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Sensitivity analysis for applied general equilibrium models in the presence of multiple Walrasian equilibria

Author

Listed:
  • Marcus Berliant

    () (Department of Economics, Washington University in St.Louis, St.Louis, MO 63130-4899, USA)

  • Sami Dakhlia

    () (Department of Economics, Culverhouse College of Business Administration, University of Alabama, Tuscaloosa, AL 35487-0224, USA)

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. We generalize Pagan and Shannon's approach to account for multiple equilibria by assuming that the choice of equilibrium is described by a 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 a model allows multiple equilibria, say $i=1,\ldots,I$, but multiplicity is ignored, then the computed solution for the i-th equilibrium generally no longer coincides with the expected value of that i-th equilibrium. The error can be large and correspond to several standard deviations of the mean's estimate.

Suggested Citation

  • Marcus Berliant & Sami Dakhlia, 2002. "Sensitivity analysis for applied general equilibrium models in the presence of multiple Walrasian equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(3), pages 459-476.
  • Handle: RePEc:spr:joecth:v:19:y:2002:i:3:p:459-476
    Note: Received: December 7, 1999; revised version: December 4, 2000
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    Keywords

    Sensitivity analysis; Delta-method; General equilibrium models; Non-uniqueness; Multiplicity.;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - 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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