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Merging simulation and projection approaches to solve high‐dimensional problems with an application to a new Keynesian model

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  • Lilia Maliar
  • Serguei Maliar

Abstract

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. 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.

Suggested Citation

  • Lilia Maliar & Serguei Maliar, 2015. "Merging simulation and projection approaches to solve high‐dimensional problems with an application to a new Keynesian model," Quantitative Economics, Econometric Society, vol. 6(1), pages 1-47, March.
  • Handle: RePEc:wly:quante:v:6:y:2015:i:1:p:1-47
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