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A Semiparametric Derivative Estimator in Log Transformation Models

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  • Chunrong Ai
  • Edward Norton

Abstract

This paper considers a regression model with a log-transformed dependent variable. The log transformed model is estimated by simple least squares, but computing the conditional mean of the dependent variable on the original scale given the explanatory variables analytically requires knowing the conditional distribution of the error term in the transformed model. We show how to obtain a consistent estimator for the conditional mean and its derivatives without specifying the conditional distribution of the error term. The asymptotic distribution of the estimator is derived. The proposed procedure is then illustrated with health expenditure data from the Medical Expenditure Panel Survey.

Suggested Citation

  • Chunrong Ai & Edward Norton, 2006. "A Semiparametric Derivative Estimator in Log Transformation Models," Health, Econometrics and Data Group (HEDG) Working Papers 06/06, HEDG, c/o Department of Economics, University of York.
    • Handle: RePEc:yor:hectdg:06/06
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    Cited by:

    1. Ciani Emanuele & Fisher Paul, 2019. "Dif-in-Dif Estimators of Multiplicative Treatment Effects," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-10, January.
    2. Devon Wilson & Donald Dantzler & Damian Evans & Richard McGregory, 0. "Do Racial Disparities Exist in the Labor Market for Educators?," Journal of Economics, Race, and Policy, Springer, vol. 0, pages 1-10.
    3. Richard McGregory, 2013. "An Analysis of Black–White Wage Differences in Nursing: Wage Gap or Wage Premium?," The Review of Black Political Economy, Springer;National Economic Association, vol. 40(1), pages 31-37, March.
    4. Richard McGregory & James Peoples, 2013. "Compensation of Foreign and Domestic Nurses in the US," Journal of Labor Research, Springer, vol. 34(2), pages 203-223, June.
    5. Shengwu Shang & Erik Nesson & Maoyong Fan, 2018. "Interaction Terms In Poisson And Log Linear Regression Models," Bulletin of Economic Research, Wiley Blackwell, vol. 70(1), pages 89-96, January.
    6. Ai, Chunrong & Li, Hongjun & Lin, Zhongjian & Meng, Meixia, 2015. "Estimation of panel data partly specified Tobit regression with fixed effects," Journal of Econometrics, Elsevier, vol. 188(2), pages 316-326.
    7. Devon Wilson & Donald Dantzler & Damian Evans & Richard McGregory, 2020. "Do Racial Disparities Exist in the Labor Market for Educators?," Journal of Economics, Race, and Policy, Springer, vol. 3(3), pages 195-204, September.
    8. Marcu, Mircea & Knapp, Caprice & Madden, Vanessa & Brown, David & Wang, Hua & Sloyer, Phyllis, 2014. "Effects of an Integrated Care System on Children with Special Health Care Needs' Medicaid Expenditures," Working Papers 2014-8, University of Alberta, Department of Economics.
    9. Aliasghar, Omid & Haar, Jarrod, 2023. "Open innovation: Are absorptive and desorptive capabilities complementary?," International Business Review, Elsevier, vol. 32(2).
    10. Zhong, Rong (Irene), 2018. "Transparency and firm innovation," Journal of Accounting and Economics, Elsevier, vol. 66(1), pages 67-93.
    11. Borislava Mihaylova & Andrew Briggs & Anthony O'Hagan & Simon G. Thompson, 2011. "Review of statistical methods for analysing healthcare resources and costs," Health Economics, John Wiley & Sons, Ltd., vol. 20(8), pages 897-916, August.

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