The attached script does just that[*], and compares execution time for both approaches, so you can play with it.

Hi,

on my machine:
             t0 =  1.3656743
             t1 =  0.42014637

My question to the community is: would it be worthwhile to implement the "specialised" algorithm natively? Something like

fols y X fac

where "fols" stands for "factorised OLS"? Or maybe as an option to the ols command? Or maybe as a function? Having such a command (or function) would of 

I'd opt for ols y X fac --factorised

Marcin