I have probably an easy problem, however I'm not really sure how to do it: Basically, I would like to estimate a linear regression with OLS. So far so good. However, the model that should estimate looks like this:

y = a0 + a1*x1 - a2*x2 + a3*x3 - a4*x4

However, the normal text book models have always only positive coefficients, unlike my x2 and x4. Now how can I do this?

I'm not sure whether it helps, but the model above is just a simplification of what I actually wanna do. I actually have two Taylor rules for two different countries, and I would like to estimate the difference between them, so i - i* = ... and then you get of course a negative -a3INFL* and a -a4OUTPUT_GAP* term and so on.