Paul Krugman, Ricardian Equivalence, and the Pigou effect

If I produce a car, and sell it, and undertake no obligation to service that car (by changing the oil), and undertake no obligation to buy back that car, and if nobody can sue me if that car goes wrong, then that car I have produced and sold is not one of my liabilities. That's why we don't list "cars sold and now owned by the public" under the liabilities section of a car producer's balance sheet (though we might list service obligations or lease buyback obligations or legal liabilities if the cars turn out to explode on impact).

If I discover a way to produce cars for free and sell them at a good price (maybe because I have a monopoly on producing cars) we still don't list the cars I have produced and sold as my liabilities.

Even if I give some of those cars away for free we still don't list the cars I have produced and given away as my liabilities. Every car I produce for free and give away is added to the wealth of the lucky person who gets it, but isn't a liability to me, so it's net wealth for the economy as a whole.

If something causes the cars I have previously produced for free and sold or given away to go up in value (because they suddenly start performing better) the wealth of the owners of those cars goes up, but my liabilities do not go up, so that is an increase in the net wealth of the economy as a whole.

It's exactly the same if we replace "cars" with "$20 notes". Provided the central bank that produces those notes undertakes no obligation to service them (by paying interest) or buy them back (replacing torn notes with a costlessly-produced new note doesn't count). That's why, under those conditions, we should not list "notes sold and now held by the public" under the liabilities section of the central bank's balance sheet. (Yes, I know lots of us economists do just that, but we are generally wrong to do just that; see my old post.)

Central bank money (or any money produced by a producer who earns monopoly profits from producing money) is net wealth. A permanent increase in the stock of that money, at the existing price level, increases net wealth. Call that "the money-wealth effect". A permanent fall in the price level, with no permanent change in the stock of that money, increases net wealth. That last thing is called "the Pigou effect".

Under those conditions central bank money is net wealth even if Ricardian Equivalence holds for government bonds so bonds are not net wealth. If those same conditions held for bonds too (they might or might not) then government bonds would be net wealth too (and Ricardian Equivalence would be false). For example, if a government could sell bonds at a rate of interest below the permanent nominal growth rate of the economy (this is generally true for money but may or may not be true for bonds) then the government could sell bonds, issue new bonds to pay the interest on the old bonds, roll over the bonds forever, and the debt/GDP ratio would still fall over time, so the government need never increase future taxes.

Paul says that in his model he found no role for a money-wealth or Pigou effect, because the Euler equation pinned down current consumption as a function of future consumption and the real rate of interest, and future consumption is pinned down by future full-employment output, when the economy eventually returns to full employment. But that does not mean there is no money-wealth or Pigou effect in his model. (The Euler equation basically says that the ratio between the marginal utility of current and future consumption equals one plus the real interest rate.)

The money-wealth or Pigou effect means an increase in net wealth. Consumption-smoothers (like in Paul's model), seeing an increase in net wealth, will plan to spread their increased consumption over all current and future periods, to satisfy the Euler equation. They plan to consume more than their income from production. But agents with rational expectations (as in Paul's model) will figure out that if all agents plan to do this (as they will in a representative agent model like Paul's) then, in each period, either production will rise to match increased planned consumption, or else the price level or real interest rate will rise to reduce planned consumption to match production. So the variables in the Euler equation will change because of the money-wealth or Pigou effect. In Paul's model, since production can rise in the current period, but not in any future period (when it's back at full-employment), what happens when there is an increase in net wealth is that the curent price level stays the same and production increases, the future price level rises for all future periods, which means the current real interest rate falls (nominal interest rate stays constant because it's at the ZLB), and all future real interest rates stay the same.

In other words: Paul's dichotomy between the money-wealth or Pigou effect and the Euler equation is a false dichotomy. The money-wealth or Pigou effect tells us that planned consumption will increase sometime, but the Euler equation tells us when that increase will happen, and the money-wealth or Pigou effect, plus the rest of the model, tells us what happens to the variables in the Euler equation. In Paul's model it will happen in the current period, which is exactly when you want it to happen, because his economy is in recession in the current period.

(In fact, if the infinite-horizon Euler equation is true, since it tells us that the real rate of interest only affects the ratio between current and future consumption, cuts in real interest rates are totally useless as a cure for permanent deficiences in aggregate demand. But that's a whole other story, that creates a massive difference between Old and New Keynesians. The Neo-Wicksellian/New Keynesians just assume that people expect the economy will eventually return to full employment, but have no mechanism whatsoever to justify that expectation, even if we ignore the effect of deflation and the ZLB. It's the New Keynesians who really really need a Pigou effect to make their models work, but it's definitely not in their Neo-Wicksellian models.)

Here's the long but relevant quote from Paul:

" Looking at Japan in 1998, my gut reaction was similar to those of today’s market monetarists: I was sure that the Bank of Japan could reflate the economy if it were only willing to try. IS-LM said no, but I thought this had to be missing something, basically the Pigou effect: surely if the BoJ just printed enough money, it would burn a hole in peoples’ pockets, and reflation would follow.

But what I did was a little different from what the MMs have done this time around: I set out to prove my instincts right with a little model, a minimal thing that included actual intertemporal decisions instead of using the quasi-static IS-LM framework. [If you have no idea what I'm talking about, you have only yourself to blame -- I warned you in the headline]. And to my considerable surprise, the model told me the opposite of my preconception: there was no Pigou effect. Consumption was tied down in the current period by the Euler equation, so if you couldn’t move the real interest rate, nothing happened.

One way to say this — which Waldmann sort of says — is that even a helicopter drop of money has no effect in a world of Ricardian equivalence, since you know that the government will eventually have to tax the windfall away. Of course, you can invoke various kinds of imperfection to soften this result, but in that case it depends very much who gets the windfall and who pays the taxes, and we’re basically talking about fiscal rather than monetary policy. And it remains true that monetary expansion carried out through open-market operations does nothing at all.

In the simple model, the only channel through which money can operate when you’re against the zero lower bound is by changing expectations of future inflation. And that’s hard to do."

Whether the Pigou effect is a strong enough force to matter is another question. Go read my previous post.

Now, please can I go to bed?

Update: I am remiss in not HTing Ashok Rao, both for his post, and for reminding me of my old post.

Comments

[Ashok Rao]

Nick, I'd written about this a few days back and wanted to forward my thoughts to you, but looks like you've reached a similar conclusion (http://ashokarao.com/2013/08/11/an-inquiry-into-the-efficacy-of-ricardos-helicopter/):

"A common refrain across blogosphere holds that Treasuries are effectively high-powered money at the zero lower bound. There is a cosmetic difference – redeemability – that plays in important role within the highly stylized, unrealistic, thought experiments that are representative agent models.

Fiat money is a final transaction. Even when the coupon rate is zero, the principal on the outstanding liability must be “redeemed” by the government. Therefore, outstanding government debt does not constitute net wealth in either the government’s or household’s budget constraint.

I’ve been toying with this distinction in my head for a while now, but Willem Buiter got there almost a decade ago. In this little-cited (according RePEc it has only self-citations, which is odd given the important result) paper, Buiter shows that a helicopter drop does not function as a tax cut. The result derives from the pithy, contradictory, but fair assumption that fiat monies are are an asset to the private holder but not – meaningfully – a liability to the public issuer.

Therefore, an dissonance between the household and government perception of the net present value (NPV) of terminal fiat stock results in discordant budget constraints in the model. In this sense, the issuance of money can increase the household’s budget constraint in a way open-market operations cannot, increasing consumption and transitively aggregate demand. (For those interested, the math is presented in the previously linked paper as well as, in better font, this lecture). The so-called “real balances effect” is, for lack of a better word, real."

And:

"It’s crucial to note this argument – while relevant to rational expectations – has nothing to do with Ricardian Equivalence. In short, the government may want to do any number of things with the issuance of fiat currency – like a future contraction – but it is not required under its intertemporal budget constraint to do anything. This is fundamentally different from the issuance of bonds where the government is required to redeem the principal even at a zero coupon rate. Therefore, in the latter scenario, Ricardian Equivalence dictates that deficits are not expansionary."

I find this to be a conversation where accounting identities – like central bank liability – create great confusion.

[Ashok Rao]

Here's my question. In Krugman's argument a helicopter drop of government issued bonds would be formally equivalent (today at the ZLB) to a helicopter drop of central bank issued fiat currency.

While the public may have any sort of expectations about future contraction that effect the viability of the latter; there is a Ricardian constraint on the former that guarantee debt neutrality.

I hope my post made sense, I was thinking very much on these lines.

[Nick Rowe]

Ashok: I had read your post, and am guilty of not HTing you (I've updated to do so). My excuse is lack of sleep. I think we might be on the same page, but I'm too tired to be sure.

[K]

I don't know if this was written in response to my comment on the previous post (and if so, I sincerely apologize for preventing you from going to bed !!?!). However, I think you may have unnecessarily delayed your nap, as I'm not sure that we disagree. When I (and I suspect also Krugman) refer to the Pigou effect, I mean the effect of a *current* expansion of money. IIRC, Pigou '42 really doesn't distinguish between different time periods, which causes significant confusion regarding *which* rate, exactly, it is that is non-zero. Krugman clarified that what's needed is a monetary expansion *in the period in which the short rate is non-zero*. If we are currently at the ZLB, that means we need a forward monetary expansion. I suppose this is what you call the Pigou effect (and I agree it's weak), but it's not at all clear to me that that was what Pigou was talking about (I don't think it was clear to him).

Unfortunately I don't think Krugman went quite far enough in elaborating the mechanism of his model. What he should point out very loudly, is that the forward monetary expansion works exactly via the reduction in forward nominal interest rates (resulting in current inflation via the expectations channel). Or equivalently:

*CONTINGENT ON THE TERM STRUCTURE OF INTEREST RATES, THE QUANTITY OF MONEY, PRESENT OR FUTURE, IS IRRELEVANT*

So QE doesn't do anything *unless* it has some kind of consequences for a forward monetary quantity, and therefore a lower forward rate during a forward period in which the short rate is not currently expected to be zero.

Ashok Rao,

Helicopter drops work, as Krugman says, if agents are not Ricardian. This is not disputed. The question is regarding the effectiveness of OMOs. (i.e. the thing that CBs are actually able to do).

[Ashok Rao]

Nick, ah, got it, no need for apologies!

What I find is the most convincing argument for helicopter drops is that government can use it to purchase real services. Either this results in inflation (yay!) or it doesn't. In the latter case, if direct monetization doesn't result in inflation – and yet we've financed real government purchases like bridges or whatever – we've found a way to get something for nothing. In other words, inflation is a necessary by product of the No Free Lunch axiom.

K, in a – as Krugman puts it – "Ricardian World" debt financing is neutral, but helicopter drops are not. The whole point of my post was that even in the Ricardian world money is a net asset on part of the holder without being a liability on part of the issuer. So whether agents are Ricardian or not is completely irrelevant.

Of course, whether agents are Ricardian or not is irrelevant for the more basic reason that if the government sends $1000 to each citizen, savings are not going to increase by $1000 per capita. I will buy that MacBook, I promise.

[Ron Ronson]

Can I clarify my understanding?

Krugman is saying that if people get new dollars in a recession they will feel wealthier but won't actually spend the new money because they know that those dollars will be taken back by the CB when the economy recovers so consumption smoothing will lead them to just save the new money.

You are saying that even if people know the dollars will eventually be taken back they will still spend more in the current period because if they have rational expectations they will know that spending the money in the present will drive up production and allow higher consumption, while not spending it in the future (when the new money is reversed out) will only prevent future inflation.

I know that's probably not quite right (I seem to be missing the role of interest rates) but I'm struggling to get my head around this.

[Ashok Rao]

Ron, there's several points Krugman might be making. He's not really "saying" anything since I highly doubt he really believes in full Ricardian Equivalence. One argument – with which Krugman fully stands – is that monetary policy (including helicopter drops, though that's a bit iffy due to quasi-fiscal effects) cannot gain traction in a liquidity trap due to contractionary expectations of future policy. You've no doubt heard this argument before.

The other Ricardian argument holds on the accounting identity that fiat currency is a liability to the Government. In a standard model where all contracts (such as debt servicing) must be held, if the government finances current purchases through deficits even at the zero coupon rate we consumers know the government must redeem the principal on the bond. Hence, we incorporate the future tax hikes necessary to cut our current consumption.

So what Krugman is saying is that monetary policy is basically like a tax cut. But what we're arguing is that fiat currency is net wealth (unlike bonds). That is to say, the face value on the $20 or $100 dollar bill is irredeemable. Therefore, since it is an asset to the private holder but not in any real sense a liability to the public issuer, if the government can change the NPV of terminal money stock, it can increase consumption by asymmetrically increasing the household's intertemporal budget constraint without messing with the government's intertemporal budget constraint.

Now, this doesn't mean monetary policy is effective, per se. Even in Ricardian Equivalence conditions, a market can expect a future contraction in monetary stock. The key is to change the NPV of terminal base. Krugman agrees with this and hence my disagreement is cosmetic. The only stylistic, but still interesting, tension is that Ricardian Equivalence has nothing to do with the efficacy of monetary policy.

I hope that makes sense. Here's a lecture that may interest: http://www.willembuiter.com/hahn.pdf

[Andy Harless]

This begs the question of why people are willing to accept money in the first place. In a world of rational agents that expect one another to be rational, I don't think liquidity value is enough, because the liquidity value depends on starting out with some fundamental value that gets people to accept it in the first place. My understanding is that, in standard models, this problem is solved either by declaring money legal tender for payment of taxes or by assuming future government surpluses that will absorb the outstanding money. But then money is not net wealth. I don't think there's an easy way to get money to be net wealth while maintaining rational expectations.

[James Hudson]

“A permanent increase in the stock of [central bank] money, at the existing price level, increases net wealth”—but there’s some sort of *ceteris paribus* clause implicit here. It is explicitly stipulated that prices do not change, but must there not be other events or processes, taking place elsewhere in the economy, in order to keep prices steady while the stock of c.b. money underwent a permanent increase, events that would entail changes in some economic variables? So what is being held constant, and what is being allowed to vary (between *ante* and *post* the c.b. increase in the stock of money), in the assertion that the increase in money would increase net wealth?

“Now, please can I go to bed?” This is a wonderful post; you’ve earned your rest, and our thanks!

[Alex Godofsky]

@K

*CONTINGENT ON THE TERM STRUCTURE OF INTEREST RATES, THE QUANTITY OF MONEY, PRESENT OR FUTURE, IS IRRELEVANT*

So QE doesn't do anything *unless* it has some kind of consequences for a forward monetary quantity, and therefore a lower forward rate during a forward period in which the short rate is not currently expected to be zero.

IOW, what Scott Sumner has been saying all along: temporary expansions in the monetary base do nothing, permanent expansions are very powerful.

[Matthew]

"It's the New Keynesians who really really need a Pigou effect to make their models work" --Good point.

On the issue of central bank liabilities, actually dollars are a central bank's liabilities in a very technical sense--the central bank technically has a legal obligation to repurchase as many dollars as the public wants to sell to them. The caveat is that, ever since the demise of the gold standard, the bank has been allowed to use other dollars to make the purchases.

[Steve Roth]

@Nick: "if the government sends $1000 to each citizen, savings are not going to increase by $1000 per capita. I will buy that MacBook, I promise."

Of course they will. Your $1000 can be passed on twenty times, or you could just hold on to it. At the end of the period, your $1000 will be in somebody's bank account. There will be a larger stock of "money savings" held by the real sector.

(Unless people use those $1000s to pay off their credit-card debt. Use their debit cards instead of their credit cards.)

Of course this gets back to that whole "eradicate 'saving'" thing, which you know I agree with, and which I won't re-enter here...

[Frank Restly]

Nick,

"Provided the central bank that produces those notes undertakes no obligation to service them (by paying interest) or buy them back (replacing torn notes with a costlessly-produced new note doesn't count). That's why, under those conditions, we should not list "notes sold and now held by the public" under the liabilities section of the central bank's balance sheet."

Not sure about Canadian notes but each and every Federal Reserve Note has the following words printed on it:

"This note is legal tender for all debts public and private"

Meaning that the Federal Reserve (or any other bank) cannot lend out dollars and then demand repayment in some other good (gold?) to satisfy the conditions of the loan. Hence, federal reserve notes are liabilities of the Federal Reserve in the sense that the Federal Reserve must accept them back when a loan is retired.

[Nick Rowe]

K: "*CONTINGENT ON THE TERM STRUCTURE OF INTEREST RATES, THE QUANTITY OF MONEY, PRESENT OR FUTURE, IS IRRELEVANT*"

Replace "quantity of money" in that sentence by "wealth". If an increase in wealth is relevant, contingent on the term structure of interest rates, and if money is net wealth, which I have shown it is, then the quantity of money is relevant.

Matthew: thanks! I'm really pleased you got that point. It took me a long time to figure it out.

Ashok: I have read a similar paper (it might have been that same paper you link to) by Willem Buiter in the past, and I think I'm saying the same thing as Willem about the Pigou effect. My "money is net wealth" argument goes back to the Pesek and Saving book he references. Where I maybe disagree with you is on Ricardian Equivalence. Under the same conditions under which money is net wealth, if those same conditions apply to bonds (they often do but are less likely to) then bonds are net wealth too. So we are mostly on the same page, but not totally.

Ron: "Krugman is saying that if people get new dollars in a recession they will feel wealthier but won't actually spend the new money because they know that those dollars will be taken back by the CB when the economy recovers so consumption smoothing will lead them to just save the new money."

It isn't fully clear to me what PK is saying about whether people expect the dollars will be taken back. He does say "One way to say this — which Waldmann sort of says — is that even a helicopter drop of money has no effect in a world of Ricardian equivalence, since you know that the government will eventually have to tax the windfall away." but it simply is not true that the government will eventually have to tax the windfall away. That is true for bonds, provided the rate of interest exceeds the growth rate of nominal GDP. But it's not true for money.

[TallDave]

"Hence, federal reserve notes are liabilities of the Federal Reserve in the sense that the Federal Reserve must accept them back when a loan is retired."

OTOH the Fed doesn't have to loan anyone money. I mean, it does lend obviously, but it can also buy assets (or just print money and give it to the government) and it never has to accept those dollars back.

[Max]

Would it be correct to say that monetarists must believe that money is net wealth, because otherwise the value of money could not be determined from the quantity? And therefore, "freeze the base" (and variations, like increase by x%/year) would not be a viable monetary policy.

[Ron Ronson]

I looked more closely at Krugman's views.

When he says that to get out of liquidity trap the CB must "commit to be irresponsible" then what he means is that at the ZLB no amount of monetary policy will work directly to boost AD. However if the CB increases the money supply in the present and commits not to remove this new money in the future when the economy has recovered then there will be inflation in that future period. Anticipation of this future inflation will then cause interest rates to rise in the present and allow normal interest rate policy to work again.

This seems like a very tortuous transmission mechanism.

Why can't CB instead just commit to keeping NGDP steady between the current period and the future period? If the economy gets into a recession it is because NGDP has fallen and on average people's income must have fallen too. People know that eventually the economy will recovers so future real income will be higher than current real income. Based on the CB's NGDPT commitment they know that the money supply will increase in the short term (to address the NGDP shortfall) and then as the economy recovers the money supply will likely be reduced again. This likely future contraction should not prevent increased spending in the present out of the new money however. As rational agents they know that they can spend some of the new money now (consume more than current income) because in the future they know that their income will be higher than in the present. The desire to consumption smooth will mean that recipients of new money will likely spend some of it because they have good reason to think that their present income is below their future average income.

So the CB does not need to commit to be irresponsible but merely to commit to be completely sensible and predictable for monetary policy to work.

(If the money supply is increased by helicopter drops rather than asset purchases then these might indeed need future tax increases to reverse out - but again as long as these reversals done as part of NGDPT this should not affect future income)

[Nick Rowe]

Max: no, that would not be correct. The wealth effect from an excess supply of money (the Pigou effect) is only one force for making the price level determinate (and not an especially strong force at that). The substitution effect from money into *all* other goods (not just bonds) will be a stronger force.

[Nick Rowe]

James Hudson: thanks!

"but there’s some sort of *ceteris paribus* clause implicit here. It is explicitly stipulated that prices do not change, but must there not be other events or processes, taking place elsewhere in the economy, in order to keep prices steady while the stock of c.b. money underwent a permanent increase, events that would entail changes in some economic variables?"

What we are trying to do here is to elucidate one of the forces that would cause the price level to go up (or output to go up). So we *provisionally* assume the price level (and output) is unaffected in all periods, then show that *if* that happened there would be an excess demand for goods, and then conclude that therefore the price level (or output) *would* go up, so that our provisional assumption would be false. It's like an argument by reductio ad absurdam, where you make an initial assumption and then derive a contradiction, in order to prove that your initial assumption must be false. Don Patinkin called it a "stability experiment", as opposed to an "equilibrium experiment".

[Andy Harless]

Nick: (from your last response to Ron)

"it simply is not true that the government will eventually have to tax the windfall away. That is true for bonds, provided the rate of interest exceeds the growth rate of nominal GDP. But it's not true for money."

If the growth rate is expected to be positive into the infinite future, then money is like a zero-interest bond, so the government can avoid taxing the wealth away, since its value becomes vanishingly small relative to the government's revenue. However, suppose that growth eventually ends. (I think this is an implication of the laws of thermodynamics, at least under some plausible cosmologies.) In that case the value of money doesn't become vanishingly small relative to the government's revenue, and it does have to tax away the wealth. If the world is going to end some day, nobody will be willing to hold money on the day the world ends, and by induction, the government will have to have taken it all out of circulation before that day in order for it ever to have had any value.

[K]

"I agree that with downward nominal price or wage rigidity... then we are unlikely to see the price level falling to near zero, but instead we would see real GDP fall to near zero instead, if the money supply fell to near zero"

But why would you assume the collapsing money supply? If prices are super-sticky downwards, the Fisher effect is inoperative, and you don't get the upward accelerating real rate. So you don't get accelerating collapse of output either. The real rate stays fixed, but too high because of the interest rate ZLB. If prices are really stuck, only bankruptcy and capital destruction can save you. But only if those things destroy supply faster than they destroy demand. Who knows???

[Nick Rowe]

Andy:

Oh dear. Can my poor brain handle the economics of infinity?

1. If people know in advance the date at which the world will end, and if the government didn't buy back that money as that date approached, I think fiat money would collapse backwards. But they might not know that in advance, or the velocity of circulation and the price level might approach infinity asymptotically in a continuous time model.

2. Even if the Bank of Canada will buy back all the money at some known future date T, money would still be net wealth, though not 100% net wealth, if r is less than n before that date, and T is in the future. And in the limit, as T approaches 2013 plus infinity, money approaches 100% net wealth. It's like an interest free loan of $100 that won't be repaid for a long time. It's worth less than $100, but more than $0, and it's worth closer and closer to $100 the longer you can postpone repayment.

[K]

Nick,

"If an increase in wealth is relevant, contingent on the term structure of interest rates, and if money is net wealth, which I have shown it is, then the quantity of money is relevant."

Yet you can't increase M out beyond the end of the ZLB without lowering future interest rates in that period. So you cannot increase wealth contingent on the term structure of interest rates, using your method. Like Andy says, I don't see how you can do this without a proper intertemporal analysis, like Krugman '98, or even better Eggertsson and Woodford 2003.

Let me quote the latter:

"This proposition implies that neither the extent to which quantitative easing is employed when the zero bound binds, nor the nature of the assets that the central bank may purchase through open-market operations, has any effect on whether a deflationary price-level path will represent a rational-expectations equilibrium. Hence the notion that expansions of the monetary base represent an additional tool of policy, independent of the specification of the rule for adjusting short-term nominal interest rates, is not supported by our general-equilibrium analysis of inflation and output determination."

Since we can (and have in the past) talk in circles about this indefinitely, maybe we can make it more concrete here. Are you saying that even if the central bank had perfect power to make commitments on forward rates, there'd still be more they could do by manipulating real balances via the money supply? If so, what specifically do you think is wrong with that paper?

[Frank Restly]

Nick,

"That is true for bonds, provided the rate of interest exceeds the growth rate of nominal GDP. But it's not true for money."

It's not even really true for bonds. Governments can experience a cash flow crisis but never a solvency crisis. The tax revenue used to service debt (make interest payments) can come from any future point in time. Meaning that a government can limit the amount of tax revenue used to service debt in any one year by altering the time over which it makes those payments.

[Nick Rowe]

K: "Yet you can't increase M out beyond the end of the ZLB without lowering future interest rates in that period."

Yes you can. You can do it both as a stability experiment (see my comment in response to James above), by helicopter, where helicopter money is equivalent to OMO (is equivalent to the Pigou effect in real terms) in a world of Ricardian Equivalence (like Paul's model). And you can do it as an equilibrium experiment, because in Paul's model a permanent increase in M will have no effect on interest rates (nominal or real) in periods past the ZLB period. The increase in M just increases P in those future periods.

I would have to re-read Eggertson and Woodford to refresh my memory, but I suspect that their paper is exactly one in which my digression above about Neo-Wicksellian models *assuming full employment*, even when not constrained by the ZLB, would apply. That aside, it is perfectly true that in (e.g.) Paul Krugman's model, which does contain a money-wealth effect, that money-wealth effect would imply a higher future price level, and you could in principle solve the model for the implied Tayloresque Rule for the nominal interest rate that would support that same higher future target price level as an equilibrium path, and the *equilibrium* time-path of nominal interest rates under that rule would be identical to the equilibrium time-path with helicopter money doing the same thing. In other words the same effect could be acheived of raising the future price level by *threatening* to hold nominal interest rates "too low for too long" unless the price level hits the higher future target, but if that threat is credible, a la Chuck Norris, it would never need be carried out.

[Mike Sproul]

The car you built is not your liability, and neither is gold you might have dug out of the ground. But if I write up a piece of paper that says "IOU 1 car", then that IOU is my liability. If I then declare that my IOU is no longer redeemable for a car, but for a basket of goods that is worth 1 car, then the IOU is still my liability. If I stop redeeming IOU's for baskets, and instead redeem IOU's mostly for bonds, the IOU is still my liability. Same if I lend my IOU's and accept them in repayment of loans. If I accept those IOU's in payment of taxes that you might owe me, the IOU is still my liability. If I cease all possible forms of convertibility, but people still know that when I die in 200 years or so, my IOU's will constitute a first lien on my assets, then that IOU is still my liability. That's why accountants record central-bank-issued paper money on the liability side of the central bank's balance sheet.

[K]

K: "Yet you can't increase M out beyond the end of the ZLB without lowering future interest rates in that period."

Nick: "Yes you can."

Cannot! I did not say that forward rate stability was inconsistent with a *globally* higher quantity of money/price level. I said that you cannot increase M in the *middle* of a period of non-zero i, without causing a drop in i. Are you denying money demand? CBs depend on the slope of the money demand in every OMO. CB increases M, short rate goes down. And vice versa. Until we hit the ZLB, and then money demand is satiated (LM is flat), and the quantity of OMOs is irrelevant.

"That aside, it is perfectly true that ... the *equilibrium* time-path of nominal interest rates under that rule would be identical to the equilibrium time-path with helicopter money doing the same thing."

Amen! (though, I still don't know why we are talking about heli drops, since RE is by no means guaranteed. The theoretical treatment of OMOs is way more unequivocal)

"In other words the same effect could be acheived of raising the future price level by *threatening* to hold nominal interest rates "too low for too long" unless the price level hits the higher future target..."

Yes...

"but if that threat is credible, a la Chuck Norris, it would never need be carried out."

Hey, you can't cheat! If the threat is going to be effective, it will have to lower (perfectly observable) forward interest rates *right now* (if forward rates aren't lower, it's because the threat is not believed, right?). But if that meant that the threat would never have to be carried out, then there is no justification for rates being low: if I know rates wont need to be low (because Chuck!), then I can carry out arbitrage by short selling bonds, waiting for higher than expected rates to be realized. And without taking any risk (again, because Chuck).

I see what you did there though! :-) You tried to claim that it's possible to create inflation expectations without actually ever having to lower rates, and that therefore rates are an unnecessary part of policy, and therefore there is no liquidity trap, and the CB is omnipotent! Fortunately, though, I already had my nap today. Nice try!

If you agree (and I'm sure you will), I think that brings us pretty close!

[Nick Rowe]

Mike: true, but:

1. In the thought-experiment that I'm arguing about with PK, we are talking about an irredeemable fiat money where the CB is not targeting the price level. The central bank permanently increases the money supply knowing this will raise the price level.

2. Even if we do have an inflation or price level targeting central bank, so some of the money *may* need to be redeemed in future, it's an interest-free loan to the central bank until such time as it will in fact be redeemed, and an interest-free loan is a valuable asset.

3. What are we: economists; or accountants? ;-)

[Mike Sproul]

Nick:

So if the CB is targeting the price level, then you'd agree that the dollar is the CB's liability? If the CB cuts the target value in half, then the dollar is half the liability it used to be? Or, what amounts to the same thing, if the CB helicopter drops enough money to raise the price level by x%, then the dollar is x% less of a liability than it used to be? The trouble is that the dollar never stops being the CB's liability in any of those scenarios.

[Ralph Musgrave]

I agree with Bill Mitchell who described Ricardian equivalence as an idea from “la-la land”. See:

http://bilbo.economicoutlook.net/blog/?p=11757

[Nick Rowe]

Mike: If someone asks "Is money a liability of the issuer (is money net wealth)?" we don't have to give a yes/no answer. We could give a percentage as an answer, (and not just 0% or 100%), and say what that percentage depends on.

Ralph: If someone asks "Is Ricardian Equivalence true (are bonds net wealth)?" we don't have to give a yes/no answer. We could give a percentage as an answer, (and not just 0% or 100%), and say what that percentage depends on.

Ooooh! I'm feeling clever!

[Nick Rowe]

K: Money demand depends on Y and P too. In PK's model, a (small) permanent increase in Ms will cause Y to increase in the current period, and P to increase in all future periods, and leave i the same in all periods.

[123]

Nick: "Money demand depends on Y and P too. In PK's model, a (small) permanent increase in Ms will cause Y to increase in the current period, and P to increase in all future periods, and leave i the same in all periods."

This is not true if central bank is buying bonds that are net wealth to the same degree as the monetary base it issues.
For example, T-bills provide grater liquidity services than monetary base (as evidenced by lower yield of T-bills). So permanent QE based on T-bills does nothing in PK's model in the US now.

[JP Koning]

If central bank money is a liability of the issuer (I think it is), I suppose the Pigou effect could still have an effect by working through central bank money's liquidity premium, insofar as it has a liquidity premium (I think it does). While the liability itself is not net wealth, the extra bit of services it provides as a highly liquid media of exchange would be considered net wealth. The issuing central bank isn't liable for the liquidity premium, nor does it have to spend resources to create or maintain that premium as long as it has market power. But by limiting the Pigou effect to operate via the wealth embodied in liquidity premia rather than the full amount of a unit of money, the Pigou effect is somewhat stunted.

[Nick, this has to do with your caveat -- "or any money produced by a producer who earns monopoly profits from producing money) is net wealth." -- since if I recall correctly, Pesek and Savings claimed that inside money was also net wealth, as long as the issuing banks enjoyed profits due to barriers to entry. The same argument applies to "inside" central bank money.]

[Max]

A currency monopoly is a valuable asset. Any monopoly is a valuable asset. But I don't see what that has to do with the question of "what is a liability". It just means that central banks can earn abnormal profits.

[Max]

A currency monopoly is a valuable asset. Any monopoly is a valuable asset. But I don't see what that has to do with the question of "what is a liability". It just means that central banks can earn abnormal profits.

[Nick Rowe]

123: good point:

In PK's model bonds are 0% net wealth and money is 100% net wealth (for a permanent monetary increase).

In the US right now, if bonds will at some future time pay higher interest than money, which seems a reasonable assumption, then a permanent QE would still raise net wealth because money would be 100% net wealth and bonds less than 100% net wealth. I think that's right.

JP: I think that's right. And then you would also get a substitution effect in addition to the wealth effect.

Max: (don't worry about the double post, I rescued one of them from spam.)

Yes a monopoly on anything is a valuable asset. And if a monopolist increases output, wealth goes up by P-MC. (And MC is roughly zero for money). But if a firm has an obligation to buy back the goods it has produced and sold, that obligation creates a liability. So if a monopolist produced goods for free, and then sold them, but everyone knew he would buy them all back tomorrow at the same price, wealth would hardly go up at all (it's just a one day interest free loan for the monopolist's profits).

[K]

Nick,

The Krugman money model is cash in advance, i.e. agents must obtain outside money to pay for all expenditures. That means that M is a hard cap on the nominal rate of consumption, which makes things simple, but it's a silly model. Also prices are perfectly rigid in the first period, and then for all intents and purposes, flexible thereafter. So yeah, first output adjusts, then prices.

So while I think what he demonstrated is cool, I don't think there is anything to be learned from the paper about the impact of OMOs on the short rate. For that you need to look at the microstructure of money demand. I'm sure we can dig up the literature, but there is *no doubt* that CB repos and purchases *reduce* the interbank rate (unless it's already at IOR). What you are saying amounts to the claim that up is, in fact, down. Sensible models of the world we actually live in (see E&W 2003) put liquidity services in the utility function in such a way that you get a monotonically decreasing short rate as a function of M. (And then show that, conditional on the path of the short rate, said utility function is irrelevant to the macro equilibrium.)

I would really recommend rereading E&W, mostly because it includes an incredibly lucid discussion of lots of the topics in this thread (everyone who cared enough to read this post should read it). At least the discussion section 1.2, and then the model in 1.1 if still interested. It would take about 10 mins to read 1.2, and for you, probably only another 10 to read 1.1 (It's a bog standard NK sticky price + monopolistic competition model plus money).

"In PK's model bonds are 0% net wealth and money is 100% net wealth (for a permanent monetary increase)."

Away from the ZLB, the real quantity of money is fixed by the cash in advance constraint and the level of Y (which is fixed from the second period on). So more money just gives you a higher price level in the second period. So a "permanent monetary increase" creates no net wealth.

[Alex Godofsky]

@K

Away from the ZLB, the real quantity of money is fixed by the cash in advance constraint and the level of Y (which is fixed from the second period on). So more money just gives you a higher price level in the second period. So a "permanent monetary increase" creates no net wealth.

Except isn't the result that a temporary monetary increase doesn't increase Y in the first period, only a permanent one? Thus a permanent monetary increase creates net wealth - just all of the new wealth represents first period Y.

[123]

Nick,

1. It is not clear that T-bills will ever pay higher interest than money in a IOR regime, and recent regulatory changes that increase the demand for safe collateral will further increase the relative attractiveness of T-bills.

2. "if bonds will at some future time pay higher interest than money, which seems a reasonable assumption, then a permanent QE would still raise net wealth because money would be 100% net wealth and bonds less than 100% net wealth"
Yet even more net wealth would be created if QE would be postponed until the moment the relative demand for T-bills and reserves flips.

3. permanent vs. temporary distinction is a little bit misleading. Temporary increases in money supply can have a very powerful effect if they correspond to periods where money demand is elevated (see recent expansion and contraction in the ECB balance sheet). Permanent increases can have no effect if in effect you are swapping nickels and dimes as happens in IOR regime with T-bill based QE.

[K]

Alex,

Agreed. It raises first period income, and has no impact on real quantities, including wealth, beyond the first period. Honestly, it's not even really a two period model. The second period is in full equilibrium, and serves as nothing more than a boundary condition for the fixed price first period. Also, apart from the cash in advance model of money and the perfectly rigid price level, the output model is a short side rule. It's really too simple to answer questions other than the very narrow ones Krugman was addressing.

[Alex Godofsky]

Boundary conditions are important. (And in this case the importance of the boundary condition is the point of the model.)

[Nick Rowe]

Alex and K: I think you are both missing something important: the distinction between (what Patinkin called) "stability experiments" and "equilibrium experiments". See my comment to James Hudson August 12 6.11.

For example, take an economy with perfectly flexible prices at full employment, so Y is fixed for all periods. Start in equilibrium. Now *provisionally* assume prices stay the same, and permanently increase the money supply. Does net wealth increase? Yes (given certain assumptions). And that increase in wealth causes an increase in consumption demand, which causes an excess demand for goods. And that excess demand for goods would cause prices to rise. ***Which proves my provisional assumption that prices would stay the same must be false.*** (And at the new equilibrium since M and P have both increased by the same percentage, M/P has stayed the same, so net wealth is unchanged.)

[K]

Alex,

I'm not complaining about the *existence* of a boundary condition! I'm just saying, that one period is too short, and and the model is too simplistic, to examine a Fisher effect.

E&W is very similar to Krugman, except:

1) Output results from monopolistic competition in the sale of a whole consumer basket, instead of an AD/AS short side rule on a single product
2) Money demand is in the utility function rather than cash in advance (extreme credit constraint)
3) Prices are sticky, not stuck
4) The model is fully dynamic so we can observe the multiperiod impact of sticky prices
5) The boundary condition is asymptotic equilibrium, not second period equilibrium

The only criticism you can make of E&W relative to Krugman is that it uses a linearization of the price setting dynamic, but even this, is not a valid criticism in the limit that the shocks are small. I'm not sure what Nick's objection to models that don't incorporate labour market disequilibrium, but both of these models, in fact, implicitly assume flexible wages, so any criticism of E&W on that front is equally a critique of Krugman '98 (which Nick seems to think is OK). So if you accept Krugman , I don't see why you wouldn't view E&W as just a (much!) better version.

[James]

Mike Sproul:

"That's why accountants record central-bank-issued paper money on the liability side of the central bank's balance sheet".

Apparently in the US coins are treated as equity, rather than as a government liability. But they're accepted in payment by the government, so by your argument they should be a liability...

[Frank Restly]

James,

See:

http://www.treasury.gov/resource-center/faqs/currency/pages/legal-tender.aspx

"The pertinent portion of law that applies to your question is the Coinage Act of 1965, specifically Section 31 U.S.C. 5103, entitled Legal tender, which states: United States coins and currency (including Federal reserve notes and circulating notes of Federal reserve banks and national banks) are legal tender for all debts, public charges, taxes, and dues."

Meaning that lenders (including the Federal Reserve) must accept coins as payment for the settlement of debt and the federal government must accept them in settling a tax obligation. Hence, coins are still liabilities of the government because the government (central bank and tax collector) must accept them as payment.

http://www.investopedia.com/terms/e/equity.asp

In finance, in general, you can think of equity as ownership in any asset after all debts associated with that asset are paid off.

[Mike Sproul]

James:

Full-bodied coins would not be the government's liability, but modern token coins are the government's liability since, as you said, the government accepts them in payment.

[James]

Mike,

the government would also accept gold and silver coins ("full-bodied" coins") in payment when they were legal tender. Doesn't that make them government liabilities too?

[James]

The reason I said 'coins are treated as equity' is because I read that claim in this IMF paper:

'The Chicago Plan Revisited', Jaromir Benes and Michael Kumhof (2012)

http://www.imf.org/external/pubs/ft/wp/2012/wp12202.pdf

"In this context it is critical to realize that the stock of reserves, or money, newly issued by the government is not a debt of the government. The reason is that fiat money is not redeemable, in that holders of money cannot claim repayment in something other than money. Money is therefore properly treated as government equity rather than government debt, which is exactly how treasury coin is currently treated under U.S. accounting conventions (Federal Accounting Standards Advisory Board (2012))."

[Frank Restly]

Nick,

"For example, if a government could sell bonds at a rate of interest below the permanent nominal growth rate of the economy (this is generally true for money but may or may not be true for bonds) then the government could sell bonds, issue new bonds to pay the interest on the old bonds, roll over the bonds forever, and the debt/GDP ratio would still fall over time, so the government need never increase future taxes."

No. If the government can sell new bonds to make the interest payments on existing bonds then the government never has to collect any taxes - ever. If the government must make interest payments on bonds from tax receipts then the amount of interest that the government must pay is a function of both of the interest rate AND the total debt owed.

Interest Expense (IE) = Interest Rate (%R) * Total Debt Owed (D)
Tax Revenue (TX) = Tax Rate (TR) * Nominal Gross Domestic Product (NGDP)

With a growing economy:

dIE / dt = d%R/dt * D + %R * dD/dt
dTX / dt = dTR / dt * NGDP + TR * dNGDP / dt

Assuming that tax rates and interest rates are unchanged over time:

dIE / dt = %R * dD/dt
dTX / dt = TR * dNGDP / dt

As long as dIE / dt (change in interest expense with respect to time) is less than dTX / dt (change in tax revenue with respect to time) you can tack on new debt and / or roll over existing debt indefinitely.

[Ponta]

Hello there from Japan

I have missed the post. Sorry for commenting this late.

"In Paul's model it will happen in the current period, which is exactly when you want it to happen, because his economy is in recession in the current period."

I'm afraid this is different from Krugman's argument. In the Krugman's model, the future price level changes already in the PRESENT peirod. Do you agree that P2 or C2 is the stochastic variable, which depends on people's expectation, in the PRESENT time, of the FUTURE variable? Accordingly, these variables in turn have an effect on the present variable, that is, C1.

Let's check this according to the model.

(C1/C2)^(-q) = D(1+i)P1/P2

If the present price level P1 decreases, then, the current consumption C1 increases. That I suppose is what you are talking about in the post.

Krugman, too, admits this case happens. He points out, in his blog article "Mechanism and Models", that "... even in a liquidity trap, deflation could be expansionary if it is perceived as temporary, so that deflation now gives rise to expectations of future inflation."

P1 decreases and people think it is temporay, which means people expect that the future price level P2 will go up. So P1/P2 decreases and the real interest rate ( (1+i)P1/P2 ) also decreases. Then the current consumption level C1 increases.

But what if people expect that the price level keeps to be decreasing? That means that P2, which is the EXPECTATION of the future price level, will go dwon or, you might say, P1, even if it actually goes down, will go up COMPARED to P2. Then, P1/P2 will increase. That will depress the present consumpiton level C1.