There have been several recent posts in the blogospere arguing about the interpretation of graphs (for several countries, but you can see Canada's here) which show a big fall in NGDP (relative to trend) at the beginning of the 2008 recession. (The latest from Ryan Avent here; Tyler Cowen's collection of links here.)
Here are my simple thoughts.
1. NGDP = RGDP x P. In words: nominal GDP = real GDP times the GDP deflator (which is one way to measure the price level). That's an accounting identity, of course. It tells us how we use words. It doesn't tell us anything about the world. Simple "hat algebra" (differentiating that identity with respect to time) lets us re-write it as NGDP^ = RGDP^ + P^, which in words means: the growth rate of NGPD equals the growth rate of RGDP plus inflation. And if people's expectations are logically consistent, expected NGDP growth will equal expected RGDP growth plus expected inflation.
2. It is easier to measure NGDP (nominal growth) than it is to measure RGDP (real growth) and P (inflation). To say the same thing another way, it is not easy to figure out how to decompose nominal growth into real growth and inflation. Because it's hard to measure things like quality changes. In that sense only, NGDP is more "real" than RGDP.
3. But how people respond to NGDP growth (or expected NGDP growth) will usually depend on how much of that (expected) NGDP growth was (expected) real growth and how much was (expected) inflation. Elasticities with respect to RGDP (or real growth) may be different from elasticities with respect to P (or inflation). If expected NGDP growth falls, the amount by which that causes current NGDP to fall might depend on how much expected real growth falls vs expected inflation falls. Adding expected real growth plus expected inflation together may be a useful simplification, but is only strictly correct if those two elasticities are the same.
4. If we observe NGDP and RGDP both suddenly fall, as they did in many countries in 2008, we cannot say from that fact alone that RGDP would not have fallen as much as it did if the central bank had held NGDP constant (growing at trend). But anyone who denies that assertion would have to believe that P would have increased (relative to trend) by the same amount that RGDP fell (relative to trend) if the central bank had held NGDP constant (growing at trend). Is that belief plausible?
5. A real business cycle theorist, who believes that prices are perfectly flexible, and who believes that monetary policy only affects nominal variables like NGDP and P, and does not affect real variables like RGDP, would believe that to be plausible.
6. Does anyone else believe that is plausible?
7. Update. I used to think that inflation targeting would be reasonably successful in preventing recessions due to deficient aggregate demand. Looking at those graphs for NGDP and P caused me to change my mind. Why? Because I saw that the Bank of Canada had been reasonably successful in keeping inflation close to target. But we still had a recession, in which both NGDP and RGDP fell sharply below trend, and it sure looked like a recession due to deficient aggregate demand. If changes in inflation had roughly matched that sharp fall in RGDP, I would have blamed the recession on the Bank of Canada failing to keep inflation on target. But that is not what happened. So instead I now blame the recession on the Bank of Canada failing to keep NGDP growing at trend, and I want the Bank of Canada to target NGDP.
Worthwhile Canadian Initiative 
No, Nick, this is a wrong answer to my question. “Better policy” is a very dangerous path. I want the one which works! And by that I mean the one which delivers better X and not better NGDP.
At the moment we have a policy which, in a broad sense, tries to deliver better X, whether it works or not. If the current policy of delivering better X fails then there is a clear pressure to “fix” something. And the theoretical basis worked until now. However bad the theoretical justification was/is there is a clear link between the facts of life (development of X) and actions triggered by these facts of life. In your policy proposal you simply wash your hands. You stop caring about life and start caring only about your theory.
I will not vote for you unless you tell me how your policy ensures progressively better X. If you are not able to do it then you just stick yourself into a dark room with Chuck in it. You will by definition face a political party which will shut down your nice experiment overnight regardless of how supercool and deeply justified your theory is.
Sergei,
Once it occurred to me the hats were supposed to display over the variable, I looked at Wolfram. I believe the idea is that if Z = X * Y -> Ln(Z) = Ln(X) + Ln(Y). Since d(Ln(X))/dt = (1/X)dX/dt. If you symbolize this as X^ [let’s pretend the ^ is over the X] -> X^ = Y^ + Z^.
This works fine, except suppose X(y,Z,t) = X(Y,t)Y(X,t). I believe this is your question. You are quite correct.
The underlying structure is a partial differential equation. NGDP(t) = RGDP(t) * P(t) is assumed to be a faithful (approximate) representation of this equation (which is almost certainly both unknown and insoluble in closed form). You can see, this representation eliminates what you are worrying about, but is this a faithful representation, and if so, why? My guess is that is within limits, and we don’t know what the limits are, but this is just a guess.
It is also may very much a question of mathematics abuse, for instance, if operating on aggregates isn’t equivalent to aggregating the results of individual operations (which it isn’t without counterfactual assumptions). While you’re looking at your qualitative question, the economagician is using his mathematical other hand to put the rabbit into the hat.
This is a classic example of begging the question, which technically means smuggling your conclusion into your premises.
The RGDP tracking story as I understand it rests on 3 pillars:
1) Stable NGDP is inherently a good thing because it represents a stable “tightness”. This is plausible, but needs some filling out to escape being a tautology.
2) NGDP is a good proxy for employment (relative to some natural rate)
3) Within some operating envelope RGDP and inflation are in a sort of equilibrium and stable ngdp allows this equilibrium to assert itself. Outside the envelope it becomes classically deflationary on the high inflation side, and stimulating through the expectations channel on the low. In fact it is supposed that the expectations associated with this as a credible policy will act to keep NGDP within a narrow range through time arbitrage, since credibility makes expectations of a profit from such arbitrage rational.
OTOH there’s the story where one of a pair of economists says “Look a $20 bill lying on the sidewalk”, and the other says “Nonsense, if it were real, someone would have picked it up already.”
I expect Nick can improve on this. I’m not an NGDP guru.
Peter N: Yep. The ^ is supposed to display over the variable. But I can’t figure out how to do that in TypePad.
There’s a whole literature on index number theory which talks about how to decompose NGDP into RGDP and P, and the limits and problems in doing so. It teaches you how to add production of apples and production of oranges, and what can go wrong. I have ignored that literature here. (All economists are familiar with the basics of it, and a few (not me) get more deeply into it.)
Peter N, you are able to express much better what I mean than I am 🙂
“My guess is that is within limits, and we don’t know what the limits are, but this is just a guess.”
Yes, the typical scope of limits is the YoY result or similar. And what I am thinking about is rather DoD where D means decade. The structure does not change fast and YoY changes can often be neglected. They however accumulate and have profound effects over the longer term as the economy changes and adapts. But adapts to what?
My concluding qualitative assessment, which I tried to express above, is that the structure of economy continuously adapts (invisible hands or whatever) in a such way as to (again might be sloppy so please try to think beyond the words) minimize its cost of hitting the exogenously set policy targets.
Looking back into the past we had inflation caring/targeting central banks and over the period of 2-3 decades the economic structure evolved into the form which allowed it to arbitrage such inflation focused central banks away. And so we have economic structure which depends on asset bubbles to function. It worked “fine” until we failed to inflate another asset bubble.
How can I be assured that either this line of thinking is wrong or that we stay away from such bad equilibrium?
“If we observe NGDP and RGDP both suddenly fall, as they did in many countries in 2008, we cannot say from that fact alone that RGDP would not have fallen as much as it did if the central bank had held NGDP constant (growing at trend). But anyone who denies that assertion would have to believe that P would have increased (relative to trend) by the same amount that RGDP fell (relative to trend) if the central bank had held NGDP constant (growing at trend). Is that belief plausible?”
When RGDP falls and inflation increases, don’t we call that stagflation?