Interpreting regression coefficients when dependent variable is percentage There is a similar question posted but this is not what I am looking for: Interpreting coefficients when dependent variable is a fraction/proportion?
I was reading a paper that ran a difference-in-differences regression and the coefficient value was -0.036. The dependent variable is vote shares and none of the variables were logged. In this case, is the coefficient just a percentage? So the impact of X on Y is a decrease of 3.6% of vote shares?
In addition, for simple OLS regressions, are coefficients usually percentages? Sometimes people say percentages and sometimes percentage points.. and this has been giving me a headache.. Can anyone help me clarify please?
 A: Talking about percents always causes confusion. For instance, if the starting value of $10\%$ undergoes an increase of $10\%$, there are legitimate claims of saying that the ending value (after the increase) is $11\%$ and $20\%$. For the latter, I would prefer to describe it as an increase of “10 percentage points,” but this is far from a universal practice.
A related question here on Cross Validated
With that out of the way, if the model is linear, the it is just a matter of taking partial derivatives and interpreting them as usual in calculus. If the derivative is $-0.0036$, this means that you expect a value $0.0036$ lower than it would have been for a predictor value one unit lower (the usual interpretation of a linear regression coefficient). In other words, this would be a decrease of 3.6 percentage points, to use my terminology (not to claim that I invented the terminology, but I do use it).
Don’t overthink it. The regression coefficients are telling you exactly what they always tell you.
(A drawback of this kind of model, however, is that it can result in predicted probabilities outside of $[0,1]$, but it is on the author to defend the decision to allow for this. Your interpretation of the coefficients does not depend on this.)
