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Confidence Intervals for Estimates of Elasticities

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

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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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
Contact details of provider: Postal: Department of Economics, The University of Melbourne, 4th Floor, FBE Building, Level 4, 111 Barry Street. Victoria, 3010, Australia
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  1. Davidson, R. & Mackinnon, J.G., 1997. "Bootstrap Testing in Nonlinear Models," G.R.E.Q.A.M. 97a39, Universite Aix-Marseille III.
  2. 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.
  3. 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.
  4. Melenberg, B. & van Soest, A.H.O., 1996. "Parametric and semi-parametric modelling of vacation expenditures," Other publications TiSEM 14de3e83-71c1-4e9a-aa5e-3, Tilburg University, School of Economics and Management.
  5. 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.
  6. 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.
  7. Thomas F. Crossley & Paul Grootendorst & Sule Kokkmaz & Michael R. Veall, 2000. "The Effects of Drug Subsidies on Out-of-Poket Prescription Drug Expenditures by seniors: regional Evidence from Canada," CEPR Discussion Papers 422, Centre for Economic Policy Research, Research School of Economics, Australian National University.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. repec:cup:cbooks:9780521780506 is not listed on IDEAS
  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. Barnett, William A, 1983. "New Indices of Money Supply and the Flexible Laurent Demand System," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(1), pages 7-23, January.
  15. 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.
  16. Richard Blundell & Alan Duncan & Krishna Pendakur, 1998. "Semiparametric estimation and consumer demand," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 435-461.
  17. 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.
  18. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
  19. 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.
  20. 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.
  21. repec:cup:cbooks:9780521785167 is not listed on IDEAS
  22. Jiazhong You, 2003. "Robust estimation of models of Engel curves," Empirical Economics, Springer, vol. 28(1), pages 61-73, January.
  23. 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.
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