A neo-Fisherian experiment that hedges its New Keynesian bets

The experience of a country like Japan, where interest rates have been at their floor for 2 decades now, and inflation is still undershooting the BoJ target of 2 per cent, is enough to test the faith of a New Keynesian and make one wonder whether the neo-Fisherians have a point.  They maintain that inflation undershoots the target because of very low interest rates, not despite them.  New Keynesians deduce from their version of the model that a temporary interest rate cut raises inflation and vice-versa.  They extended that logic to deduce that an extremely protracted recession and undershoot of the inflation target should be responded to by keeping interest rates at their floor indefinitely.  Neo Fisherians think that indefinitely low interest rates is what keeps inflation low, not what will cure it.

The 'Fisherian' bit of the name comes from the Fisher relation, which asserts that in the very long run central bank rates and inflation move one for one in step with each other.  Neo-Fisherians are those who argue that inflation would rise in step with central bank rates from their current starting points not only in the long run, but also in the short run too.

What about experimenting with temporarily higher rates to see if the Neo-Fisherians have a point?  This could be ruled out using logic along the lines of Pascal's wager.  (Pascal decided to feign belief in God on the grounds that if there was no God, he had simply wasted some time.  But if he stuck with his atheism proper and that was wrong, he would be damned for an eternity.)

The cost of trying out a Neo-Fisherian rise in rates, if vanilla New Keynesianism turns out to be true is, in the worst case, another recession and losing control of inflation on the downside.  By contrast, if the past is  reliable guide, then the cost of continuing vanilla New Keynesian policy when the world is actually Neo Fisherian is another period of inflation somewhat below target and reasonable growth.

However, a modification to the experiment makes it more attractive for a policymaker playing according to Pascal's wager:

Suppose instead we pre-announce two things:  1) a temporary increase in interest rates, relative to some previously expected and intended path;  2) a temporary fiscal stimulus, calibrated to offset the interest rate rise under the assumption that the world was vanilla New Keynesian.

If the world turns out to be New Keynesian after all, there is no harm done.  The monetary tightening and fiscal loosening offset.  If the world turns out to be Neo-Fisherian, we get a temporary boost to inflation.  Which can be locked in after the experiment with a more determined effort, and without the need for a further fiscal stimulus.

There are communication and practical issues that would have to be thought through.   But if the concepts are right here those issues might, for a central bank with few other options, be worth trying to surmount.