Price levels and inflation in regressions How would we include price levels in a regression? Would we just take the log of the price index number, e.g.: Consumer Price Index number provided by the Office of National Statistics (UK statistical agency)? If not, then how would we include it? Is it acceptable to just put in the log of the inflation rate as a regressor on the RHS? If I am modelling savings and want to see how it responds to price levels, how would I do this?
 A: Price levels are nonstationary: both means and variances tend to grow. We usually treat them as exponentially growing series. 
In practice all combinations are used: $P_t$, $\Delta P_t$, $\ln P_t$, $\Delta\ln P_t$ etc. It depends on the problem. 
For instance, the GDP deflator is essentially $P_t$, i.e. the level. It is used to convert nominal GDP into real GDP.
Inflation is usually in simple percentages, i.e. $P_t/P_{t-1}-1\approx \Delta\ln P_t$, but researches often use the continuously compounded version $\Delta\ln P_t$.
In your case of savings on prices, I would first look at what researchers are doing, by that I mean review the papers. It's not my field, so I can't give you a direct advice. I would start with reviewing the basic macroeconomic theories in this regard, like new Keynesian stuff which you can find in any textbook (Mankiw?). There's also a difference between a realized inflation, and inflation expectations.
I work with somewhat similar problem but in banking (deposits), not macroeconomic context. In deposits we usually look at sensitivity to the rates, not inflation. Economists in this context would probably look at real rates, i.e. interest rates minus inflation. So, if you regress savings, then make sure you don't double count the inflation. 
