Interpretation of regression - logarithm

[Milla Hanzon]

Hello,

I have a question regarding these two outputs from a DiD-model. First of all, sorry about the Norwegian, but I'll try to explain the models.

The models show the effect on sales on four different stores from treatments that happened at different times. The variable butikk_behandling#etablering is the DiD-estimator of the treatment on the four different shops.


In the first output, the dependent variable is the natural logarithm of sales, and in the second output, the dependent variable is sales in absolute values. Apart from this, the models are identical, which is why I cannot understand why I am left with two positive and two negative DiD-estimators in the first model, whereas in the second model there is only one negative value. Shouldn't the results be the same, only represented in different values (ln and non-ln?)?

I have a feeling this has got something to do with the fact that using ln_sales as dependent variables only gives me an approximation. However, I'm struggling to understand this and would really appreciate some help!

[Carlo Lazzaro]

Milla:
not quite.
In a log-linear regression model, the contribution of each predictor (when adjusted for the remaining ones) to the variation of the regressand shoud be read in percentage terms.
Example: when butikk_behandling increases from 0 to 2 when etaberling is 0, the regressand increases by:

. di exp(.4379019)-1
.5494529

that is, about 54.94%.

[Milla Hanzon]

Thank you Carlo,

I was a but unclear about my interpretation. I would also interpret the change the way you do. However, I still don't understand why the coefficient in front of butikk_behandling#etablering 2.1 is positive when measured in absolute whereas it is negative when it is measured as a logarithm. How can (e^-0,0761 - 1) = - 0,073 represent the same change as 29132,41?

Best regards,
Mia

[Carlo Lazzaro]

Milla:
is the number of observations the same in both datasets?

[Milla Hanzon]

Yes, the number of observations are the same. No values are negative or equal to zero.

Best,
Mia

[Carlo Lazzaro]

Milla:
due its lack of significance (mirrored by the width of its 955 CI) it's not surprising the coefficient -2 1- flipped its sign over the two models.
I do not think that is indeed an issue for your analysis.