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Re: st: Reconcile Log Transformed with Untransformed Results


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Reconcile Log Transformed with Untransformed Results
Date   Sat, 13 Feb 2010 08:03:26 -0500

Erasmo Giambona <e.giambona@gmail.com>:
No, not correct: a regression of ln(y+1) on ln(x+1) does not estimate
an elasticity, and a change from -0.45 to +0.4 does not correspond to
any well-defined percentage point change.  If you are unsure of the
correct functional form, consider -lpoly- or -fracpoly- or -mkspline-
or -pspline- (on SSC).

On Sat, Feb 13, 2010 at 7:10 AM, Erasmo Giambona <e.giambona@gmail.com> wrote:
> 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,
>
> Erasmo
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