On Thu, 25 Mar 2004, Hans J. Baumgartner wrote:
> If Salary is in log, then nonwhites earn on averarge _b[nonwhite]
> percentage more than the repecitve dummy base.
> Best wishes
> Hans
>
Hans has made a very common mistake in interpreting the coefficient on a
dummy variable. There is a paper by Halvorsen and Palmquist (American
Economic Review, 1980) that discusses this issue, and there is a
user-written command called -logdummy- by Richard Goldstein that was
introduced in the Stata Technical Bulletin (issue 5, package srd8).
Following H & P, say we have estimated the following equation:
ln Y = a + b'x + c*D
where D is a dummy variable, x is a vector of continuous variables,
and a, b, and c are estimated parameters. Then
Y = exp(a + b'x + c*D)
= (1 + g)^D exp(a + b'x)
where the second equality makes use of the fact that D is a 0/1
dummy and g is the relative impact on Y when D=1. Thus, c is
an estimate of ln(1 + g), and what we really want to know is g.
c = ln(1 + g) => g = exp(c) - 1
Hence, if salary is in logs, then nonwhites earn on average
100*(exp(_b[nonwhite]) - 1) more than whites.
-- Brian
-- bpoi@stata.com
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