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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.

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File URL: http://www.uvic.ca/socialsciences/economics/assets/docs/econometrics/ewp1101.pdf
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Bibliographic Info

Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 1101.

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Length: 24 pages
Date of creation: 31 Jan 2011
Date of revision:
Handle: RePEc:vic:vicewp:1101

Note: ISSN 1485-6441
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Keywords: Semi-logarithmic regression; dummy variable; percentage change; confidence interval;

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  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. Nicolas G. Vaillant & Fran├žois-Charles Wolff, 2013. "Understanding diamond pricing using unconditional quantile regressions," Working Papers halshs-00853384, HAL.
  3. Mick Silver, 2012. "Why House Price Indexes Differ," IMF Working Papers 12/125, International Monetary Fund.

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