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Coherent optimal prediction with large nonlinear systems: an example based on a French model

Author

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  • Brillet, Jean-Louis
  • Calzolari, Giorgio
  • Panattoni, Lorenzo

Abstract

The drawbacks of predictors obtained with the usual deterministic solution methods in nonlinear systems of stochastic equations have been widely investigated in the literature. Most of the proposed therapies are based on some estimation of the conditional mean of the endogenous variables in the forecast period. This however provides a solution to the problem which does not respect the internal coherency of the model, and in particular does not satisfy nonlinear identities. At the same time, for analogy with univariate skewed distributions, the conditional mean may be expected to lie on the wrong side of the deterministic solution, meaning that it moves towards values of the variables which are less likely to occur, rather than towards the most probable values. Estimation of the most likely joint value of all endogenous variables is proposed as an alternative optimal predictor. Experimentation is performed on a large scale macroeconomic model of the French economy, and some considerations are drawn from the results.

Suggested Citation

  • Brillet, Jean-Louis & Calzolari, Giorgio & Panattoni, Lorenzo, 1986. "Coherent optimal prediction with large nonlinear systems: an example based on a French model," MPRA Paper 29057, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:29057
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    File URL: https://mpra.ub.uni-muenchen.de/29057/1/MPRA_paper_29057.pdf
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    References listed on IDEAS

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    1. Brundy, James M & Jorgenson, Dale W, 1971. "Efficient Estimation of Simultaneous Equations by Instrumental Variables," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 207-224, August.
    2. Amemiya, Takeshi, 1983. "Non-linear regression models," Handbook of Econometrics,in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 6, pages 333-389 Elsevier.
    3. Calzolari, Giorgio, 1979. "Antithetic variates to estimate the simulation bias in non-linear models," Economics Letters, Elsevier, vol. 4(4), pages 323-328.
    4. Brown, Bryan W & Mariano, Roberto S, 1984. "Residual-Based Procedures for Prediction and Estimation in a Nonlinear Simultaneous System," Econometrica, Econometric Society, vol. 52(2), pages 321-343, March.
    5. Fair, Ray C, 1980. "Estimating the Expected Predictive Accuracy of Econometric Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(2), pages 355-378, June.
    6. Wallis, Kenneth F., 1982. "'Time-series' versus 'econometric' forecasts : A non-linear regression counterexample," Economics Letters, Elsevier, vol. 10(3-4), pages 309-315.
    7. Hall, S G, 1986. "The Application of Stochastic Simulation Techniques to the National Institute's Model 7," The Manchester School of Economic & Social Studies, University of Manchester, vol. 54(2), pages 180-201, June.
    8. Bianchi, Carlo & Calzolari, Giorgio & Corsi, Paolo, 1976. "Divergences in the results of stochastic and deterministic simulation of an Italian non linear econometric model," MPRA Paper 21287, University Library of Munich, Germany.
    9. Fisher, Paul & Salmon, Mark, 1986. "On Evaluating the Importance of Nonlinearity in Large Macroeconometric Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(3), pages 625-646, October.
    10. James M. Brundy & Dale W. Jorgenson, 1971. "Efficient estimation of simultaneous equations by instrumental variables," Working Papers in Applied Economic Theory 3, Federal Reserve Bank of San Francisco.
    11. Bianchi, Carlo & Brillet, Jean-Louis & Calzolari, Giorgio, 1984. "Analyse et mesure de l'incertitude en prevision d'un modele econometrique. Application au modele mini-DMS
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    12. Bianchi, Carlo & Calzolari, Giorgio, 1980. "The One-Period Forecast Errors in Nonlinear Econometric Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 201-208, February.
    13. Mariano, Roberto S & Brown, Bryan W, 1983. "Asymptotic Behavior of Predictors in a Nonlinear Simultaneous System," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 523-536, October.
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    Citations

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    Cited by:

    1. Bianchi, Carlo & Calzolari, Giorgio & Brillet, Jean-Louis, 1987. "Measuring forecast uncertainty : A review with evaluation based on a macro model of the French economy," International Journal of Forecasting, Elsevier, vol. 3(2), pages 211-227.
    2. Calzolari, Giorgio & Panattoni, Lorenzo, 1990. "Mode predictors in nonlinear systems with identities," International Journal of Forecasting, Elsevier, vol. 6(3), pages 317-326, October.
    3. Gajda, Jan B. & Markowski, Aleksander, 1998. "Model Evaluation Using Stochastic Simulations: The Case of the Econometric Model KOSMOS," Working Papers 61, National Institute of Economic Research.

    More about this item

    Keywords

    Macroeconometric model; French economy; mean and mode; joint distribution; coherent prediction;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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