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st: Reconcile Log Transformed with Untransformed Results

From   Erasmo Giambona <>
To   statalist <>
Subject   st: Reconcile Log Transformed with Untransformed Results
Date   Sat, 13 Feb 2010 13:10:22 +0100

Dear All,

I am estimating the following model using simple OLS: Y=a+bX+e. The b
coefficient is equal to 0.006. The 25th percentile of X=-0.45 and the
75th percentile of X=0.40. The mean of Y is equal to 0.026. I use this
information to gauge a sense of the economic effect of X on Y. I find
that a 1 interquartile range (IQR) change in X =(0.40+0.45) has an
effect on Y equal to 0.006*0.85=0.0051, which is a 20% change in Y
(obtained as 0.0051/0.026) and seems quite sizable.

Next, I re-estimate the same model, but first I log transform both RHS
and LHS as follows: LNY=ln(1+Y) and LNX=ln(1+X). Therefore, I estimate
the following model: LNY=A+B*LNX+E. The B coefficient is equal to
0.008 in this case. It seems the interpretation of this coefficient is
the following: a 1% change in X casuses a 0.008% increase in Y.
Alternatively, if I consider a 189% change in X (i.e., the percentage
increase from the 25th to the 75 percentile) I find that this causes a
1.51% increase in Y (obtained as 189*0.008).

My question is: is this calculation correct? I find it hard to
reconcile it with the untransformed results, where a 1 IQR change in X
causes Y to increase by 20%.

Thanks for any suggestions on the issue,

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