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Nonparametric estimation of a heterogeneous demand function under the Slutsky inequality restriction

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  • Richard Blundell
  • Joel L. Horowitz
  • Matthias Parey

Abstract

Economic theory rarely provides a parametric specification for a model, but it often provides shape restrictions. We consider nonparametric estimation of the heterogeneous demand for gasoline in the U.S. subject to the Slutsky inequality restriction of consumer choice theory. We derive conditions under which the demand function can be estimated consistently by nonparametric quantile regression subject to the Slutsky restriction. The estimated function reveals systematic variation in price responsiveness across the income distribution. A new method for estimating quantile instrumental variables models is also developed to allow for the endogeneity of prices. In our application, shape-constrained quantile IV estimates show similar patterns of demand as shape-constrained estimates under exogeneity. The results illustrate the improvements in the finite-sample performance of a nonparametric estimator that can be achieved by imposing shape restrictions based on economic theory.

Suggested Citation

  • Richard Blundell & Joel L. Horowitz & Matthias Parey, 2013. "Nonparametric estimation of a heterogeneous demand function under the Slutsky inequality restriction," CeMMAP working papers 54/13, Institute for Fiscal Studies.
  • Handle: RePEc:azt:cemmap:54/13
    DOI: 10.1920/wp.cem.2013.5413
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    Cited by:

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    2. Denis Chetverikov & Daniel Wilhelm, 2017. "Nonparametric instrumental variable estimation under monotonicity," CeMMAP working papers 14/17, Institute for Fiscal Studies.
    3. Sam Cosaert & Thomas Demuynck, 2018. "Nonparametric Welfare and Demand Analysis with Unobserved Individual Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 349-361, May.
    4. Denis Chetverikov & Daniel Wilhelm, 2017. "Nonparametric Instrumental Variable Estimation Under Monotonicity," Econometrica, Econometric Society, vol. 85, pages 1303-1320, July.
    5. Horowitz, Joel L. & Lee, Sokbae, 2017. "Nonparametric estimation and inference under shape restrictions," Journal of Econometrics, Elsevier, vol. 201(1), pages 108-126.
    6. Denis Chetverikov & Daniel Wilhelm, 2015. "Nonparametric instrumental variable estimation under monotonicity," CeMMAP working papers 39/15, Institute for Fiscal Studies.
    7. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2023. "Constrained Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 91(2), pages 709-736, March.
    8. Xiaohong Chen & Timothy Christensen, 2013. "Optimal Sup-norm Rates, Adaptivity and Inference in Nonparametric Instrumental Variables Estimation," Cowles Foundation Discussion Papers 1923R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2015.
    9. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    10. Joel L. Horowitz & Sokbae (Simon) Lee, 2015. "Nonparametric estimation and inference under shape restrictions," CeMMAP working papers 67/15, Institute for Fiscal Studies.
    11. Xiaohong Chen & Timothy M. Christensen, 2015. "Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation," CeMMAP working papers 32/15, Institute for Fiscal Studies.
    12. Denis Chetverikov & Daniel Wilhelm, 2016. "Nonparametric instrumental variable estimation under monotonicity," CeMMAP working papers 48/16, Institute for Fiscal Studies.
    13. Stefan Hoderlein & Jörg Stoye, 2015. "Testing stochastic rationality and predicting stochastic demand: the case of two goods," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 313-328, October.

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