Skip to main content

A Practical Method for Explicitly Modeling Quotas and Other Complementarities

Abstract

To make CGE models realistic, inequality constraints (e.g., import quotas) or non-differentiable functions (e.g., income tax schedules) are sometimes needed. Both situations may be described using complementarity conditions, which state that either an equation is true or itscomplementary variable is at a boundary value. The paper describes a practical way to solve CGE modelsthat contain such conditions. The technique, which is different from complementarity algorithms commonly used elsewhere (e.g., GAMS), has been implemented in the current version of the GEMPACK system, and has been used in a number of applications.This paper explains why the solution methods used in previous versions of GEMPACK do not handle complementarity conditions well, and describes how a two-pass procedure can overcome these difficulties. The key insight is that if we knew in advance which constraints would be binding in the accurate solution, the complementarity conditions could be reformulated in terms of smooth functions only, via a closure change which allows us to ignore the troublesome equations.

This is a preview of subscription content, access via your institution.

References

  • Atkinson, K.E. (1989). An Introduction to Numerical Analysis, 2nd edn. Wiley, New York.

    Google Scholar 

  • Bach, C. and Pearson, K.R. (1996). Implementing quotas in GTAP using GEMPACK or how to linearize an inequality. GTAP Technical Paper No. 04, September 1996, pp. 37 + 4.

  • Berkhout P., van Bruchem, C., Helming, J. and van Tongeren, F. (2002a). Hervorming EU-zuivelbeleid (Reforming the EU dairy industry). LEI report, The Hague.

  • Berkhout, P., Helming, J.F.M., van Tongeren, F.W., de Kleijn, A.J. and Van Bruchem, C. (2002b). Zuivelbeleid zonder melkquotering? Mogelijke gevolgen voor Nederland en de EU (Dairy policy without quota?). LEI report 6.02.03, The Hague.

  • Berkhout, P., van Berkum, S., Helming, J.F.M., Lips, M. and van Meijl, J.C.M. (forthcoming). Herziening van de suikermarktordening: mogelijke gevolgen voor Nederland en de EU (Reform of sugar policy: possible implications for the Netherlands). Netherlands Agricultural Economics Research Institute, Report (forthcoming).

  • Dirkse, S.P. and Ferris, M.C. (1995). The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems. Optimization Methods and Software, 5, 123–156.

    Google Scholar 

  • Elbehri, A. and Pearson, K.R. (2000). Implementing bilateral tariff rate quotas in GTAP using GEMPACK. GTAP Technical Paper No. 18, December 2000, pp. 47 + 4.

  • Ferris, M.C. and Kanzow, C. (2000). Complementarity and related problems: A survey. In P.M. Pardalos and M.G.C. Resende (eds.), Handbook of Applied Optimization, Oxford University Press (forthcoming).

  • Francois, Joseph, van Meijl, Hans and van Tongeren, Frank (2002). Economic benefits of the Doha round for The Netherlands. Report submitted to the Ministry of Economic Affairs, Directorate-General for Foreign Economic Relations. LEI report 6.03.02, The Hague.

  • Francois, Joseph, van Meijl, Hans and van Tongeren, Frank (2003). Economic implications of trade liberalization under the Doha round. Paper prepared for the 6th annual conference on Global Economic Analysis, The Hague, June 2003.

  • Harrison, W.J. and Pearson, K.R. (1996). Computing solutions for large general equilibrium models using GEMPACK. Computational Economics, 9, 83–127.

    Google Scholar 

  • Harrison, W.J. and Pearson, K.R. (2002a). GEMPACK user documentation for release 8.0 (7 volumes). Centre of Policy Studies,Monash University, Clayton (October 2002), downloadable from http://www.monash.edu.au/policy/gpdoc.htm.

    Google Scholar 

  • Harrison, W.J., Horridge, M., Pearson, K.R. and Wittwer, G. (2002b). A practical method for explicitly modeling quotas and other complementarities. Centre of Policy Studies and Impact Preliminary Working Paper No. IP-78, Monash University, Clayton (April 2002), pp. 19, downloadable from http://www.monash.edu.au/policy/elecpapr/ip-78.htm.

    Google Scholar 

  • Horridge, M., Dixon, P. and Rimmer, M. (1993). Water pricing and investment in Melbourne: General equilibrium analysis with uncertain stream flow. IMPACT PreliminaryWorking Paper No. IP-63, December 1993, downloadable from http://www.monash.edu.au/policy/elecpapr/ip-63.htm.

  • Lips, Markus and Rieder, Peter (2002). Endogenous adjusted output quotas-the abolishment of the raw milk quota in the European Union. 5th Conference on Global Economic Analysis, Taiwan, June 2002.

  • Malakellis, M. (2000). Integrated Macro-Micro Modelling under Rational Expectations. Physica-Verlag, Heidelberg, ISBN 3-7908-1274-9.

    Google Scholar 

  • Meijl, Hans van and van Tongeren, Frank (2002). The Agenda 2000 CAP reform, world prices and URAA GATT-WTOexport constraints. European Review of Agricultural Economics, 29(4), 445–470.

    Google Scholar 

  • Pearson K.R. (1991). Solving nonlinear economic models accurately via a linear representation. Impact Preliminary Working Paper No. IP-55, Melbourne (July), pp. 39.

  • Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T. (1986). Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge.

    Google Scholar 

  • Rutherford, T. (1993). MILES: A Mixed Inequality and Nonlinear Equation Solver. Working Paper 93-20, Department of Economics, University of Colorado.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Harrison, W.J., Horridge, M., Pearson, K. et al. A Practical Method for Explicitly Modeling Quotas and Other Complementarities. Computational Economics 23, 325–341 (2004). https://doi.org/10.1023/B:CSEM.0000026795.44450.4a

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:CSEM.0000026795.44450.4a

  • complementarity
  • applied general equilibrium
  • quotas
  • tariff-rate quotas
  • inequality constraints
  • algorithm