Is the demand for money interest-elastic?

Read the ongoing debate over at EconLog.  Bryan Caplan writes:

When I’ve asked economists "Do you hold less money when
interest rates rise?," they usually admit that they don’t. And we’re
trained to think we should! If we asked non-economists the same
question, I bet that most would simply be baffled.

I have much sympathy for this view as long as we are talking about currency.  But it is a trickier question for the broader monetary aggregates.  High measured nominal interest rates alter the real interest rates faced by some market participants.  We don’t all face the same rate of price inflation.  High nominal rates of interest, for this reason, proxy for a high variance of real interest rates (across individuals) and perhaps a more general greater future uncertainty as well.  I would not be surprised if these effects kept down the broader measures of money demand, albeit not the demand for currency through the mechanism of portfolio substitution. 

Let’s not forget the Litterman and Weiss result (Econometrica, 1983) that high nominal interest rates in a VAR model predict bad times ahead.  Who knows why, but they do.  So why can’t they predict money demand as well?

Sometimes a nominal interest rate is not just "a nominal interest rate," to turn Freud’s aphorism on its head.