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A neural network demand system with heteroskedastic errors

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Author Info

  • McAleer, Michael
  • Medeiros, Marcelo C.
  • Slottje, Daniel

Abstract

In this paper we consider estimation of demand systems with flexible functional forms, allowing an error term with a general conditional heteroskedasticity function that depends on observed covariates, such as demographic variables. We propose a general model that can be estimated either by quasi-maximum likelihood (in the case of exogenous regressors) or generalized method of moments (GMM) if the covariates are endogenous. The specification proposed in the paper nests several demand functions in the literature and the results can be applied to the recently proposed Exact Affine Stone Index (EASI) demand system of [Lewbel, A., Pendakur, K., 2008. Tricks with Hicks: The EASI implicit Marshallian demand system for unobserved heterogeneity and flexible Engel curves. American Economic Review (in press)]. Furthermore, flexible nonlinear expenditure elasticities can be estimated.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 147 (2008)
Issue (Month): 2 (December)
Pages: 359-371

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Handle: RePEc:eee:econom:v:147:y:2008:i:2:p:359-371

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Demand functions Estimating demand systems Flexible forms Exact affine Stone index (EASI) Neural networks Asymptotic theory Heteroskedasticity Engel curves;

References

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  1. White,Halbert, 1994. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521252805, October.
  2. Swanson, Norman R. & White, Halbert, 1997. "Forecasting economic time series using flexible versus fixed specification and linear versus nonlinear econometric models," International Journal of Forecasting, Elsevier, vol. 13(4), pages 439-461, December.
  3. Mayte Suarez Farinãs & Carlos Eduardo Pedreira & Marcelo C. Medeiros, 2003. "Local-global neural networks: a new approach for nonlinear time series modelling," Textos para discussão 470, Department of Economics PUC-Rio (Brazil).
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  7. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
  8. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  9. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1975. "Transcendental Logarithmic Utility Functions," American Economic Review, American Economic Association, vol. 65(3), pages 367-83, June.
  10. McAleer, Michael & Chan, Felix & Hoti, Suhejla & Lieberman, Offer, 2008. "Generalized Autoregressive Conditional Correlation," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1554-1583, December.
  11. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
  12. Alston, Julian M & Foster, Kenneth A & Green, Richard D, 1994. "Estimating Elasticities with the Linear Approximate Almost Ideal Demand System: Some Monte Carlo Results," The Review of Economics and Statistics, MIT Press, vol. 76(2), pages 351-56, May.
  13. Medeiros, Marcelo C. & Teräsvirta, Timo & Rech, Gianluigi, 2002. "Building neural network models for time series: A statistical approach," Working Paper Series in Economics and Finance 508, Stockholm School of Economics.
  14. Walter Beckert & Richard Blundell, 2004. "Invertibility of Nonparametric Stochastic Demand Functions," Birkbeck Working Papers in Economics and Finance 0406, Birkbeck, Department of Economics, Mathematics & Statistics.
  15. Medeiros, Marcelo C. & McAleer, Michael & Slottje, Daniel & Ramos, Vicente & Rey-Maquieira, Javier, 2008. "An alternative approach to estimating demand: Neural network regression with conditional volatility for high frequency air passenger arrivals," Journal of Econometrics, Elsevier, vol. 147(2), pages 372-383, December.
  16. Blundell, Richard & Pashardes, Panos & Weber, Guglielmo, 1993. "What Do We Learn About Consumer Demand Patterns from Micro Data?," American Economic Review, American Economic Association, vol. 83(3), pages 570-97, June.
  17. Pashardes, Panos, 1993. "Bias in Estimating the Almost Ideal Demand System with the Stone Index Approximation," Economic Journal, Royal Economic Society, vol. 103(419), pages 908-15, July.
  18. Gibson, John, 2002. " Why Does the Engel Method Work? Food Demand, Economies of Size and Household Survey Methods," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 64(4), pages 341-59, September.
  19. Donald J. Brown & Rosa L. Matzkin, 1998. "Estimation of Nonparametric Functions in Simultaneous Equations Models, with an Application to Consumer Demand," Cowles Foundation Discussion Papers 1175, Cowles Foundation for Research in Economics, Yale University.
  20. Foster, Andrew & Hahn, Jinyong, 2000. "A consistent semiparametric estimation of the consumer surplus distribution," Economics Letters, Elsevier, vol. 69(3), pages 245-251, December.
  21. Suhejla Hoti & Michael McAleer & Daniel Slottje, 2006. "Intellectual Property Litigation Activity In The Usa," Journal of Economic Surveys, Wiley Blackwell, vol. 20(4), pages 715-729, 09.
  22. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
  23. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
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Citations

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Cited by:
  1. Julien Boelaert, 2013. "A Neural Network Demand System," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00917810, HAL.
  2. Harin, Alexander, 2014. "General correcting formulae for forecasts," MPRA Paper 55283, University Library of Munich, Germany.
  3. Julien Boelaert, 2013. "A Neural Network Demand System," Documents de travail du Centre d'Economie de la Sorbonne 13081, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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