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Conditional heteroskedasticity in nonlinear simultaneous equations

  • Calzolari, Giorgio
  • Fiorentini, Gabriele

We show in this paper that the treatment of conditional heteroskedasticity inside nonlinear systems of simultaneous equations is a sufficiently manageable matter for some types of multivariate ARCH error structures. Reparameterization makes it possible to estimate the model by means of the (nearly) standard algorithms developed in the past and widely used for estimating nonlinear simultaneous equations where the error structure is of the i.i.d. type with unrestricted contemporaneous covariance matrix. The method is discussed in this paper and empirical applications exemplify the efficiency gains.

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File URL: https://mpra.ub.uni-muenchen.de/24428/1/MPRA_paper_24428.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 24428.

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Date of creation: Sep 1994
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Publication status: Published in Florence: European University Institute Working Paper ECO No. 94/44 (1994): pp. 1-19
Handle: RePEc:pra:mprapa:24428
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  1. Jerry A. Hausman, 1974. "Full Information Instrumental Variables Estimation of Simultaneous Equations Systems," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 641-652 National Bureau of Economic Research, Inc.
  2. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-37, July.
  3. Calzolari, Giorgio & Sampoli, Letizia, 1993. "A Curious Result on Exact FIML and Instrumental Variables," Econometric Theory, Cambridge University Press, vol. 9(02), pages 296-309, April.
  4. 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 207-24, August.
  5. Amemiya, Takeshi, 1977. "The Maximum Likelihood and the Nonlinear Three-Stage Least Squares Estimator in the General Nonlinear Simultaneous Equation Model," Econometrica, Econometric Society, vol. 45(4), pages 955-68, May.
  6. Oliver Linton, 1993. "Adaptive Estimation in ARCH Models," Cowles Foundation Discussion Papers 1054, Cowles Foundation for Research in Economics, Yale University.
  7. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
  8. Ng, Lilian, 1991. " Tests of the CAPM with Time-Varying Covariances: A Multivariate GARCH Approach," Journal of Finance, American Finance Association, vol. 46(4), pages 1507-21, September.
  9. Fiorentini, G. & Maravall, A., 1995. "Unobserved Components in ARCH Models: An Application to Seasonal Adjustment," Papers 9509, Centro de Estudios Monetarios Y Financieros-.
  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. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
  12. Robinson, P M, 1991. "Best Nonlinear Three-Stage Least Squares Estimation of Certain Econometric Models," Econometrica, Econometric Society, vol. 59(3), pages 755-86, May.
  13. Gourieroux Christian & Monfort Alain & Trognon A, 1981. "Pseudo maximum likelihood methods : theory," CEPREMAP Working Papers (Couverture Orange) 8129, CEPREMAP.
  14. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  15. Calzolari, Giorgio & Panattoni, Lorenzo & Weihs, Claus, 1987. "Computational efficiency of FIML estimation," Journal of Econometrics, Elsevier, vol. 36(3), pages 299-310, November.
  16. Bianchi, Carlo & Calzolari, Giorgio & Sterbenz, Frederic P., 1991. "Simulation of interest rate options using ARCH," MPRA Paper 24844, University Library of Munich, Germany.
  17. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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