Can you use an index as an independent variable in linear regression? My y is an interest rate. The independent variable I would like to use is one index divided by another: both indexes have a base of year 2012 = 100. So my independent variable is the ratio of one index to another over many periods. Is there any issue if I use this ratio as my independent variable in a regression to predict y?
I am wondering if there are technical reasons for why this may be flat out wrong to do. My thinking is it shouldn’t matter whatsoever… in this case, every one unit increase in my ratio which is based on two very particular indexes corresponds to an increase in y equal to the coefficient. As long as I know how the interpret the coefficient then this is fine?
Here’s the ratio but with base year 2007. https://fred.stlouisfed.org/graph/?g=qLC

It is difficult to say without additional context, but so long as the indices are exchangeable then there should be no problem.
Exchangeability manifests as invariance in the joint distribution of the parameters of the model.  If, for example, I could reassign the indices to show a negative relationship/positive relationship then the model would be non-exchangeable.
