Quantitative Economics 6 (2015) - Merging simulation and projection approaches to solve high-dimensional problems - Numerical algorithm

Sep 18, 2026

Introduces a numerical algorithm for solving dynamic economic models by merging stochastic simulation with projection techniques. The method approximates the ergodic measure via simulation, then covers its support using a fixed grid whose construction is the central innovation. Instead of using a dense cloud of simulated points, the approach replaces it with a smaller set of representative points. Three methods are proposed for constructing these points—clustering, ε-distinguishable sets, and a locally adaptive ε-distinguishable variant—validated on neoclassical growth and large new Keynesian models with a zero lower bound.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages69

Reading Time2 h 54 min

AccessFree to download

Introduction

Numerical algorithm overview

Construction of fixed grids via representative points

Three techniques for representative points

Quantitative Economics 6 (2015), 1–47 1759-7331/20150001 Merging simulation and projection approaches to solve high-dimensional problems with an application toa new Keynesian model Lilia Maliar Stanford University Serguei Maliar Santa Clara University We 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. [Lilia Maliar:](Lilia Maliar: maliarl@stanford.edu)[ maliarl@stanford.edu](Lilia Maliar: maliarl@stanford.edu) Serguei Maliar: [smaliar@scu.edu](smaliar@scu.edu) This 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 . Copyright © 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). DOI: 10.3982/QE364 2 Maliar and Maliar Quantitative Economics 6 (2015) Keywords. Ergodic set, ε-distinguishable set, clusters, adaptive grid, discrepancy, large-scale model, new Keynesian model, ZLB, stochastic simulation. JEL classification. C61, C63, C68, E31, E52 . 1. Introduction We 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

FAQs

What problem does the paper address?

The paper addresses solving dynamic economic models in high-dimensional settings by developing a tractable numerical algorithm.

How does the proposed method combine simulation and projection?

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.

What are the key techniques for constructing representative points?

The paper presents three options: a clustering method, an ε-distinguishable set method, and a locally adaptive variant of the ε-distinguishable set method.

Sep 18, 2026

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