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Interpreting Dummy Variables in Semi-logarithmic Regression Models: Exact Distributional Results

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Abstract

Care must be taken when interpreting the coefficients of dummy variables in semi-logarithmic regression models. Existing results in the literature provide the best unbiased estimator of the percentage change in the dependent variable, implied by the coefficient of a dummy variable, and of the variance of this estimator. We extend these results by establishing the exact sampling distribution of an unbiased estimator of the implied percentage change. This distribution is nonnormal, and is positively skewed in small samples. We discuss the construction of bootstrap confidence intervals for the implied percentage change, and illustrate our various results with two applications: one involving a wage equation, and one involving the constructions of an hedonic price index for computer disk drives.

Suggested Citation

  • David E. Giles, 2011. "Interpreting Dummy Variables in Semi-logarithmic Regression Models: Exact Distributional Results," Econometrics Working Papers 1101, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:1101
    Note: ISSN 1485-6441
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    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp1101.pdf
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    References listed on IDEAS

    as
    1. Kees Jan Van Garderen & Chandra Shah, 2002. "Exact interpretation of dummy variables in semilogarithmic equations," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 149-159, June.
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    More about this item

    Keywords

    Semi-logarithmic regression; dummy variable; percentage change; confidence interval;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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