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Approximating high-dimensional dynamic models: sieve value function iteration

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  • Peter Arcidiacono
  • Patrick Bayer
  • Federico A. Bugni
  • Jonathan James

Abstract

Many dynamic problems in economics are characterized by large state spaces, which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of high-dimensional dynamic models based on sieves and establish results for the: (a) consistency, (b) rates of convergence, and (c) bounds on the error of approximation. We embed this method for approximating the solution to the dynamic problem within an estimation routine and prove that it provides consistent estimates of the model’s parameters. We provide Monte Carlo evidence that our method can successfully be used to approximate models that would otherwise be infeasible to compute, suggesting that these techniques may substantially broaden the class of models that can be solved and estimated.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Cleveland in its series Working Paper with number 1210.

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Date of creation: 2012
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Handle: RePEc:fip:fedcwp:1210

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Keywords: Estimation theory ; Quantitative policy modeling ; Simulation modeling;

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  1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
  2. Igal Hendel & Aviv Nevo, 2006. "Measuring the Implications of Sales and Consumer Inventory Behavior," Econometrica, Econometric Society, vol. 74(6), pages 1637-1673, November.
  3. Victor Aguirregabiria & Pedro Mira, 1999. "Swapping the Nested Fixed-Point Algorithm: a Class of Estimators for Discrete Markov Decision Models," Computing in Economics and Finance 1999 332, Society for Computational Economics.
  4. Gregory S. Crawford & Matthew Shum, 2005. "Uncertainty and Learning in Pharmaceutical Demand," Econometrica, Econometric Society, vol. 73(4), pages 1137-1173, 07.
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Cited by:
  1. Meredith Fowlie & Mar Reguant & Stephen P. Ryan, 2012. "Market-Based Emissions Regulation and Industry Dynamics," NBER Working Papers 18645, National Bureau of Economic Research, Inc.

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