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Bayesian Estimation for Partially Linear Models with an Application to Household Gasoline Consumption

Author

Listed:
  • Haotian Chen

  • Xibin Zhang

Abstract

A partially linear model is often estimated in a two-stage procedure, which involves estimating the nonlinear component conditional on initially estimated linear coefficients. We propose a sampling procedure that aims to simultaneously estimate the linear coefficients and bandwidths involved in the Nadaraya-Watson estimator of the nonlinear component. The performance of this sampling procedure is demonstrated through Monte Carlo simulation studies. The proposed sampling algorithm is applied to partially linear models of gasoline consumption based on the US household survey data. In contrary to implausible price effect reported in the literature, we find negative price effect on household gasoline consumption.

Suggested Citation

  • Haotian Chen & Xibin Zhang, 2014. "Bayesian Estimation for Partially Linear Models with an Application to Household Gasoline Consumption," Monash Econometrics and Business Statistics Working Papers 28/14, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2014-28
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    References listed on IDEAS

    as
    1. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    2. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    3. repec:aen:journl:2008v29-01-a06 is not listed on IDEAS
    4. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    5. repec:aen:journl:2007v28-01-a02 is not listed on IDEAS
    6. Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.
    7. Wadud, Zia & Noland, Robert B. & Graham, Daniel J., 2010. "A semiparametric model of household gasoline demand," Energy Economics, Elsevier, vol. 32(1), pages 93-101, January.
    8. Dahl, Carol A, 1979. "Consumer Adjustment to a Gasoline Tax," The Review of Economics and Statistics, MIT Press, vol. 61(3), pages 427-432, August.
    9. Hausman, Jerry A & Newey, Whitney K, 1995. "Nonparametric Estimation of Exact Consumers Surplus and Deadweight Loss," Econometrica, Econometric Society, vol. 63(6), pages 1445-1476, November.
    10. Angus Deaton & Christina Paxson, 1998. "Economies of Scale, Household Size, and the Demand for Food," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 897-930, October.
    11. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
    12. Sebastiano Manzan & Dawit Zerom, 2010. "A Semiparametric Analysis of Gasoline Demand in the United States Reexamining The Impact of Price," Econometric Reviews, Taylor & Francis Journals, vol. 29(4), pages 439-468.
    13. Dahl, Carol & Sterner, Thomas, 1991. "Analysing gasoline demand elasticities: a survey," Energy Economics, Elsevier, vol. 13(3), pages 203-210, July.
    14. 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, March.
    15. Su, Qing, 2011. "The effect of population density, road network density, and congestion on household gasoline consumption in U.S. urban areas," Energy Economics, Elsevier, vol. 33(3), pages 445-452, May.
    16. Kayser, Hilke A., 2000. "Gasoline demand and car choice: estimating gasoline demand using household information," Energy Economics, Elsevier, vol. 22(3), pages 331-348, June.
    17. Golubev, Georgi & Härdle, Wolfgang, 2000. "On adaptive estimation in partial linear models," SFB 373 Discussion Papers 2000,21, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    18. Adonis Yatchew & Joungyeo Angela No, 2001. "Household Gasoline Demand in Canada," Econometrica, Econometric Society, vol. 69(6), pages 1697-1709, November.
    19. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    20. Liang, Hua, 2006. "Estimation in partially linear models and numerical comparisons," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 675-687, February.
    21. Stoker, Thomas M., 1996. "Smoothing bias in the measurement of marginal effects," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 49-84.
    22. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    23. Dongfeng Chang & Apostolos Serletis, 2014. "The Demand For Gasoline: Evidence From Household Survey Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(2), pages 291-313, March.
    24. Richard Schmalensee & Thomas M. Stoker, 1999. "Household Gasoline Demand in the United States," Econometrica, Econometric Society, vol. 67(3), pages 645-662, May.
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    Keywords

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: 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
    • Q41 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Demand and Supply; Prices

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