« On the percentage of Canada covered by water (totally off topic) | Main | If Canada used American racial categories... »

Comments

Feed You can follow this conversation by subscribing to the comment feed for this post.

Nick, is your point that the model in the link is somehow "misspecified"? In particular, that it is "misspecified" in a fashion that is akin to the model having an upward sloping AD curve?

If it's not, then I am totally confused by this post (and the upward sloping AD curve in particular).

Nick,

I can tell that the AD curve in your model is sloping upwards because the central bank is targeting nominal interest rates. I can tell because you explicitly stated that. I am guilty of not understanding why the central bank targeting nominal interest rates leads to the AD curve being upwardly sloped, even though I read your last post on AS-AD and tried to digest it.

Could you explain, Nick? Maybe you should do a series of posts on AS-AD (or link to them if you already have), especially on why the different monetary policy regimes lead to different sloping and shaped AD curves. I'm still struggling to get my head around it. If not, can you recommend a text that explains these facets of the model in full?

Cheers!

If the CB is targetting a nominal interest rate, i, then a higher inflation implies a lower REAL interest rate, r, since by definition r = i - inflation. A lower real interest rate, conventionally, encourages higher investment expenditure and possibly higher consumption expenditure too. So under the assumed conditions - the CB setting the nominal interest rate - a higher inflation rate raises AD.

Nigel gets it, and explains it.

Ben: see Nigel's answer. I don't think there is such a textbook, though you might see bits of it in some textbooks. Maybe I will do a post on it. Nobody should be teaching poncy stuff like DSGE until they have made damned sure their students understand what AD curves look like and why they shift under various different monetary policy targets.

Evan: the model is not (necessarily) misspecified. The monetary policy is just a stupid one, because it leads to an unstable equilibrium. And the author doesn't understand his model, and why he's getting his results, and why they don't mean anything. Because he doesn't understand AS-AD. Even though he is much smarter than me.

Nigel: By the way, how come you get it? Did someone teach you AS-AD? Did you figure it out for yourself? Does it seem obvious to you? (My apologies for asking it this way, but I know nothing about you, and you could be an econ prof or some guy that just wandered in off the street, or anything in between!)

Ha, ha, good one Prof. Rowe. Stability of equilibrium. Ha, ha! I like that.

I see that Nigel's explanation is correct but don't see the mechanism by which the inflation rate will be driven up.
If wages are totally flexible then won't they (and other prices) initially fall when AD moves left ? With nominal rates targeted this deflation will increase real rates and cause investment to fall. What will trigger the inflation that is needed to lower real interest rates ?

Somewhat unrelated to this post but I was struck by the "Employment-Population Ratio" chart in Kocherlakota's presentation. The ratio flat-lines between 2003-2008, drop 8% or 9% between 08 and 09, then flat-lines again at this new lower value up until today.

If that was the only chart I had ever seen on the great recession I wouldn't say "Demand for money increased in 2008 and has stayed high ever since and prices never really adjusted" but rather "we moved from one equilibrium in 2008 to a new one that had a lower level of employment". I would then look for reasons why this may have happened. Demand for money would probably be part of the answer but I would mostly be interested in what had sustained AD at the pre-2008 levels so long and why this proved to be unsustainable.

That chart just made me look at this in a different way.

Ron: "I see that Nigel's explanation is correct but don't see the mechanism by which the inflation rate will be driven up."

Nor does anyone see it. Because there isn't one. That's the point of my post. What NK *should* have said was "Inflation would *need to* rise for the new equilibrium to be reached, but there is no reason why inflation would *in fact* rise, instead it would fall without limit."

Nick: there had been hope in the last few months, but we're back into CoC territory...

Ok, thanks guys, that makes sense.

Jacques Rene: that's exactly what I thought. I thought he had gotten it this last year or two, but it seems not. I had to restrain myself from uttering CoC thrice.

(Your seventh cousin twice removed makes excellent strong cider. 15% by volume!!! The Brits would be stunned, in both senses.)

What also surprised me is that none of the Americans noticed this. It was a public speech, and Mark Thoma linked it. It took me literally about 5 minutes to see what was going on. (Actually, there's another problem, that I ignored in my post: in the sticky wage version he assumes that wages are sticky *up*, not down. And you can see why he made that assumption, because in his way of thinking, if AD fell, and wages were sticky down but flexible up, wage inflation would immediately *rise* to the new higher equilibrium!). But none of the Americans seem to be watching what's happening at their own central bank. Maybe I shouldn't have "buried the lede" (is that the right expression?) like I did. Too deadpan. Where's PK when you need him? (Or maybe that should be *they* need him, because it's their country and Fed.)

Nick
This should be required reading:
http://faculty-web.at.northwestern.edu/economics/gordon/GRU_Combined_090909.pdf
Best quote from article:
“As combined in 1978-era theories, empirical work, and pioneering intermediate macro textbooks, this merger of demand and supply resulted in a well-articulated dynamic aggregate demand-supply model that has stood the test of time in explaining both the multiplicity of links between the financial and real economies, as well as why inflation and unemployment can be both negatively and positively correlated. The achievement of 1978-era macro was to retain the best of Keynesian demand-side economics while dropping the negatively sloped inflation-unemployment tradeoff with its neglect of supply shocks. 1978-era macro recognizes that the correlation between inflation and unemployment can be either negative or positive, just as microeconomics has long predicted that the correlation between the price and quantity of wheat can be either negative or positive depending on the size of the shocks to demand and supply.”

When I studied graduate macro, my professor Locke Anderson imbued on us the Correpndence Principle regarding Comparative Statics exercises. The system needs to be stable:
As Richard Goodwin said a long time ago, an "equilibrium state that is unstable is of purely theoretical interest, since it is the one place the system will never remain."

And the Kocherlakota 'model' you mention has been on his head for a long time. Remember three years ago the "low interest rate is deflationary" controversy?:
http://www.minneapolisfed.org/news_events/pres/speech_display.cfm?id=4525

marcus: yep. And it might be worth adding, at the end of that quote:"...and on the supply and demand elasticities". Because the whole point of e.g. inflation targeting is to make the AD curve flat and not move, so that we should observe zero correlation.

When I studied graduate macro, my professor, Locke Anderson, imbued on students the Correspondence Principle in comparative statics exercises. If the system has no stable equilibrium no use doing comparative statics:
As Richard Goodwin said a long time ago, an "equilibrium state that is unstable is of purely theoretical interest, since it is the one place the system will never remain.":

marcus: Yep, I remember 3 years ago. That was my cryptic reference at the end.

Marcus, what's the correspondence principle?

Not sure I understand the objections raised above…this is how I see it.

Let π = inflation rate, πe = inflation rate, r = real interest rate, i = nominal interest rate, A = autonomous expenditure, Y = output, Y* = full-employment output. Suppose aggregate expenditure depends on the real interest rate, according to:

(1) r = (1/φ)A –(1/μ)(1/φ)Y

where μ = simple Keynesian income multiplier, φ = (real) interest elasticity of expenditure, and μ, φ > 0. If the CB is bent on fixing i at some target level i* then it must take steps to ensure πe = i* - r whatever the circumstances. Under perfect foresight this requires π = i* - r. Substituting this into (1):

(2) π = i* -(1/φ)A + (1/μ)(1/φ)Y.

This equation describes the “AD curves” represented in the above diagram. The target nominal interest rate and level of autonomous expenditure determine the position of each such curve. The inflation rate rises with Y along a given curve: an increase in Y, given A, implies an endogenous decline in r (i.e. a movement down the corresponding IS curve), which in turn implies a policy-induced rise in π (the latter being required if the CB is to keep i = i* in the face of the fall in r).

Now suppose perfect price/wage flexibility, so that Y = Y*. Then, according to (2):

(3) dπ/dA = -(1/φ) < 0.

Why? A decline in autonomous expenditure reduces the natural real rate of interest. To keep i = i* the CB must raise the inflation rate, presumably by adopting a higher rate of monetary expansion.

What am I missing?

Knew it had to be Kocherlakota, even before I clicked the link.

BH: See where Marcus quotes Richard Goodwin? that's basically it (or one way of saying it).

Giovanni: you have (though I haven't checked) correctly solved for how the equilibrium rate of inflation will change if A changes, holding i constant. But you haven't asked whether that equilibrium would be stable, if the CB holds i constant.

Take a simple micro example. Suppose the supply of rice was perfectly inelastic. Suppose rice was a Giffen good, so the demand curve sloped up. Would an exogenous decrease in the demand for rice (demand curve shifts left) cause the equilibrium price of rice to rise? Yes. Would we actually get to that new equilibrium, even if we started at the old equilibrium by sheer chance? No.

Saturos: I wonder how many people would have guessed that?

Nick, in your reply to Giovanni I think you mean "Suppose the SUPPLY OF rice was perfectly inelastic..."

Matteo: Ooops! Yes, I edited it now.

Nick:

Your unstable rice market analogy would be apt if changes in the inflation rate provided the equilibrating mechanism by which output demand = output supplied. But that's not the case here...it's movements of the real interest rate that do that work, as per the "classical case" of an IS curve in output/real-interest space with output fixed at the full-employment level. The inflation rate is determined recursively, given autonomous expenditure, the full-employment level of output and the target nominal interest rate...the "AD curves" in your diagram are really schedules showing how the inflation rate must respond under interest rate targeting to changes in these factors.

So in the light of Giovanni's comments:

- The AD curve moves to the left
- Initially if prices are flexible, they fall
- This puts downward pressure on the nominal interest rate
- As the nominal interest rate is the target, the CB has to adjust the money supply to maintain the rate.
- It may initially try to raise the rate by reducing the money supply but finds the real rate just falls more. Eventually it will discover that with perfectly flexible pricing that inflation/deflation is the only way to adjust real interest rates with a nominal target.
- Once it has hit the required rate of inflation that maintains the required real and nominal rates of interest it should remain in a stable equilibrium as far as I can see.

correction:

"It may initially try to raise the rate by reducing the money supply but finds the real rate just falls more. Eventually it will discover that with perfectly flexible pricing that inflation/deflation is the only way to adjust real interest rates with a nominal target."

should be

"It may initially try to MAINTAIN the rate by reducing the money supply but finds the real rate just falls more AND CAUSES FURTHER DOWNWARD PRESSURE ON THE NOMINAL RATE. Eventually it will discover that with perfectly flexible pricing that inflation/deflation is the only way to adjust real interest rates with a nominal target."

Giovanni: I'm balancing a pole upright on the palm of my hand. The top of the pole is in equilibrium, directly above my hand. If I move my hand north by 1 yard, the top of the pole would also need to move 1 yard north to re-equilibrate. But the top of the pole will actually move south.

Nigel and Nick,

Minor complaint on the verticle AS curve. I don't think it allows for value added to raw materials. Obviously this is a world of fixed supply raw materials. But the price level is for both raw goods and finished products.

"A lower real interest rate, conventionally, encourages higher investment expenditure and possibly higher consumption expenditure too."

I believe it is more heavily weighted to consumption expenditures primarily because production of finished goods and resource extraction (in some instances) can be funded by either debt or equity issuance. Whereas consumption is realized either from current income or from borrowing. If you are going to make the argument that lower interest real rates fuel consumption then you need to look at those rates (credit card rates or home equity loan rates for instance) rather than the rate set by the central bank.

And I won't even start into consumption is made from after tax income, not wages.

Nick,

I think I see your point now. Using my previous notation, suppose out-of-equilibrium adjustments of the inflation rate are governed by

(1) dπ/dt = θ(Y - Y*)
= θ[μA - μφ(i* - π) - Y*]

with θ > 0. Let n = equilibrium inflation rate (that is, the value of π that solves μA - μφ(i* - π) = Y*) and z = π - n. Then (1) becomes

(2) dz/dt = λz

where λ = θμφ. But then λ > 0, which implies any adjustment path derived from (1) will be explosive in the direction of the initial displacement from equilibrium. Give this system a jolt and it will go off toward ever-worsening hyper-inflation or -deflation, rather than converge to a new equilibrium inflation rate.

Is this what you have in mind?

Giovanni: Yes.

Sir.
Quality, sheer quality.
But potaTO potAto.
Definitely something Giffen good'ish about this.

Sorry for the multiple questions: So, Nick, are you basically saying that an equilibrium doesn't exist in Kocherlakota's model?

Nick,

Fair enough. There are two prices in this system that will need to adjust in the face of a shock: the rate at which units of output trade for units of money (i.e. the price level), and the rate at which units of present goods trade for units of future goods (i.e. the real interest rate). Seems to me there is any number of assumptions one could make about the process governing these adjustments. My equation (1) above is one possibility. Another - the one I had in mind in my earlier comment about inflation being determined recursively – would be for the real interest rate to follow

(1’) dr/dt = ψ(μA - μφr - Y*]

with ψ > 0. This would yield a convergent adjustment path r(t) for the real interest rate and - with i* = r(t) + π(t) under interest rate targeting - the inflation rate. Beyond this, one could readily think up a two-equation adjustment process for π and r that included (1) and (1’) as special cases, and produced stable or unstable adjustments paths, depending on parameter values.

The comments to this entry are closed.

Search this site

  • Google

    WWW
    worthwhile.typepad.com
Blog powered by Typepad