The impact of monetary expansion on nominal interest rates is unclear. The liquidity effect implies that in the short run they will fall. However the Fisher effect implies that in the long run they will rise. Whether the monetary expansion ultimately leads to a nominal interest rate that is higher or lower than the original rate depends on the relative strength of these effects. If the liquidity effect dominates the Fisher effect then expansionary policy will cause rates to fall. If the Fisher effect dominates the liquidity effect then the expansionary policy will cause rates to rise. (I'm neglecting several things, but I hope the above still makes sense).
This is important, because whether or not a low interest rate is a sign of expansionary monetary policy depends on inflation expectations.
if monetary policy reveals information about economic developments, interest rates of all maturities move in the same direction in response to a policy innovation. If, on the other hand, monetary policy reveals information about the central bank's policy preferences, short and long interest rates move in opposite directions.
My interpreration of this is that when there is a policy surprise the Fisher effect dominates the liquidity effect. But this poses two really interesting questions:
1. Is there anything important about the surprise, other than its impact on inflation expectations?
2. Does this adhere to the Lucas critique?
Update: I've just seen that Samuel Hammond and Ben had a disagreement about what the paper implies about the liquidity and Fisher effects on Twitter. I would love to see a longer discussion.