Capital Controls Increase Monetary Policy Autonomy

I saw a Tyler Cowen link to a paper under the text “Are capital controls actually effective?” I assumed the conclusion of the paper must be that they’re not. But actually it seems to me that Nicolas Magud, Carmen M Reinhart, and Kenneth Rogoff are finding that capital controls have some important effects. Specifically, controls on capital inflows:

Make monetary policy more independent,
— Alter the composition of capital flows, and
— Reduce real exchange rate pressures (although the evidence on the latter is more controversial).
— Do not reduce the volume of net flows (and hence the current-account balance).

The question facing policymakers is whether the distorting effect of altering the composition of capital flows is a bigger deal than the increased ability to fight recessions. Presumably the question “at what margin?” is relevant here. But this seems like a very relevant consideration.