Exact interpretation of dummy variables in semilogarithmic equations

This paper considers the percentage impact of a dummy variable regressor on the level of the dependent variable in a semilogarithmic regression equation with normal disturbances. We derive an exact unbiased estimator, its variance, and an exact unbiased estimator of the variance. The main practical contribution lies in a convenient approximation for the unbiased estimator of the variance, which can be reported together with Kennedy's approximate unbiased estimator of the percentage change. The two approximations are very simple, yet highly reliable. The results are applied to teacher earnings and further illustrated by examples from the literature.