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Sensitivity Analysis for Applied General Equilibrium Models in the Presence of Multiple Equilibria

Author

Listed:
  • Marcus Berliant

    (Washington University)

  • Sami Dakhlia

    (Washington University)

Abstract

Pagan and Shannon's (1985) widely used approach employs local linearizations of a system of non-linear equations to obtain asymptotic distributions for the endogenous parameters (such as prices) from distributions over the exogenous parameters (such as estimates of taste, technology, or policy variables, for example). However, this approach ignores both the possibility of multiple equilibria as well as the problem (related to that of multiplicity) that critical points might be contained in the confidence interval of an exogenous parameter. Critical equilibria occur for parameter values that generate a singular excess demand Jacobian at the equilibrium prices. At such points, the equilibrium correspondence might not be lower hemi-continuous and the selection of equilibria made by a computation algorithm (or by a tatonnement process) can jump. From a statistical viewpoint, the presence of critical economies means that statistical error in the parameter estimates can have a large and discontinuous impact on error in the endogenous variables, such as prices. We generalize Pagan and Shannon's approach to account for critical economies and multiple equilibria by assuming that the choice of equilibrium is described by a continuous random selection. We develop an asymptotic theory regarding equilibrium prices, which establishes that their probability density function is multimodal and that it converges to a weighted sum of normal density functions. An important insight is that if multiple equilibria exist but multiplicity is ignored, the computed solution will be an inconsistent estimator of the true equilibrium, even if the computation algorithm tracks the same equilibrium as the economy's tatonnement.

Suggested Citation

  • Marcus Berliant & Sami Dakhlia, 1997. "Sensitivity Analysis for Applied General Equilibrium Models in the Presence of Multiple Equilibria," GE, Growth, Math methods 9709003, EconWPA.
  • Handle: RePEc:wpa:wuwpge:9709003
    Note: Type of Document - LaTeX; prepared on UNIX Sparc TeX; to print on PostScript; pages: 25 ; figures: included
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    References listed on IDEAS

    as
    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, March.
    2. Mas-Colell, Andreu & Nachbar, John H., 1991. "On the finiteness of the number of critical equilibria, with an application to random selections," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 397-409.
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    Cited by:

    1. Christos FLOROS & Pierre FAILLER, "undated". "Development of a Computable General Equilibrium (CGE) Model for Fisheries," EcoMod2004 330600052, EcoMod.

    More about this item

    Keywords

    critical equilibria multiplicity uniqueness computation applied general equilibrium models delta method jumps catastrophy continuous random selection sensitivity analysis asymptotic distribution;

    JEL classification:

    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models

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