<p>Care must be taken when interpreting the coefficients of dummy (“indicator”) variables in a semi-logarithmic regression model. 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 non-normal, 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 construction of an hedonic price index for computer disk drives.</p>

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

  • David E. Giles

摘要

Care must be taken when interpreting the coefficients of dummy (“indicator”) variables in a semi-logarithmic regression model. 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 non-normal, 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 construction of an hedonic price index for computer disk drives.