# How to calculate inflation rate in order to perfom VAR model?

For an assignment I need to perform a VAR model on the three variables real GDP, short term interest rate and inflation. While for the first two variables I have not any problem, I am struggling to understand how to obtain a reliable "inflation" time series to be used for the model.

An expression I found on "Vector Autoregressions" by James H. Stock and Mark W. Watson is: $$\pi_t = 400 \ln \left(\frac{P_t}{P_{t-1}}\right)$$ where $P_t$ is the chain-weighted GDP index. However, I don't understand the reasoning behind this expression (why 400?) and I'd prefer to avoid using the chain-weighted GDP index since is an index I don't know very well.

I'd like to start from the GDP deflator. I tried with some reasoning to obtain an useful expression and I came to the conclusion that maybe a good variable is: $$\pi_t = \frac{DEF_t -DEF_{t-1}}{DEF_t}$$

Is that correct? Which is the best series to use as inflation for the VAR model?