Instantaneous Deflation as a Macro Solution
I think this analysis is correct, under the maintained assumption that prices (including wages) are completely and instantaneously flexible. But if prices are sticky, then the immediate deflation and concurrent increase in expected inflation won't occur painlessly. Instead, it would take a while for the price level to fall, and as we wait, the economy would suffer through a period of depressed economic activity.
Let's stipulate for the sake of argument that the "equilibrium real interest rate" is negative, and that the nominal interest rate goes all the way down to zero. But oh no! Given the current array of prices and the expected array of prices next year, the implied real interest rate is too high for the market to clear. What to do?
Mankiw's suggestion is that the Fed should credibly promise to dump gobs of new dollars into the economy in twelve months, thus raising the future price "level" and giving people an incentive to unload their dollars today, while they have some purchasing power.
But there is another alternative, and that is for market prices today to fall very steeply until the market clears. The short-term collapse in prices during the present month, say, will then allow for a rapid price inflation back up to "normal" prices a year from now. [Emphasis in the original.]
According to conventional new Keynesian analysis, sticky prices are the ultimate market imperfection that makes aggregate demand matter. If you deny that prices are sticky and assume they can instantaneously jump downward to new equilibrium levels, many macroeconomic problems become much easier to solve. Indeed, you don't need to solve them at all, as the market would do it.
I wish we lived in the world that Mr Murphy describes, but my reading of the evidence is that we don't.