On the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Space

Acknowledgments: The author wishes to thank Professor Anna Chojnowska-Michalik and the referee for many helpful suggestions and comments.We study a class of stochastic evolution equations in a Banach space E driven by cylindrical Wiener process. Three different analytical concepts of solutions: generalised strong, weak and mild are defined and the conditions under which they are equivalent are given. We apply this result to prove existence, uniqueness and continuity of weak solutions to stochastic delay evolution equations. We also consider two examples of these equations in non-reflexive Banach spaces: a stochastic transport equation with delay and a stochastic delay McKendrick equation

Replication data for: Price-setting heterogeneity and robust monetary policy in a two-sector DSGE model of a small open economy

Research data associated with the manuscript: [1] Górajski, M., Kuchta, Z., Leszczyńska-Paczesna, A., 2021, Price-setting heterogeneity and robust monetary policy in a two-sector DSGE model of a small open economy The Readme file describes all user-defined MATLAB functions that solve the robust monetary policy rules (see problems (44) and (45)) and replicate the main results from Section 4. We group them into three folders: main_estimation, main_robust_simple_rules, and main_sensitivity_analysis. This work is supported by the National Science Centre in Poland under Grant No. 2017/26/D/HS4/00942. Abstract This paper offers a welfare analysis of robust simple monetary policy rules in a multi-sector dynamic stochastic general equilibrium model of a small open economy. The model assumes price-setting heterogeneity between two sectors of the economy: the production of food and energy goods, and the remaining consumption goods and services. We determine monetary policy rules that minimise the Bayesian risk and take into account the uncertainty of the economic environment. Using this approach we propose a robust price index. To illustrate an application, we estimate the model on Polish data and compare expected welfare losses under implementable monetary policy rules. We show that reacting to core inflation improves social welfare more than responding to headline inflation. Moreover, the choice between the robust headline and core inflation rules may depend on country-specific factors, such as the share of food and energy in a consumption bundle or the level of competitiveness

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., 2021, 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 from Section 4 and replicate all results. We group them into seven folders: 1. main_data It performs the data preparation process. 2. main_estimation It estimates 24 versions of the Erceg, Henderson, and Levine (2000) small-scale DSGE model (EHL model). They differ by the Talor-type rule. We consider eight sets of the response variables in the policy rule (see Table 1) with three different dynamic specifications: backward-looking, cotemporaneous and forward-looking. 3. main_measuring_uncertainty It evaluates the MWL and OPFC distributions for 24 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 from Section 4. 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 This paper offers 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 who 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 for verifying the k-degree stochastic dominance relation. Third, we apply our approach to a dynamic stochastic general equilibrium model, estimated for the U.S. economy. We show that using stochastic dominance to rank simple policy rules yields different rankings than using well-established robust approaches. The contemporaneous monetary policy rule that reacts to inflation and the output gap, with an interest rate smoothing mechanism, minimises the welfare loss for all decision-makers who admit infinite degree stochastic dominance preferences