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A Log-linear Homotopy Approach to Initialize the Parameterized Expectations Algorithm

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Abstract

In this paper I present a proposal to obtain appropriate initial conditions when solving general equilibrium rational expectations models with the Parameterized Expectations Algorithm. The proposal is based on a log-linear approximation to the model under study, so that it can be though of as a particular variant of the homotopy approach.The main advantages of the proposal are: i. it guarantees the ergodicity of the initial time series used as an input to the Parameterized Expectations algorithm; ii. it performs well as regards speed of convergence when compared to some homotopy alternatives; iii. it is easy to implement. The claimed advantages are successfully illustrated in the framework of the Cooley and Hansen (1989) model with indivisible labor and money demand motivated via a cash-in-advance constraint, as compared to a procedure based on the standard implementation of homotopy principles.

Suggested Citation

  • Javier J. Pérez, 2001. "A Log-linear Homotopy Approach to Initialize the Parameterized Expectations Algorithm," Economic Working Papers at Centro de Estudios Andaluces E2001/02, Centro de Estudios Andaluces.
  • Handle: RePEc:cea:doctra:e2001_02
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    References listed on IDEAS

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    1. Duffy, John & McNelis, Paul D., 2001. "Approximating and simulating the stochastic growth model: Parameterized expectations, neural networks, and the genetic algorithm," Journal of Economic Dynamics and Control, Elsevier, vol. 25(9), pages 1273-1303, September.
    2. Albert Marcet & David A. Marshall, 1994. "Solving nonlinear rational expectations models by parameterized expectations: convergence to stationary solutions," Working Paper Series, Macroeconomic Issues 94-20, Federal Reserve Bank of Chicago.
    3. Alfonso Novales & Emilio Dominguez & Javier J. Perez & Jesus Ruiz, 1998. "Solving Non-linear Rational Expectations Models By Eigenvalue-Eigenvector Decompositions," QM&RBC Codes 124, Quantitative Macroeconomics & Real Business Cycles.
    4. Jensen, Mark J, 1997. "A Homotopy Approach to Solving Nonlinear Rational Expectation Problems," Computational Economics, Springer;Society for Computational Economics, vol. 10(1), pages 47-65, February.
    5. Albert Marcet, 1991. "Simulation analysis of dynamic stochastic models: Applications to theory and estimation," Economics Working Papers 6, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Albert Marcet & Guido Lorenzoni, 1998. "Parameterized expectations approach; Some practical issues," Economics Working Papers 296, Department of Economics and Business, Universitat Pompeu Fabra.
    7. Eaves, B. Curtis & Schmedders, Karl, 1999. "General equilibrium models and homotopy methods," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1249-1279, September.
    8. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
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    Cited by:

    1. Antonio Morales & Pablo Brañas Garza, 2003. "Computational Errors in Guessing Games1," Economic Working Papers at Centro de Estudios Andaluces E2003/11, Centro de Estudios Andaluces.
    2. Paul Pichler, 2005. "Evaluating Approximate Equilibria of Dynamic Economic Models," Vienna Economics Papers 0510, University of Vienna, Department of Economics.

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    Keywords

    Parameterized Expectations Algorithm; initial conditions; log-linear approximations; homotopy; rational expectations;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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