anti-logarithm after linear regression

[Kenny Ostel]

Hi Statalists,
in my linear regression I integrated the logarithmized GDP via log(GDP). Now after my estimation I want to compute the anti-log for the coefficient of GDP. How can I do that?

Cheers,
Kenny

[Carlo Lazzaro]

Kenny:
did you log your depvar but keep the predictors in their raw scale or else?

[Rich Goldstein]

the simple answer is to use the "exp()" function

however, as implied by Carlo, that is probably not what you want to do; please show at least your regression command (in code blocks please - see the FAQ) and tell us what you want to know from that regression

[Alfonso Sánchez-Peñalver]

Carlo's question is very valid. I will extend on his request to ask that you explain exactly what regression model you ran and what you actually want to accomplish by taking the antilog of the coefficient on ln(GDP). Carlo's question, I imagine, is directed towards knowing if the coefficient is an estimate of a sem-elasticity (if you logged only the dependent variable or only the explanatory variable) or the estimate of the elasticity (if you logged both). My question extends that to see what you're trying to achieve, and give us more information to answer. If you're trying to calculate an estimate of the effect that GDP would have on the dependent variable, I don't see how exponentiating it achieves that. So please explain more. Thanks.

[Carlo Lazzaro]

Rich wrote what was my jerk knee reaction when I first read Kenn's post (and I shared Rich's foreboding that -exp()- was not what the original poster was looking for).
Alfonso explained exactly the core meaning of my previous reply.
Kenny: the gist of all the replies you have received so far is: please, provide us with further details (as recommended by FAQ #12). Thanks.

[Kenny Ostel]

I'm gonna try to explain it in a nutshell:
- I ran an xtmixed-model
- I did not log the depvar, but only the GDP per capita to correct some violations against the model assumptions
- so I guess Rich might be right: So I only have to put the coefficient of GDP per capita into the brackets of exp()?

Best,
Kenny

[Nick Cox]

I don't see any explanation here of why you think you need to exponentiate the coefficient at all.

[Kenny Ostel]

I've read in a textbook that you can do it at least in two cases:
- to correct violations of the model assumptions
- for modelling the assumption, that the effect of GDP could decline the higher the GDP ist, e.g. the effect between a GDP of 2.000 and 3.000 is higher than between 50.000 and 51.000.

[Alfonso Sánchez-Peñalver]

I agree with Nick and it is something that I pointed to in my previous comment. The estimate you have is an estimate of a semi-elasticity. In particular you have an estimate of the following derivative: s = d y/d ln(GDP). What I'm assuming you want is an estimate of the partial with respect to GDP: b = d y / d GDP. Since d ln(GDP) = d (GDP) / GDP, it must be then that b = s GDP. So all you have to do is to multiply the coefficient you have by average GDP. The question then arises as to what average GDP to use, since you're using xtmixed which indicates that there are clusters (panels) for which you can use their own average. In any case, there is no need to exponentiate the coefficient.

[Kenny Ostel]

Thanks, Alfonso! First, since I'm very new to multivariate methods, those letters convey nothing to me but still, it's clear what I have to do. But how do I have to interpret the result. My coefficient for GDP per capita is 0.255 an the average e.g. 27,516, the multiplication result is 7,029. How can I interpret this?

[Alfonso Sánchez-Peñalver]

Kenny I made a mistake. The transformation you need is b = s / GDP, not times. My bad. Your estimate is then 0.0000093. Assuming that GDP is measured in dollars, an increase of GDP of a million dollars will increase your dependent variable by 9.3. The problem is that the relationship is nonlinear, so at different values of GDP the estimate of the slope will be different.

[Roman Mostazir]

If Alfonso's reply #9/10 does not convey any message to you, for the ease of interpretation, you may have a look at this UCLA page