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Semiparametric estimation of consumer demand systems in real expenditure

  • Krishna Pendakur

    (Department of Economics, Simon Fraser University, Burnaby, BC, Canada)

  • Stefan Sperlich

    (Georg-August Universitat Gottingen, Institut fur Statistik und ÷konometrie, Gˆttingen, Germany)

Microdata concerning consumer demand typically show considerable variation in real expenditures, but very little variation in prices. We propose a semiparametric strategy for the consumer demand problem in which expenditure share equations are estimated nonparametrically in the real expenditure direction and estimated parametrically (with fixed or varying coefficients) in price directions. In our model, Engel curves are unrestricted: demands may have any rank. Because the demand model is derived from a cost function, it may be restricted to satisfy integrability and used for consumer surplus calculations. Since real expenditure is unobserved, but rather estimated under the model, we face a semiparametric model with a nonparametrically generated regressor. We show efficient convergence rates for parametric and nonparametric components. We illustrate the feasibility of our proposed strategy using Canadian expenditure and price data: Engel curves display curvature which cannot be encompassed by standard parametric models. We also find that the rationality restriction of Slutsky symmetry is rejected in the fixed-coefficients model, but not in the varying-coefficients model. Copyright © 2009 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/jae.1085
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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 25 (2010)
Issue (Month): 3 ()
Pages: 420-457

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Handle: RePEc:jae:japmet:v:25:y:2010:i:3:p:420-457
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  1. K. K. Gary Wong & Keith R. McLaren, 2005. "Specification and Estimation of Regular Inverse Demand Systems: A Distance Function Approach," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(4), pages 823-834.
  2. Arthur Lewbel & Krishna Pendakur, 2006. "Tricks With Hicks: The EASI Demand System," Boston College Working Papers in Economics 651, Boston College Department of Economics, revised 26 Nov 2008.
  3. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2003. "Nonparametric IV estimation of shape-invariant Engel curves," CeMMAP working papers CWP15/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2001. "Bootstrap Inference in Semiparametric Generalized Additive Models," Finance Working Papers 01-3, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  5. Pendakur, K., 1999. "Taking Prices Seriously in the Measurement of Inequality," Discussion Papers dp99-7, Department of Economics, Simon Fraser University.
  6. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
  7. 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.
  8. Haag, Berthold R. & Hoderlein, Stefan & Pendakur, Krishna, 2009. "Testing and imposing Slutsky symmetry in nonparametric demand systems," Journal of Econometrics, Elsevier, vol. 153(1), pages 33-50, November.
  9. Hengartner, Nicolas W. & Sperlich, Stefan, 2005. "Rate optimal estimation with the integration method in the presence of many covariates," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 246-272, August.
  10. Crossley, Thomas F. & Pendakur, Krishna, 2010. "The Common-Scaling Social Cost-of-Living Index," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 523-538.
  11. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
  12. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
  13. Camilo Sarmiento, 2005. "A Varying Coefficient Approach to Global Flexibility in Demand Analysis: A Semiparametric Approximation," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(1), pages 38-47.
  14. James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November.
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