{"title":"Pseudospectral methods for continuous-time heterogeneous-agent models","authors":"Constantin Schesch","doi":"10.1016/j.jedc.2024.104856","DOIUrl":null,"url":null,"abstract":"<div><p>We propose a pseudospectral method to solve heterogeneous-agent models in continuous time. The solution is approximated as a sum of smooth global basis functions, in our case polynomials represented by their values at Chebyshev nodes. We illustrate the method by applying it to a Krusell-Smith model. It solves the differential equations characterizing the steady-state efficiently and precisely, despite using only very few nodes. System dynamics are then automatically differentiated to simulate a linearized model. The full solution takes a third of a second and only uses standard software. A benchmark against finite differences shows that pseudospectral methods achieve far greater precision for a given number of nodes and for a given runtime. We conclude by discussing the methods' applicability, which is promising for smooth multi-dimensional models.</p></div>","PeriodicalId":48314,"journal":{"name":"Journal of Economic Dynamics & Control","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Economic Dynamics & Control","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165188924000484","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
Abstract
We propose a pseudospectral method to solve heterogeneous-agent models in continuous time. The solution is approximated as a sum of smooth global basis functions, in our case polynomials represented by their values at Chebyshev nodes. We illustrate the method by applying it to a Krusell-Smith model. It solves the differential equations characterizing the steady-state efficiently and precisely, despite using only very few nodes. System dynamics are then automatically differentiated to simulate a linearized model. The full solution takes a third of a second and only uses standard software. A benchmark against finite differences shows that pseudospectral methods achieve far greater precision for a given number of nodes and for a given runtime. We conclude by discussing the methods' applicability, which is promising for smooth multi-dimensional models.
期刊介绍:
The journal provides an outlet for publication of research concerning all theoretical and empirical aspects of economic dynamics and control as well as the development and use of computational methods in economics and finance. Contributions regarding computational methods may include, but are not restricted to, artificial intelligence, databases, decision support systems, genetic algorithms, modelling languages, neural networks, numerical algorithms for optimization, control and equilibria, parallel computing and qualitative reasoning.