IDEAS home Printed from https://ideas.repec.org/p/mlb/wpaper/1053.html
   My bibliography  Save this paper

Confidence Intervals for Estimates of Elasticities

Author

Listed:
  • 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.

Suggested Citation

  • J. G. Hirschberg, J. N. Lye & D. J. Slottje, 2008. "Confidence Intervals for Estimates of Elasticities," Department of Economics - Working Papers Series 1053, The University of Melbourne.
    • Handle: RePEc:mlb:wpaper:1053
    as

    Download full text from publisher

    File URL: http://fbe.unimelb.edu.au/__data/assets/pdf_file/0006/802743/1053.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. William A. Barnett, 2000. "New Indices of Money Supply and the Flexible Laurent Demand System," Contributions to Economic Analysis, in: The Theory of Monetary Aggregation, pages 325-359, Emerald Group Publishing Limited.
    2. Melenberg, Bertrand & van Soest, Arthur, 1996. "Parametric and Semi-parametric Modelling of Vacation Expenditures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(1), pages 59-76, Jan.-Feb..
    3. 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.
    4. 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, May.
    5. 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.
    6. Alan, Sule & Crossley, Thomas F. & Grootendorst, Paul & Veall, Michael R., 2002. "The effects of drug subsidies on out-of-pocket prescription drug expenditures by seniors: regional evidence from Canada," Journal of Health Economics, Elsevier, vol. 21(5), pages 805-826, September.
    7. Jeffrey H. Dorfman & Catherine L. Kling & Richard J. Sexton, 1990. "Confidence Intervals for Elasticities and Flexibilities: Reevaluating the Ratios of Normals Case," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 72(4), pages 1006-1017.
    8. 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.
    9. 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 829-844, September.
    10. McDonald, John F & Moffitt, Robert A, 1980. "The Uses of Tobit Analysis," The Review of Economics and Statistics, MIT Press, vol. 62(2), pages 318-321, May.
    11. Sonia Bhalotra & Cliff Attfield, 1998. "Intrahousehold resource allocation in rural Pakistan: a semiparametric analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 463-480.
    12. Hongyi Li & G. S. Maddala, 1999. "Bootstrap Variance Estimation Of Nonlinear Functions Of Parameters: An Application To Long-Run Elasticities Of Energy Demand," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 728-733, November.
    13. 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.
    14. 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.
    15. 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.
    16. Davidson, Russell & MacKinnon, James G, 1999. "Bootstrap Testing in Nonlinear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 487-508, May.
    17. Stephen E. Miller & Oral Capps & Gary J. Wells, 1984. "Confidence Intervals for Elasticities and Flexibilities from Linear Equations," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 66(3), pages 392-396.
    18. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, January.
    19. Wayne A. Fuller, 1962. "Estimating the Reliability of Quantities Derived from Empirical Production Functions," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 44(1), pages 82-99.
    20. 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.
    21. 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.
    22. 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.
    23. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
    24. 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 715-719, November.
    25. Wayne A. Fuller & James E. Martin, 1961. "The Effects of Autocorrelated Errors on the Statistical Estimation of Distributed Lag Models," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 43(1), pages 71-82.
    26. Dorfman, Jeffrey H. & Kling, Catherine L. & Sexton, Richard J., 1990. "Confidence Intervals for Elasticities and Flexibilities," 1990 Annual meeting, August 5-8, Vancouver, Canada 270866, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    27. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, January.
    28. Jiazhong You, 2003. "Robust estimation of models of Engel curves," Empirical Economics, Springer, vol. 28(1), pages 61-73, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rossini, Gustavo & Arancibia, Rodrigo García & Depetris Guiguet, Edith, 2014. "Argentine Beef Demand and Household Choices of Retail Channels," International Journal on Food System Dynamics, International Center for Management, Communication, and Research, vol. 5(1), pages 1-10, June.
    2. Rodrigo García Arancibia, 2013. "Curvas de Engel de alimentos fuera del hogar según circunstancia de consumo. el caso de Argentina," Revista Cuadernos de Economia, Universidad Nacional de Colombia, FCE, CID, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hirschberg, J.G. & Lye, J.N. & Slottje, D.J., 2008. "Inferential methods for elasticity estimates," Journal of Econometrics, Elsevier, vol. 147(2), pages 299-315, December.
    2. Seebens, Holger, 2009. "Child Welfare and Old-Age Security in Female Headed Households in Tanzania," IZA Discussion Papers 3929, Institute of Labor Economics (IZA).
    3. Carson, Richard T. & Czajkowski, Mikołaj, 2019. "A new baseline model for estimating willingness to pay from discrete choice models," Journal of Environmental Economics and Management, Elsevier, vol. 95(C), pages 57-61.
    4. 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.
    5. Nicholas E. Piggott, 2003. "Measures of precision for estimated welfare effects for producers from generic advertising," Agribusiness, John Wiley & Sons, Ltd., vol. 19(3), pages 379-391.
    6. Timothy K.M. Beatty & Erling Røed Larsen, 2005. "Using Engel curves to estimate bias in the Canadian CPI as a cost of living index," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(2), pages 482-499, May.
    7. Kling, Catherine L., 1991. "Estimating the precision of welfare measures," Journal of Environmental Economics and Management, Elsevier, vol. 21(3), pages 244-259, November.
    8. Kim, Jae H. & Fraser, Iain & Hyndman, Rob J., 2011. "Improved interval estimation of long run response from a dynamic linear model: A highest density region approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2477-2489, August.
    9. Hirschberg, J.G. & Lye, J.N., 2010. "Two geometric representations of confidence intervals for ratios of linear combinations of regression parameters: An application to the NAIRU," Economics Letters, Elsevier, vol. 108(1), pages 73-76, July.
    10. Caffey, Rex H. & Kazmierczak, Richard F., Jr., 1994. "Factors Influencing Technology Adoption In A Louisiana Aquaculture System," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 26(1), pages 1-11, July.
    11. Shimshack, Jay P. & Ward, Michael B. & Beatty, Timothy K.M., 2007. "Mercury advisories: Information, education, and fish consumption," Journal of Environmental Economics and Management, Elsevier, vol. 53(2), pages 158-179, March.
    12. Syed Abul Hasan, 2016. "Engel curves and equivalence scales for Bangladesh," Journal of the Asia Pacific Economy, Taylor & Francis Journals, vol. 21(2), pages 301-315, April.
    13. Johnston, Robert J. & Swallow, Stephen K. & Weaver, Thomas F., 1999. "Estimating Willingness to Pay and Resource Tradeoffs with Different Payment Mechanisms: An Evaluation of a Funding Guarantee for Watershed Management," Journal of Environmental Economics and Management, Elsevier, vol. 38(1), pages 97-120, July.
    14. Bolduc, Denis & Khalaf, Lynda & Yélou, Clément, 2010. "Identification robust confidence set methods for inference on parameter ratios with application to discrete choice models," Journal of Econometrics, Elsevier, vol. 157(2), pages 317-327, August.
    15. David Aristei & Luca Pieroni, 2008. "A double-hurdle approach to modelling tobacco consumption in Italy," Applied Economics, Taylor & Francis Journals, vol. 40(19), pages 2463-2476.
    16. Carlin, Paul S. & Flood, Lennart, 1997. "Do children affect the labor supply of Swedish men? Time diary vs. survey data," Labour Economics, Elsevier, vol. 4(2), pages 167-183, June.
    17. Xiaodong Gong & Laurie Brown, 2017. "The Impacts of the Presence of Disabled Members on Intra-household Allocation in Older Australian Households," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 50(4), pages 398-411, December.
    18. Lanfranco, Bruno A. & Ames, Glenn C.W. & Huang, Chung L., 2001. "A Censored System Estimation Of Hispanic Household Food Consumption Patterns," Faculty Series 16720, University of Georgia, Department of Agricultural and Applied Economics.
    19. Abdul Malik Iddrisu & Michael Danquah & Alfred Barimah & Williams Ohemeng, 2020. "Gender, age cohort, and household investment in child schooling: New evidence from sub-Saharan Africa," WIDER Working Paper Series wp2020-9, World Institute for Development Economic Research (UNU-WIDER).
    20. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.

    More about this item

    Keywords

    Engel curves; Fieller method; Tobit; robust regression; semiparametric;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mlb:wpaper:1053. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Dandapani Lokanathan (email available below). General contact details of provider: https://edirc.repec.org/data/demelau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.