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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. 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.
  2. McDonald, John F & Moffitt, Robert A, 1980. "The Uses of Tobit Analysis," The Review of Economics and Statistics, MIT Press, vol. 62(2), pages 318-21, May.
  3. 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.
  4. Cragg, John G, 1971. "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods," Econometrica, Econometric Society, vol. 39(5), pages 829-44, September.
  5. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, November.
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  7. Deaton, Angus & Irish, Margaret, 1984. "Statistical models for zero expenditures in household budgets," Journal of Public Economics, Elsevier, vol. 23(1-2), pages 59-80.
  8. 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.
  9. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, November.
  10. 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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  16. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, November.
  17. Davidson, R. & Mackinnon, J.G., 1997. "Bootstrap Testing in Nonlinear Models," G.R.E.Q.A.M. 97a39, Universite Aix-Marseille III.
  18. Jean-Thomas Bernard & Nadhem Idoudi & Lynda Khalaf & Clément Yélou, 2007. "Finite sample inference methods for dynamic energy demand models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(7), pages 1211-1226.
  19. 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.
  20. Daniel Polsky & Henry A. Glick & Richard Willke & Kevin Schulman, 1997. "Confidence Intervals for Cost-Effectiveness Ratios: A Comparison of Four Methods," Health Economics, John Wiley & Sons, Ltd., vol. 6(3), pages 243-252.
  21. Cliff Attfield & Sonia R Bhalotra, 1998. "Intrahousehold Resource Allocation in Rural Pakistan: A Semi-parametric Analysis," STICERD - Development Economics Papers - From 2008 this series has been superseded by Economic Organisation and Public Policy Discussion Papers 11, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  22. Kling, Catherine L. & Dorfman, Jeffrey & Sexton, Richard, 1990. "Confidence Intervals for Elasticities and Flexibilities: Re-Evaluating the Ratios of Normals Case," Staff General Research Papers 1582, Iowa State University, Department of Economics.
  23. Jiazhong You, 2003. "Robust estimation of models of Engel curves," Empirical Economics, Springer, vol. 28(1), pages 61-73, January.
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