New Keynesians really need the Pigou effect

Because otherwise their models won't work.

And yet the canonical versions of their models, which don't even have money, cannot have a Pigou effect.

And so New Keynesians are guilty of the Old Keynesian accusation of "just assuming full employment".

Here's why: In Old Keynesian models, if Aggregate Demand is too low, a cut in real interest rates will (usually) increase Aggregate Demand to get the economy to full employment. But in New Keynesian models a cut in real interest rates may merely redistribute Aggregate Demand from future to present. Because in New Keynesian models it is only the ratio of present to future Aggregate Demand that depends on the real rate of interest. The overall level of Aggregate Demand, present plus future, is indeterminate, unless you just assume the economy will eventually get back to full employment.

In the olden days, when the Old Keynesians were young, the young Keynesians had a sure-fire way of demolishing an unprepared "classical" economist. "But your model just assumes full employment!" was how they attacked. (Several decades later, "But your model just assumes sticky prices/ignores the Lucas Critique" played a similar role for different young macroeconomists.)

A well-prepared "classical" economist needed some sort of answer ready to defend himself against the young Keynesian accusation.

He might say that if there were an excess supply of goods then the price level would fall, and that fall in the price level would increase the real money supply, and that would cause an excess supply of money, which would mean an increased demand for goods, which would get the economy back to full employment.

Or he might invoke Keynes himself, and say that if there were an excess supply of goods then the price level would fall, and that fall in the price level would increase the real money supply, and that would cause an excess supply of money, which would mean an excess demand for bonds, which would cause bond prices to rise, which would mean interest rates fall, which would cause desired investment and maybe desired consumption to rise, which would mean an increased demand for goods, which would get the economy back to full employment.

Only a really desperate classical macroeconomist would invoke the Pigou effect to defend his assumption of full employment. It was a defence of last resort, to be used only if the young keynesians said "But what if there's a liquidity trap so interest rates can't fall, or what if interest rates do fall but desired investment and consumption are perfectly interest-inelastic?" He would then invoke the Pigou effect, and say that an increase in the real money supply would increase real wealth which would increase desired consumption.

Now let's take one of those vicious young Old Keynesians from more than half a century ago, put him in a time-machine, and wake him up in a seminar where a Woodfordian New Keynesian is presenting his very simple model.

It's a very simple model, with no investment, government expenditure or taxes, or net exports. The only source of Aggregate Demand is consumption. "OK", says the young Old Keynesian, "so let's see the consumption function". And the New Keynesian writes down an Euler equation in which the ratio of today's consumption to tomorrow's consumption is a negative function of the real rate of interest. "OK", says the young Old Keynesian, "that looks a bit strange to me, but I will take your word for it".

There is next a long and confused discussion in which the young Old Keynesian eventually learns that the new name for "full employment" seems to be "the natural rate of unemployment".

Then the New Keynesian says: "The economy will always be at the natural rate of unemployment provided the central bank continuously adjusts the real rate of interest in response to shocks to keep the real interest rate at the right level".

The young Old Keynesian sticks up his hand: "Hang on" he says "I can see that keeping the real interest rate at the right level is a necessary condition for keeping the economy always at full employment in your model, but it's not a sufficient condition. What happens if the real interest rate is always at the right level but consumption is always 50% below full employment output? The ratios between today's and tomorrow's consumption would still be exactly the same, so your Euler equation consumption function thingy is still satisfied."

The young Old Keynesian then makes his old accusation: "Your model just assumes full employment!"

How could the New Keynesian defend his model?

He cannot say that if consumption was too low the central bank would just cut the real interest rate. Because the young Old Keynesian would reply: "But you have already assumed the real rate of interest was at the right level. And in any case, even if the central bank did cut the real interest rate, all you know is that the ratio of today's to tomorrow's consumption will increase, and that might equally well happen by tomorrow's consumption falling with today's consumption staying the same, which doesn't help us get back to full employment today, and simply takes us even further away from full employment tomorrow. Cutting real interest rates only gets us to full employment today if you just assume we're at full employment tomorrow. I repeat my accusation: your model just assumes full employment!"

And he's right.

The young Old Keynesian then decides to say something kind, as well as uncharacteristic. "You know" he says "you could make your model work by adding a Pigou effect to get you to full employment. And unlike those stupid classical economists, your model only needs a really tiny Pigou effect to make it work. Because provided the central bank gets the right rate of interest there is nothing to prevent your model being at full employment; it's just that there's nothing to prevent it not being there either. Maybe if the central bank got the interest rate wrong in a big way, then you would need a big Pigou effect to offset it, like in Samuelson 1958 where M/P has to be really big because people want to save so much and can't invest, and only the really big Pigou effect keeps Samuelson's model at full employment. Trouble is, your model doesn't have 'M' in it, so you would need to change that, if you wanted to add a Pigou effect ."

But it's too late for this kind and uncharacteristic suggestion. The New Keynesian already knows that "M" doesn't matter and that only "r" does. He's off thinking about transversality conditions.

Comments

[Gregor Bush]

Great post Nick,
I have one (possibly stupid) question: dosen't the standard NK model also have an Phillips curve equation and monetraty policy reaction function. And if so, if both current and future consumption were 50% below the full employment level the output gap would be massive and inflation would fall below the central banks' traget. And this of course would cause the central bank to cut the actual intertest rate to a level below the natural interest rate until the output gap starts to close and inflation moves back to target. It's pinning down inflation that keeps the economy at full employment in the NK model. Is it not?

I'm not sure how to sqaure that with the Euler equation being the ratio of present to future consumption.

[Nick Rowe]

Gregor: Thanks!

"I'm not sure how to sqaure that with the Euler equation being the ratio of present to future consumption."

It can't be squared with "And this of course would cause the central bank to cut the actual intertest rate to a level below the natural interest rate until the output gap starts to close and inflation moves back to target."

If the central bank cuts the actual interest rate below the natural interest rate, all we know is that the ratio of today's to tomorrow's consumption will rise. So it is perfectly possible that cutting the rate of interest will simply reduce tomorrow's consumption instead, leaving today's output gap the same, and making tomorrow's output gap even worse. Even if the central bank *permanently* cuts the actual rate of interest below the natural rate, it is perfectly possible that today's consumption will stay the same but the growth rate of consumption will permanently fall.

In a continuous time version, it is the growth rate (not the level) of consumption that is a positive (not a negative) function of the real rate of interest.

And if we add in the distinction between real and nominal interest rates, since lower future consumption means a lower future price level, things might get even uglier.

[Scott Sumner]

Nick Rowe, Excellent post again. Does long run wage flexibility help? Or is that already assumed by NKs?

(Not sure how this relates to Gregor's question.)

[Nick Rowe]

Scott: Thanks!

Long run wage or price flexibility doesn't help at all, unless we add a Pigou effect to the model. I'm assuming that the central bank can set any real rate of interest it wants. Price and wage flexibility just complicates things, by introducing a distinction between real and nominal interest rates. Of course, if real wages were at the wrong level, that would be an additional force preventing full employment, but I'm ignoring that, and (implicitly) assuming real wages are always at the right level.

[Gregor Bush]

Thanks Nick.

I see. So in other words there's nothing about the standard NK model that necessarily results in the central bank hitting its own inflation target. It's perfectly possible for it to systematically miss its target forever, even if interest rates aren't at zero. In some NK models I've seen there is an expectations term in the Phillips curve equation that causes inflation to drift back to the target for any given output gap - a "gravitational pull term" if you will. So with respect to that model I suppose you would say there’s nothing to ensure that the output gap will close but if inflation expectations stayed close to the target actual inflation would also tend stay close to the target. Hmmm, there’s something familiar about that.

[Nick Rowe]

Gregor: I think that's right. Just assuming that the central bank eventually hits its inflation target is equivalent to just assuming eventual full employment, given the Phillips curve and Rational Expectations. I've simplified by assuming perfect foresight, assuming the central bank sets a real interest rate (indexed bonds), so I can solve the model without talking about the Phillips Curve. And it still can't guarantee to hit full employment.

[Ed]

Neat post. I haven't digested all of it, but it was a joy to read. I actually had one general question that's always kind of nagged at me. It's probably obvious but I'll ask anyways: what does it really mean for overall Aggregate Demand to increase in real terms?

You noted in the beginning that in canonical NK models there isn't an overall change in Aggregate Demand but rather a distributional change. I guess I'm having trouble wrapping my head around what it actually means for overall real aggregate demand to rise or fall. Does it just mean, as you put it, that everyone wants more output today *and* tomorrow? Which would seem to imply that everyone would prefer to work more today and tomorrow? Am I thinking about this right? Or do you need to think of it in terms of money?

[Nick Rowe]

Ed: Thanks!

"Or do you need to think of it in terms of money?"

We need to think in terms of money. If this were a barter economy, we could never have a problem of deficient aggregate demand. If there were unemployed workers who wanted more work, and firms who wanted more customers, the unemployed would just go to the firms, offer to work, and ask for some of the output they produced in return. And unless the workers demanded too much output per hour of work (unless they demanded too high a real wage) the firm's new customers would be the very same people as its new workers, and so the firm would say "yes!"

It's when there isn't that double coincidence of wants, and so the workers want to be paid in money, and the firm needs to find (different) customers who want to pay money, and everyone wants to hang onto their money, that we get a problem of not enough aggregate demand.

[W. Peden]

Brilliant post. My views on the Pigou Effect have been like a yo-yo while reading recent blogosphere debates on it.

One question-

"There is next a long and confused discussion in which the young Old Keynesian eventually learns that the new name for "full employment" seems to be "the natural rate of unemployment"."

I was under the impression that Keynes's meaning of 'full employment', the way Old Keynesians tended to use 'full employment', the NAIRU, and the natural rate of unemployment, all refer to different things:

Keynes: the level of unemployment at which an increase in investment results purely in an increase in prices rather than output.

The (vulgar) Keynesians: not too sure, but they seem to have thought that it was a fairly fixed and predicatable percentage that could be sustained at a particular rate of change of prices.

NAIRU: any rate of unemployment which is consistent with (most) rates of inflation, provided that the rate of inflation is stable.

The natural rate: any rate of unemployment at which expected inflation = actual inflation.

Have I got some or all of those wrong? If not, then isn't it incorrect to equivocate the natural rate of unemployment and full employment?

[K]

Nick,

Can we agree on a representative NK paper that we can refer to for the purposes of this discussion? Then we can discuss exactly what is wrong with what equation. If we are going to criticize a model, don't we have a better chance of making progress if we agree exactly what we are talking about? Personally, I would propose Eggertsson and Woodford 2003, because it's a standard NK model *and* they explicitly include money for the purposes of examining real balances effects (i.e. the Pigou effect).

Also, when we talk about the Pigou effect do we mean the mechanism as described in Pigou 1943? Again, in all the discussion over the past few days, it seems like everyone maps "the Pigou effect" into their own internal economic model, and it's not at all clear that anyone is talking about the same thing.

Wouldn't we have a better chance of making progress if we agree on the terms of the disagreement (if any)?

[Nick Rowe]

W Peden: Thanks!

"My views on the Pigou Effect have been like a yo-yo while reading recent blogosphere debates on it."

Truth be told, my poor old brain yo-yo's a bit too. NO! SCRATCH THAT! I'm right I tell ye! And all them others are wrong, wrong, WRONG!

Yes, very strictly speaking, all those many different concepts of 'full employment" may not be exactly the same. For example, we can imagine an economy in which inflation is accelerating but actual and expected inflation are the same.

But it doesn't matter for this post. If the model has no automatic tendency towards the natural rate, even if the central banks sets r right, it won't have any automatic tendency towards "full employment" for any non-vacuous definition.

K: My young Old Keynesian time-travelling alter ego borrows a line from Joan Robinson: "You want to hide behind thickets of algebra?"

For this post, all you need is:

Representative infinitely-lived agent with perfect foresight who maximises V = sum over all t B^t.Log(C(t)) subject to Present value of C(t) = Present Value of Y(t) discounted at rate r(t), which gives you the Euler equation C(t)/C(t+1) = 1/B.(1+r(t)) for all t.

Accounting identity given I=G=T=X=Im=0: Y(t) = C(t)

Exogenous full employment income Y*(t)

Central Bank sets r(t) such that Y(t)=Y*(t)

The only role of the Phillips Curve and supply-side is to relax the assumption of exogenous Y*(t) and define Y*(t) that is compatible with the inflation target.

[Edited to fix my usual math mistakes.]

[Nick Rowe]

And the solution to that model, assuming Y*(t) is constant for all t, for simplicity:

The CB sets r(t) = (1/B)-1.

[Edited to fix my usual math mistakes, but it's probably still wrong, sod it, who cares.]

[W. Peden]

"But it doesn't matter for this post. If the model has no automatic tendency towards the natural rate, even if the central banks sets r right, it won't have any automatic tendency towards "full employment" for any non-vacuous definition."

Hmm, now that's something I'd never realised.

[Ashok Rao]

Nick, I will add to the chorus: a very enjoyable read!

I'm still absorbing it all, but I have a few questions. Isn't this a somewhat contrived way to force a Pigou effect into NK models? To force NKs not to assume full employment, we are stipulating that "consumption is always 50% below full employment output". It seems like we're creating a model that tautologically requires a Pigou-type effect to make it work. So is this a mathematical identity or a real insight? Would this kind of a result hold in an open economy with investments, with depreciation?

To me, the most interesting implication of your post isn't necessarily that a Pigou effect is necessary as much as the equivalency of assuming full employment to assuming the central bank hits its target. I think that is particularly relevant today.

Again, I'm still absorbing it and will think more of it later.

[K]

Nick,

OK, so I think you are saying that since there is no link between the nominal and the real economy, money has no real effect. I.e. you've proved your claim for a simple RBC economy, but you claimed you were talking about the NK economy. The NK model works by adding sticky prices so that inflation has real effects. That's how you get the NK Philips curve. Sticky (e.g. Calvo) prices are the additional equation that tie together the real and nominal economies and make expectations of nominal variables unique.

[HJC]

Finally! A well-worded piece highlighting this problem is long overdue and most welcome. Would you also care to comment on Kalecki's 'demolition' of the Pigou effect in 1944?

[Kevin Donoghue]

In fairness, I think the New Keynesians acknowledge at the outset that they are assuming long-run full employment in some sense. Gali's book refers in passing to "the assumption that the effects of nominal rigidities vanish asymptotically" which lets the cat out of the bag. But for that matter, even Keynes was willing to concede that the classical verities hold in the long run. I don't think his State of Long-term Expectation can involve involuntary unemployment lasting centuries, though it does allow stagnation as an end state.

[Nick Rowe]

Ashok: Thanks!

"To force NKs not to assume full employment, we are stipulating that "consumption is always 50% below full employment output"."

We are not *forcing* or *stipulating* that consumption (and hence output) is always 50% of full-employment output. We are saying that the NK model does not prove that that cannot happen, even if the CB sets r correctly at a level compatible with output being at full employment.

K: Add a Calvo Phillips Curve to my model. Then define my Y*(t) as the level of Y(t) consistent with inflation always being equal to the CB's inflation target given that Phillips Curve. That Calvo Phillips Curve then tells us how inflation will deviate from target if Y(t) is not equal to Y*(t). But that has no implications for my argument here.

HJC: Thanks!

I can't remember reading Kalecki on the Pigou effect. My guess is that he would have said: "The Pigou effect is really small, and it will be overwhelmed by much bigger forces, such as the effect of a changing price level on real wages and the distribution of income, given that workers have a higher marginal propensity to consume than capitalists, and money wages adjust more slowly than prices, so we can reasonably ignore the Pigou effect."

Is my guess right?

Kevin: my point here is quite independent of whether or not the effect of nominal rigidities vanish asymptotically. If prices are fixed forever my model still works. And if the long run Phillips Curve is vertical at Y* all that means is that since there is nothing to prevent Y being bigger or smaller than Y* there is nothing to prevent inflation going to plus or minus infinity even if the CB gets r(t) right for all t. When they just assume inflation does not go to plus or minus infinity and just assume inflation stays on target provided the CB sets the right r(t) they are just assuming full employment.

[Ashok Rao]

Nick, if I recall correctly Kalecki actually rejected the Pigou effect on the grounds that it would increase the real value of debts which would crash demand. The source (possibly gated) is here, I have not reread it so forgive any errors: http://www.jstor.org/discover/10.2307/2959845?uid=3739640&uid=2134&uid=2473548943&uid=2&uid=70&uid=3&uid=2473548933&uid=3739256&uid=60&sid=21102556749203

"We are not *forcing* or *stipulating* that consumption (and hence output) is always 50% of full-employment output. We are saying that the NK model does not prove that that cannot happen, even if the CB sets r correctly at a level compatible with output being at full employment."

Right I understand that, I phrased my question incorrectly. Not able to express my point cogently at the moment, but it is the always that does not sit well, especially in a model where the only source of Aggregate Demand is restricted to consumption. If we restrict said source to always remain at 50% of full-employment output, the required enhancements necessary to obtain full employment seem like red herrings. Not sure if I'm expressing my doubts more clearly here.

I decided to go back and read Kalecki's piece, it really is quite beautiful. Here's the key:

The following reservations must be made with regard to this argument. The increase the real value of the stock of money [implies that for each] gain of money holders there corresponds an equal loss of the bank debtors. The total real value of possessions in creases only to the extent to which money is backed by gold […] If in the initial position the stock of gold is small as compared with the national wealth, it will take an enormous fall in wage rates and prices to reach the point when saving out of the full employment income is zero. The adjustment required would increase catastrophically the real value of debts, and would consequently lead to a wholesale bankruptcy and a "confidence crisis".

[Roger Gomis]

Nick great post! Lately you are considering very interesting topics but my head is starting to hurt a bit too much. At the peril of behaving like your NK character...

(All variables are in log deviations) I think that the issue can be solved with a better real rate rule. Taking the usual output gap Euler equation in log deviations and ignoring uncertainty we have:

y(t)= y(t+1) - r(t)

If we follow your policy of constant real rate (in a precise level but constant):

y(t)= y(t+1)

we see that we are only guaranteeing that the output gap will remain constant. But we can consider the system:

y(t)= y(t+1) - r(t)
r(t)=reaction_coefficient*y(t+1)

If we set the reaction coefficient to negative, like a threat to increase real rate if the output gap tomorrow is positive, the solution of the system is unique, if we impose a non explosive path for the output gap (which I don't find unreasonable), since the only non explosive solution is zero output gap at all periods as the overall coefficient is higher than one.

reaction_coefficient less than 0

y(t)= y(t+1)*(1-reaction_coefficient) thus y(t)=0 for all t, otherwise consumption explodes and this cannot be an equilibrium.

I hope this a useful and not totally off topic answer!

PS: Other policy coefficients (including crazy ones) and endogenous policy rules might work.

[Nick Rowe]

Ashok: thanks for that quote from Kalecki. He's roughly right about the Pigou effect, for a world under the gold standard (though he misses the Pesek and Saving point that money produced by a bank that earned monopoly profits would also be net wealth even if it weren't backed by gold). And his point about the "equal loss to bank debtors" is badly stated, because it should be an "equal rise in bank liabilities". But he doesn't say anything about fiat currency, so we can't really apply his analysis today and say whether it's right or wrong.

His offsetting effect via real value of debts sounds like Fisher's earlier debt-deflation view, and not the wage/profits distribution view that I guessed he would talk about.

BTW, your comment went into spam, and I had to fish it out manually. (This is a common problem; the same thing happens to all of my comments!) So if any future comment does not appear, just wait a bit.

[Nick Rowe]

Roger: Thanks!

(BTW, your comment went into spam too.)

It's definitely on-topic.

I think it's useful.

I think (not 100% sure) it doesn't affect my point:

First, because you have to *just assume* the economy doesn't go on an explosive path, which isn't much better than *just assume* full employment.

Second, because I think (not sure) you could get the same results if you assumed a central bank reaction function like r(t) = r*(t) + c[Y(t)-Y*(t)] which is a bit like the CB saying "If you don't go to Y*(t) when I go to r*(t) then I will do something crazy and the economy will explode, and since the economy can't explode you had better go to Y*(t) when I go to r*(t)".

[Ashok Rao]

Nick, since Kalecki's point should hold true for all outside money (which was restricted to gold backed currency in his time) is there any reason the Pigou effect wouldn't be insignificant if fiat currency and reserves represent a sizable portion of all money? That may not be the case, but should give at least epsilon oomph, speaking technically. I see no reason, were that logic to be true, that it not be extended to any outside money including foreign holdings.

[Kevin Donoghue]

Nick: my point here is quite independent of whether or not the effect of nominal rigidities vanish asymptotically. If prices are fixed forever my model still works.

Too subtle for me I'm afraid. I can't see fixed prices without nominal rigidities. Brain hurtz. Never mind.

[Frank Restly]

Nick,

"I've simplified by assuming perfect foresight, assuming the central bank sets a real interest rate (indexed bonds), so I can solve the model without talking about the Phillips Curve. And it still can't guarantee to hit full employment."

A central bank by buying and selling indexed bonds would be setting the price of the bonds. The market interest rate would move in the opposite direction as the price. Even with indexed bonds the central bank may not be able to set the real component as high as it would like if the issuer of the bonds has the ability to buy the bonds back when they trade below par.

For instance, a government sells indexed bonds at auction with a 2% real component, the central bank tries to push the real component to 3% but the government buys them back at any discount to par. Since the central bank cannot directly participate in bond auctions (central bank independence) it is at the mercy of the government and the rest of the market.

[Nick Rowe]

Ashok: the consensus is that the Pigou effect is small, because it only applies to central bank money, which is a small part of total wealth.

Kevin: my fault for not writing clearly.

Yes, nominal rigidities = sticky prices (in this context).

I was saying:

My point holds if prices are fixed in the long run.
My point holds if prices are perfectly flexible in the long run.
It doesn't make any difference, except that if prices are perfectly flexible in the long run, the price level will implode to zero if Y is less than Y*, even if r is at the correct level.

[Nick Rowe]

Frank: central banks buy and sell bonds. And that's a red herring anyway. No more discussion on that point please.

[Ashok Rao]

Isn't the implication said consensus that not only can a helicopter drop be beneficial, but its value increases superlinearly with each dollar, in a situation like today's? Same with QE. Of course, alpha epsilon is still epsilon.

[HJC]

Nick and Ashok:

First, thanks for taking up the challenge!

Kalecki's point is about inside money, since outside money, either fiat or commodity, is significantly smaller. Perhaps to clarify, the point that there is an "equal loss to bank debtors" is that any real gain that money holders have (by price falls) is offset by the loss that debtors incur since their debts are fixed nominally. Is that "badly stated"?

Also, as you say Nick, his argument is not as you first suspected (a good guess since he is probably more well known for his theory of profits) and is perhaps is akin to Fisher's (or Koo's?) view, although there may be some subtle differences that I am not aware of. I am not sure that I see why it is not relevant to a fiat currency though. Outside money, i.e. central bank reserves, are (excepting QE) a tiny proportion of bank balance sheets, in some cases zero or negative. So it seems to me that his conclusion still follows if you imagine the kind of price and wage drops necessary to raise real balances on outside money alone.

[Nick Rowe]

Ashok: "Of course, alpha epsilon is still epsilon."

Not if alpha is very very big, which it is in this NK model. The economy is like a ball on a perfectly flat frictionless surface (if the central bank sets r right). An epsilon push in the right direction will move it.

HJC: Here is my recent post on the Pigou effect.

[Max]

"(though he misses the Pesek and Saving point that money produced by a bank that earned monopoly profits would also be net wealth even if it weren't backed by gold)."

Suppose the Fed were privatized. This would convert the currency monopoly into money. If the Fed then paid out this money to the government as a dividend, it would have a money liability that offset the currency monopoly asset. The national debt would be reduced, but the government is no better off.

[Nick Rowe]

Max: true. But if the newly-privatised monopoly central bank then permanently increased the money supply beyond what had been expected when it was privatised, the owners of that bank would be wealthier.

[Roger Gomis]

(Reviewing the post I have seen the terrible grammatical/spelling/etc mistakes, I apologize for any remaining error)

Nick: Yes the reaction function that you state is much more intuitive and simple to interpret. I agree that the BK conditions reasoning sounds odd when thinking about the economy.

For point 2, this interpretation is similar to yours: For some reason (before the CB acts) Y is larger than Y* the CB raises the real rate so the agents have two options (In fact they have all combinations between the 2 but is useful to ignore it) either lower C(t) or increase C(t+1), if they increase C(t+1) the CB will increase the real rate in the next period, again the agents have two options decrease C(t+1) or increase C(t+2), and so on. The agents know therefore that they will have to increase consumption to infinity, but they cannot do that due to their inter temporal budget constraint, or any other reason(like nature). Thus their reaction must be to lower C(t) when the real rate increases.

For point 1 I would say that it is not a harmful assumption that the consumption in real terms cannot explode, rather it reflects a physical or budget constraint that a forward looking consumer will take into account when he sets the optimal consumption plan.

Of course this reasoning does not resemble any reasonable behavioral approximation, and I am sure that a better model of the economy would have to include another mechanism (although I am not convinced that it is the Pigou effect).

But in my opinion, almost all equilibrium models with rational expectations have this same taste. In particular equilibrium seems to immediately and automatically arise without any mechanism that pushes to that equilibrium, other than the assertion that other solutions are not an equilibrium.

PS: The argument of the CB threat might be more interesting to consider in an OLG model.

[Nick Rowe]

Roger: "...but they cannot do that due to their inter temporal budget constraint,..."

Hang on. Each individual agent has an intertemporal budget constraint, and cannot have a present value of consumption greater than the present value of his income. But for the economy as a whole it doesn't work like that. Starting with Y(t) below Y*(t) for all t, if C(t) increases by $1 for all t, then Y(t) increases by $1 for all t too.

Now ultimately there is a resource constraint that prevents Y(t) going to infinity, and you would just get shortages and queues if people tried to go there, so Y(t) would not rise with C(t) past that point. (Maybe that's what you had in mind). But there is nothing to prevent Y(t) and C(t) falling to zero.

[Frank Restly]

Ashok,

"The increase the real value of the stock of money [implies that for each] gain of money holders there corresponds an equal loss of the bank debtors."

Only true if the increase in the real value of the stock of money is caused by an increase in the demand for money over goods (increase liquidity preference).

If the increase in the real value of the stock of money is caused by an increase in productivity then this implication does not hold true.

With higher productivity more goods are produced for the same amount of debt and liquidity preference falls to absorb these additional goods - Nominal GDP stays the same, prices fall, quantity sold rises, nominal debt is serviced from nominal GDP.

[Max]

The point I was trying to make (rather badly) is just that the value of the currency monopoly isn't infinite, it's the present value of future seignorage profits, the value of a central bank as a business. You can put a number on it (ok, there's uncertainly, but still).

If a central bank did a "helicopter drop" that exceeded this value, then it would be insolvent (holding the price level constant). The price level would have to rise. Below this value, the price level doesn't have to rise.

Likewise if the price level fell too much, the central bank would be insolvent. And the demand for the liabilities of an insolvent bank is surely small (if not zero), so the Pigou effect never has a chance to operate.

[Nick Rowe]

Roger: "PS: The argument of the CB threat might be more interesting to consider in an OLG model."

Samuelson 1958 is the ur-OLG model, and I alluded to it in the post. There is something in that model Samuelson calls "money", but its only role is as an intergenerational savings vehicle. People only hold "money" as a store of wealth. And what makes the price level determinate in that model is precisely a Pigou effect. (It is a pure fiat money in fixed quantity and no "backing" whatsoever.)

[Nick Rowe]

Max: "If a central bank did a "helicopter drop" that exceeded this value, then it would be insolvent..."

I disagree. If the central bank pays 0% (nominal) interest on its currency, and is never under any obligation to redeem its currency, it can never be insolvent. Simply because someone who never owes anyone anything can never be insolvent.

(If it wanted to maintain some inflation or price level target it might become insolvent if it does too big a helicopter and had to subsequently buy back currency to hit its target.)

[Max]

In what non-totalitarian system can people be forced to hold a pure bubble money? Why wouldn't entrepreneurs demolish the demand for such a lousy money?

[Alex Godofsky]

Nick is assuming no one ever just drops their money on the ground and abandons it.

[Nick Rowe]

Max: It's the world we live in. Yes, we can imagine competition would either eliminate the demand for government's currency, or force the government to pay interest, but it hasn't happened yet. (Maybe because of legal restrictions, or maybe because it's a natural monopoly, but that's a side question.) So bubble money is valued, and it's useful because it's valued, and valued because it's useful, and nobody drops it on the ground.

[Roger Gomis]

Nick: You are right, I need to use a physical constraint at some point and of course this does not bind for consumption falling to zero.

However,couldn't we rule it out by plain maximization? We have two consumption paths that obey the Euler equation (given the kind of policy rule that you mentioned). 1) We have a plan that equates consumption to potential output every period. 2)We have a path that starts below potential output, and takes a exponential decay to zero. Thus plan 1 strictly dominates the 2nd. Each individual agent will never choose the inferior plan and the economy will not collapse.

Anyway I'm not sure, because nobody told me that the NK assumptions weren't enough to make the Euler equation a sufficient condition.

[Frank Restly]

Max,

"In what non-totalitarian system can people be forced to hold a pure bubble money? Why wouldn't entrepreneurs demolish the demand for such a lousy money?"

Imagine a monetary system where money has a fixed life span determined by the central bank. Currency has an expiration date. The central bank is not in a technical sense redeeming the currency when the currency reaches end of life.

Alex,

Nick is also assuming that the central bank creates money that has an infinite life - $1 created today is the same as $1 created 100 years from now.

[Alex Godofsky]

Frank:

That happens to be a pretty good description of the world we live in, so I'm not sure why it's notable.

[Frank Restly]

Alex,

Credit based money can contract as well as expand.

[Alex Godofsky]

The central bank doesn't create credit based money. The dollars that the central bank produces really are identical between cohorts, modulo wear-and-tear on actual paper.

Why are you still talking about this? It is completely irrelevant to Nick's point, and a blatant attempt to hijack his discussion.

[Nick Rowe]

Frank: stop now please.

Roger: "Each individual agent will never choose the inferior plan and the economy will not collapse."

He wants everyone else to choose full-employment consumption, and if he expects them to do that, he will too. But if he expects everyone else to choose the inferior plan, so will he.

It needs someone to step in and say "We have nothing to fear except fear itself. All together now, on the count of three, we will all start spending more and earning more." A conductor of the orchestra to get them all to speed up the tempo. Or someone to announce higher NGDP target. Or a Pigou effect.

Formally, the game is staghunt.

[Max]

We live in a world of floating exchange rate money, not a world of irredeemable money. They aren't the same thing.

What is stopping Canadians from switching to the U.S. dollar, causing hyperinflation (regardless of interest rate)? More than inertia - the central bank won't allow it. If they had to, they could and would peg the currency to stop an inflation. They have both the ability and the will. Hence the money has, as they say, a firm foundation of value; it's not a bubble. It's a redeemable money.

[Nick Rowe]

Max:

We have learned from experience that there is an incredible amount of ruin in even a really crappy currency. Witness hyperinflations. It takes massive money growth before people abandon a currency altogether.

It is *fixed* exchange rates that would make money redeemable, because the Bank of Canada would promise to redeem its currency for US dollars at a fixed price. So if it exogenously printed more Canadian dollars, the exchange rate would depreciate, unless it immediately bought them all back again.

[Max]

"It is *fixed* exchange rates that would make money redeemable, because the Bank of Canada would promise to redeem its currency for US dollars at a fixed price."

Yes, but redeemability is defined by whether the bank could and would fix the exchange rate, not whether the exchange rate is currently fixed.

[Greg Hill]

Great post Nick. Wouldn't the Fisher effect dominate the Pigou effect under plausible assumptions?

[Matthew]

I was thinking about this issue some more.

First point: Im not sure what you mean when you say the canonical models don't have money. If you look at, say, Christiano Eichenbaum and Rebelo (2011), which is about as canonical a paper I can think of for recent New Keynesian theory, there is money in the utility function, which relates money to interest rates and prices, as well as a taylor rule that implicitly defines monetary policy in terms of interest rates, the output gap, and prices. The actual open-market-operations that the central bank uses to set nominal interest rates is not explicitly modeled in the paper, but that is just because it is trivial to the model, not because it doesn't exist (ie, you could solve for the time-path of money supply, if you wanted).

Second point is that I think a couple of papers on "expectations-driven" equilibria have essentially already examined this issue, though they did not make explicit reference to the pigou effect. Benhabib, Schmitt-Grohe and Uribe (2001) explore multiple expectations-driven equilibria in a non-linearized New Keynesian model. This may not seem to have a direct relationship to what you are saying, but in fact it is the process of linearization that forces us to assume reversion around a fixed steady state. More recently, Mertens and Ravn (2012) have adapted a similar framework to show a permanent liquidity trap can arise when policy thwarts expectations of returning to steady state. Both models stay within the liquidity trap framework, which is appropriate because in the absence of a liquidity trap, the central bank can use monetary policy to thwart expectations of these undesirable alternate equilibria--do the extent that the central bank fails to do so, it is simply replicating liquidity trap conditions, even if it is not at the zero lower bound.

As a final note, I think Krugman is playing a slight of hand here (I don't think its deliberate, he just sees it through a different filter). Krugman claims there was "no role whatsoever" for the pigou effect in his 1998 liquidity trap paper: http://www.brookings.edu/~/media/projects/bpea/1998%202/1998b_bpea_krugman_dominquez_rogoff.pdf I don't think this is true. In the flexible price part of the paper, output does not fall in a liquidity trap. Krugman argues that this is only because a fall in prices generates expectations of future inflation (the assumed trend-reversion Nick mentions), not because of the pigou effect. However, an equally valid way of seeing this is that the central bank is only capable of "reflating" the economy in the future because the pigou effect keeps the flexible price economy at full employment/output. So far, Krugman's much more recent paper on debt deflation http://www.princeton.edu/~pkrugman/debt_deleveraging_ge_pk.pdf is the only New Kenesian model I know of that exhibits the "paradox of flexibility" where falling prices does not incrementally return us to full employment. But I'm not so sure Krugman isn't still relying on a Pigou effect in that paper, even if it never gets realized. That's because Krugman needs expectations of trend-reversion (ie, a pigou effect) to subvert the possible multiple equilibria discussed in Mertens and Ravn. This trend reversion expectation never gets realized because deflation actually shifts the demand curve backwards due to magnification of real debt obligations. The problem, though, is that if expectations shift so that people now believe in a permanent liquidity trap, then the comparative statics all get reversed: fiscal stimulus is actually contractionary.