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Why do you emphasize that at the *previously existing price level* for 2014 net wealth is increased? After the changes have gone into effect and new prices have emerged, wouldn't the value of central bank liabilities in the public's hands have declined so that once again no net wealth has been created?

JP: "After the changes have gone into effect and new prices have emerged, wouldn't the value of central bank liabilities in the public's hands have declined so that once again no net wealth has been created?"

Yes. (At least, in a simple model where money is neutral.)

That is what Patinkin calls an "equilibrium experminent".

"Why do you emphasize that at the *previously existing price level* for 2014 net wealth is increased?"

Because we want to explain **why** that previously existing price level (path) is no longer an equilibrium. We want to explain why there will be upward pressure on the existing price level.

We are doing what Patinkin calls a "stability experiment"

When you raise the price level (or NGDP) target, that is essentially an unanticipated one-time tax on current money holders, a transfer of net wealth from current money holders to future taxpayers. The wealth effects cancel. So I think you are correctly pointing out here that Willem Buiter and Tony Yates are both wrong to be focusing on wealth effects when what really matters is the substitution effect (away from money toward real goods and services).

Great Article.

I have a question on "We also know that the halving of Pm in 2525 will double the price level in 2525. Which in turn will increase the price level in 2524 relative to what it would have been. Because if the 2524 price level were to remain unchanged, the expected inflation rate in 2524 would increase by 100%, which would cause upward pressure on the price level in 2524. And so on, by backwards induction, all the way back to 2014."

Do you mean "expected inflation rate in 2524 would increase TO 100%"? Is the implication of this that a commitment to the doubling of the price level on 2524 will lead to a doubling in 2014, or just that prices will rise gently between now and 2525 to reach that higher level ? What would happen in the BoC said "we are committed to a stable price level between now and 2524, and 100% inflation in 2525". I assume they would (in theory) be able to meet this commitment?

Andy: I was trying to think through the wealth vs substitution effects here, and my brain gave up. But it seemed to me, that when I was doing my backward induction from 2525, I was doing substitution effects.

I think this is related to the equilibrium experiment vs stability experiment question.

My brain is not yet clear on this.

MF: thanks!

I should have said "100 percentage points". I will edit.

Whether the price level doubles instantly or slowly in 2014 and onwards depends on how sticky prices are. With perfectly flexible prices and neutral money we would get an instant doubling in 2014, and at all t from 2014 to 2525, relative to what it would otherwise have been.

It seems to me that this discussion reflects differing base concepts of money supply and base path for money creation.

Using some base assumptions, an equation between GDP, government tax rate, and money supply can be found. Derivation of the equation can be found at


In the limit, GDP = money supply / tax rate. You can see that if the tax rate is zero (which is the case if government spends all tax receipts), any money supply can support an infinite GDP. Actual GDP would depend upon the velocity of money.

The derivation of this equation and result seem to support the argument of Buiter (but I am saying that without completely reading the papers of either Buiter or Yates). The assumptions of this equation, derivation, and results could provide a reference point for this (Nick's post) and many other discussions.

Nick, Very good post. And unless I'm mistaken Andy's comment seems exactly right to me.

"Let us suppose, with Tony, that the government will eventually redeem all the money it has issued in the past, for real goods, and will re-start the monetary system anew. Specifically, in the year 2525 the government will redeem all the money at a price Pm, so every $1 will be redeemed for Pm units of real goods, and people know this in 2014."

I presume this to mean that all money will be redeemed for new real goods produced in 2525, not real goods that the government purchased and stored in a warehouse sometime in 2014. I presume also that redemption is coerced - an individual holding currency cannot refuse redemption - and people know in 2014 that this redemption will be coerced.

"What this also means is that the price of real goods in terms of money, at the beginning of 2525, will be 1/Pm, and people know this in 2014 too."

But the government does not know the quantity of new real goods available in 2525. Isn't there the possibility that the government would not be able to honor all redemptions in 2525 for the price 1/Pm set in 2014? There seems to be a government credibility problem here, unless the government is producing real goods to handle the redemptions (government ownership of means of production).

> I presume this to mean that all money will be redeemed for new real goods produced in 2525

Be careful, you're mixing units. Money is a stock, goods are a stock, production is a flow. To simplify, we can assume that produced goods have some finite and known lifespan, or that we're in an apple-economy and everything rots after a period.

> I presume also that redemption is coerced - an individual holding currency cannot refuse redemption

Or simply they credibly believe that after the redemption date, their currency will have no residual value.

> There seems to be a government credibility problem here

You can say that about any monetary system. If we were redeeming goods next week we'd find it highly credible. If we were redeeming goods in the year 102,014, we'd probably find it incredible.

Existing central banks get around that by using short to medium-term targets, no more than a few years out. The development of central bank credibility in general sounds like a very interesting field of study that I for one know little about. (The first inflation targets were controversial, after all).

Much of it seems to rely on CB methodology, such that they take actions that would result in financial losses for anyone fighting the stream. Helicopter money works regardless of whether an individual believes in it, but it works better when people do believe.

Suppose the government's only asset is a stream of future taxes receivable, which has a present value of 100 oz. of silver. The government has no liabilities, so its net worth is 100 oz. Then the government drops $40 by helicopter, promising a redemption value that yields $1=1 oz. today. Government net worth just dropped to 60 oz., while the net worth of the public rose by 40 oz. If the government helicopter drops another $60, while keeping the price target at $1=1 oz, then government net worth is zero, and the public's net worth is 100 oz. If the government helicopter dropped another $100, then the public's net worth stays at 100 oz, the government's at zero, and the value of the dollar is cut in half.

Conclusion: Helicopter drops don't affect combined net worth of the government and the public, and they only affect the price level once the government's net worth has dropped below zero.

Scott: Thanks! I think that the thought-experiment for helicopter drops is the worst-case scenario, where the economy will be stuck in a liquidity trap from 2014 until 2525. So there cannot be a substitution effect. But if the government halves Pm and doubles P in 2525, it seems we will get both a wealth effect and a substitution effect, rolling all the way back to 2014.

I'm still not sure I understand this perfectly clearly.

Mike: "Conclusion: Helicopter drops don't affect combined net worth of the government and the public, and they only affect the price level once the government's net worth has dropped below zero."

Once the price level adjusts, there is no effect on net wealth (assuming money neutral etc.) But one reason why they do cause the price level to rise is that net wealth would be increased if the price level did not rise. And the government's net worth is always zero, if we assume the government budget constraint holds.

Roger: I don't understand any of that.

OK. I now think that Andy and Scott are right.

OK. I've changed my mind again. If a financial asset trades at a price above its fundamental value, it is net wealth. And in the stability experiment, where P(2014) stays the same, but P(2525) doubles, money is trading above its fundamental value. Pesek and Saving.

Taking L for Tim Hortons and a walk, to clear my head.

I think there's a mix of effects.

The wealth effect is caused by a rational agent smoothing consumption over time: finding it has more financial resources, it seeks to consume more now and more later.

The substitution effect is caused by a rational agent smoothing the duration of its assets: it has more money now than it wishes, so it instead seeks to invest in loner-duration instruments.

If the conversion was imminent, then:

*) If the government doubled money supply but halved the conversion rate, we'd see a wealth effect. Money neutrality suggests that the true price level should double, but sticky prices and wages suggest that in the meantime we should overconsume goods that are priced below their fundamental value.

*) If the government doubled money supply but the *same* conversion rate, then the wealth effect would be "sterilized". Since production can't double in a week, to exchange money for newly-produced goods the government will be forced to levy taxes to meet its budget constraint. Most of that newly-issued money will be returned to the government to offset its printing. (To put it another way, the at-par convertibility is not credible, so the government will have to vacuum up money an instant before the conversion)

Interesting things happen when we push the redemption date out further, because now capital has time to do its thing. It's possible to react to changes in the money stock by increasing the output of real goods.

*) In the first case, not much is likely to change. A doubled money stock but halved conversion rate means that the same amount of real goods will be exchanged upon conversion. Wealth/neutrality effects are likely to prevail in the same way.

*) In the second case, *now* we see interesting things. The expected future tax burden is increased, but not by a great deal (spread over however many years). Instead of saving half of their money under the mattress, agents will seek to save somewhat less in the form of profit-bearing investments (and spend the rest). Individually, this is the substitution effect; society-wide it represents a shift in time preference.

Is this latter case stable? Probably not as specified. If it worked "in equilibrium," then the additional present consumption (as agents believed they could meet future demands partially via investment) would lead to an increase in short-term prices. Than in turn sets up deflationary expectations, since current prices would be above the conversion level.

That may be an artifact of construction, however. If the government drops or vacuums money on a regular basis, that wouldn't necessarily be deflationary. (On the other hand, we're now approaching the Fischer equation from the other side; do this on a continual basis and the nominal rate = real rate + inflation; with inflation = 0 the government seeks to set r=r')

Your model creates an increase in money supply using the method of "helicopter money". "Helicopter money" is the concept of money out of the sky, which, in turn, yields the concept that the new money is printed, not borrowed from the existing economy.

The printing of new money could be accomplished as simply as government edict to mark all accounts in cents instead of dollars. Following the printing, the yen dollar ratio would change from about 100:1 to 1:1 (yen/cent). To me, that seems to be an innocuous change.

Your model never makes assumptions of how the "helicopter money" is delivered. To my way of thinking, the path of delivery is crucial. Is every person treated the same? Is every worker treated the same? Is every saver treated the same? Is government worker treated the same as private worker? Is a city dweller treated the same as a rural dweller?

The path of "helicopter money" delivery will guide the expectations and the final result of change in money supply. Without definitions of pathway, the entire argument becomes nebulous.

Comment for Mike Sproul: What you say make sense but leads to unlikely conclusions. Say a govt is worth $1000 and issues $100 of notes (by giving them away) each of which it will redeem for a certain bundle of goods. The bundle of goods would be worth 10% of the govt assets. If I understand your logic you are saying that if they then issues (by giving away) another $900 of notes each redeemable for the same bundle of goods this will not be inflationary since the assets of the govt will be exactly matched by the notes it has issued.

My problem with this logic is that when the second set of notes is given away people will be holding more notes than they wish to hold and will try to spend them on goods, which will increase the price of goods. This may cause the value of the notes to fall below market value of the bundle of goods and people will start redeeming them , and will continue to do so until the notes are again valued the same as the bundle of goods.

In other words when the govt issues notes valued and redeemable against an external measure (like a unit of precious metal or a bundle of goods) then it is limiting itself to the qty of these notes in away that is independent of its net worth.

"When you raise the price level (or NGDP) target, that is essentially an unanticipated one-time tax on current money holders, a transfer of net wealth from current money holders to future taxpayers."

Is this always true ?

Say you are in a recession and people's wealth is made up of money and real assets (like machines and factories) that have a monetary value.

The CB doubles the money supply by giving money away. As we are in a recession this act will probably lead to a less than doubling of the price level, and as production will increase (compared to the recession level) the value of real assets will increase by more than the general price level.

So: While giving money away may represent a relative wealth shift away from current money holders towards the recipients of the new money (and the tax payers who would otherwise have to pay more future taxes) overall there will be an increase in real net wealth and any increase in spending will be due to both wealth and substitution effects.

"OK. I've changed my mind again. If a financial asset trades at a price above its fundamental value, it is net wealth. And in the stability experiment, where P(2014) stays the same, but P(2525) doubles, money is trading above its fundamental value. Pesek and Saving."

I'm still trying to understand this post + comments, but on your last point, that reminds me of a conversation we've had before.


I think you're saying that the actual current stock of base money is irrelevant here. So, if the government halved the 2525 redemption price Pm, but rather than doubling the supply of base money as in your example, it did a helicopter drop of bonds for the same face value, that would have the same effect. Because all that matters here is Pm. Which sort of makes sense, because any bonds are going to be redeemed for base money before 2525 (presumably, else who would buy them?), so they also add to the government final redemption bill.

I would say though that the Pm that matters here is what people believe. The government might say what they want Pm to be. But they will have to make it happen, which means they need to impose real taxes to provide the real goods to effect the redemption (of bonds and money). And people may not believe that the government will stick to its Pm target rather than run politically expedient deficits (and quite frankly, they would right not to do so). So an expected Pm based on some form of FTPL may be much more plausible than the government's stated target.

Market fiscalist:

Instead of thinking of a government whose "taxes receivable" has a present value of 100 oz, think of a landlord whose only asset is a stream of "rents receivable" with a PV=100 oz. That landlord can go around town buying stuff by writing out IOU's that say "good for 1 oz rent on my property". He can issue anywhere from 1 IOU to 100 IOU's before he gets in trouble. (Actually people would start doubting his credit once he issued more than maybe 40, but I won't worry about that for now.) Now suppose that instead of spending his IOU's, he helicopter drops them, just giving them away. All he is doing is transfering his wealth to the public. He's not creating wealth, except to the extent that his IOU's are better than other moneys and make trading easier.

So let's say starts by giving away 1 IOU, and then gives away another 99 IOU's, thus increasing the money supply by 100x. There are more IOU's relative to goods, but those IOU's don't have to be spent on goods. They can reflux to the landlord, or they can be hoarded for some future rent payment, but they won't drop much below 1 oz of silver, or the arbitragers will step in and get a free lunch.

That's one virtue of the backing theory: it doesn't force you to believe in free lunches. (Of course, for Keynesians who already believe in free lunches this is not a problem.)


You say these IOUs can "can reflux to the landlord,". That's my point. IOU's, in addition to needing to be backed by assets of sufficient value, also need sufficient "demand to hold" otherwise they will either reflux (if that is an option) or lose value. Backing is a necessary but not a sufficient condition.

Market fiscalist:

I think we'd agree that money has to have (1) backing (2) a way to get at that backing i.e., some open channels of reflux (3) a demand to hold that money. If enough reflux channels are closed, then that is tantamount to a loss of backing. But the more demand there is to hold the money, the less reflux is needed.

Mike: Yes, I think I would agree with that.

Thanks for the comments. I'm still reading, but not replying (much), because I'm thinking back to the basics of the "Is money net wealth?" question, and planning a post.

Nick E: first paragraph: I agree.

Second paragraph. "I would say though that the Pm that matters here is what people believe." I agree. Regarding the rest of that paragraph: if the government reduces Pm, then the government budget constraint implies that G *must* increase or T *must* fall, sometime between 2014 and 2525.


"if the government reduces Pm, then the government budget constraint implies that G *must* increase or T *must* fall, sometime between 2014 and 2525."

And that's where I'm a little sceptical. In the few years leading up to 2525, is the government really going to start adjusting G and T in order to ensure they hit the Pm target set 500 years ago? Seems unlikely. So I don't think anyone in 2014 would believe the Pm target.

This is an extreme case, but I think it illustrates a general problem. Most modelling involving forward looking agents requires assuming some kind of policy rule which is exogenous and permanent. But in reality it is never exogenous. Policy is dictated by circumstance and politics.

So which is going to be the more important in determining the actual Pm at which the government carries out the redemption? The target they previously set? Or the level of public debt, i.e. the extent to which they have to levy taxes or cut spending? I'd go with the latter.

(looking forward to the "Is money net wealth?" post)

Nick E: Yes, it all depends on expectations. But the 2% inflation target does seem to have been credible (at least in Canada). And people did not expect 2% inflation before that target was announced.

"Tony says that if money is irredeemable, the existence of an equilibrium in which intrinsically worthless money has positive value becomes problematic."

Well, that would also be the case on a metallic standard, as long as the face value of the coins are worth more than the value of the metal content. Which was, OC, the normal state of affairs.

Perhaps the problem lies in the assumption of an equilibrium?

"Is money net wealth?"

I look forward to that post, too.

My 2 Cts. up front:

I think one has to ask oneself net of what or, even better, net of whom? And, to preconclude, thinking of money as a net claim on government (or a bank, or the central bank) is wrong, I'd say.

It is always a measure of one private entity relative to another because governments (or banks, or the central bank) do not actually produce anything. Governments can merely commission entities to deliver goods or services for the benefit of the community. Whereas banks are the designated QCs of the process - they (should) make sure claims are equal, both between entities and over time. CBs are the QCs of banks.

Government debt signifies an excess of pblic commissions over private claims previously collected. One can argue over which must logically come first.

Consequently, I have trouble with the term helicopter drop. It doesn't specify who benefits and for having done what, which probably matters in terms of its effects on an individual sense of entitlement (wealth effect).

Nick, Andy, JPKonig

There are wealth effects plus substitution effects in a helicopter drop.

Think of the assets of the sovereign + CB complex. They're mostly future tax libilities of citizens. The effective discount rate is perhaps mildly above the NGDP growth rate, to preserve dynamic efficiency in an OLG economy. However, the sovereign complex wants this discount rate to be *just* above the expected NGDp growth rate, as otherwise it is charging too high a premium for risk not doing its job of the inter-tenporal risk coordination focal point well enough.

When the fiscal authority issues bonds, that is an attempt to reduce the applicable discount rate (because r on govt bonds should be lower than r on average capital) , which increases net wealth. When the monetary authority swapas money for bonds, that is an attempt to reduce the applicable discount rate, which increases net wealth. When the two do in lockstep, that is, well an attempt to reduce the applicable discount rate. But by the strongest possible tool (lowest possible discount rate) at the sovereign's disposal.

Of course any of these actions only have effect if they are in some sense, unanticipated. I'm assuming that throughoutfor the moment. Also, all of this is obviously about *real* discount rates

So what is asymmetric irredeemability? Nothing much, except for the fact that due to historical/ institutional reasons, the unanticipation/permanence of a helicopter drop is presumed to be higher than a tax cut or an OMO/QE. Ergo, the likeliood that the economy will signal-process a helicopter drop as a *net* wealth effect is higher, thereby inreasing the expected magnitude of the actual wealth effect. That is all. The substitution effect Andy has already identified. In top of wealth + substitution effects, we can obviously build credit constraints, institutional frictions (e.g. payment systems, counterintuitive effects of policy due to collateral drianage etc.) blah blah. Depending on the magnitude of the wealth + substitution effects, sometimes these 3rd order effects may even dominate.

In an economy that is presumed to be growing rather than static, where sovereign debt is presumed to be rolled over or inflated away rather than paid down, and where even base money may pay positive (or for that matter, negative) interest, concepts like asymnmetric irredeemability are simply historical legacies, useful to make sense of current or past institutions, but conceptually unclarifying because they are dirty mish-mashes of two or more 'base' concepts(Nick, I always keep in mind your story around Borges and the various ways to slice and dice the universe).

Until we integrate short term macro with proper capital theory (rather than mickey mouse DSGEs), we are doomed to keep wallowing such.

I suggest Nick’s “monetary policy target” is irrelevant because it’s just not something that 99% of households think about. In short helicoptering works because (revelation of the century this) when people are given money, they tend to spend it. It’s that simple.

The “monetary policy target” stuff is a bit like Ricardian equivelnence, which also assumes that households calculate what government will do in the future. That sort of stuff is great for keeping academic economists employed with their mathematical models. So far as reality goes, it’s irrelevant. As Stiglitz put it, “Ricardian equivalence is taught in every graduate school in the country. It is also sheer nonsense.”

Ralph: see Scott Sumner's post on Japan. It didn't happen.

So Japan was able to engage in a massive spending spree, accumulate politically toxic levels of debt but unable to announce a target?

"What makes helicopter money truly helicopter money -- a permanent increase in the money supply that does not imply increased tax liabilities or future government spending cuts -- is the announced increase in the price level target or NGDP level path target that accompanies the helicopter."

I would think that the virtue of helicopter money lies in having a significant portion of the helicopter drop land in the hands of those whose behavior is not affected by future taxes or gov't spending cuts; or price level or NGDP targets.


The Japanese are well known as compulsive savers. Thus the country where helicoptering is likely to have the least effect (per dollar printed and spent) is Japan.

As regards Scott's claim that Japan "did an almost unbelievably large money-financed fiscal expansion over the past 20 years", I just looked up some figures. Far as I can see the increase in the monetary base per person over that period was equivalent to $15,000 (US). That's less than $1,000 a year per person.

Given the Japanese propensity to save, it isn't surprising that $1,000 did not have much effect, seems to me.

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