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Interpolating Value Functions in Discrete Choice Dynamic Programming Models

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  • Sullivan, Paul

Abstract

Structural discrete choice dynamic programming models have been shown to be a valuable tool for analyzing a wide range of economic behavior. A major limitation on the complexity and applicability of these models is the computational burden associated with computing the high dimensional integrals that typically characterize an agent's decision rules. This paper develops a regression based approach to interpolating value functions during the solution of dynamic programming models that alleviates this burden. This approach is suitable for use in models that incorporate unobserved state variables that are serially correlated across time and correlated across choices within a time period. The key assumption is that one unobserved state variable, or error term, in the model is distributed extreme value. Additional error terms that allow for correlation between unobservables across time or across choices within a given time period may be freely incorporated in the model. Value functions are simulated at a fraction of the state space and interpolated at the remaining points using a new regression function based on the extreme value closed form solution for the expected maxima of the value function. This regression function is well suited for use in models with large choice sets and complicated error structures. The performance of the interpolation method appears to be excellent, and it greatly reduces the computational burden of estimating the parameters of a dynamic programming model.

Suggested Citation

  • Sullivan, Paul, 2006. "Interpolating Value Functions in Discrete Choice Dynamic Programming Models," MPRA Paper 864, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:864
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    File URL: https://mpra.ub.uni-muenchen.de/864/1/MPRA_paper_864.pdf
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    Cited by:

    1. Christian Belzil & Jörgen Hansen, 2020. "The evolution of the US family income–schooling relationship and educational selectivity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(7), pages 841-859, November.
    2. Christian Belzil & Jörgen Hansen, 2020. "Reconciling Changes in Wage Inequality With Changes in College Selectivity Using a Behavioral Model," CIRANO Working Papers 2020s-36, CIRANO.

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    More about this item

    Keywords

    dynamic programming models; interpolation; simulation methods; estimation of dynamic programming models;
    All these keywords.

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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