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

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  • Richard Blundell

    () (Institute for Fiscal Studies and IFS and UCL)

  • Joel L. Horowitz

    () (Institute for Fiscal Studies and Northwestern University)

  • Matthias Parey

    () (Institute for Fiscal Studies and University of Essex)

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 CWP54/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:54/13
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    File URL: http://www.cemmap.ac.uk/wps/cwp541313.pdf
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    References listed on IDEAS

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    1. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
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    4. Richard Blundell & Joel L. Horowitz & Matthias Parey, 2012. "Measuring the price responsiveness of gasoline demand: Economic shape restrictions and nonparametric demand estimation," Quantitative Economics, Econometric Society, vol. 3(1), pages 29-51, March.
    5. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    6. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, March.
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    Cited by:

    1. Sam Cosaert & Thomas Demuynck, "undated". "Nonparametric welfare and demand analysis with unobserved individual heterogeneity," ULB Institutional Repository 2013/251988, ULB -- Universite Libre de Bruxelles.
    2. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2015. "Constrained conditional moment restriction models," CeMMAP working papers CWP59/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Sam Cosaert & Thomas Demuynck, 2015. "Revealed preference theory for finite choice sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 169-200, May.
    4. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    5. Xiaohong Chen & Timothy M. Christensen, 2015. "Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation," CeMMAP working papers CWP32/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. 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.

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