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Department ofEconomics


Merging Simulation and Projection Approaches to Solve High-Dimensional Problems with an Application to a New Keynesian model

Serguei Maliara and Lilia Maliar

Quantitative Economics Volume 6(1), pp.1-47, March 2015

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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.

LSB Research, ECON, 2015, Serguei Maliar