# Re: st: Reconcile Log Transformed with Untransformed Results

 From Erasmo Giambona To statalist@hsphsun2.harvard.edu Subject Re: st: Reconcile Log Transformed with Untransformed Results Date Sat, 13 Feb 2010 19:10:31 +0100

```Thanks Austin. This is really helpful. Assuming I want to use the log
specification, can I still compuet economic significance?

That is, in the example, could I say that a 1 IQR change in X (i.e.,
0.85) is approximately associated with a 0.008*0.85=0.0068 change in
Y?

Thanks you,

Erasmo

On Sat, Feb 13, 2010 at 2:03 PM, Austin Nichols <austinnichols@gmail.com> wrote:
> 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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