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Corcoran in the Financial Post today:


He seems to stray in his last paragraph?

JKH: Thanks! Well-spotted! Yes, he definitely does stray on that last paragraph.

"An increase in expected future real income increases current consumption demand."

What I dont understand is how inflation (either with a rate target or NGDP target) leads to an increase in real output? Is this because people will reduce their savings rate in the face of expected future inflation thereby increasing current consumption? Or is there some other method that creating inflation increases real output?

Ian: for a given nominal interest rate, an increase in expected inflation reduces the real interest rate, which increases current consumption and investment demand, which increases either current output or current prices (depending on the slope of the SR Phillips Curve). That's the New Keynesian version. A more monetarist version is that expected inflation reduces the demand for money, which means people try to spend that money by demanding more goods, which again increases either output or prices.

Isnt the nominal interest rate simply what investors believe the real interest rate is plus the addional interest they charge to protect their investments against inflation? I dont really see how an increase in inflation can cause the real rate to decrease. I understand you can set up an identity that says the real rate is the nominal rate minus expected inflation but I dont understand what that means in "real" terms, ie how can moving terms in an identity reverse the causation?

In the Monetarist version I dont see how producers are going to meet that new demand for goods if they dont have access to the real savings required for the capital formation that is required to produce those goods. Does demand create its own supply?

Ian: The New Keynesian story has the central bank set the nominal interest rate. So it's the real rate that must adjust down if expected inflation increases.

In both Keynesian and monetarist versions, in a recession, demand creates its own "supply". "If they come, we will build it". Using the word "supply" more correctly, there is excess of supply over demand in a recession. Producers are able to produce more, and willing to sell more. But they can't sell more because there isn't enough demand. The existing stock of capital, and workers, sit idle.

The coxswain metaphor is great. I don't suppose that I'm the only one whose thinking about monetary policy owes a great deal to Hume's thought experiment?

The rub here, though, is that Hume's inflation mechanism -- an extra pound slipped into every Englander's pocket overnight -- is exceedingly blunt. Similarly, Milton Friedman's statement that inflation is always and everywhere a monetary phenomenon is very blunt. The change in the amount of money need not be primary, it may be the effect rather than the cause. If there is a widespread belief that prices will increase due to an increase in the amount of money, then prices will rise in anticipation. It's terrifyingly close to a con game, but if it works then so be it.

Thanks Nick, I see now why the new demand will be met. I still dont understand why the real interest rate must fall in response to an increase in the nominal interest rate because as far as I can tell its the nominal interest rate that gets set partially by the central bank creating inflation and partially by the real rate of interest. There's nothing within my understanding that says that the nominal inflation rate should effect the real rate.


I'm curious why you've ignored this part of Ip's post:

In a model developed by Larry Ball in 1996, NGDP targeting produces systematic over- and under-shooting of both inflation and output. It is “not just inefficient, but disastrous. It causes both output and inflation to wander arbitrarily far from their long-run levels.”

Also, from the abstract to Ball's paper:

inflation targets are efficient. Indeed, the set of
efficient rules is equivalent to the set of inflation-target policies with different
speeds of adjustment. Finally, nominal-income targets are highly
inefficient: they create great volatility in both inflation and output.

Any comments?

As Brad Delong likes to point out, the USA has been missing its inflation target by quite a bit lately - on the low side. If the target is 2% why is 1% considered success? Should not (one of) the question be: why is inflation targeting failing?

Since inflation is expected to be a help growing things, why not cut the ambiguity and simply raise the inflation target?

Will: Yep. Hume is very good on money. His oarsmen metaphor (which is similar to the Staghunt game) is influential in theories of property rights and government, but I hadn't thought of applying it to monetary economics.

In a sense, all money is a con game. We accept money because we believe someone else will accept it from us. This is more so with paper money, but also true to some extent with commodity money.

Ian: because, by assumption, the central bank holds the nominal interest rate constant until the NGDP target is met.

Adam: Yep. It's on my "to read" list. The MMs have been discussing Larry Ball's paper by email. IIRC his results have something to do with the assumed lag structure in the IS and Phillips curves, and don't generalise.

There's potentially a similar problem with IT, if targeting is too strict. You get "instrument instability" if the lagged effect of interest rates on inflation is bigger than the contemporaneous effect. If inflation starts to rise above target you need a big increase in r to stop it rising immediately. But the lagged effect causes inflation to fall below target next period, unless you have an even bigger cut in r. And so on, with bigger and bigger swings in r.

The way this problem is solved in practice in IT is to avoid strict IT. The BoC only targets inflation at a 2 year horizon, to avoid the wild swings in interest rates and exchange rates that would be needed to keep inflation at target instantly. An NGDP target would also (I think) need a targeting horizon for much the same reason.

I'm a bit scared to look at Larry Ball's paper because I'm afraid my math won't be up to it, and I will have to try to figure everything out intuitively (as usual). But yes, I need to gather up my courage and tackle this whole "horizon" question. The practical policy question would be whether the horizon under NGDP level path targeting could be shorter than the horizon under IT. My intuition says it would not have to be longer, simply because Y responds more quickly than P. My guess is that they would need the same horizon.

Another, related, issue is inflation inertia. It is one reason to prefer IT over PLPT, unless the return to path is slow enough that inertia is not a problem. Calvo pricing models do not have inflation inertia, because the Calvo fairy visits all firms with equal probability. But if the Calvo fairy is instead a Taylor fairy, and visits each firm after n periods, rather than randomly, you get inflation inertia.

Chris: a serious IT would be good, but I think an NGDP target, especially in the US, would be better. As I argue in the post, it would be more credible, because of the "mix" feature. It also handles supply shocks better. Politically, it's also closer in spirit to the Fed's dual mandate.

Adam, again: Here's another way of thinking about it.

Some prices in the CPI are very flexible, and some prices are very sticky. Inflation targeting targets a mix of flex and sticky prices. If you do very strict IT, you would get big swings in relative prices, and potentially explosive oscillations in each component.

NGDP also targets a "mix" of Y and P. And Y is more "flexible" (adjusts more quickly) than P, which is sticky. Larry Ball's paper (I still haven't read it) is saying that this mix of flexible plus sticky in the target variable is a problem. OK, but there's the exact same problem (conceptually) with IT. And the solution to both is a sufficiently long targeting horizon.

Ball's 1999 paper only deals with NGDP growth targeting, which he shows to be unstable. You'd probably be more interested in the 1997 NBER version (wp.5952), which deals with level targeting. I would like to see how he handles that myself, but unfortunately I don't have an NBER subscription.

Nick, I don't think that's right.

As I see it the fundamental problem is that in just about all models the pricing problem of the single firm depends on expectations of the future aggregate price level but not expectatons of future aggregate output, because under monopolistic competition they'll adjust outpu to absrob demand shocks. The same is true of the wage setting problem for labour.

Thus, as real growth shifts today if NGDP expectations don't shift then the entire phillips curve shifts instead. This feeds back to the correspondence between the real interest rate and the level of ouptput (essentially induces a shift in the IS curve) and causes the level of output to be inconsistent with the rate of inflation, even though it was to begin with. This process continues in a cycle of increasing amplitude, destabilizing the whole system.

to be clear:

I should have said, they'll adjust output to absorb transient demand shocks. In some sense then the contradiction is that if NGDP targeting works then all demand shocks must be transient, but if that's true then NGDP targeting can't work.

And no, neither inflation targeting no price level targeting has this problem.

But yes, the problem applies just as much to NGDP level targeting as to NGDP growth targeting.

Adam. Hmmm. Thinking about this.

Tentatively, I disagree with your first paragraph, and you lost me on the second.

Take the simplest case. An individual monopolistically competitive firm sets p one period in advance, and lets y be demand-determined. The firm sets p according to its expectation for next period's demand, MR, and MC curves.

Put nominal p on the vertical axis, and real y on the horizontal. Let P and Y be aggregate versions of p and y.

Start in full equilibrium.

If E(P) increases by 10%, holding E(Y) constant, the individual firm's expected demand curve, MR curve, and MC curve, all shift up vertically by 10%, so it sets a 10% higher p for next period. OK.

If E(Y) increases by 10%, holding E(P) constant, the individual firm's expected demand curve shifts right by 10% (at the existing p, assuming representative firm), which will *normally* (except for weird preferences that don't give constant elasticity) shift the MR curve right too, plus the expected MC curve will shift up vertically too because other firms will be hogging all the labour, and paying higher real wages. So the individual firm will set a higher p.

OK. The only case I can think of where an increase in E(Y) does not change p is where elasticity of demand is invariant to E(Y), and where the MC curve is horizontal and does not shift up when E(Y) increases. But in that case, equilibrium Y is indeterminate anyway. It's a knife edge case where the LRAS curve is very thick.


here: "If E(Y) increases by 10%, holding E(P) constant, the individual firm's expected demand curve shifts right by 10% (at the existing p,..."

I'll assume you meant capital P, and not little p.

But then what you said for a firm that can change price today but not tomorrow is only true if the increase in E(Y) is permanent, if it's transient then p is set based on the demand curve that corresponds to long run E(Y). (See my follow up).

Now we're back to what I said above: if NGDP targeting works then all demand shocks must be transient, but if that's true then NGDP targeting can't work.

Or, if demand curves get much more elastic in booms, so MR rises by enough to offset the upward shift and upward movement along the MC curve, so a firm might actually lower p when E(Y) increases. This means that E(y) rises by more than E(Y), so the LRAS/AD equilibrium is macroeconomically unstable.

BTW, McCallum answers Ball's critique in

The McCallum paper only establishes that nominal GDP targeting doesn't necessarily imply explosive variances, it does not show it to be optimal.

Ball actually responds in the paper we've been discussing:

The result that output and inflation have infinite variances may appear
too extreme to believe. Indeed, recent work by McCallum (1997) and Dennis
(1998) shows that the result is not robust. Reasonable modifications of the
Phillips curve, equation (2), produce finite variances of output and inflation
under income targeting. Dennis, for example, shows that the variances are
finite if inflation depends on both past inflation and expected future inflation.
This is true even if the future-inflation term has a small weight, so the Phillips
curve is close to my purely backward-looking equation.
These results do not, however, overturn the conclusion that income targeting
is an undesirable policy.While infinite variances are a special result, it appears
that income targeting produces finite but large variances under a broad
range of assumptions. The reason is the overshooting phenomenon discussed
above. The overshooting result appears robust; it arises, for example, in Dennis’s
model, as long as the lagged-inflation term in the Phillips curve has a positive
weight. In that model, the oscillations die out over time, implying finite variances.
But the variances are still large relative to efficient policies.4

Adam: simple monopolistic competition macro model:

Elasticity of demand is a constant, so price is a markup (1+m) over marginal cost. Assume a production function Y=n, so Y=N in aggregate. Assume an inverse labour supply function W/P=F(N).

Firms set price for one period, in advance.

The expected profit-maximising price to set for next period is p=(1+m).F(E(Y)).E(P)

(I've ignored all the variance and covariance terms, of course.)

Will be back later, maybe tomorrow.

Ball's model is completely backward-looking. I think there's an analogy here w/ the literature on price-level path targeting. There's an early literature using backward-looking models that finds price-level targeting to lead to more volatile fluctuations in inflation and output. Forward-looking expectations moderate the impact of shocks on current inflation because price-setters calculate that the central bank will offset the impact of shocks on future inflation. Most of the arguments in favor of nominal GDP targeting involve the link between future expected inflation and/or real expenditures on current expenditures.

Steve, the quote from Ball I posted just above addresses that. Even with the forward looking IS and Philips curverve NGDP targeting is inferior to inflation targeting.

for a given nominal interest rate, an increase in expected inflation reduces the real interest rate, which increases current consumption and investment demand, which increases either current output or current prices (depending on the slope of the SR Phillips Curve).

But in the real world, isn't it the case that changes in the nominal interest rates are exceedingly sensitive to changes in inflation expectations? If I begin to expect higher inflation, my bank is going to begin to expect higher inflation right along with me. So there is no reason to expect real interests rates to go down.

Also, the connection between expected inflation and the propensity to hold or spend money doesn't seem as simple as it is usually painted as being. For example, suppose my nominal income is relatively fixed, and suppose I live on canned fruits and vegetables. Then it is true that if I expect the price of canned vegetables to start to rise, I will spend more money now to stock up rather than wait for the value of my dollars to decline.

But suppose I live on fresh fruits and vegetables. Then I will expect to have to a higher proportion of my future money income on food than I spend now. Assuming I want to maintain a constant level of consumption, the rational response would be to re-balance my consumption pattern, diminish my spending and consumption a bit now, and save more money, so I can consume the same amount later at the higher prices.

Dan Kervick: It should not matter what inflation banks expect as it is assumed that nominal interest rate is in the hands of the Central Bank. All they should be interested in, is their customers risk profile and actual (expected) nominal interest rate.

The only channel via which banks may be interested in increased inflation is through its impact on increasing future nominal interest rates of the CB, and even then only in case they offer credit in a nominally fixed rates or if they expect inflation to increase risk profile of their customers. So in short if banks think that future inflation will lead CB to increase its nominal interest rate, they will probably increase their rate on let's say 5-year fixed-interest loans.

It should not matter what inflation banks expect as it is assumed that nominal interest rate is in the hands of the Central Bank. All they should be interested in, is their customers risk profile and actual (expected) nominal interest rate.

That assumption seems incorrect. The central bank can control certain fundamental interest rates - the Fed funds rate and the overnight rate for example - but it can't control interest rates throughout the economy. Those fundamental rates determine the costs of acquiring additional reserves, but surely it cannot be the case that the interest a bank charges for a loan is independent of how much the bank expects the principle to be worth when the loan is repaid. The inflation risk has to be factored in along with other aspects of customer risk.

If there is presently a close connection between the fundamental rates and commercial bank lending rates, that is only because we have had very low inflation. But if you are recommending a move to higher inflation, then I would think that will produce a correspondingly larger gap between the rates the Fed determines for reserves and the rates banks charge their customers for loans.

Dan Kervick: "but surely it cannot be the case that the interest a bank charges for a loan is independent of how much the bank expects the principle to be worth when the loan is repaid" Actually, I think it can be the case. The point is that banking works on a margin, they just offer transaction services. They do not play with their own money (or to be precise, they have their own capital highly leveraged). Banks have some sum of money on saving accounts on behalf of their customers. Banks may either lend this money, or they may just let it sit there to be eaten by inflation. If the latter is the case, for banks it it sufficient to offer 0% interest on savings accounts and then they could not care less. It is their customers-depositors who bear the loss from inflation. Banks will profit from any loans that they make with yield beyond that of the cost (nominal interest) of funding minus risk level of their creditors. Then they pay out this as profit to their shareholders and that is that is the end of story.

Just a note, banks have to be regulated. If they could use deposits for their own speculative trades, then we have a problem. They could speculate that inflation will increase price of commodities and buy those - but that is not "banking" in that old boring and conservative meaning - as facilitating loans. Nor is any similar scheme when a bank gives a loan to somebody speculating in a similar manner - namely using deposits to conduct speculations.

Adam: I have now read Larry Ball's 1999 paper. OK, I didn't really read it, but I looked at the model. (The math wasn't anyway near as scary as I thought!)

The intuition behind his result is exactly as I guessed. Assume r causes y with a one period lag, and r causes p (inflation in this case) with a two period lag. Larry Ball says that targeting inflation gives you good results, and targeting NGDP gives you bad results.

That is correct. And it will also generalise beyond the strict assumptions in his model.

But that result has nothing to do with whether the target variable is inflation or NGDP. What his model really shows is that if you target with a 2 period horizon you get better results than if you target with a 1 period horizon.

Suppose half the components of the CPI react to r with a 1 period lag, and the other half of the CPI reacts with a 2 period lag. If you target inflation at a 2 period horizon all is well. If you target inflation with a 1 period lag you will get low variance in total inflation but big oscillations in relative prices.

The real message out of his paper is: regardless of the target variable you choose, don't make the targeting horizon too short.

Now, AFAIK, the topic of the optimal targeting horizon is one that doesn't get enough attention. Too many macro models assume the CB has contemporaneous information, and there are no lags from monetary policy to inflation. That would make strict inflation targeting trivially easy. We need to recognise that different prices and different real variables react with different lags.


Your wrong, the problem is exactly the same if the CB targets 2 period ahead NGDP as it is if the CB targets one period ahead NGDP.

The reason for this is very simple, the policy rule that stabilizes 2 period ahead NGDP is the same as the one that targets 1 period ahead NGDP by the law if itereated expectations!

Now, you're correct that the ocillatory outcome is driven by the fact that monetary policy causes y with a one period lag and pi with a 2 period lag but that is necessary for money to have any real effect at all, it's just the sticky price assumption. So you can't dispense with that assumption very easily.

This is not a result you can cheat so easily, this model, or any simillar one will imply NGDP targeting to be grossly inferior to inflation targeting for any targeting horizon!

And changing the timing assumptions will destroy monetary policy's ability to have any effect at all on RGDP which would also imply inflation targeting is far superior to NGDP targeting!

more details here:


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