Interpreting ratio as dependent variable in regression

Question

I am running a linear multiple regression model, looking at various businesses' change in income due to the COVID-19 lockdowns. So, as DV, I am calculating a ratio of post-pandemic income over pre-pandemic income. I have two questions:

1. If one of the predictors has a significant Beta of, let's say, -.01, would it make sense to interpret this as: "a one unit increase in that predictor is associated with a 1 percentage point loss in income?" In other words, should I read it as a 1 percentage point loss or a 1 percent loss?
2. Would using a ratio as DV make sense in light of Kronmal 1993? Intuitively speaking, at least, regressing change of income makes a lot of sense to me, but that is a ratio.

Thanks a lot!

Answer 1

Usually, the closer you are to the original observations with your model the fewer chances there are for hidden assumptions to lead you astray.

With respect to ratios, the Kronmal paper you cite and the answer linked by kjetil b halvorsen in a comment show the dangers.

With respect to using differences as outcomes, there are also problems. See for example this discussion. There's a big problem if you use the baseline value as a predictor in the model; see here for example.

If your interest is in fractional changes in income and all values are strictly positive, a log transformation might be useful. Otherwise, it's usually best to build your model on the original observations and do your estimates of changes, ratios, etc thereafter.