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A Practical Method for Explicitly Modeling Quotas and Other Complementarities


  • W. Jill Harrison
  • Mark Horridge
  • K.R. Pearson
  • Glyn Wittwer


To make CGE models realistic, we sometimes need to include inequality constraints (eg, import quotas) or non-differentiable functions (eg, income tax schedules). Both situations may be described using complementarity conditions, which state that either an equation is true or its complementary variable is at a boundary value. The paper describes a practical way to solve CGE models, which contain such conditions. The technique, which is different from complementarity algorithms commonly used elsewhere (eg GAMS), has been implemented for the next version of the GEMPACK system. In the Euler (and similar) methods used by GEMPACK, derivatives are calculated to work out the approximate effects of exogenous changes. To get more accuracy, we can divide exogenous changes into several smaller steps. We interpret this procedure as a path-following algorithm. If all equations in the model are smooth (have continuous derivatives) we can always choose sufficiently many steps to be sure that approximation errors are a smooth and decreasing function of the number of steps. At this point we can invoke extrapolation procedures which use results from, say, Euler computations of 10, 15 and 20 steps, to compute results which are as accurate as machine precision allows. The extrapolation also allows us to compute error bounds for our computation. Unfortunately, complementarity conditions are equivalent to kinked schedules; they contain points where derivatives change sharply. The lack of smoothness precludes the use of extrapolation. Without extrapolation, very many tiny Euler steps might be needed to ensure sufficient accuracy -- leading to unacceptably lengthy computations. Our paper describes one way of overcoming this problem. 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. With all remaining functions smooth, extrapolation again becomes effective. This leads to a two-pass procedure. First, a single Euler computation, of limited accuracy, is used to discover which constraints will finally bind. Using this information the equations are recast into an equivalent smooth system which is then solved accurately. Similar methods have been used in Australia and elsewhere for years. They are simple and intuitive -- but tedious and difficult to implement manually, especially where many complementarity conditions interact. GEMPACK now offers a syntax for expressing complementarity conditions in a standard way. This enables the software to take over the boring work: running the approximate simulation, making the closure change and identifying target values for the newly exogenous variables, and finally re-solving accurately. We illustrate the technique with WAYANG, a SAM-based CGE model of Indonesia. Here, import quotas yield large rents to some richer households. We expect that removing the quotas should improve income distribution. However, the simulation results contain some surprises.

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  • W. Jill Harrison & Mark Horridge & K.R. Pearson & Glyn Wittwer, 2002. "A Practical Method for Explicitly Modeling Quotas and Other Complementarities," Centre of Policy Studies/IMPACT Centre Working Papers ip-78, Victoria University, Centre of Policy Studies/IMPACT Centre.
  • Handle: RePEc:cop:wpaper:ip-78

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    References listed on IDEAS

    1. K.R. Pearson, 1991. "Solving Nonlinear Economic Models Accurately Via a Linear Representation," Centre of Policy Studies/IMPACT Centre Working Papers ip-55, Victoria University, Centre of Policy Studies/IMPACT Centre.
    2. Elbehri, Aziz & Ken Pearson, 2000. "Implementing Bilateral Tariff Rate Quotas in GTAP using GEMPACK," GTAP Technical Papers 475, Center for Global Trade Analysis, Department of Agricultural Economics, Purdue University.
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    Cited by:

    1. Antimiani, Alessandro & Finizia, A. & Henke, Roberto & Manfredi, G. & Merciai, S., 2008. "The impact of the reform of the milk quota regime on the Italian dairy sector," 2008 International Congress, August 26-29, 2008, Ghent, Belgium 43658, European Association of Agricultural Economists.
    2. Dixon, Peter B. & Rimmer, Maureen T., 2011. "You can't have a CGE recession without excess capacity," Economic Modelling, Elsevier, vol. 28(1-2), pages 602-613, January.
    3. repec:oup:ecpoli:v:32:y:2017:i:92:p:651-705. is not listed on IDEAS
    4. Swati Dhingra & Hanwei Huang & Gianmarco Ottaviano & João Paulo Pessoa & Thomas Sampson & John Van Reenen, 2017. "The costs and benefits of leaving the EU: trade effects," Economic Policy, CEPR;CES;MSH, vol. 32(92), pages 651-705.
    5. Keith Walsh & Martina Brockmeier & Alan Matthews, 2005. "Implications of Domestic Support Disciplines for Further Agricultural Trade Liberalization," The Institute for International Integration Studies Discussion Paper Series iiisdp99, IIIS.
    6. M. Kohlhaas & K.R. Pearson, 2002. "Introduction to GEMPACK for GAMS Users," Centre of Policy Studies/IMPACT Centre Working Papers ip-79, Victoria University, Centre of Policy Studies/IMPACT Centre.
    7. Ashley Winston, 2005. "The Theory of Tariff Rate Quotas: An Application to the U.S. Sugar program using MONASH-USA," Centre of Policy Studies/IMPACT Centre Working Papers ip-83, Victoria University, Centre of Policy Studies/IMPACT Centre.
    8. Glyn Wittwer & Marnie Griffith, 2011. "Modelling drought and recovery in the southern Murray‐Darling basin," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 55(3), pages 342-359, July.
    9. Peter B. Dixon & Maureen T. Rimmer, 2010. "Simulating the U.S. Recession with and without the Obama package: the role of excess capacity," Centre of Policy Studies/IMPACT Centre Working Papers g-193, Victoria University, Centre of Policy Studies/IMPACT Centre.
    10. Beckman, Jayson & Arita, Shawn & Mitchell, Lorraine, 2015. "The Transatlantic Trade and Investment Partnership and Agriculture: A Quantitative Analysis," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205056, Agricultural and Applied Economics Association;Western Agricultural Economics Association.
    11. repec:eee:rensus:v:77:y:2017:i:c:p:596-603 is not listed on IDEAS
    12. Naudé, Wim & Rossouw, Riaan, 2008. "South African quotas on textile imports from China: A policy error?," Journal of Policy Modeling, Elsevier, vol. 30(5), pages 737-750.

    More about this item


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

    JEL classification:

    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models


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