What's the best shape for the AD curve?

Economists usually talk as if the slope of the Aggregate Demand curve were a positive question: what is the slope of the AD curve? I think it's best to treat it as a normative question: what slope of the AD curve ought the central bank choose?

That leads us to a simple way to think about the choice of target variable for monetary policy.

Those who want to target real GDP (or employment, or unemployment) want a vertical AD curve. Those who want to target inflation (or the price level) want a horizontal AD curve. And halfway in between, those who want to target Nominal GDP want a downward-sloping (rectangular hyperbola) AD curve.

Which is best?

At first sight, the vertical AD curve looks best. Real output, employment, and unemployment, matter a lot more than the price level or the rate of inflation. And monetary policy should target what matters most.

And that's what many countries used to do. Then, sometime in the 1970's, economists and policymakers learned from both theory and experience that it was a bad idea. With a vertical AD curve, and vertical Long Run Aggregate Supply curve (or Long Run Phillips Curve), the price level and inflation rate are indeterminate. There's no nominal anchor. If you try to increase real output beyond what's sustainable, the result is ever-accelerating inflation. And we don't know what's sustainable.

So nearly all economists have decided that a vertical AD curve is a bad idea.

That leaves two main alternatives: the horizontal AD curve of inflation targeting; and the rectangular hyperbola of NGDP targeting.

(There's also an important distinction between levels and rates of change, but I'm ignoring that distinction here. I want to focus on the difference between P as the target variable, and NGDP as the target variable. I'm ignoring the distinction between price level path targeting and inflation targeting. I'm ignoring the parallel distinction between NGDP level path targeting and NGDP growth targeting.)

Inflation targeting and NGDP targeting have a lot in common. In both cases the central bank tries to prevent fluctuations (unpredictable shifts) in the AD curve. An inflation targeting central bank tries to make the AD curve horizontal, and slowly moving upwards over time at a fixed pace. An NGDP targeting central bank tries to make the AD curve a rectangular hyperbola, and slowly moving North-Easterly at a fixed pace.

One curve isn't enough. The simplest (sensible) macroeconomic model will have two more curves. There's the vertical LRAS curve (or long run Phillips curve), and the upward-sloping Short Run Aggregate Supply Curve (or short run Phillips curve). And those two curves shift too.

Start in long run equilibrium, at the point where all three curves intersect. Suppose the LRAS curve shifts left, and the SRAS curve shifts left by exactly the same amount. A bad harvest in an agricultural economy, for example, would shift the LRAS curve left. Whether it would also shift the SRAS curve left by exactly the same amount is not certain. It depends. But suppose it does.

In this example, a horizontal AD curve would be best. Inflation targeting beats NGDP targeting, precisely because it lets output fall by the full amount of the leftward shift in the LRAS curve. The same applies if the shock causes the LRAS curve to shift to the right, provided the SRAS curve shifts right too by exactly the same amount. The horizontal AD curve lets output rise by the full amount of the rightward shift in the AD curve. The optimal level of output is not a constant. If the LRAS curve represents optimal level of output (more weakly, if fluctuations in the LRAS curve correspond to equal-sized fluctuations in the optimal level of output), then we want actual output to fluctuate to match fluctuations in LRAS. NGDP targeting results in smaller fluctuations in output than inflation targeting, and, in this case, that is a bad thing.

But, as I said above, it is not at all obvious that "supply shocks"  shift the LRAS and  SRAS curves right or left by the same amount. It depends. I can rig up a model where the SRAS curve shifts either more or less than the LRAS curve, or even shifts in the opposite direction. For example, suppose nominal wages are set one year in advance, before the weather is known. And suppose the price of output is perfectly flexible. Bad weather (and a bad harvest) will cause the SRAS curve to shift left by the same amount as the LRAS curve only if bad weather leaves the flexible equilibrium real wage unchanged. That is very unlikely to happen. Bad weather may either increase or decrease the marginal product of labour and shift the labour demand curve either right or left. ("We need more labour to harvest this wet corn" vs. "We need less labour to harvest the little corn that survived the drought"). Plus, there may be income effects of a bad harvest on labour supply ("We had better work harder to harvest every last bit of corn that remains, or we will all starve").

If the flexible equilibrium real wage falls when there is an adverse supply shock, and the nominal wage is fixed, then you need a rise in the price level to reduce real wages to keep the economy on the LRAS curve. In this case, the SRAS curve shifts further left than the LRAS curve. The horizontal AD curve of inflation targeting prevents the real wage falling, and causes a bigger than optimal drop in output. The downward-sloping AD curve of NGDP targeting allows the price level to rise and the real wage to fall, so there is a smaller drop in output. It might be still a larger drop in output than is optimal. It might be a smaller drop in output than is optimal. If the output drop is far too small, it might even be worse than the too large drop in output with the horizontal AD curve of inflation targeting. It depends.

Theory does not tell us whether inflation targeting or NGDP targeting will be better in the face of genuine supply shocks that shift the LRAS curve. It depends on the shock, it depends on the parameters of the model, and it depends on the exact source of the nominal rigidity.

But I just can't get too excited about shifts in the LRAS curve. Sure, in an agricultural economy in a small country the weather could be a biggie. But in the sorts of diversified economies we are mostly talking about, only Real Business Cycle Theorists think that shifts in the LRAS curve are a big deal and the major source of economic fluctuations. And they don't care much about monetary policy anyway.

The SRAS curve can shift independently of the LRAS curve. Let me give two examples: one hypothetical, and one real.

Suppose government shifts the legal incidence of an employment tax from workers to employers. This ought to be economically irrelevant. The wage should fall by exactly the same amount, leaving output and employment unchanged. The LRAS curve stays put. But if nominal wages are sticky. the SRAS curve will shift left. With the horizontal AD curve of inflation targeting, there will be a fall in output and employment in the short run. With the downward-sloping AD curve of NGDP targeting, the price level will rise, real wages will fall, and there will be a smaller fall in output and employment. Neither AD curve is optimal in this case, but NGDP targeting is less suboptimal.

When Canada introduced the GST (VAT) it replaced a less efficient tax. Presumably, this improvement in the tax system should have caused the LRAS curve to shift right, if at all. But given nominal rigidities, everyone, including the Bank of Canada, expected the GST would cause an upward/leftward shift in the SRAS curve. (There was little if any economics in the reasoning; it was based on simple atheoretical accounting, AFAIK.) The Bank of Canada said it would allow a small one-shot increase in the price level to accommodate the upward shift in SRAS, but would then prevent any further "second round" inflationary effects. And that's basically what happened. But this means that the Bank of Canada deliberately abandoned its inflation target, even if only temporarily, and in a very small way.

Why did the Bank of Canada abandon its inflation target? Because it knew that if it tried to prevent this small temporary increase in inflation the result would be a fall in output and employment.

Even though, in my opinion, shocks to LRAS are small and rare, that doesn't mean there are no supply shocks at the microeconomic level. Equilibrium relative prices are changing all the time. Some prices are stickier than others. Since some prices won't adjust, at least not quickly, the flexible prices need to do all the adjusting. If flexible prices need to rise relative to sticky prices, the SRAS curve shifts up. If flexible prices need to fall relative to sticky prices, the SRAS curve shifts down. The LRAS curve rarely shifts much, IMHO, because most supply shocks more or less cancel out at the macroeconomic level. But the SRAS curve is shifting up and down all the time.

AD shocks can also cause the SRAS curve to shift. Under both inflation targeting and NGDP targeting, the central bank tries to stop the AD curve shifting. But it will fail, of course, because central banks lack a crystal ball, don't have full contemporaneous information, and can only react to AD shocks with a lag. If the AD curve does shift, then output will rise above the LRAS curve, and prices will rise too. And if there are nominal rigidities, so that the price level has inertia, or the inflation rate has inertia, the SRAS curve will shift up. Inevitable past mistakes made by the central bank cause the SRAS curve to shift without causing the LRAS curve to shift.

Suppose you live in an economy where the LRAS curve does not shift, but the SRAS curve is shifting up and down all the time. That, I think, is roughly the economy we live in. A downward-sloping AD curve beats a horizontal AD curve. NGDP targeting beats inflation targeting. Neither is optimal, but NGDP targeting is less suboptimal than inflation targeting.

Inflation targeting central banks are fully aware of everything I have written above. That's why inflation targeting central banks don't in fact target inflation. At least not strictly. They know that bad things would happen if they tried to prevent any fluctuations in inflation. They know that bad things will happen if they tried to bring inflation immediately back to target. They know that strict inflation targeting would result in non-optimal fluctuations in relative prices, as the more flexible prices had to move double or treble the amount to make up for the failure to move of the less flexible prices. They know that strict inflation targeting would result in non-optimal fluctuations in real output because real output adjusts if sticky prices don't want to adjust to the bank's target.

Only "inflation nutters" strictly target inflation. All actual existing inflation targeting central banks are flexible inflation targeters. They think about the possible effects on output and employment if they tried to keep inflation exactly on target at all times. They partially accommodate SRAS shocks. If inflation deviates from target, they try to bring it back to target slowly, over a horizon of about two years (more, or less, depending on their view of those side-effects on output).

Actual existing inflation targeting central banks, most of the time, do something that looks a lot closer to NGDP targeting than strict inflation targeting. They are secret believers, to a certain extent, in the NGDP heresy.

In normal times, when central banks don't make big mistakes, there really isn't much difference between actual existing inflation targeting and NGDP targeting. It's only in abnormal times it might matter. It's only the experience of the last three years that makes me lean towards NGDP targeting.

NGDP targeting is not optimal. But it might be a reasonable compromise between the vertical AD curve of the Old Keynesians and the horizontal AD curve of inflation targeting.

(There's a separate question of whether inflation targeting or NGDP targeting would lead to smaller mistakes by the central bank when it fails to prevent the AD curve fluctuating. One target might lead to smaller undesired AD shifts than the other. But I'm going to leave that question for now.)

(I thank Adam P. for inspiring me to write this post.)

Update: The Bank of Canada and government have decided to renew the existing 2% inflation target for another 5 years. Ah well. They avoided the mistake of cutting the target rate below 2%, thank God! There's a lot worse than a 2% inflation target. Like having a really stupid target, or no target at all.

Comments

[Bill Woolsey]

I think a good bit of the analysis here assumes a one good economy.

The reason I think nominal GDP targeting is better is that I am assuming that when there is a change in supply in a particular market, those setting prices in that market adjust the price of that particular good. The problem with price level targeting is that an excess supply or demand for money needs to be generated to force all the other prices to what amounts to an artificial target.

If there is only one good, then this effect isn't relevant. Though I am not sure why it is bad that a decrease in long run aggregate supply might result in a higher price for the single good in the single good economy. For example, I am not sure I understand how this would result in production failing to decrease enough. People are confused that higher price means demand increased for the one good that everyone is producing and buying? Well, suppose the corn harvest fails in Iowa. Is it "confusing" to farmers in Nebraska that the higher price of corn signals that they produce more? Would it be a mistake for the Iowa famers to increase effort to reduce waste from the harvest?

If it is persisent, what exactly is the benefit to having aggregate demand fall next period so the price level goes back down? (On the other hand, having the price level rise next period if it didn't rise before would be a bit pointless too.)

I can barely imagine real wages rising in the face of a decrease in output in a one product economy. (real income falls, but labor's share increases enough so that real wages rise on net?)

I guess I need to worry more about the sticky priced good having its supply decrease and there are shortages. Shortages, of course, are always a problem when the target is demand but what you observe is prices and output. If it persists, and the price remains sticky, creating an excess supply of money so that other prices rise would disruptive.

Still, I think the basic approach that adverse supply shocks reduce output and raise prices in particular markets and reduce aggregate output and raise the price level as a matter of arithmetic. The reduction in real income requires a reducing in all factor incomes, including real wages. The aritmetically higher price level reduces real wages.

Trying to keep inflation (or the price level) on target is a mistake. The least bad opition is to let things be.

Isn't it better for disruptions in the corn market to mostly be solved by changing the price of corn? Isn't having everyone else in the economy think about the corn harvest when setting their price, (so that inflation will hit a target) a bad idea?

Now, coming up with some complicated formula for inflation and real output based upon what markets are likely to have the supply shocks and what their supply and demand elasticies will be would improve expected welfare, but how far will that get outside the ivory tower?

[Nick Rowe]

Bill: my corn model was (implicitly) assuming a one good economy.

"I can barely imagine real wages rising in the face of a decrease in output in a one product economy. (real income falls, but labor's share increases enough so that real wages rise on net?)"

Agreed, but it might happen. It depends on how the production function shifts. For example, with L on the horizontal, and Y on the vertical axis, a downward shift in the production function that also made it steeper at the existing level of L would do this. The MPL increases. Sure, it's a bit weird. But that's roughly what happens in a wet harvest. The corn is still there, but it takes more work to get it into the silo. (I'm using "corn" in Ricardo's sense, like my father, to mean wheat, barley, oats, etc., and not maize.)

I wasn't thinking of a one-good model in the rest of the post. When I'm talking about relative supply shocks causing the SRAS curve to shift, I'm thinking a bit along your lines.

I need to think some more about your comment. It reminds me of a paper (by Mankiw???) about how dispersion in relative price shocks can cause the SRAS curve to shift, when all prices are sticky. Those goods most affected change price, and those least affected don't. You need a 3 (or more) good model for that.

[Min]

Stupid question: Why should we think that there is an AD curve at all? A quick look online at the definition makes me wonder if there is a functional relationship at all? Why not an AD blob, for instance?

If you respond, just giving me a reference would be fine. Thanks. :)

[Too Much Fed]

If possible, some graphs would help.

[Nick Rowe]

Min: well, I've seen economists argue against the existence of the AD curve on the grounds you can't aggregate. I've seen economists argue that the AD curve is kinked. I've seen economists argue that the concept is meaningless. I think I can rig up a model where the AD curve is thick; is that what you mean by a "blob"? Any macroeconomic textbook will give a model or story of the AD curve.

TMF: Yep, I thought of doing graphs. But it would have taken about a dozen graphs to show everything I wanted. And most people who have done basic macro and seen the standard AD/LRAS/SRAS picture will be able to see it all in their mind's eye.

[Adam P]

Nick,

I haven't really read the post, just scanned it but it already seems you're speaking a different language here.

The question is, how does a bad harvest shift the LRAS curve? A bad harvest is a good example here exactly because it's transitory. The LRAS doesn't move, the SRAS shifts.

(Not sure this actually matters to much for your argument thoug...)

[Nick Rowe]

Adam: Yep. The LRAS/SRAS terminology is really bad/confusing. But we seem to be stuck with it. "LRAS" doesn't mean "permanent". It means (something like) "where the economy would be if we ignored nominal rigidities". It's the Real Business Cycle Theory AS curve. It's the natural rate of output. It's Y* in the Phillips Curve. If there were no nominal rigidities, we could ditch the SRAS curve, and the economy would always be on the AD/LRAS curve intersection. Bad/good harvests would cause the vertical LRAS curve to shift left/right annually.

We should call it the "no nominal rigidities AS curve" instead of "LRAS curve". The only reason we call it the "Long Run" AS curve is because we believe it takes time for prices to adjust and so the SRAS curve will shift over time so that it tends to move towards the AD/LRAS intersection.

[Nick Rowe]

Damn! I was trying to make an argument that is both reasonably sophisticated and yet accessible by being couched in the language of the first year textbook's AD/LRAS/SRAS model. Looks like my two objectives are in conflict. Damn!

[Nick Rowe]

Bill: suppose we had a two good economy. Corn and milk. Both goods are 50% of GDP on average. Suppose there are productivity shocks to both goods, but the shocks are independent of each other. And suppose both prices are equally sticky. Ignore wages, because each good is produced by self-employed yeoman farmers. Suppose there's a bad corn harvest, but milk production is normal. We want the price of corn to rise relative to milk, so people shift demand from one good to the other. Prime facie, it would seem the best way to achieve this is to have both prices adjust, by equal amounts. There seems to be no reason to prefer having the price of corn rise over having the price of milk fall.

If you have three goods, and lump sum menu costs, then it does seem easier to have one price adjust up rather than two prices adjust down. I think that's what's behind your intuition.

[Nick Rowe]

Adam: here's a simpler/better answer: think of LRAS as representing the (constrained) optimal level of output. It's the level of output a central bank would target if it had full information (plus a crystal ball).

[Adam P]

Nick: "I was trying to make an argument that is both reasonably sophisticated and yet accessible by being couched in the language of the first year textbook's AD/LRAS/SRAS model. Looks like my two objectives are in conflict. "

On this, I agree. However....

I think I disagree with your interpretaton. This part, "It's the Real Business Cycle Theory AS curve" I agree with. The LRAS is the RBC one, but the bad harvest is most definitely NOT a shift in this curve.

In RBC language the aggregate productivity process is usually modelled as something like the following AR(1):

A(t) = c + rho*A(t-1) + e;

The long run mean of productivity is c/(1-rho) and the LRAS supply curve is vertical is the implied output level with full employment and A = c/(1-rho), that is A is at it's long run mean. Thus, a shift in the LRAS is exactly a shift in c or rho.

Now, a bad harvest is NOT a shift in c or rho.

A bad harvest is a negative realization of e.

[Nick Rowe]

OK. I'm talking about AS conditional on A(t), not AS conditional on c/(1-rho). RBC says that realisations of e cause fluctuations in Y. My "LRAS" curve (call it what you like) is what Y would be if RBC were true. It fluctuates when e fluctuates.

[Nick Rowe]

When the weather is bad, the optimal level of Y falls. The leftward shift in my "LRAS" curve represents the fall in the optimal level of output, whether it's temporary or permanent.

[reason]

Nick,
are you looking for an argument here? I think you are right. Its on the choice of policy tools that we differ.

[Adam P]

Nick,

I think you want to call it the PAS curve, the potential aggregate supply curve.

It's the level of AS with a zero output gap, employment at the NAIRU.

agree?

[Nick Rowe]

reason: I'm not really looking for an argument on this post. Yep, the whole question of policy instruments, and *how* the central bank/fiscal authorities gets the AD curve into the shape and position it wants, is a whole other question. I was trying to get my own head clear on whether/why NGDP targeting might be better in the face of supply shocks. Plus, I thought that thinking of the whole question in terms of the best shape of the AD curve was a neat way of looking at it.

Now, I'm trying to figure out a way to express the LRAS/SRAS distinction differently, maybe in math, so I can try to make the same point in different "words". At the root of the whole problem is that different people mean different things by "supply shocks". So they are arguing at cross purposes. I thought my LRAS/SRAS distinction would help clear it up. But maybe not. Because the LRAS/SRAS distinction also means different things to different people.

Oh well. Such is life. We keep plugging away, striving for clarity, so we can at least understand where we disagree.

[Nick Rowe]

Adam: Yep. I *think* we mean the same thing. Trouble is, I dislike the term "potential" output too (because output can be above potential, which is a bit oxymoronic). And I don't like the term "NAIRU" either, for complicated reasons. But, words aside, I think we are now on the same page. I am using "LRAS" to mean the same thing that other people mean when they say "potential" output or "NAIRU" output.

(Worse, the LRAS and SRAS curves aren't even, really, *supply* curves. Sometimes I hate it when descriptive words become names for things, even when we change our minds and believe the original description is false).

[Min]

Nick Rowe: "well, I've seen economists argue against the existence of the AD curve on the grounds you can't aggregate. I've seen economists argue that the AD curve is kinked. I've seen economists argue that the concept is meaningless. I think I can rig up a model where the AD curve is thick; is that what you mean by a "blob"?"

When I tried to think of a functional relationship, what came to mind was a curve in n-space that could be quite complicated. Projecting it onto two dimensions could, in the limit, produce a surface. Hence, the blob. ;)

What did sort of make sense to me was the AD curve as a snapshot, something that would hold (approximately) over a relatively short period of time. The slope of such a curve might be vertical or horizontal, or somewhere in between, but it would not make much sense to extend it very far. You could not, from such a snapshot, argue runaway inflation, I don't think.

Nick Rowe: "Any macroeconomic textbook will give a model or story of the AD curve."

Many thanks, Nick. As always. :)

[Nick Rowe]

Min: Yep. In principle it has lots of dimensions. If we draw it in 2 dimensions we are saying that a change in the variable on any of the other dimensions causes it to shift. But, in principle, the central bank could take offsetting action to shift it back to where it wants it to be.

I did a quick Google to try to find a good article about the AD curve online. Most were terribly bad. This one looks just about OK: http://www.amosweb.com/cgi-bin/awb_nav.pl?s=wpd&c=dsp&k=aggregate+demand+curve

This one looks good: http://people.uleth.ca/~richard.mueller/MacroChap09.pdf

[himaginary]

Let's interpret this post in terms of Ball's paper, with which all the arguments have begun.

In terms of Ball's paper, LRAS is potential output (although Nick dislikes the term -- maybe "trend" is better? Anyway, I denoted this variable as T in my comment here), and SRAS shift is included in white-noise shocks in equation (1) and (2).

AD curve is equation (5), E[y] = -q*E[pi].

And loss function is equation (3), Var[y] + mu*Var[pi].

Strict inflation targeting corresponds to q=1/alpha and mu=infinity, where alpha is the Phillips-curve slope. Policy-makers care only about inflation variance in this case.

NGDP targeting corresponds to q=1 (as I showed in above-mentioned comment) and mu=1/(1-alpha). When policy-makers care about output variance for 1, they care about inflation variance for 1/(1-alpha).

So, in general, Var[y] is more taken care of in NGDP targeting than in strict inflation targeting; NGDP targeting is better than strict inflation targeting from the point of view of output.

However, in strict inflation targeting, E[pi] = 0, which means E[y] = 0. Therefore, output is always equal to potential output.

On the other hand, in NGDP targeting, E[y] is not always zero. Therefore, output does not necessarily follow potential output.

So, if you focus on how well output follows potential output, strict inflation targeting is better.

[Nick Rowe]

himaginary: "Let's interpret this post in terms of Ball's paper, with which all the arguments have begun."

Unfortunately, I'm not sure that works. You can build a model in which IT is optimal, and also build a model in which NGDPT is optimal.

And E(y)=0 isn't really enough, because there might be a large variance in y. It doesn't mean y=0 always. Or maybe I have misunderstood you.

[Min]

Nick Rowe: "I did a quick Google to try to find a good article about the AD curve online. Most were terribly bad. This one looks just about OK: http://www.amosweb.com/cgi-bin/awb_nav.pl?s=wpd&c=dsp&k=aggregate+demand+curve

"This one looks good: http://people.uleth.ca/~richard.mueller/MacroChap09.pdf"

Thanks again, Nick! :)

I would say that I am in your debt, but that might be a dangerous thing to say in an economics blog. ;)

[Min]

@ Nick Rowe:

Yes, the slides for the Mueller chapter are quite helpful. :)

{bows down}

[Andrew F]

Hey Nick, you might be interested in a CD Howe commentary on the Bank of Canada's mandate and why they feel sticking to inflation targeting was the best move.

http://www.cdhowe.org/the-roads-not-taken-why-the-bank-of-canada-stayed-with-inflation-targeting/15625

[JW Mason]

This is a very good post. Very clarifying. (I am actually teaching intermediate macro for the first time right now, and these discussions are very helpful.)

But it seems to me that something is missing. Isn't the main task of monetary policy to stabilize the economy n terms of shocks to demand? In other words, isn't assuming the central bank can get whatever AD curve it wants, assuming that the most important problem of monetary policy has already been solved? In the real world,don;t we think that in most of the short-term variation in output comes from shifts in the AD curve?

[Rob]

Assume a stable economy with 0% productivity growth that hits a permanent supply shock that cause RGDP to undergo a 1 time fall fall.

The CB has a choice between a 0% inflation target and a 0% NGDP growth target.

If the supply shock causes prices to rise immediately:
An inflation-target suppresses these prices rises by reducing the money supply and RGDP falls beyond what it otherwise needs to
An NGDP-target accommodates the price rises by leaving the money-supply unchanged and the only RGDP fall is due to the supply shock.
NGDP-target is clearly better.

If the supply shock causes RGDP to fall immediately but prices to rise next period:
Period 1:
An inflation-target leaved money supply unchanged since there is no inflation
An NGDP-target requires money supply to grow since otherwise the RGDP-fall would cause an NGDP shortfall. This causes unnecessary inflation and perhaps sets higher inflation expectations.
Period 2:
Both targets face rising prices and a fixed RGDP. Both have to reduce the money supply to meet the target. However because of the inflation from period 1 this may need to be sharper under NGDP than inflation targetting.
In this case it seems inflation targeting wins.

I'm probably missing something but to me this looks like (given price stickiness, which is after all why it is needed) NGDP targetting may have a downside.

[JW Mason]

Rob-

That's not what Nick is talking about, tho. He assumes (and I agree) that those kinds of supply shocks are not an important source of macroeconomic fluctuations.

[Adam P]

Nick,

Can you explain this rectangular hyperbola a bit and how it's supposed to come about?

I mean, the usual AD curve is derived from fixing the money supply M and varying P. Lower P means highr real balances M/P which increases demand, either by lowering the interest rate (if you're Keynsian) or directly (if you're a monetarist).

Now, let's speak your language and use a quantity equation framework. MV = PY. The CB sets M which, for each value of V will determine PY but the CB has no seperate control of P or Y.

Inflation targeting first: the CB varies M until it gets the P it wants, Y is whatever value is consistent with that P. I can see how you can call this a flat AD curve although there is a bit of a catch, if P responds with a bit of a lag (which is just the assumption of sticky prices) then you really need short run and long run AD curves, only the long run AD curve would be horizental. But the second point is a bit of an aside.

Now NGDP targeting: How do we get a rectangular hyperbola? I take it that you mean that there is some point (Y*,P*), where Y* is then potential output, such that to the left of (Y*,P*) the curve is horizental and then it goes up vertically from (Y*,P*). Is that what you mean?

But in any event, whatever we mean, how do you actually get it? I mean, the CB varies M to get the PY they want, but how do they make the curve horizental sometimes and veritcal others? I don't see it.

[Nick Rowe]

Min: glad to be able to help. What shocked me (though I expect it shouldn't) was how bad most of those things I found by Googling were.

Andrew: thanks. Chris Ragan is a good economist. I liked and agreed with most of what he wrote, but he was very weak on NGDP targeting. Didn't really give any argument against it. But he had to write it quickly, for a general audience.

The Bank of Canada backgrounder was very very good. Gave me confidence in them.

http://www.bankofcanada.ca/2011/11/press-releases/bank-of-canada-releases-background-information/

JW: Thanks! I seem to have found an audience after all.

"But it seems to me that something is missing. Isn't the main task of monetary policy to stabilize the economy n terms of shocks to demand? In other words, isn't assuming the central bank can get whatever AD curve it wants, assuming that the most important problem of monetary policy has already been solved? In the real world,don;t we think that in most of the short-term variation in output comes from shifts in the AD curve?"

Basically, yes. Whether the Bank tries to make the AD curve horizontal and not move around, or downward sloping and not move around, it will fail in each case. There will be AD shocks in each case, because the Bank does not have perfect information.

*If* the fluctuations in the AD curve are of equal size under both IT and NGDPT, and *if* those fluctuations have the same correlation with supply shocks under both IT and NGDPT, then I don't think that affects my argument in any way. But those are both big "ifs".

Yes. My analysis is incomplete.

Rob: in your first example, I think you have the SRAS curve shifting left by more than the LRAS curve. That might happen, but might not. If it did, then IT is not optimal, and NGDPT might be better than IT.

In your second example, I'm not sure. I think you have the SRAS and LRAS shifting left by exactly the same amount in the first period, then an additional leftward shift in SRAS in the second period. I'm not sure which would be better in this case.

But, as JW says, I don't think LRAS shocks are big and common, in practice. RBC economists would disagree.

[Nick Rowe]

Adam: For simplicity lets compare Price level targeting with NGDP level targeting, with a fixed target P=Pbar or P.Y=Nbar, in each case. The central bank has an instrument i (doesn't matter for this post if i is a nominal interest rate or a money stock).

This is one way of looking at it:

The Bank makes a (one period ahead?) forecast for P and for Y, conditional on i, and conditional on all its other information I. These forecasts are functions E(P)=F(i,I) and E(Y)=G(i,I).

Under P targeting, the Bank ignores G(.), and sets i=i' such that F(i',I)=Pbar. (That is roughly what the Bank of Canada does now, except Pbar is 2% inflation and the horizon is 2 years.)

Under NGDP targeting, the Bank looks at both F(.) and G(.), and chooses i=i" such that F(i",I).G(i",I)=Nbar.

(OK, on re-thinking, what I have written above isn't exactly right, because I've ignored the covariance term in P and Y. It would really need to find a new function which is an amalgam of F(.) and G(.) taking that covariance term into account. And I've forgotten how to do the math.)

[Adam P]

Nick,

I don't think you've answered the question. An AD curve traces out aggregate quantity demanded as P varies. You haven't explained what exactly you mean by "recatngular hyperbola" and how exactly an NGDP target implies this.

I'm looking for a story that is direclty analagous to the sequence of implications -- with fixed M lower P means higher M/P and this means higher quantity demanded.

Can you spell it out for me please?

[Nick Rowe]

Adam: the story I gave above is how I think it would likely be implemented in practice. Remember, the Bank can *try* to hold the AD curve fixed, and *try* to make it horizontal or downward sloping, but it will fail to do so exactly, unless it has perfect information. An inflation targeting Bank *tries* to make the AD curve horizontal, and moving upwards at 2% per year.

Ignore all that. Here's another story. Take the ISLM, for example. When you solve the ISLM model with M fixed, it gives you a downward sloping demand curve Y=D(M/P,X), where X is all the other stuff. In more general terms Bank just adopts a money supply function M=m(P,Y). Under inflation targeting, the money supply function needed is M=m(P), where m(.) becomes perfectly elastic wrt P at Pbar. Under NGDP targeting, the money supply function needed is M=m(PY), where m(.) becomes perfectly elastic wrt PY at Nbar.

[Nick Rowe]

For example, in the textbook ISLM, lower P means higher M/P which means lower r which means higher Y. But, if you look at the math of the ISLM, a 1% fall in P will give a less than 1% rise in Y (unless the IS is horizontal, and the income elasticity of money demand is exactly 1). So the Bank would need to increase Ms by just enough when P falls to ensure that Y rises by exactly 1%.

That story assumes the Bank observes P contemporanously, and knows the parameters (elasticities) of the ISLM model, and that the effects of Ms are instant. If it doesn't have all that information, you get back to my first story. There's a lag in the Bank getting the *expected future* AD curve in the shape and position it wants it to be. But since expected future AD strongly affects current AD, the belief that the Bank wants a rectangular hyperbola AD, and will make the expected future AD a rectangular hyperbola, will tend to make the current actual AD a rectangular hyperbola too. Though not exactly.

[Adam P]

Nick,

You haven't told me what exactly "rectangular hyperbola" means let alone how one obtains. An AD curve is a set of points in (Q,P) space, quantity Q on the horizental axis and price P on the vertical.

So the bank has set i, or M, based in their information and what they hope to achieve. Now, given that fixed value of i or M let P vary and match each value of P with a value of quantity demanded Q to trace out the curve.

What does a "rectangular hyperbola" acutally look like? And how is the you trace out actually obtained in the model?

For example, you said in the post that under price level targeting the AD curve is horizental. But then @8:05 you said "sets i=i' such that F(i',I)=Pbar" where F(i',I) = E(P). This does not generate a horizental AD curve, the AD curve is only horizental if it's not possible for P to differ from E(P)! But you implied that this is possible because you said the bank doesn't have perfect information.

I think you have in mind that the CB sees P before trading begines and then gets to adjust i or M to ensure that the P that obtains during trading is the right one. That would get you a horizental AD curve but that is not at all what you said @8:05.

[Adam P]

The point here is essentially the one JW Mason made above, the bank doesn't choose the entire AD curve.

The AD curve traces out (Q,P) pairs but not all those pairs is a point of general equilibrium. Only one point is the equilbrium point.

An inflation targeting CB tries to make the equilibrium P equal Pbar, that may or may not mean that P = Pbar at out of equilibrium points. You're saying that an inflation targeting central bank gets a horizental AD curve, thus P = Pbar even out of equilibrium. I want you to explain how that happens.

[Nick Rowe]

Adam: Assume ISLM.

Under full information, the central bank can make the AD curve any shape it wants, simply by choosing the correct money supply function M=m(P,Y).

Example 1.: assume the money demand function (in logs) is Md=P + Y -li. If the bank sets the money supply function Ms=P + Y* -li then we get a vertical LM curve at Y*, and the AD curve is also vertical at Y*.

Example 2. If the Bank sets the money supply function Ms=P* + Y - li, then we get a horizontal AD curve at P*.

Example 3. If the Bank sets the money supply function Ms= Nbar -li then we get a downward sloping AD curve that sets NGDP = P+Y = Nbar. (That's rectangular hyperbola when we antilog it.)

Under imperfect information it can't do this. It can only make the expected future AD curve any shape it wants. Do the same as above, but just put an E(.) around all the symbols (and let someone who is math competent figure out the covariance stuff).

[Nick Rowe]

Ooops. Third line should read (that has taught me something): "...correct money supply function M=m(P,Y,i)."

[himaginary]

Nick@02:09 "You can build a model in which IT is optimal, and also build a model in which NGDPT is optimal."

The merit of Ball's method is that you can compare that optimality by way of parameter mu in his loss function, i.e. equation (3).

"And E(y)=0 isn't really enough, because there might be a large variance in y."

That is, how well output follows potential output isn't really enough. I think that observation also gives support to Ball's loss-function method.

Nick@11:04 "It can only make the expected future AD curve any shape it wants. Do the same as above, but just put an E(.) around all the symbols (and let someone who is math competent figure out the covariance stuff)."

I think Ball's paper did that (although he didn't use M). See the following passage:
"The policy-maker can adjust E[y(+1)] to any level he chooses by setting the appropriate r given (4) and the current value of y. We can therefore view the policy-maker’s problem as choosing E[y(+1)]. Given a rule for E[y(+1)], equation (4) determines the implied rule for r.
When the policy-maker chooses E[y(+1)], what variables are relevant? Inspection of (1) and (2) shows there is only one state variable. This variable is expected inflation in the next period, E[pi(+1)], which equals pi + ay. When the policymaker chooses E[y(+1)], he takes E[pi(+1)] as given because it affects inflation only after two periods. The future of the economy is determined by the state variable E[pi(+1)], the policy-maker's rule for E[y(+1)], and future shocks. Thus policymakers set E[y(+1)] as a function of E[pi(+1)]."
That leads to equation (5), which I cited in my previous comment.

[Rob]

Nich,

Thanks very much for taking the time to review my beginners attempts to understand how these 2 types of targeting play-out in simple model. Based on your comments I see that i was implicitly(and stupidly) assuming a vertical AS curve (and LRAS=SRAS) that moved left, which of course means that monetary policy only ever affects prices and not output. Once one assumes an upward sloping AS then it becomes apparent that a whole bunch of variables (price stickiness,which particular prices are sticky and to what degree , and how long it takes to move from SRAS to LRAS etc) come into play and make it impossible to see from a simple model which form of targeting is optimal - which is of course what your post is all about.

[Nick Rowe]

himaginary: I'm not ignoring your comment. I'm thinking about how to translate between my graphs and your and Larry's math. This may take me some time (like days or weeks or months). It's running through the back of my mind. One day (I hope) it may all suddenly come clear to me.

Rob. Thanks. Yep. That was my point in this post.