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



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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    References listed on IDEAS

    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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    Cited by:

    1. Mick Silver & Brian Graf, 2014. "Commercial Property Price Indexes; Problems of Sparse Data, Spatial Spillovers, and Weighting," IMF Working Papers 14/72, International Monetary Fund.
    2. Rajendran, Srinivasulu & Afari-Sefa, Victor & Karanja, Daniel Kimani & Musebe, Richard & Romney, Dannie & Makaranga, Magesa A. & Samali, Silvest & Kessy, Radegunda Francis, 2016. "Farmer-Led Seed Enterprise Initiatives to Access Certified Seed for Traditional African Vegetables and its Effect on Incomes in Tanzania," International Food and Agribusiness Management Review, International Food and Agribusiness Management Association, vol. 0(Issue 1), pages 1-24, February.
    3. repec:eee:transa:v:112:y:2018:i:c:p:18-28 is not listed on IDEAS
    4. Jackson, Kristoffer, 2016. "Do land use regulations stifle residential development? Evidence from California cities," Journal of Urban Economics, Elsevier, vol. 91(C), pages 45-56.
    5. Blane Lewis, 2016. "Local political fragmentation: Fiscal and service delivery effects in Indonesia," Departmental Working Papers 2016-16, The Australian National University, Arndt-Corden Department of Economics.
    6. Alwin Keil & Alwin D’souza & Andrew McDonald, 2015. "Zero-tillage as a pathway for sustainable wheat intensification in the Eastern Indo-Gangetic Plains: does it work in farmers’ fields?," Food Security: The Science, Sociology and Economics of Food Production and Access to Food, Springer;The International Society for Plant Pathology, vol. 7(5), pages 983-1001, October.
    7. Nicolas Vaillant & François-Charles Wolff, 2013. "Understanding Diamond Pricing Using Unconditional Quantile Regressions," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 3(11), pages 1540-1561, November.
    8. Alwin Keil & Alwin D’Souza & Andrew McDonald, 2016. "Growing the service economy for sustainable wheat intensification in the Eastern Indo-Gangetic Plains: lessons from custom hiring services for zero-tillage," Food Security: The Science, Sociology and Economics of Food Production and Access to Food, Springer;The International Society for Plant Pathology, vol. 8(5), pages 1011-1028, October.
    9. Mick Silver, 2016. "How to Better Measure Hedonic Residential Property Price Indexes," IMF Working Papers 16/213, International Monetary Fund.
    10. Franz Fuerst & Jorn van de Wetering, 2015. "How does environmental efficiency impact on the rents of commercial offices in the UK?," Journal of Property Research, Taylor & Francis Journals, vol. 32(3), pages 193-216, September.
    11. Mick Silver, 2012. "Why House Price Indexes Differ; Measurement and Analysis," IMF Working Papers 12/125, International Monetary Fund.
    12. Fuerst, Franz & McAllister, Patrick & Nanda, Anupam & Wyatt, Peter, 2015. "Does energy efficiency matter to home-buyers? An investigation of EPC ratings and transaction prices in England," Energy Economics, Elsevier, vol. 48(C), pages 145-156.

    More about this item


    Semi-logarithmic regression; dummy variable; percentage change; confidence interval;

    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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