Take a standard New Keynesian macroeconomic model, where the central bank sets the one-period interest rate. Now let's hit it with an unexpected shock. For simplicity and concreteness, let the shock be a reduction in government spending that will last for n periods, after which government spending will return to normal. So government spending was 100, will now be 90 for n periods, then will be 100 again in period n+1 and thereafter.

If n=1, the model says the central bank should cut the real interest rate for one period, then raise it again to its original level.

If n=2, the model says the central bank should *leave the real interest rate unchanged for one period*, then cut it in the second period, then raise it again to its original level in the third period.

If n=3, the model says the central bank should *leave the real interest
rate unchanged for two periods*, then cut it in the third period, then
raise it again to its original level in the fourth period.

Etc.

If n=infinity, the New Keynesian model says the central bank should leave the real interest rate unchanged.

My hunch is that most students of New Keynesian macroeconomics knew about the results for n=1 and n=infinity, but did not know about the results for n=2 and n=3 etc., and had to think about it. Am I right?

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