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Stochastic simulation approximates the ergodic measure, while the method covers its support using a fixed grid. Projection techniques then solve the model accurately on that grid. The core novelty is replacing a large cloud of simulated points with a smaller set of representative points. Three construction techniques are compared: clustering, epsilon-distinguishable sets, and a locally adaptive variant. The approach targets high-dimensional state spaces and is illustrated using neoclassical growth and large-scale New Keynesian models with a zero lower bound.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/merging-simulation-and-projection-approaches-to-solve-high-dimensional-problems-with-an-application-to-a-new-keynesian-model/297118/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/merging-simulation-and-projection-approaches-to-solve-high-dimensional-problems-with-an-application-to-a-new-keynesian-model/297118.png","ImageObject",300,407,{"name":92,"@type":93},"8796093062539","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-22","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does the proposed algorithm address?","Question",{"text":112,"@type":113},"It addresses solving dynamic economic models with high-dimensional state spaces efficiently, using an approach that remains tractable on a desktop computer.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the method combine simulation and projection?",{"text":117,"@type":113},"Simulation approximates the solution’s ergodic measure, a fixed grid covers its support, and projection techniques then compute accurate solutions on that grid.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the main novelty in the paper’s grid construction?",{"text":121,"@type":113},"The grid replaces a large cloud of simulated points with a smaller set of representative points, constructed via clustering, epsilon-distinguishable sets, or a locally adaptive variant.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},297118,1789740721,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":66,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":133,"file_id":134,"file_url":135,"file_type":136,"file_size":137,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":138,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143,"preview_page_count":4},8796093062539,"Merging Simulation and Projection Approaches to Solve High-Dimensional Problems with an Application to a New Keynesian model  \nLilia Maliar and Serguei Maliar  \nMarch 9, 2014  \nAbstract  \nWe introduce a numerical algorithm for solving dynamic economic models that merges stochastic simulation and projection approaches: we use simulation to approximate the ergodic measure of the solution, we cover the support of the constructed ergodic measure with a Öxed grid, and we use projection techniques to accurately solve the model on that grid. The construction of the grid is the key novel piece of our analysis: we replace a large cloud of simulated points with a small set of \"representative\" points. We present three alternative techniques for constructing representative points: a clustering method, an epsilon-distinguishable set method, and a locally-adaptive variant of the epsilon-distinguishable set method. As an illustration, we solve one-and multi-agent neoclassical growth models and a large-scale new Keynesian model with a zero lower bound on nominal interest rates. The proposed solution algorithm is tractable in problems with high dimensionality (hundreds of state variables) on a desktop computer.  \nJEL classification : C61, C63, C68, E31, E52  \nKey Words : ergodic set; \"-distinguishable set; clusters; adaptive grid; discrepancy; large-scale model; new Keynesian model; ZLB; stochastic simulation  \n Ken Judd was also an author on this paper. See page 43   \n1 Introduction  \nWe introduce a numerical algorithm for solving dynamic economic models that merges stochastic simulation and projection approaches: we use simulation to approximate the ergodic measure of the solution, we cover the support of the constructed ergodic measure with a Öxed grid, and we use projection techniques to accurately solve the model on that grid. The construction of the grid is the key novel piece of our analysis: wereplace a large cloud of simulated points with a small set of \"representative\" points. We present three alternative techniques for constructing representative points: a clustering method, an epsilon-distinguishable set method, and a locally-adaptive variant of the epsilon-distinguishable set method. As an illustration, we solve one-and multi-agent neoclassical growth models and a large-scale new Keynesian model with a zero lower bound on nominal interest rates. The proposed solution algorithm is tractable in problems with high dimensionality (hundreds of state variables) on a desktop computer.  \nOne broad class of numerical methods for solving dynamic economic models buildson stochastic simulation. First, this class includes iterative methods for solving rational expectations models; see, e.g., Marcet (1988), Smith (1993), Maliar and Maliar (2005) and Judd et al. (2011a) . Second, it includes learning-based analysis; see, e.g., Marcet and Sargent (1989), Bertsekas and Tsitsiklis (1996), Pakes and McGuire (2001) and Powell (2011) . Finally, it includes methods that use simulation to reduce information sets of decision makers; see, e.g., Krusell and Smith (1998), and Benkard et al. (2008) . The key advantage of stochastic simulation methods is that the geometry of the set on which the solution is computed is adaptive. Namely, these methods solve dynamic economic modelson a set of points produced by stochastic simulation, avoiding thus the cost of Önding solutions in areas of the state space that are e§ectively never visited in equilibrium; see Judd et al. (2011a) for a discussion. However, a set of simulated points itself is not ane¢ cient choice either as a grid for approximating a solution (it contains many closelylocated and hence, redundant points) or as a set of nodes for approximating expectation functions (the accuracy of Monte Carlo integration is low) .  \nAnother broad class of numerical methods for solving dynamic economic models relies on projection techniques; see, e.g., Wright and Williams (1984), Judd (1992), Christiano and Fisher (20","cbCaiuAyqozBp2gt","https://ap.wps.com/l/cbCaiuAyqozBp2gt","pdf",815913,51,"English","# Abstract\n# Introduction\n## Stochastic simulation methods\n## Projection techniques\n## Combined approach and example (Figures 1a-1d)","[{\"question\":\"What problem does the proposed algorithm address?\",\"answer\":\"It addresses solving dynamic economic models with high-dimensional state spaces efficiently, using an approach that remains tractable on a desktop computer.\"},{\"question\":\"How does the method combine simulation and projection?\",\"answer\":\"Simulation approximates the solution’s ergodic measure, a fixed grid covers its support, and projection techniques then compute accurate solutions on that grid.\"},{\"question\":\"What is the main novelty in the paper’s grid construction?\",\"answer\":\"The grid replaces a large cloud of simulated points with a smaller set of representative points, constructed via clustering, epsilon-distinguishable sets, or a locally adaptive variant.\"}]","Merging Simulation and Projection Approaches to Solve High-Dimensional Problems with an Application to a New Keynesian model | PDF",129]