Sunday, October 4, 2015

Whither Econometric Principal-Components Regressions?

Principal-components regression (PCR) is routine in applied time-series econometrics.

Why so much PCR, and so little ridge regression? Ridge and PCR are both shrinkage procedures involving PC's. The difference is that ridge effectively includes all PC's and shrinks according to sizes of associated eigenvalues, whereas PCR effectively shrinks some PCs completely to zero (those not included) and doesn't shrink others at all (those included). 

Does not ridge resonate as more natural and appropriate? 

This recognition is hardly new or secret. It's in standard texts, like the beautiful Hastie et al. Elements of Statistical Learning.  

Econometricians should pay more attention to ridge.