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Confidence Intervals for Estimates of Elasticities

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  • J. G. Hirschberg, J. N. Lye
  • D. J. Slottje

Abstract

Elasticities are often estimated from the results of demand analysis however, drawing inferences from them may involve assumptions that could influence the outcome. In this paper we investigate one of the most common forms of elasticity which is defined as a ratio of estimated relationships and demonstrate how the Fieller method for the construction of confidence intervals can be used to draw inferences. We estimate the elasticities of expenditure from Engel curves using a variety of estimation models. Parametric Engel curves are modelled using OLS, MM robust regression, and Tobit. Semiparametric Engel curves are estimated using a penalized spline regression. We demonstrate the construction of confidence intervals of the expenditure elasticities for a series of expenditure levels as well as the estimated cumulative density function for the elasticity evaluated for a particular household.

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Bibliographic Info

Paper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 1053.

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Length: 42 pages
Date of creation: 2008
Date of revision:
Handle: RePEc:mlb:wpaper:1053

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Keywords: Engel curves; Fieller method; Tobit; robust regression; semiparametric;

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  1. Thomas F. Crossley & Paul Grootendorst & Sule Korkmaz & Michael R. Veall, 2000. "The Effects of Drug Subsidies on Out-of Pocket Prescription Drug Expenditures by Seniors: Regional Evidence from Canada," Quantitative Studies in Economics and Population Research Reports 350, McMaster University.
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  7. Tansel, AysIt & Bircan, Fatma, 2006. "Demand for education in Turkey: A tobit analysis of private tutoring expenditures," Economics of Education Review, Elsevier, vol. 25(3), pages 303-313, June.
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  12. Ping Zhang & Arthur van Soest & Xiaodong Gong, 2005. "The effects of the gender of children on expenditure patterns in rural China: a semiparametric analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 509-527.
  13. Sonia Bhalotra & Cliff Attfield, 1998. "Intrahousehold resource allocation in rural Pakistan: a semi-parametric analysis," LSE Research Online Documents on Economics 6679, London School of Economics and Political Science, LSE Library.
  14. Krinsky, Itzhak & Robb, A Leslie, 1986. "On Approximating the Statistical Properties of Elasticities," The Review of Economics and Statistics, MIT Press, vol. 68(4), pages 715-19, November.
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  16. Krinsky, Itzhak & Robb, A Leslie, 1991. "Three Methods for Calculating the Statistical Properties of Elasticities: A Comparison," Empirical Economics, Springer, vol. 16(2), pages 199-209.
  17. J.G. Hirschberg & J. N. Lye, 2007. "Providing Intuition to the Fieller Method with Two Geometric Representations using STATA and Eviews," Department of Economics - Working Papers Series 992, The University of Melbourne.
  18. Joseph G. Hirschberg & Jenny N. Lye, 2004. "Inferences for the Extremum of Quadratic Regression Models," Department of Economics - Working Papers Series 906, The University of Melbourne.
  19. Jiazhong You, 2003. "Robust estimation of models of Engel curves," Empirical Economics, Springer, vol. 28(1), pages 61-73, January.
  20. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, Fall.
  21. Davidson, R. & Mackinnon, J.G., 1997. "Bootstrap Testing in Nonlinear Models," G.R.E.Q.A.M. 97a39, Universite Aix-Marseille III.
  22. Timothy Beatty, 2009. "Semiparametric quantile Engel curves and expenditure elasticities: a penalized quantile regression spline approach," Applied Economics, Taylor & Francis Journals, vol. 41(12), pages 1533-1542.
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