Take $y=\alpha + \beta_1 x_1 + \beta_2 x_2 + ... + \beta_3 x_5 + \epsilon$
The Bai-Perron sequential approach allows to identify multiple structural break dates for the regression coefficients in the regression above. However, the structural breaks are common across coefficients. What if I have good reason to believe the structural breaks are different for $x_1$ and $x_2$ and perhaps nonexistent for $x_3$ but still find it relevant to include all variables in the regression for the sake of controlling for omitted variable biases?
I could in principle test for all possible combinations of arbitrary breaks in the regression coefficients using the chow tests. But not only is this computationally unfeasible in my case due to the large sample size, it is also the case that the chow tests are for known break dates. The Andrews sup-F test for unknown break dates focus on single breaks and do not detect multiple break dates.
Which methods would you recommed to do this?