Are Japan and Switzerland havens for terrorists and drug lords? High-denomination bills are in high demand in both places, a trend that some politicians claim is a sign of nefarious behavior. Yet the two countries boast some of the lowest crime rates in the world. The cash hoarders are ordinary citizens responding rationally to monetary policy.

The Swiss National Bank introduced negative interest rates in December 2014. The aim was to drive money out of banks and into the economy, but that only works to the extent that savers...