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Solving Nonlinear Economic Models Accurately Via a Linear Representation

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  • K.R. Pearson

Abstract

This paper focuses on one way a linearized representation of a nonlinear economic model can be used to obtain arbitrarily accurate solutions to simulations. The key is a method for translating a simulation problem directly to a so-called initial value problem. Since many different methods for solving initial value problems are known and well understood, and since each one converts to an algorithm for solving simulation problems, this insight greatly expands the computational tool kit for conducting simulations. This paper contains a survey of the theoretical results guaranteeing convergence and forming the basis for extrapolations of two important methods for solving initial value problems. Theoretical considerations suggest that the faster rate of convergence of one of these methods (the modified midpoint method) is likely to cause it to dominate the other (Euler's method) in many situations faced by applied general equilibrium modellers. The other main points of the paper are: (a) to emphasize that linearized (symbolic) representations of models lead naturally to efficient algorithms which can be used to compute solutions having any desired degree of precision; and (b) to suggest that such accurate methods (rather than Johansen's method) should be the default when solving models (especially applied general equilibrium models) represented in linearized form.

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Bibliographic Info

Paper provided by Victoria University, Centre of Policy Studies/IMPACT Centre in its series Centre of Policy Studies/IMPACT Centre Working Papers with number ip-55.

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Date of creation: Jul 1991
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Handle: RePEc:cop:wpaper:ip-55

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References

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  1. K.R. Pearson, 1986. "Automating the Computation of Solutions of Large Economic Models," Centre of Policy Studies/IMPACT Centre Working Papers, Victoria University, Centre of Policy Studies/IMPACT Centre ip-27, Victoria University, Centre of Policy Studies/IMPACT Centre.
  2. Thomas W. Hertel & J. Mark Horridge & K. R. Pearson, 1991. "Mending the Family Tree: A Reconciliation of the Linearization and Levels Schools of CGE Modelling," Centre of Policy Studies/IMPACT Centre Working Papers, Victoria University, Centre of Policy Studies/IMPACT Centre ip-54, Victoria University, Centre of Policy Studies/IMPACT Centre.
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Cited by:
  1. Hertel, Thomas W. & Mark Horridge, J. & Pearson, K. R., 1992. "Mending the family tree a reconciliation of the linearization and levels schools of AGE modelling," Economic Modelling, Elsevier, Elsevier, vol. 9(4), pages 385-407, October.
  2. Maureen T. Rimmer & Alan A. Powell, 1992. "Demand Patterns Across the Development Spectrum: Estimates for the AIDADS System," Centre of Policy Studies/IMPACT Centre Working Papers, Victoria University, Centre of Policy Studies/IMPACT Centre op-75, Victoria University, Centre of Policy Studies/IMPACT Centre.
  3. W. Jill Harrison & Mark Horridge & K.R. Pearson & Glyn Wittwer, 2004. "A Practical Method for Explicitly Modeling Quotas and Other Complementarities," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 23(4), pages 325-341, 06.
  4. Michael Malakellis, 1992. "Solving a Large-Scale Intertemporal Applied General Equilibrium Model," Centre of Policy Studies/IMPACT Centre Working Papers, Victoria University, Centre of Policy Studies/IMPACT Centre op-74, Victoria University, Centre of Policy Studies/IMPACT Centre.
  5. M. Kohlhaas & K.R. Pearson, 2002. "Introduction to GEMPACK for GAMS Users," Centre of Policy Studies/IMPACT Centre Working Papers, Victoria University, Centre of Policy Studies/IMPACT Centre ip-79, Victoria University, Centre of Policy Studies/IMPACT Centre.
  6. Maureen T. Rimmer & Alan A. Powell, 1992. "An Implicitly Directly Additive Demand System: Estimates for Australia," Centre of Policy Studies/IMPACT Centre Working Papers, Victoria University, Centre of Policy Studies/IMPACT Centre op-73, Victoria University, Centre of Policy Studies/IMPACT Centre.

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