Interpretations of dummy variables in regressions with log. depen. variable
---------------------------------------------------------------------------
by Richard Goldstein, Qualitas, Brighton, MA,  EMAIL goldst@@harvarda.bitnet

                  ^logdummy^ varlist

No options are allowed or needed.

When the dependent variable in a linear regression is a logarithmic transform,
the interpretation of the right-hand-side variables is that they show the
percentage change in the untransformed dependent variable per one-unit change
in the right-hand-side variable, if the right-hand-side variable is in
original units; if the variable has been transformed also, by taking logs,
then it's coefficient is interpreted as the percentage change in the
untransformed dependent variable for a 1 percent change in the untransformed
right-hand-side variable.  This is fine for continuous variables, but is
biased for dummy (categorical) variables (this provides the estimated median
of the distribution rather than the mean).  ^logdummy^ gives a simple change
for dummy variables that is consistent and, though still biased, is very close
to the unbiased result and is much easier to compute.  For discussion, see R.
Halvorsen and R. Palmquist (1980), "The Interpretation of Dummy Variables in
Semilogarithmic Equations", American Economic Review, 70, pp. 474-5; P.E.
Kennedy (1981), "Estimation with Correctly Interpreted Dummy Variables in
Semilogarithmic Equations", American Economic Review, 71, p. 801; D.E.A.
Giles (1982), "The Interpretation of Dummy Variables in Semilogarithmic
Equations", Economics Letters, 10, pp. 77-79.