Sorry for the very cryptic title, but I do not know how to describe my problem in another way and I'm sure the solution is rather straightforward.
I am currently running a regression where the dependent and independent variables are transformed to natural logarithms. The problem I have is that one IV, DC-ratio, has a lot of values of 0% and log(0) is undefined and thus results in a missing value in Stata. If I use this value, Stata will drop the missing values and my sample would be biased since it only uses the funds which actually have a DC-ratio >0%. This is an issue as more than half of my dataset have a DC-ratio of 0%. My idea was to turn all values of 0% DC-ratio to 0.0000001%.
My councelors solution, which according to him is often used in research, is to add 1 to all values of the DC-ratio, turning 0% DC-ratio in 100% and 30% in 130%. I have followed his solution.
Besides the fact that I am wondering is this is at all possible when in the original values a DC-ratio of 100% is the maximum, I can't figure out how to interpret the results. Do I need to subtract the +1 somewhere?
I am familiair with interpreting the log-log results, but I can't figure out how to deal with this adjustment of original values. In the picture (regression results), regression number 9 is preferred and I know that a 1% increase in the DC-ratio will lead to an increase of 1.01^7.126= 1.0735-1= 7.35% increase in the geometric mean of the dependent variable. But I can tell you right now that this does not make any sense in an economic context.
I hope someone could shed some light on this problem.
Many thanks in advance!