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1759-7331/20150001  \nMerging simulation and projection approaches to solve high-dimensional problems with an application toa new Keynesian model  \nLilia Maliar  \nStanford University  \nSerguei Maliar  \nSanta Clara University  \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 fixed 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 ε-distinguishable set method, and a locally-adaptive variant of the ε-distinguishable set method. Asan 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.  \n[Lilia Maliar:](Lilia Maliar: maliarl@stanford.edu)[ maliarl@stanford.edu](Lilia Maliar: maliarl@stanford.edu)  \nSerguei Maliar: [smaliar@scu.edu](smaliar@scu.edu)  \nThis paper is a substantially revised version of NBER working papers 15965 and 18501 titled “A cluster-grid projection method: Solving problems with high dimensionality” and “Merging simulation and projection approaches to solve high-dimensional problems,” respectively. We started this project with Kenneth L. Judd who subsequently withdrew as an author. We are very grateful to him for his contribution to this paper. We thank the editor of Quantitative Economics, FrankSchorfheide, for many thoughtful comments and suggestions that led to a substantial improvement of the paper. We are also indebted to the editor of Econometrica, Jean-Marc Robin, and five anonymous referees for a large number of useful comments and suggestions in three rounds of revision. Also, we benefited from the comments of seminar participants at University of London, Canadian Central Bank, Cornell University, Federal Reserve Bank of San Francisco, Penn State University, Santa Clara University, Stanford University, University Autonoma de Barcelona, University of Alicante, University of Bilbao, University of California at Berkeley, University of Chicago, University of Edinburgh, and University of Oxford, as well as from participants of the 2011 Society of Economic Dynamics meeting, the 2011, 2012, and 2013 meetings ofthe Society of Computational Economics, the 2013 meeting of the Macro Financial Modeling Group at the University of Chicago, the Summer 2013 Computation in CA Workshop at Stanford University, and the 2014 American Economic Association meeting in Philadelphia. Errors are ours. Lilia Maliar and Serguei Maliar acknowledge support from the Hoover Institution and the Department of Economics at Stanford University, Santa Clara University, University of Alicante, Ivie, MECD, and FEDER funds under the project ECO2012-36719 .  \nCopyright © 2015 Lilia Maliar and Serguei Maliar. Licensed under the Creative Commons AttributionNonCommercial License 3.0. Available at [http://www.qeconomics.org](http://www.qeconomics.org).  \nDOI: 10.3982/QE364  \n2 Maliar and Maliar Quantitative Economics 6 (2015)  \nKeywords. Ergodic set, ε-distinguishable set, clusters, adaptive grid, discrepancy, large-scale model, new Keynesian model, ZLB, stochastic simulation.  \nJEL classification. C61, C63, C68, E31, E52 .  \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 constru","cbCaik3PA0mIzgyi","https://ap.wps.com/l/cbCaik3PA0mIzgyi","pdf",3254276,69,"English","# Introduction\n## Numerical algorithm overview\n## Construction of fixed grids via representative points\n## Three techniques for representative points","[{\"question\":\"What problem does the paper address?\",\"answer\":\"The paper addresses solving dynamic economic models in high-dimensional settings by developing a tractable numerical algorithm.\"},{\"question\":\"How does the proposed method combine simulation and projection?\",\"answer\":\"It uses stochastic simulation to approximate the solution’s ergodic measure, then applies projection techniques to solve the model accurately on a fixed grid that covers the ergodic measure’s support.\"},{\"question\":\"What are the key techniques for constructing representative points?\",\"answer\":\"The paper presents three options: a clustering method, an ε-distinguishable set method, and a locally adaptive variant of the ε-distinguishable set method.\"}]","Quantitative Economics 6 (2015) - Merging simulation and projection approaches to solve high-dimensional problems - Numerical algorithm | PDF",174]