Perhaps we should think about monetary policy this way.
If all prices were perfectly flexible, monetary policy wouldn't matter much. Monetary policy matters because not all prices are perfectly flexible, which means that bad monetary policy causes monetary disequilibrium, which is what happens when prices want to change but don't change. Recessions and booms are examples of monetary disequilibrium.
What we want is a monetary policy that minimises monetary disequilibrium.
But monetary disequilibrium is a theoretical construct. We don't observe it directly. So we need an empirical proxy for monetary disequilibrium, so we can tell the central bank to minimise that empirical proxy.
Deviations of actual unemployment from full employment might look like one possible proxy. Trouble is, "full employment" (or the "natural rate of unemployment", or "potential output" etc.) is itself a theoretical construct. It's not something we can observe. So telling the central bank to target "full employment", so as to minimise deviations of actual unemployment from full employment, didn't work very well.
So we switched to telling central banks to target a fixed rate of inflation instead. We told them to minimise deviations of actual inflation from target.
Is "deviation of inflation from (a fixed) target" a good empirical proxy for monetary disequilibrium?
Well, it's empirical all right, because we can measure inflation (more or less), and the data arrives with a fairly short lag (around one month). And 2% (or some such target) is simply a number, not a theoretical construct like "full employment".
But is "deviation of inflation from 2%" a good proxy for monetary disequilibrium?
On the face of it, it looks like a very bad proxy.
We are trying to measure something that happens because some prices don't change, so we look at the prices that do change? How the hell is that supposed to work? Well, perhaps surprisingly, there is one case where deviations of inflation from target would be a perfect proxy for monetary disequilibrium. That's the case where the firms that do change prices are exactly like the firms that don't change prices, except for that one difference.
And that one very special case is exactly the case assumed by the Calvo Phillips curve. Calvo's fairy flies around at random, touching firms with her wand, giving them permission to change prices. And precisely because she flies around at random, and there is a very large number of firms, the sample of firms that do change their prices are exactly the same as the remaining population of firms that don't change their prices. So if we see some firms cutting prices, we know that the remaining firms want to cut their prices too, but cannot, so there must be a monetary disequilibrium at those other firms, and it must be a recessionary monetary disequilibrium.
The randomness of the flight of the Calvo fairy is precisely the assumption that makes it easy to do the math. And it's precisely the assumption that makes inflation targeting the optimal monetary policy for minimising monetary disequilibrium. But if you think about it for a bit, it's not a very plausible assumption.
For example, suppose that all firms are identical, but some firms change their prices once a month and other firms can change their prices once a year. Assume a 0% inflation target, just for simplicity. If we see negative inflation in January, and 0% inflation in February, does that mean we have monetary disequilibrium in January, but no monetary disequilibrium in February? Of course it doesn't. In February, the firms that can only change prices once a year still want to cut their prices, but cannot. The economy is still in recessionary monetary disequilibrium, even though inflation is back at the 0% target.
If that were the only difference between firms, then price level path targeting would be the best way to minimise monetary disequilibrium. The central bank should aim to bring February's price level back up to where it was in December.
But presumably there are reasons why some firms change prices more frequently than others, and the two sets of firms will not be exactly the same in all other respects.
And even if all firms did change prices at the same frequency, on average, it is very unlikely that the firms that do change prices in any particular period are exactly the same as the firms that don't change prices in that period. There must be a reason why some firms did change prices and other firms didn't. Maybe there was a real shock, that caused relative demand to shift away from some firms, towards other firms. And if there is some threshold, like a small menu cost, so a firm won't change its price unless it wants to change it a lot, then if the distribution of relative demand changes is skewed, the prices that do change won't even tell us the correct sign of the monetary disequilibrium. All we are observing is one tail of the distribution of monetary disequilibrium.
Thinking about good monetary policy as minimising some empirical proxy for monetary disequilibrium does not tell us what the best proxy is. But it might help us think more clearly about the question. And it does help us understand why inflation targeting might not work. And it does tell us that using mathematically tractable assumptions, like the random flight of the Calvo fairy, could badly bias our search for the best monetary policy.
Worthwhile Canadian Initiative 
I’m surprised that this post didn’t move onto a discussion of why NGDP levels make a superior proxy to the others you discuss.
Tom: I suppose NGDP targeting was implicit. But I wanted a post that was more general than NGDP targeting. First we have to understand why inflation targeting failed. And it’s very unlikely that NGDP-level target would be a perfect proxy.
Nick said: “So we switched to telling central banks to target a fixed rate of inflation instead. We told them to minimise deviations of actual inflation from target.”
Tom, would you interpret that to mean the central bank has one target and no other target, buy a bond if price inflation falls below target, and sell a bond if price inflation rises above target?
TMF: yes, basically. Although perhaps just their publicly announced intention to do so if necessary would suffice (according to my understanding of what Nick has stated in the past: i.e. he’s stated that what the CB signals is of primary importance, not necessarily the mechanics of open market operations).
Let’s skip the intention would suffice part for right now.
What if the system does not work like that? What if there is another target that takes priority over the price inflation target?
TMF: another target such as price levels or NGDP levels or the stock of base money or paper money in circulation or employment rates?
All those could be targets AFAIK. But I don’t know about successfully hitting all those targets nor do I know the advantages or disadvantages of each (even if the CB could successfully hit their target). Nick obviously has an opinion on some of the disadvantages of some of them here in this post. I’m really not qualified to offer an informed opinion on the subject.
“I’m really not qualified to offer an informed opinion on the subject.”
Not a problem. Just keep following along for now.
Let’s put the central bank on a gold standard with a 100% reserve requirement. 1 oz of gold = $1, and $1 = 1 oz of gold. The reserve requirement is 100% for demand deposits (with currency).
The central bank also has a price inflation target of 2%. The gold standard is primary.
Next, the “unimaginable” happens, and gold starts being mined so it is growing by 12% per year causing 7% price inflation. If the central bank can’t get some entity(ies) to save, the price inflation target will be violated. The fixed exchange rate will not be violated.
Now what the central bank really needs is for gold to grow by less than 12% per year to hit the price inflation target.
So far so good?
TMF: “So far so good?”
No. So far so bad.
This is not the place for you to collar other commenters and drag them into random off-topic conversations. Jeez!
Tom, do you still have your blog?
I’m not convinced.
Inflation seems to me like a perfectly natural target for monetary policy. That the target is positive isn’t central here, so suppose the CB just targeted a fixed P. Then if P starts to rise, the CB knows that there is upward pressure on prices and wages, which is prima facie evidence of excess demand, and so it raises r / lowers M to offset.
You seem to be saying that this relies on the firms that change their prices being identical. But I think your point is really about how we measure inflation, and maybe in part about how a price index designed for optimal monetary policy might differ from one that measures consumer purchasing power (i.e. you care more about more sticky prices when setting monetary policy).
Your comment about identical firms is hinting at issues arising from the bias of a price index by which firms change their prices, for instance because of differential productivity growth across sectors, new products, etc. But these are just the classic issues of measuring inflation. If we manage to successfully observe a true AGGREGATE price level, I don’t think this is an issue (with the above caveat about the optimal index from the perspective of MP).
jonathan: “…and maybe in part about how a price index designed for optimal monetary policy might differ from one that measures consumer purchasing power (i.e. you care more about more sticky prices when setting monetary policy).”
I think that’s a very important point. For example, note the silly arguments over whether house price inflation is really inflation. The only sensible way to answer that question is to ask another question: what do we want to use our measure of “inflation” for?
But that last bit “(i.e. you care more about more sticky prices when setting monetary policy)” is what leads us into a reductio ad absurdam. Take it to the limit. The prices whose changes we most care about are those prices that don’t change at all. The optimal weights are inversely related to the things they are weighting. The most important signal is the signal we never see.
Nick: I don’t think this is a reductio ad absurdum. You’re just taking a limit, and you want to make sure that your policy behaves reasonably in the limit. As prices become more sticky, they will change less in response to a given demand shock, and therefore a given change in those prices is evidence of a larger demand shock. This is just an information extraction problem.
By the way, here is a paper that discusses this question:
http://onlinelibrary.wiley.com/doi/10.1162/154247603770383398/abstract
(Mankiw Reis, 2010)
From the abstract:
“[T]he [optimal] weight of a sector in the stability price index depends on the sector’s characteristics, including size, cyclical sensitivity, sluggishness of price adjustment, and magnitude of sectoral shocks.”
NBER version:
http://www.nber.org/papers/w9375
(should be ungated)
jonathan: well, inflation targeting seems to behave unreasonably in the limit, (but my calling that “RAA” wasn’t very clear or precise). It seems to me we need to look at fluctuations in quantities as an additional signal. And if we take the sum of those two signals (the P-signal and the Q-signal), we get the PQ-signal, which is NGDP targeting.
This is also sort of why it’s pretty much impossible to think in any meaningful way about currency areas in the Calvo/NK framework; you pretty much have to assume that the firms in one country are identical to firms in another country, PPP holds, complete markets etc. etc., effectively assuming away all the interesting questions relevant to optimal currency areas.
The Mankiw & Reis paper doesn’t have Calvo, it’s got, if I understand it correctly (I’ve only skimmed it so far) Fischer style fraction-of-prices are fixed and fraction are flexible. And that has some problems of its own – only unexpected monetary policy matters for output gap – which might be why M&R limit it to a bank which just cares about inflation.
notsneaky “This is also sort of why it’s pretty much impossible to think in any meaningful way about currency areas in the Calvo/NK framework”
Hmmm. Interesting thought.