use of the suggested approach to a dynamic stochastic general equilibrium model, estimated for the U.S. economy. We show that using stochastic dominance to rank simple monetary policy rules yields different rankings than well-established robust approaches. The contemporaneous monetary policy rule that reacts to inflation and the output gap, with an interest rate smoothing mechanism, minimizes the welfare loss for all decision-makers who admit infinite degree stochastic dominance preferences.

本研究数据关联学术论文[1]：Górajski, M., Kuchta, Z., 2022, 《参数不确定下的最优宏观经济政策规则设计：随机占优方法》。本研究工作得到波兰国家科学中心资助，资助编号为2017/26/D/HS4/00942。
本数据集包含所有用于实现本文算法、复现全部研究结果的用户自定义MATLAB与R函数，划分为7个功能文件夹：
1. main_data：用于执行数据预处理流程。
2. main_estimation：对Erceg、Henderson与Levine(2000)提出的小型动态随机一般均衡（Dynamic Stochastic General Equilibrium, DSGE）模型（下称EHL模型）的25种变体进行估计。这些变体的差异在于货币政策规则的设置：本文共考虑8类泰勒型规则（Taylor-type rules，详见表1）与1类名义GDP盯住规则（nominal GDP targeting rule，H.2，详见附录H）。
3. main_measuring_uncertainty：针对所有EHL模型变体，评估其边际福利损失（Marginal Welfare Loss, MWL）与最优政策前沿曲线（Optimal Policy Frontier Curve, OPFC）的分布特征。
4. main_compare_losses：包含本文4.2节提出的用于检验随机占优（Stochastic Dominance, SDk）关系的新型期望损失（Expected Loss, EP）贝叶斯检验方法，用于对比各模型的边际福利损失。
5. main_robust_simple_rules：复现全部贝叶斯与极小极大稳健策略。
6. main_simulations：收录所有用于模拟搭载随机占优最优规则与估计得到的政策规则的EHL模型的代码。
7. main_performance_BayesEP_SDk_tests：评估针对随机占优关系的EP贝叶斯检验的性能表现。

## 摘要
本文提出一种基于贝叶斯决策理论的分析框架，用于理性预期模型中的政策评估。其一，本文阐明了在模型结构参数存在不确定性的情境下，如何基于福利损失最小化准则，对简单政策规则开展合理评估与排序。本文假设贝叶斯政策制定者通过比较福利损失的分布特征，借助随机占优序关系来衡量政策行动的有效性。其二，本文提出了一种全新的贝叶斯检验程序，可用于验证高阶乃至无穷阶的随机占优关系。其三，本文以针对美国经济估计得到的动态随机一般均衡模型为案例，演示了所提方法的应用潜力。研究结果表明，相较于已被广泛采用的稳健政策评估方法，利用随机占优对简单货币政策规则进行排序会得到截然不同的规则排名。对于所有遵循无穷阶随机占优偏好的决策者而言，同时对通胀与产出缺口做出反应并搭载利率平滑机制的同期货币政策规则，能够实现福利损失最小化的目标。