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Efficient Computation with Taste Shocks

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  • Grey Gordon

Abstract

Taste shocks result in nondegenerate choice probabilities, smooth policy functions, continuous demand correspondences, and reduced computational errors. They also cause significant computational cost when the number of choices is large. However, I show that, in many economic models, a numerically equivalent approximation may be obtained extremely efficiently. If the objective function has increasing differences (a condition closely tied to policy function monotonicity) or is concave in a discrete sense, the proposed algorithms are O(n log n) for n states and n choice--a drastic improvement over the naive algorithm's O(n2) cost. If both hold, the cost can be further reduced to O(n). Additionally, with increasing differences in two state variables, I propose an algorithm that in some cases is O(n2) even without concavity (in contrast to the O(n3) naive algorithm). I illustrate the usefulness of the proposed approach in an incomplete markets economy and a long-term sovereign debt model, the latter requiring taste shocks for convergence. For grid sizes of 500 points, the algorithms are up to 200 times faster than the naive approach.

Suggested Citation

  • Grey Gordon, 2019. "Efficient Computation with Taste Shocks," Working Paper 19-15, Federal Reserve Bank of Richmond.
  • Handle: RePEc:fip:fedrwp:19-15
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    Cited by:

    1. Cristina Arellano & Yan Bai & Gabriel Mihalache, 2018. "Inflation Targeting with Sovereign Default Risk," Department of Economics Working Papers 18-14, Stony Brook University, Department of Economics.
    2. Grey Gordon & Pablo Guerron-Quintana, 2019. "A Quantitative Theory of Hard and Soft Sovereign Defaults," 2019 Meeting Papers 412, Society for Economic Dynamics.
    3. Mihalache, Gabriel, 2020. "Sovereign default resolution through maturity extension," Journal of International Economics, Elsevier, vol. 125(C).
    4. Cristina Arellano & Yan Bai & Gabriel Mihalache, 2019. "Monetary Policy and Sovereign Risk in Emerging Economies (NK-Default)," Department of Economics Working Papers 19-02, Stony Brook University, Department of Economics.

    More about this item

    Keywords

    Computation; Monotonicity; Discrete Choice; Taste Shocks; Sovereign Default; Curse of Dimensionality;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • F34 - International Economics - - International Finance - - - International Lending and Debt Problems
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics
    • F44 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - International Business Cycles

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