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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 University College London)

  • Joel Horowitz

    ()
    (Institute for Fiscal Studies and Northwestern University)

  • Matthias Parey

    ()
    (Institute for Fiscal Studies)

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.

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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP54/13.

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Date of creation: Oct 2013
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Handle: RePEc:ifs:cemmap:54/13

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  1. Stefan Hoderlein & Anne Vanhems, 2011. "Welfare analysis using nonseparable models," CeMMAP working papers CWP01/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. 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, 03.
  3. Whitney Newey & Guido Imbens, 2004. "Identification and Estimation of Triangular Simultaneous Equations Models without Additivity," Econometric Society 2004 North American Summer Meetings 594, Econometric Society.
  4. Richard Blundell, 2005. "Presidential Address: How Revealing Is Revealed Preference?," Journal of the European Economic Association, MIT Press, vol. 3(2-3), pages 211-235, 04/05.
  5. Brown, Bryan W & Walker, Mary Beth, 1989. "The Random Utility Hypothesis and Inference in Demand Systems," Econometrica, Econometric Society, vol. 57(4), pages 815-29, July.
  6. Manning, Willard G. & Blumberg, Linda & Moulton, Lawrence H., 1995. "The demand for alcohol: The differential response to price," Journal of Health Economics, Elsevier, vol. 14(2), pages 123-148, June.
  7. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762.
  8. Stefan Hoderlein & Jörg Stoye, 2014. "Revealed Preferences in a Heterogeneous Population," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 197-213, May.
  9. Frondel, Manuel & Ritter, Nolan & Vance, Colin, 2012. "Heterogeneity in the rebound effect: Further evidence for Germany," Energy Economics, Elsevier, vol. 34(2), pages 461-467.
  10. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, September.
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