Recommended tests do detect breaks in time series What tests do you recommend for finding breaks in the following time series: log of inward FDI, log of nominal GDP, log of outward FDI from 1980 to 2012?
For a multivariate regression:

If you're testing for a break at a known date, say at a historic event or change in policy regime, I would recommend that you use a Chow test (a special case of an F-test). This will give you an idea of whether the coefficients are constant on each side of the proposed break.

On the other hand, if you want to test for a break at an unknown date, you have three options. You could try a Quandt, Mann-Wald, or Andrews-Ploberger statistic. The choice is up to you, but I like Mann-Wald. To me, it's more intuitive than the others because it's basically the Mean Value Theorem evaluated using a Riemann sum of the F-test at each potential break. Of course, the asymptotic distributions necessary to use any of these methods are beyond my knowledge, but you don't need those if you're modeling in a nice software package with pre-loaded diagnostic tests. 

Lastly, testing for "breaks" (as in multiple breaks) is a computational nightmare. You probably have deeper issues with your model (like omitted variables or some sort of misspecification) if you need multiple breaks.