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Re: st: Calculating an average effect

From   "Brian P. Poi" <[email protected]>
To   [email protected]
Subject   Re: st: Calculating an average effect
Date   Thu, 25 Mar 2004 17:14:31 -0600 (CST)

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
  -- [email protected]

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