I have a panel data model with double-log functional form. I have 4 variables, one of which is a dummy. What is the best way to transform the values of 0 for my dummy to be able to take natural logs (since you can't take logs from zero)? I have found 2 options so far, but I dont know which is the best (or perhaps there is a 3rd option).
1) Transform all the values of 0 into a very small value (0.00000000001) and then take the logs. I'm not sure this wouldn't still change the outcome of my model quite a bit. 2) Change the values of 0 into 1 and the dummy values of 1 into e (the base of natural logarithm). The log of this newly defined dummy then takes on the values of zero and one and the interpretation of my betas would remain the same.
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