The fact that inflation is so stable when interest rates are stuck at zero has profound implications. If inflation is stable at a zero peg, it must be stable at a higher peg as well, which means raising interest rates must sooner or later raise inflation. The open question, which this paper goes after, is whether inflation can temporarily decline when interest rates rise. (Graphs from an earlier blog post here.)
Classical "Keynesian" or "Monetarist" models say that inflation is unstable in a peg. They must be wrong. "New-Keynesian" models say that inflation is stable in a peg, a good point in their favor. The important difference is rational expectations. If people drive a car looking in the rear view mirror, cars are unstable and veer off the road. If people look forward, then cars are stable and get back on the road on their own.
But the standard new-Keynesian model also predicts that inflation goes up if interest rates rise, as shown in the graph. Interest rates are blue, inflation is red, output is black. The dashed line is when people know the rise is coming, the solid line for when it's a surprise. Raising rates does lower output, just as you thought.
The paper tries everything to revive the idea that higher interest rates lower inflation, without luck.
The standard new-Keynesian model accounts well for the fact that inflation has been stable at a zero interest rate peg. However, If the Fed raises nominal interest rates, the same model model predicts that inflation will smoothly rise, both in the short run and long run. This paper presents a series of failed attempts to escape this prediction. Sticky prices, money, backward-looking Phillips curves, alternative equilibrium selection rules, and active Taylor rules do not convincingly overturn the result. The evidence for lower inflation is weak. Perhaps both theory and data are trying to tell us that, when conditions including adequate fiscal-monetary coordination operate, pegs can be stable and inflation responds positively to nominal interest rate increases.