An economy is humming along very nicely in full long run equilibrium. All real variables are at their natural rates. Actual and expected inflation are both equal to the 2% inflation target. As the years go by, the price level goes: 90, 92, 94, 96, 98, and everybody expects it to continue 100, 102, 104, forever and ever.
Then a negative Aggregate Demand shock hits, and the central bank is slow to respond. Instead of going to 100, as everyone had expected, the price level in year 0 is 99. What else happens?
There's a recession. Real output and employment fall below their natural rates, and unemployment rises above its natural rate. But the story doesn't end there.
1. Now suppose that the central bank wakes up, announces that it will make sure the price level rises at 2% per year from now on, and everybody fully expects the central bank will do what it says, and the price level does in fact go: 99, 101, 103, 105, etc.
Question 1: in year 1, when the price level is 101, and the actual and and expected and target rates of inflation are all equal, will this economy still be in recession, or will it have completely recovered to the natural rates of output, employment, and unemployment?
2. Now suppose instead that the central bank wakes up, announces that the price level will rise by 3% in year 1, and 2% thereafter, and everyone fully expects the central bank to do what it says, and the price level does in fact go: 99, 102, 104, 106, etc.
Question 2: in year 1, when the price level is 102, and the actual and expected and target rates of inflation are all equal, will this economy still be in recession, or will it have completely recovered to the natural rates of output, employment, and unemployment?
Question 3 (just for clarification): Are you saying that the levels of output, employment, and unemployment, will be the same in year 1 in both questions 1 and 2, even though the price level is 101 in question 1 and 102 in question 2?
The Calvo Phillips Curve, which is the theory of price adjustment most commonly used in New Keynesian macroeconomic models, basically answers "yes" to all three questions.
(I stuck in that weasel-word "basically" for two reasons: first, the variance of prices, output and employment across individual firms will be different in the Calvo model between 1 and 2, and this variance might affect aggregate output and employment, though this effect is usually ignored; second, because the recession in year 0 might have hysterisis affects, and this might affect the short run natural rates, but this still shouldn't prevent the answer to question 3 being "yes", because it would affect 1 and 2 equally.)
I think I would answer the three questions: 1. no; 2. probably (except for hysterisis); 3. no.
We can restate the question this way: are those recessions that are caused by drops in Aggregate Demand only (no "supply shocks") associated with: the inflation rate being below the previous trend path; or the price level being below the previous trend path? What belongs on the vertical axis of the Short Run Aggregate Supply/Short Run Phillips Curve: the inflation rate; or the price level?
The answer really matters for monetary policy. If you answer "yes" to all three questions, then there is nothing to choose (in this particular case) between Inflation Targeting and Price Level Path (or NGDP Level Path) Targeting. If you answer "no", "yes", "no" that is a very strong argument for PLPT (or NGDPLPT) over IT. And it's an argument that has nothing to do with: Zero Lower Bounds; automatic stabilisers for AD; supply shocks; risk-sharing between debtors and creditors.
I think this argument for PLPT (or NGDPLPT) is implicit in what Scott Sumner says, but I don't remember him laying it out explicitly. I'm not sure whether other supporters of NGDPLPT or PLPT, across the whole monetarist-keynesian spectrum, would or would not agree with with this particular argument.
Why do I answer those three questions the way I do?
Well, mostly it's the data. It must be the data, because I didn't use to think like this. If you had told me, back in 2009, that the inflation rate would quickly return to target (or to its previous trend in countries without an explicit target) I think I would have said "Right, no worries then, because inflation lags output and employment, so if inflation returns quickly to target there must be a very quick V-shaped recovery after a very short recession." I might have made a few caveats about hysterisis, I suppose.
The data don't tell a story that is anywhere near as clean as I would like, and if the SRAS/SRPC is fairly flat (which it seems to be), and if there are supply shocks (which there may be), it will be very hard to tell the two stories apart empirically. But I think it is a little easier to force the data to fit my story than to force the data to fit the Calvo Phillips Curve story.
Take Canada for example. Very crudely, inflation fell below the 2% target in early 2009, and returned to target by late 2010, but the real economy (unemployment for example) seemed to take a couple more years to recover (you could argue it has still not recovered fully). Here are the price data. What do you see? Remember there is total CPI and 3 different measures of core, and we could look at monthly as well as annual inflation rates. Note that the price level (both total and core) seems to still be a little below the pre-recession trend.
So much for the data. What about the theory?
Maybe something like Mankiw and Reis? The basic idea is that people just don't listen to the news very often, and keep on raising their prices at 2% per year regardless of what is happening around them, until they do eventually pay attention. It sounds daft, but it does seem to fit the facts.
Maybe some sort of convention in a model of multiple equilibria? Most people try to follow the convention, as long as they expect most other people will follow the convention. And if the convention is to raise prices at 2% per year, most people keep on raising prices by 2% per year.
So when AD fell only a few people cut their prices, so there was a recession. The recession then continues, with a slow recovery. Every year a few people listen to the news, or break convention, and raise their prices by less than 2%. But a few others, who had originally cut their prices when the recession hit, now raise their prices by more than 2% because the economy is slowly recovering so they don't want their relative prices to be quite so low as before. So the average inflation rate is 2%, even though the economy is still in recession and in a slow recovery
Any other theory?
We really do not know very much about the Short Run Aggregate Supply Curve/Short Run Phillips Curve. And yet it's really important. If something like the Mankiw/Reis model is roughly right, even if it's right for the wrong reasons, Inflation Targeting is bad policy, and something like Price Level Path Targeting or NGDP Level Path targeting would be much better policy. Quite apart from any other reasons for preferring some sort of level path target.