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Endogenous Gridpoints in Multiple Dimensions: Interpolation on Non-Linear Grids


  • Matthew N. White

    () (Department of Economics, University of Delaware)


In dynamic optimization problems with multiple continuous state variables and multiple continuous controls, the method of endogenous gridpoints (ENDG) generates an irregular collection of gridpoints for which standard interpolation techniques do not apply, while alternative interpolation methods are extremely slow. This paper presents an interpolation technique that allows ENDG to be used in multi-dimensional problems in an intuitive and computationally e?cient way. The method translates irregular grid sectors onto the unit square (unit cube, unit hypercube, etc) and then applies standard linear interpolation. This method’s superiority to traditional solution approaches, in terms of speed and accuracy, is demonstrated on a benchmark model. At commonly used grid densities, the method of endogenous gridpoints with non-linear grid interpolation is 7.7 times faster than the traditional solution method, with slightly greater accuracy. This computational acceleration erodes only very slowly as grid density increases, unlike with alternative interpolation methods.

Suggested Citation

  • Matthew N. White, 2014. "Endogenous Gridpoints in Multiple Dimensions: Interpolation on Non-Linear Grids," Working Papers 14-17, University of Delaware, Department of Economics.
  • Handle: RePEc:dlw:wpaper:14-17

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    References listed on IDEAS

    1. Giulio Fella, 2011. "A Generalized Endogenous Grid Method for Non-concave Problems," Working Papers 677, Queen Mary University of London, School of Economics and Finance.
    2. Carroll, Christopher D., 2006. "The method of endogenous gridpoints for solving dynamic stochastic optimization problems," Economics Letters, Elsevier, vol. 91(3), pages 312-320, June.
    3. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    4. John Rust & Bertel Schjerning & Fedor Iskhakov, 2012. "A generalized endogenous grid method for discrete-continuous choice," 2012 Meeting Papers 1162, Society for Economic Dynamics.
    5. Hintermaier, Thomas & Koeniger, Winfried, 2010. "The method of endogenous gridpoints with occasionally binding constraints among endogenous variables," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 2074-2088, October.
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    More about this item


    Dynamic models; numerical solution; endogenous gridpoint method; non-linear grid interpolation; endogenous human capital;

    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
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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