Good morning all,
I am having some trouble interpreting my regression output. My model is LN of transaction volume = alpha + beta1_RER + control variables
RER is defined as the change in the average exchange rate from one period (half year) to another. And it is expected to have an impact on the transaction volume.
Log-level : %Δy = (100*β1)Δx
The coefficient for RER is -12. In my opinion this means that :
- An increase of 1 unit in the exchange rate change (100 percentage points) would mean a 1200% drop in transaction volume
- An increase of 1p.p. in exchange rate change would mean a 15,98% decrease in transaction volume
With standard deviation :
STD : 0,0535
0,0535 * -12 = 0.642
- A one standard deviation increase in RER means a 64% drop in transaction volume
Is that correct?
I have just very confused because I am interpreting a change in a change and am unsure how to deal with the coefficient.
Start by working through the math very methodically.
LN is natural log, or log base e. It is often written lower case ln.
ln(volume)=alpha - 12*ln(RER) + Ln(control variables)
An increase in RER by 1 will have different outcomes depending on the starting value of RER.
RER old=0.2, so RER new = 1.2. ln(0.2) is -1.60944 and therefore the old volume was antilog(-12*(ln(0.2))=244137453. If I do the same calculations with RER new I get ln(1.2)=0.18 and antilog(-12*ln(1.2))= 0.11216.
RER old=1.2, so RER new=2.2. Same math, so volume old is 0.11216 and volume new is 0.0000779.
My guess is that I have not interpreted the question correctly, but this is how I interpreted what you wrote. Hopefully I provide enough detail for this to be helpful. An obvious mistake I might have made is to use 1 rather than 1%. The correct value is determined by how the data were entered in building the model.
Hi Thoms thanks for your reply my model does not use ln(RER) it uses delta(RER) and interpretation of delta(RER) is what i am not sure about. I am interpreting the effect in % on volume (due to ln form) of an increase in a change. I am unsure on how to interpret the coefficient. Could you please have a look above on my proposed interpretation?
So how did you get an answer of 1200% ?
Assuming no interactions then ln(volume)=-12RER. If RER=1 then volume=0.0000067. If RER=2 then volume=0.00000000004.
You are correct that increasing RER will result in a decrease in volume.
For standard deviation example you have a mistake. A one standard deviation increase in RER means a 0.64 point decrease in ln(volume). That part is very important. A one standard deviation increase in RER means a 0.64 point decrease in ln(volume) is good. However you cannot change that simple statement to get rid of the log transformation. If I start with an RER of 0.9 then the difference in volume from 0.9 to 0.9535 is 0.02, while the difference in volume from 1.114 to 1.1675 is 0.017. The log relationship is linear, not the anti-log.
Beware of an RER of zero as the ln(0) is not defined.
If RER can be negative you may also have some interesting issues. where a 0.05 point change in RER results in huge changes in volume.
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