Do tax cuts to the rich lower interest rates?
You may want to look at the literature of the effects of taxation on savings. A survey is given in: Sandmo. A. (1985) The effects of taxation on savings and risk-taking, in: Auerbach &amp; Feldstein, Handbook of Public Economics, Elsevier.

In this survey, the (simpler) problem of the overall effect of taxation on saving behavior is analyzed. A change in tax progression is much more subtle and harder to measure.

The survey states the problems associated with estimation of this simpler problem and the author comes to the conclusion that the empirical results are inconclusive. Since then there may have been some move in the literature, however.