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Approximating high-dimensional dynamic models: sieve value function iteration

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

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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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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  1. Igal Hendel & Aviv Nevo, 2006. "Measuring the Implications of Sales and Consumer Inventory Behavior," Econometrica, Econometric Society, vol. 74(6), pages 1637-1673, November.
  2. 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.
  3. Gregory S. Crawford & Matthew Shum, 2005. "Uncertainty and Learning in Pharmaceutical Demand," Econometrica, Econometric Society, vol. 73(4), pages 1137-1173, 07.
  4. 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.
  5. Hugo Benitez-Silva & John Rust & Gunter Hitsch & Giorgio Pauletto & George Hall, 2000. "A Comparison Of Discrete And Parametric Methods For Continuous-State Dynamic Programming Problems," Computing in Economics and Finance 2000 24, Society for Computational Economics.
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