We know the economy needs a bubble; but how big?

This isn't as clear as I want it to be. Sorry.

Mr Ponzi issues a financial asset. Assume that the demand to hold that asset grows at the same rate as GDP. If people are willing to hold that asset at a rate of return less than the growth rate of GDP, Mr Ponzi can run a sustainable Ponzi scheme. He can issue new assets to pay the interest on the existing assets, and still issue a few more to provide some income for himself. Another name for a sustainable Ponzi scheme is a rational bubble.

Consider paper currency. Bank of Canada notes, for example. The Bank of Canada promises that this asset will earn a rate of return, in real terms, equal to minus 2% on average. That is below the expected growth rate of the economy. It is a sustainable Ponzi scheme, and a profitable one for the Bank of Canada. It is a rational bubble.

"Does the economy need a bubble?" is the wrong question. We know it needs a bubble. The empirical evidence is right there in our pockets. The only question is: how big a bubble does it need? Or, what does it depend on?

People willingly hold paper currency, even at a very low rate of return, because it is more liquid than other assets, which need to pay a higher rate of return.

We can imagine an economy in which the only liquid asset is paper currency, and all other assets are much less liquid, and in which paper currency is the only Ponzi asset, and all other assets pay a rate of return greater than the growth rate of GDP. If the issuer of that paper currency promises a real rate of return of minus 2%, and people choose to hold (say) 5% of their annual income in paper currency, then that economy needs a bubble equal to 5% of GDP.

Now suppose the issuer of that paper currency promises a 0% real rate of return instead. (The Bank of Canada targets 0% inflation instead of 2% inflation). And suppose people now want to hold (say) 10% of their annual income in paper currency. Then that economy needs a bubble equal to 10% of GDP.

Let's keep going. What would happen if the issuer of paper currency promised a rate of return equal to the growth rate of GDP? (The Bank of Canada targets zero growth in nominal GDP, so the inflation rate is minus the growth rate in real GDP.) Suppose people now want to hold (say) 123% of their annual income in paper currency. Then that economy needs a bubble equal to 123% of GDP. That is the exact borderline between paper currency being a bubble asset and not a bubble asset. The Bank of Canada issues an amount of paper currency equal to 123% of GDP, then issues no more ever again (assuming the demand for currency is proportional to GDP).

Now suppose there were some exogenous change in the demand for currency, that caused it suddenly to double, as a percentage of people's annual incomes. The economy would need a bubble twice as big as before. And if the issuer of paper currency didn't satisfy that need for a bubble twice as big, the price level would have to halve to satisfy it. And if the price level couldn't halve instantly (because prices are sticky) there would be a recession, because of the excess demand for currency, which serves as the medium of exchange.

But currency is not the only liquid asset. Some assets are more liquid than others. Some may be liquid enough that people will hold them even if they expect a rate of return that is permanently below the growth rate of the economy. Any such asset can be used for a sustainable Ponzi scheme (a rational bubble).

Let us imagine an economy with a spectrum of Mr Ponzi's. And let's line up all the Mr Ponzi's in order of how liquid their liabilities are.

The first Mr Ponzi (the Bank of Canada) can issue the most liquid liabilities. The second Mr Ponzi (the Government of Canada?) can issue the second most liquid liabilities. And so on down the line of Mr Ponzi's.

If he wants to, the first Mr Ponzi can drive all the other Mr Ponzi's out of business. He simply needs to promise a rate of return just slightly below the growth rate of the economy. Since all the other Mr Ponzi's, who issue less liquid liabilities, would need to pay a rate of return above his if they wanted people to buy their liabilities, they wouldn't be able to run a sustainable business.

Suppose the first Mr Ponzi doesn't do that. He then leaves room for the second Mr Ponzi. And if the second Mr Ponzi wants to, he can drive all the other Mr Ponzi's out of business. Suppose the second Mr Ponzi doesn't want to do that. He then leaves room for the third Mr Ponzi. And so on.

You can think of this post as a continuation of my post on Turgot's land beating Samuelson's money.

Samuelson said you could have an economy which needed a bubble, because the rate of interest is below the growth rate of the economy. People would want to hold what Samuelson called "money" (but which might better be called "government bonds") purely as a way of saving, even if they knew it was a pure Ponzi asset.

Stefan Homburg said that Samuelson was wrong, because land would be just as good a savings vehicle as Samuelson's "money", since land too lasts forever, and land is even better, because land pays rent, because land is productive.

But if land is less liquid than Samuelson's "money", the economy might still need a bubble. We know that land is less liquid than currency, and we know that the economy needs a bubble, because people are willing to hold currency even though its rate of return is below the growth rate.

But what Finance tries to do is convert less liquid assets into more liquid assets. For a while, Finance succeeded in making land (in particular, the land on which houses are built) into a more liquid asset. If Finance succeeded in making land as liquid as currency, the economy would not need a bubble. If Finance succeeded in making land nearly as liquid as currency, the economy would only need a small bubble. But if Finance suddenly fails, and land becomes less liquid, the economy suddenly needs a much bigger bubble.

Comments

[Bill Woolsey]

I don't understand.

The economy needs a bubble?

Suppose nominal GDP grows the same as potential on average, and so the price level is stable on average.

All money takes the form of interest bearing deposits. The amount issued matches the demand to hold them.

The deposits are liquid, but the interest rate is less than the interest rate on nonliquid securities because there is a cost of intermediation. The liquidity premium equals the cost of providing intermediation services.

Is there a bubble in this economy? What is the problem with this economy?

What is missing that will be solved by adding zero interest currency and causing 2 percent inflation?

[Evan]

Maybe I am focusing too much on the terminology, and not enough on the argument, but I feel like I need a concrete definition of what you mean by "bubble".

[Nick Rowe]

Bill: I'm trying to understand it too!

I think the key is the cost of providing intermediation services. If an asset pays a rate of interest less than the growth rate, but there is a cost to the issuer of servicing that asset, and it's a zero-profit business, then it's not a Ponzi asset, and there is no dynamic inefficiency.

Evan: My old post may help.

[Lord]

It needs a lot of bubbles so the failure of any one is small enough to be taken up by the others. When there are only a few, they are large, and the failure of one is difficult to compensate for.

[Nick Rowe]

Lord: you might have a point there. Unless the failure of bubbles is correlated.
Or, we make the central bank bubble big enough to eliminate all the other bubbles, and make sure the central bank adjusts the size of its bubble to equal demand.

[Roger Sparks]

A bubble can only be found when measuring against a stable reference. Would anyone be satisfied with "only a bubble"? So we move from stability (where in the last 40 years might that be?) to a bubble (how do we define it?). You have me totally lost by now.

It is great to provide employment for all. Does anyone want to retire? How much might our bubblees need for retirement? If bubblees find it imprudent (or impossible) to retire, we need to provide even more jobs, enough to employ both young and old. Guess that would just take a little more annual deficit, to provide more savings for those who refused to help increase AD.

This is getting a little confusing for me.

[Jacques René Giguère]

Just to throw a monkey wrench in the spanners: if Bernard madoff had floated his scheme on NYSE ( and a lot of weird things got floated...) so that its clients could sell their shares instead of trying to redeem from him, would that still count as a Ponzi scheme or just as a failed stock?
Either I'm OT or I am geting confused and not only out of maturity...

[Bob Murphy]

Nick I can't tell if this post is brilliant or ridiculous. I'll let you know...

In the meantime, can you clarify: Are you using "bubble" and "Ponzi scheme" interchangeably? I think that's what's throwing some of us.

[Philippe]

cryptic.

[Richard H. Serlin]

I find the whole premise terrible. Aggregate demand will be regularly deficient due to secular stagnation, so we should make bubbles? Or encourage people to spend more on frivolous, high positional externality, goods? Wouldn't it create ridiculously more total societal utils if we increased aggregate demand by spending 10 times the ridiculously small amount we spend on basic scientific and medical research, having universal high quality preschool and daycare, universal high nutrition school breakfasts and lunches (truly high nutrition, not ketchup is a vegitable), universal free bachelor's degree,...

We have to try to increase demand wastefully and inefficiently, when there are so many high return investments?

Oh yeah, we have dogmatic, brain dead Republicans undemocratically blocking (extreme gerrymandering, etc.) anything that involves government investment.

[Ritwik]

Finally! Do I see some Wicksellian-monetarist convergence? And shall we thank J P Koning for banging on about liquidity and 'moneyness'? :)

[Ralph Musgrave]

Nick asks, “We know the economy needs a bubble; but how big?” The answer is easy: “Big enough to raise employment as far as is possible without causing excess inflation, or put another way, big enough to cut unemployment to NAIRU” At least that’s the standard MMT answer.

I.e. the solution to excess unemployment advocated by MMT (and the group linked to below) is simply to have the central bank create more bubbly stuff (monetary base) and spend it into the economy (and/or cut taxes).

http://www.positivemoney.org.uk/wp-content/uploads/2010/11/NEF-Southampton-Positive-Money-ICB-Submission.pdf

As to making land or other assets like shares as liquid as money, that will never happen. Though as Nick rightly points out, finance can make those assets a bit more liquid than they might otherwise be. E.g. government debt is used in lieu of money in the world’s financial centres. But it’s useless for buying cars or your groceries or houses.

[Martin]

"But if Finance suddenly fails, and land becomes less liquid, the economy suddenly needs a much bigger bubble."

I like this idea, but perhaps I am reading what I want to read into it.

If we take the "World's Smallest Macroeconomic Model"* and replace "M" by "M_0 + M_1(M_0)" where M_1'>0 and M_0 is interpreted as the asset issued by the central bank which serves as an input for the production of the asset M_1 by a representative financial intermediary, and which is backed by the M_0 held by the financial intermediary. If the financial intermediary 'fails' then we need a much larger M_0 to offset the drop in M_1.

There are three differences with the model described above:
1. M_0 is the only "Ponzi Asset";
a) Individuals only hold M_1 because the intermediary holds a stock of M_0;
2. There is no explanation for why individuals hold M_0;
3. M_1 is not produced using any other asset than M_0.

The result is the same though. Start in equilibrium M_1>0 and M_0>0, now finance 'fails' a larger bubble (M_0) is needed.

What I read into this is that finance is a technology for reducing the use of M_0 and a technological shock to finance explains recessions if M_0 is constant. Funny how finance reduces the size of 'bubbles'.

*http://web.mit.edu/krugman/www/MINIMAC.html

[Nick Edmonds]

Nick

Two points

First, I don't think it's right to describe this process as a bubble. An essential feature of bubbles is that they are prone to bursting. With a bubble, what we expect to see is that people are buying assets on the basis of expected returns. Once the expected returns can no longer be delivered, demand collapses.

In Samuelson, people are buying the asset because they want to defer consumption and it's the only way open to them. If the return disappears (the economy stops growing), people will still need to buy the asset, so demand will not collapse. (You can build in some element where demand depends partly on returns, but that's just an add-on.) It is true, of course, that there is a confidence element to Samuelson's money - people accept it because they think other people will accept it - but this is just the wider issue of why people accept worthless bits of paper. It has nothing to do with returns.

Secondly, the thing I take away from Samuelson, is not that the economy needs bubbles, but rather that a growing economy needs public sector deficits. Samuelson's money is outside money. The return arises simply because the real stock needs to grow. As there are no public sector flows in Samuelson, there is no primary surplus or deficit, so the economy has to create an inflation adjusted deficit by generating a real rate of return on the outside assets. If you extend Samuelson's model to include a public sector running a primary deficit, then the assets no longer need to grow in value, because the growth is provided by the flow of new assets.

[Herbert]

Deep and interesting posting, Nick. Let me see if I got it straight, introducing some notation in order to elaborate your argument. I consider four assets:

1. Land with price q and fixed quantity L. If individuals want to hold a certain multiple of NGDP in the form of land, qL/NGDP is constant and q increases at the rate n, the growth rate of NGDP. Because land also yields a rent, its total rate of return, to be called i, exceeds n.

2. Reproducible fixed capital which is similarly illiquid as land, must also yield a total return of i. This follows from arbitrage. The important point is that the existence of land prevents overaccumulation: No investment returning n or less is undertaken.

3. Money whose nominal rate of return equals zero. Money is held because it is more liquid than land and reproducible fixed capital, its opportunity cost equals the marginal utility of liquidity.

4. Now your most interesting point: Asset backed securities (ABS). These should ideally yield the same return as the underlying land. But they are almost as liquid as money. In this sense, ABS dominate all aforementioned assets.

Before I proceed: Do you agree with these considerations?

[Nick Rowe]

Herbert: basically yes. You are being much clearer than I was. Start with Samuelson 1958, then add your 1,2,3,4. Then ask what happens if the production of liquid ABS's suddenly fails.

Minor points:
2. fixed capital depreciates, land doesn't, so introducing capital into Samuelson doesn't necessarily overturn Samuelson, in the way introducing land does. (You very probably already knew that, just checking).
4. We might still want some currency for buying coffee, if it's more convenient than ABS for buying small stuff. But we can ignore that as a modelling strategy.

[Nick Rowe]

Everybody: read Andy Harless' post. Andy introduces risk, where I introduce liquidity.

[Nick Rowe]

Roger: read my old post for background. See my reply to Evan above.

Jacques Rene: imagine if Bernie Madoff had floated his scheme, but had told everyone everything about it, and they still lent him money, and did so rationally, and assumed all future people who lent to BM were rational too. That's what I'm talking about here. Whether he accepts deposits, or issues tradeable securities, doesn't matter.

Bob: bubble = ponzi scheme = chain letter. All 3 are economically equivalent. I'm using the words interchangeably. Fiat money is a chain letter, except you typically send goods of less value to the person who sent you the letter than he sent to the person before him.

Richard: you really need to read Samuelson 58 to get the argument. See my old post.

Ritwik: yes to both, I think.

Ralph: banks have illiquid assets and liquid liabilities. You can think of a bank as a factory that converts less liquid assets into more liquid assets.

Martin: I think you are on the right track. Or think of M_1 as backed by land.

Nick Edmonds. Start with Samuelson 58, with no government. There are two types of shells, just laying on the ground, in fixed supply. There are 3 (4?) equilibria: no shells are used as money r < g. Type1 shells are used as "money" r=g. Type2 shells are used as money r=g. (And maybe both types of shells are used as money, r=g). We have multiple equilibria. Bubbles burst, when we switch from one equilibrium to another.

[Nick Edmonds]

Nick,

The same applies though even when g = 0, so there is no inflating going on. Again, it's not really what I think of as a bubble, so much as the question of why we would accept intrinsically worthless objects as money. But maybe that's just the way I understand the term. In any event, if what you mean when you say that we need bubbles, is simply that we need to have an intrinsically worthless asset that people will accept in exchange for goods, then yes I agree, but it's not what I think is meant when I hear that "we need bubbles".

[Nick Rowe]

Nick Edmonds: sure. When people hear the word "bubble" they don't think about currency. But currency is a bubble, and this post is reminding people that it is a bubble.

[Dan Kervick]

Nick could you go into a little more detail about the second paragraph? I don't understand what kinds of instruments you have in mind exactly, so I don't understand the conditions for whatever form of sustainability you are positing. But if I understand you correctly, then I don't think you are describing bubbles. You are just describing sustainable patterns of promises to make payments among the members of some population, where the prices paid for these promises are always in line with the real returns that come from them.

Suppose we have two people A and B, who make the following promises to each other: A agrees that at the end of each odd numbered year, A will pay B an amount equal to the growth rate in GDP during the year just completed, multiplied by some fixed initial dollar value X. And B agrees that at the end of each even number year, B will pay A an amount equal to the growth rate in GDP during the year just completed.

Let's assume the payments are to last for 30 years, so 15 payments each for A and B, and assume A and B are very young and healthy with good prospects, so there is no reason to assume the promises can't easily be kept.

For each of the participants A and B, the expected value of the the other participant's promise is X*(Y/2), where Y is the expected 30-year growth rate of the economy. Risk considerations aside, that would be a rational price for each to pay for the other's promise. If the two participants sell each other their promises for that amount, then the net cost of the total transaction for each participant is $0, which is also the net expected value of entering the two-sided arrangement.

Suppose these kinds of promises between pairs of friends become very popular. They catch on like wildfire. Sometimes the transaction is one-sided: one friend buys a promise from the other friend, paying X*(Y/2) up front for the promise, and expecting at the outset to collect roughly that amount in 15 payments over the next 30 years. Sometimes the transaction is two-sided, as in the above case of A and B.

Yet, no matter how popular these waves of promises become, it doesn't seem like what we are describing is a bubble: not so long as the prices paid for the promises are in line with the real returns from them.

[Nick Rowe]

Dan: Here is an example closer to Samuelson's:

Suppose people live for 2 periods. They work when they are young, but cannot work when they are old. There are no assets in the economy. The economy lasts forever. Output is backscratching services. The government orders the young to give half their income to the old (they spend half their time scratching old people's backs). That's an unfunded pension plan. It can (and will in this case) make everyone better off. They are happy to give up half their backscratches when young to get their backs scratched when old.

Now let's suppose there are useless shells, laying on the beach. People pick up all those shells. Every period, the young buy shells off the old by scratching the old people's backs. Those shells are their pension plan. If the growth rate of the population is g, those shells will earn a rate of return equal to g. Those useless shells are just a different way of implementing the same unfunded pension plan.

I call those shells a bubble/Ponzi asset, because they are intrinsically worthless. But unlike most bubble/Ponzi assets, this one is sustainable. It does not rely on there being a "greater fool". Everyone is fully rational and understands that the shells are intrinsically worthless.

Some people would object to my terminology. They want to define "bubbles" and "Ponzi's" as being irrational/unsustainable. I see their point. But I find it useful.

[Herbert]

Nick: "2. fixed capital depreciates, land doesn't, so introducing capital into Samuelson doesn't necessarily overturn Samuelson, in the way introducing land does. (You very probably already knew that, just checking)."

Sure. I mentioned fixed capital because the reverse holds true: Land prevents overaccumulation of fixed capital which can occur in the Diamond (1965) model but not in a model witch land.

Last point, an empirical one: For Canada 2010, qL/NGDP equals roughly 1.2 whereas M1/NGDP equals roughly 0.4. This suggests that the land bubble is thrice as large as the money bubble.

[Nick Rowe]

Herbert: "For Canada 2010, qL/NGDP equals roughly 1.2..."

Neat! 120% of annual GDP. Does that include all land (farmland + building land)? Where did you get that info?

I'm not sure about M1. Currency is a bubble. But demand deposits can be thought of as government plus private bonds-made-more-liquid, at a cost.

[Frank Restly]

Nick,

Liquidity is one risk measurement property of all asset classes. There are others

1. Market volatility risk - for instance central bank oscillates between a 5% inflation target and a -5% inflation target
2. Legal risk - every financial asset is someone else's liability, what recourse does the owner of the asset have if the seller fails to deliver as promised - for instance the central bank targets 5% inflation and gets 20% instead
3. Solvency / Bankruptcy - obviously not possible for central banks, but still a concern for other financial assets

"If people are willing to hold that asset at a rate of return less than the growth rate of GDP, Mr Ponzi can run a sustainable Ponzi scheme. He can issue new assets to pay the interest on the existing assets, and still issue a few more to provide some income for himself."

People must be willing to hold that asset that offers a rate of return less than the growth rate of GDP + the growth rate in the nominal quantity of assets for the Ponzi scheme to be successful. For instance, if the growth rate of an economy is 5%, the interest rate is 3%, but Mr Ponzi wants to sell 10% more assets every year, then people must be willing to accept a -12% rate of return (3% nominal interest - 5% nominal GDP growth - 10% nominal asset growth rate = -12% not -2%).

[Nick Rowe]

Frank: "Liquidity is one risk measurement property of all asset classes."

No it isn't.

Last paragraph: sure, there is a limit to how much income you can earn from producing a Ponzi asset. Robert Mugabe tried to go past that limit.

[Andy Harless]

OK, I'm going to push back on your response to Frank, because I was going to make the same point. Isn't illiquidity just a form of risk? Thinly traded stocks are considered inherently risky precisely because they are illiquid: if you own one, you risk that, when you try to sell it, you will not be able to get a good price because there won't be any buyers at that particular time. To put it another way, there is volatility in the bid price (and the ask price, too, but that's a separate issue), which makes the asset risky for the owner. And when we say that T-bills are less liquid than Federal Reserve notes, it's essentially the same issue: if you want to "sell" your Federal Reserve note (in the US), say to buy a latte, you're fairly well assured of getting a good price -- maybe not as good a price as you want, but the price won't be idiosyncratically bad. If you walk into a Starbucks with a T-bill, chances are you won't get much of a bid. Somebody might be willing to make a market, given that there's a lot of potential profit in making change for a T-bill, but you won't get a very good bid. So there is a risk associated with holding T-bills instead of FR notes: the reason people hold some of their assets in FR notes (and forms that can be immediately converted thereto), rather than holding T-bills and always doing the conversion on a just-in-time basis, is that there's a risk of wanting to sell (i.e., buy something) when you can't easily sell your T-bill.

[Nick Rowe]

Andy: lottery tickets (before the winning numbers are announced) are very risky, but quite liquid, because there is symmetric information about the risks (except for people who have lucky numbers).

Frank was talking about the risks to a bank, and wants to list liquidity as just one of a number of risks that banks face. If we want to introduce risk into the bubble/secular stagnation debate, I would rather do it the way you did. Just say that risk-averse people value safe assets, and are prepared to accept a lower expected rate of return on safe assets than on risky assets.

[Nick Rowe]

Or, suppose you know for certain you will need to sell your car soon, because you will be leaving the country, and you know for certain that used cars sell for a low price because of the market for lemons problem. So you rent a car instead of buying a car, if you are only going to visit a country for a short while.

[Martin]

Andy, imagine that there is a 30 year time deposit that cannot be traded nor can it can be used as collateral in any shape or form. This asset is not very liquid. Now imagine that the principal and interest are covered by a government backed deposit insurance scheme. This asset is thus no more risky than a bond issued by the same government. If the government is very solvent, then this asset is not very liquid, but not very risky either.

[Dan Kervick]

Sorry Nick. I can't see how the shells + backscratching economy is either a Ponzi scheme or a bubble. It seems to me that you are using these terms in novel senses that are not the way most others use them. If the price of an asset is rising in a sustainable and rational way, then it seems to me that by definition that is not a bubble. It is only when there is some discrepancy between the prevailing rate of increase of some risk-fraught market exchange price and some other, less risk-fraught source of the asset's value that it makes sense to speak of a "bubble".

Suppose the shells are signs of binding contracts. There is a special group G of back scratchers that puts the shells into circulation, issuing them in exchange for getting their own backs scratched in the present. The shells record the commitment of the members of G to scratch the back of the bearer and returner of a shell at a rate of one-minute of back-scratching per shell. That is the redemption value of a shell.

But the shells also come to have a non-contractual exchange value. If you have one of these shells, you can probably find some person not in G who is willing to scratch your back for one minute in exchange for a shell, since the shell can be redeemed later with the members of G. People start out scratching other people's backs in exchange for shells at a rate of one minute of backscratching per shell. That is, the exchange value is equal to the redemption value.

But then people come to realize that human backscratching productivity is growing, and that one minute of backscratching in the future will be significantly more wonderful and intense than backscratching in the present. As a result, people are increasingly willing to obtain a single shell in exchange for more than a single minute of present backscratching. The exchange value of a shell, measured in terms of minutes of backscratching is higher than the redemption value measure in minutes of backscratching. But this is rational at this stage, because a minute of future backscratching is worth more than a minute of present backscratching.

But soon, the price of shells begins to rise at a rate that outstrips the growth in the productivity of backscratching. People are paying back scratches for these shells whose values are much higher than the value of whatever back scratches they will ever get by redeeming them from the members of G. We can imagine that some, or even all market participants are aware of this discrepancy.

Nevertheless the price of the shells continues to rise at a high and steady rate. Why? Adaptive expectations. There is a general perception of the rate of price increase for the shells, and that perception is somewhat self-sustaining so long as there is widespread confidence in the continuance of this rate of price increase. People know that the prevailing exchange value of the the shells is higher than the redemption value and increasing at a rate higher than the redemption value. But at this point all they care about is the exchange value.

But there is risk involved. Nobody is contractually obligated to exchange back scratches for shells at the rates that happen to prevail, and the market price increase is just a self-emergent pattern of self-reinforcing expectations and behaviors that could easily be disrupted and fall apart. It is entirely possible that some people will suddenly start saying "no" to the shells, or start only say "yes" in exchange for ewer back scratches than the market was fetching the day before, and that the price will rapidly collapse back to its expected redemption value. One might think that the greater the gap between the prevailing exchange value and the redemption value, the greater the risk and the greater the likelihood of such a disruption occurring. One might also think that the awareness of risk depends on how many people know of the discrepancy between the market exchange value and the redemption value.

If there is no redemption value for some asset - or at least some other lower-risk, more inherently stable source of value for the asset besides the market exchange value - than I don't think its increase in market value can be called a bubble. In that case, where the expected exchange value is the entire source of the asset's value, then all we have is something like an informal medium of exchange with price deflation. That's not the same thing as a bubble. A bubble is a discrepancy between a present market value and some other source of value that is more "real".

[Nick Rowe]

Dan: some economists do talk about "rational bubbles" and are using the words in the same sense I use them. But yes, most people don't use the words the same way. But then maybe most people are wrong, because they fail to understand how it is possible that people could rationally buy an asset that isn't backed by anything, just like Mr Ponzi's assets. But it is possible.

"Suppose the shells are signs of binding contracts. There is a special group G of back scratchers that puts the shells into circulation, issuing them in exchange for getting their own backs scratched in the present."

But the whole point of Samuelson 1958 is that there cannot be some such special group. The old people, who want to get a backscratch from you today, will be dead by the time you are old and want to redeem the promise, and you will want to get a backscratch from the people who aren't yet born.

[Nick Rowe]

Put it another way. There is an exchange of backscratches that can make every cohort better off. But in order to make that exchange, you would need an infinite number of cohorts all meeting together at the same time. But at any given time, only two cohorts are alive. You need to bring the unborn into the deal, and you can't. So you start a chain letter, and hope they don't break the chain.

[Andy Harless]

Nick,

My contention is that illiquidity is one type of risk. A lottery ticket does not have that form of risk, but it does have another type of risk. Risk is general; (il)liquidity is a special case.

Martin,

For a typical individual, an insured 30-year time deposit is not very risky because liquidity is the only risk associated with it, and usually that risk has been largely diversified away with other assets. It would be quite risky to hold your entire portfolio as an insured 30-year time deposit, because you'd be totally screwed if you had an unanticipated need to sell part of it. On the other hand, if you have a portfolio that already has enough liquidity in it, adding an illiquid asset produces only a tiny increase in the risk (unless your future liquidity needs are extremely uncertain): from your point of view, this risk is idiosyncratic. Now if liquidity were to become so plentiful that reducing the liquidity of the market portfolio would not reduce its value, that is equivalent to saying that liquidity would become a zero-beta asset that no longer adds risk to the market portfolio. Liquidity would no longer be priced, but it would still be an idiosyncratic risk from the point of view of portfolio construction.

[Frances Coppola]

Martin, if your illiquid asset is fully backed by a government insurance scheme, then the liquidity risk has been transferred to the government, which we assume can always produce enough liquid assets (currency) to enable you to sell your asset and buy beers. So the liquidity risk doesn't disappear, but it is mitigated by faith in the government. If the government refuses to honour the insurance - as Iceland did - you will go thirsty.

[Nick Rowe]

Suddenly, I want a beer. Mmmm, sipping Sleeman's porter, while waiting for the winter storm to hit. Thanks Frances! Why do only Brits, Irish(?) and Quebecers drink porter?

[rp1]

People hold cash because of the bubble. It is a rational thing to do because bubbles burst. And what happens then? It depends on how much of the economy was driven by the excesses of the bubble. You can't predict the turn or how exactly it will play out, but you can easily estimate the magnitude of the shock if markets simply revert to the mean, which they always do.

I read stuff here occasionally and I just shake my head. It's so half-baked and utterly devoid of common sense. The economy needs a bubble? Really? Who pays the price for that? Families, usually. But in a just world, it would include amoral economists who say things like "the economy needs a bubble". I wonder what Adam Smith would make of that?

People build their lives and livelihoods around economic pretences which, in a bubble, turn out to be spectacularly false. Yet this incredible cost is blithely ignored. I'm only half-jokingly expecting the day when we hear "the economy needs a war", as if the world itself were an externality.

[Martin]

But Frances, in my example the time deposit cannot be sold nor transferred. So even if the government can produce currency it will have to break the law to enable me to sell my asset and buy beers.

In any case, the point is that an asset that is not liquid is not necessarily risky. To go with the beer example, I don't think this is an example of liquidity risk.

For example, let's say that at t=0 I know that I want to have two pints of beers at t=2. At t=0 I have barely enough currency to purchase one beer. At the start of t=0 I however have the option to purchase an asset, but this asset comes with a restriction that it cannot be sold or transferred before t=2, and if it is transferred I will have to pay a fine that leaves me with barely enough currency to cover half a pint of beer. Now if I can perfectly anticipate my own consumption, then purchasing the asset is a no brainer. If I don't however, I run the risk of having instead of two beers or one beer, not even half a pint of beer if I get thirsty at t=1.

Now what is the problem here? Is the problem that I cannot forecast my own consumption perfectly or is it the restriction on the asset? If I can forecast my own consumption perfectly, then the restriction is no problem and the asset is neither risky or liquid. The lack of liquidity is not sufficient for an asset to be risky.

[Nick Rowe]

rp1: Look at those bits of paper in your pocket. They are only worth something if you can sell them to someone else, who will only buy them if he in turn thinks he can sell them to someone else....etc. And yet they are depreciating at 2% per year.

[Andy Harless]

Hmm...it seems my other comment (responding to Martin and Nick) has disappeared. Maybe caught in a spam filter? Or did I forget to click "Post"?

Anyhow, I wanted to say something else about land. Even absent risk and/or liquidity concerns, I don't think land necessarily solves the problem. That is, it will solve the milder version of the problem, in which the bubble is efficient but people still have positive marginal time preference. But I find it quite conceivable that people, in some possible equilibria at least, have negative time preference: people lay up treasures for themselves on earth, where moth and rust destroy, etc.; if saving is expensive, they're willing to pay the price. And if the equilibrium is one with negative marginal time preference, and if there is no "end of the world" time period, then I don't think any land price will be an equilibrium. Any price of land tomorrow implies it would be more expensive today, and by pushing the relevant tomorrow arbitrarily far into the future, I think you can show by induction that any price one might choose is too low to be an equilibrium. In other words, if the price of land is going to keep going down forever at a constant rate, it has to start out at infinity.

Now that I think about it, I'm not even sure land solves the milder version. Land provides services. In order for there to be an equilibrium, the total return on land, including the services it provides, has to be able to equal the rate of time preference, which means, if the rate of time preference is near zero, the value of the land has to fall almost enough to offset the value of the services. But again I argue the value can't keep falling forever. Although I'm not sure, because the value could be so high that the services become nearly irrelevant. I have to think about that case some more.

[Nick Rowe]

Andy: I found your other comment in the spam filter. Sorry about that.

Years ago, I tried to do a post arguing that asset prices could be infinite. Never did get my head straight on it. With negative rates of time preference, and infinite horizons, it does look like land might have infinite value. Or, even with positive time-preference, if the rent on land is growing faster than the rate of time preference. Dunno.

[Philippe]

Nick, this 2007 paper by Wynne Godley and Marc Lavoie might interest you, regarding the sustainability of 'bubbles' and the real rate of interest on government debt:

http://www.levyinstitute.org/pubs/wp_494.pdf

"... we arrive at two unconventional conclusions: first, that an economy (described within an SFC framework) with a real rate of interest net of taxes that exceeds the real growth rate will not generate explosive interest flows, even when the government is not targeting primary surpluses; and, second, that it cannot be assumed that a debtor country requires a trade surplus if interest payments on debt are not to explode."

[Herbert]

Nick: "Herbert: "For Canada 2010, qL/NGDP equals roughly 1.2...
Neat! 120% of annual GDP. Does that include all land (farmland + building land)? Where did you get that info?
I'm not sure about M1. Currency is a bubble."

The value of Canada's land is reported by www.stats.oecd.org. Look under National Accounts, Detailed Tables, Table 9B. According to 10.175 in SNA 2008, this includes farmland and building land, but excludes land improvements, buildings, and structures, which are booked under fixed capital.

qL/NGDP=1.2 for Canada is low, compared with numbers over 2.0 or 3.0 for countries like France, Japan, or Korea. But compared with currency/NGDP, land is unequally more important than currency.

[Herbert]

@Andy Harless and Nick Rowe:

You discuss the relation between land and time preference, and this is the central point. In order to simplify let us consider Turgot's stationary state:

1. The land's price q and the land rent x are constant positive numbers. A land investment yields the return (q + x)/q. This equals 1 + i in a stationary state. Hence the interest rate i is positive.

2. If time preference were negative we had a contradiction. But time preference cannot become negative in an economy with land.

3. To see why observe that in an OLG model the old land owners sell land in order to consume. The young earn wage income wN and buy land in order to save. With excess saving the land price goes up which makes it possible for the elderly to consume more.

4. The land price does not increase infinitely but is bounded from above by qL = wN where the young use their entire wage income to buy land. Given the usual indifference curves (with Inada properties, to make the argument air-tight), the marginal rate of time preference would move to infinity if qL approached wN.

The core point is the direction of causation: The land's price prevents the marginal rate of time preference from becoming negative. This contradicts Austrian thinking, of course, where time preference is an exogenous number that drives accumulation.

[Nick Rowe]

Herbert: (Again, very good comments).

Yep, the key is the overlapping generations bit. In a stationary economy, infinite lives means stationary consumption, which means the rate of interest must equal the rate of time preference *proper* (i.e the "pure" rate of time-preference, when C(t) = C(t+1) ).

In an OLG economy each agent can have growing (or declining) consumption, even though aggregate consumption is stationary, so the marginal rate of time preference is not pinned down, until you know something about the assets and demographics.

But in a Barro-Ricardian model, with bequests, it could be different. Land could be passed down through the generations, even if it had infinite value. They could always "afford" it, since they already own it.

[Frank Restly]

Nick,

"Frank was talking about the risks to a bank, and wants to list liquidity as just one of a number of risks that banks face."

Actually, for Mr. Ponzi, I was listing possible risks to buyer's for his scheme and thus risks to his ability to continue to sell those assets.

From your original post:

"He can issue new assets to pay the interest on the existing assets, and still issue a few more to provide some income for himself."

That is assuming that the market volatility of those assets is relatively small, that buyers of those assets have legal recourse if Mr. Ponzi fails to deliver on his promised return on investment, that Mr. Ponzi does not go bankrupt / insolvent, and that the assets that Mr. Ponzi sells are fairly liquid / transferrable. In short I wasn't speaking to banks specifically, but to the general case of Mr. Ponzi selling "interest" bearing assets and continuing to sell those assets.

And even then (assets are low volatility, legally protected, fairly liquid / transferrable, and Mr. Ponzi has a monopoly), the buyers of those assets must be willing to accept a rate of return of the stated "interest" rate - GDP growth rate - quantity growth rate of securities sold.

[Herbert]

Nick: I must confess that I always think about intertemporal problems in terms of OLG. Your comment helps me understanding your above exchange with Andy Harless:

1. In the OLG model with exogenous land L, consumption when young equals cy = wN - qL wheras consumption when old equals co = (q + x)L. In a stationary state, the interest factor (q + x)/q is exogenous, and the actual rate of time preference adjusts to it. The price of land regulates the distribution of consumption between the young and the elderly.

2. In a model with one infinitely lived agent, the interest factor equals the exogenous pure rate of time preference. The price of land, I suppose, is not defined in this model because there is no market for land. The infinitely lived monster possesses all land from the outset, as you put it, and the aggregate resource constraint demands that C = Y in every period, there is no distribution issue.

Comparing the two models reinforces my uneasiness with the infinite-horizon model which trivializes important issues as pensions, government debt, or dynamic inefficiency.

[Steve Roth]

For years I've been pondering your "The economy wants a Ponzi scheme" line. Just haven't had the guts to write the post that arises from my thinking:

The Economy *Is* a Ponzi Scheme.

A magical log-rolling exercise.

Thanks for writing it for me.

[Nick Rowe]

Herbert: Yep. I tend to switch randomly between OLG and infinite horizon!

1. Take the case of logarthmic preferences: U = Log(Cy) + B.log(Co)

Then the interest factor is Co/BCy = (q + x)/q . I would say the rate of interest and marginal rate of time preference are co-determined. If instead we had linear preferences, U = Cy + BCo, then B determines the interest rate.

2. With identical agents, there would be no trade in land, but we could still define a price of land they would be willing to buy and sell extra land for.

[rp1]

Nick Rowe: "Look at those bits of paper in your pocket. They are only worth something if you can sell them to someone else, who will only buy them if he in turn thinks he can sell them to someone else....etc. And yet they are depreciating at 2% per year."

Do you own any stocks that don't pay a dividend?

I am perfectly aware of the scam that has been run so successfully over and over again on society: jack up risk to unconscionable levels by inflating asset prices. The government and monetary authorities keep it going as long as possible. Nobody likes the inflation tax so they eventually succumb and the majority suffers a _large capital loss_ on stocks, bonds, real estate, whatever. They can even be coerced to sell at the bottom. This is how money is made today. The middle class is soon to be extinct in this country because they can not cope with this game. Like the dodo, they may not be coming back.

How long should you pay an inflation tax of 2% if the alternative is to buy an asset that is 35% overvalued and yields 1% ? This is an actual high-stakes question that many Canadians faced. In that environment, would you rather hold cash or a 10 year bond at 1.5%? I think a lot of people failed that one recently. Of course you have to look for undervalued assets. The correct way to treat cash is as an option. The penny-wise and pound-foolish are looking at the 2%. With the markets being driven to extremes, that option is much more valuable than most of us are comfortable believing.

[Nick Rowe]

rp1: "Do you own any stocks that don't pay a dividend?"

Yes. But I think (and hope) there are some real assets matching those stocks, and the returns from those real assets will eventually be used to either pay me dividends or to buy back stocks (same thing). So I expect those stocks to appreciate over time. I wouldn't hold them unless I expected them to appreciate.

But that doesn't work with paper currency. I know the Bank of Canada has assets, but I also know they will simply hand over the returns from those assets to the government, and not use those returns to pay dividends and buy back currency. I expect that currency to depreciate over time, at 2% per year. The Bank of Canada has promised it will try to make it depreciate at 2% per year.

[Roger Sparks]

Nick,

I was inspired by your comment "currency is a bubble" (written in response to Nick Edmonds) to write a post "Fiat Money is a Bubble" (found at http://mechanicalmoney.blogspot.com/2013/12/fiat-money-is-bubble.html).

The comment struck me as SO TRUE! In the post, I mention your comment as containing a startling depth of insight.

I expect you might not agree with my further associations but such is the stuff of economic exploration. Thanks for your post and comments.

[rp1]

I think you're misunderstanding. We agree that cash should not be a long term investment. It's a defensive measure that one might hold if they discern a predatory investment climate. Because it is an extremely valuable option in such an environment. That is, in addition to protecting you, it can also make you lots of money which you might need if things continue on their trip to hell.

Here is a weekly chart of the DJIA. http://i.imgur.com/akKU7o4.png

Your arguments against holding cash were proclaimed just as loudly in 2000 and 2007, and by American homeowners in 2005, and by Canadians 2010-present. If you have not considered the possibility that we are in a secular bear market, then I suggest you do so. That is my contention, but I have also considered a secular bull market and managed risk as best I can. It's easier with global investment options.

I would like to point out that much of what has been called investment since the mid 1990's is purely speculation on price, and the trend towards speculation has intensified as interest rates and real yields fell. This is not conductive towards productive investment that leads to future growth.

I would also like to point out that the financial system has been abused to such an extent that it has damaged the real economy and the prospect of earned income for large swaths of the population in the developed world, and we now have governments and central banks running wild experiments which affect financial markets greatly but do little for the real economy.

My point here is that risk and opportunity are two sides of the same coin, and to take advantage of an opportunity, you need cash. For five years we have had financial assets rising seemingly without limit as real economies stagnate, with many choosing to put 100% of their net worth into that. I think this lacks common sense. History is replete with strange trends that persist longer than anyone expects before coming to an end. The only real surprise is that anyone is surprised when things change.

[rp1]

To Roger: of course fiat currency is a bubble. It has to be. Without such a bubble you would not have economic freedom.

[Jon]

So maybe the great moderation wasn't due to CB policy so much as a combination of low currency growth and a free-banking alternative (shadow banking)

[The Keystone Garter]

Mr Ponzi, in trying to put lower tier Ponzi's out of biz, will cause hyperinflation, and the selection by investors of a sane currency. If the expected growth rate of the economy is 3.0%, and Ponzi ups the return from 1.5% to 2.9%, next years expected return will be 4.4%, and Ponzi will have to pony up a 4.3% return...The Senate would stop such a Central Banker in this country, at least for 8 years.

[Dan Kervick]

You guys have all gone nuts. I sincerely hope nobody in a position of actual authority is listening to you.

[Nick Rowe]

Roger: thanks!

rp1: we are not talking about the same things. Currency is a good long term investment. I like to hold about $100 on average. It is a good investment because it makes it easier for me to buy stuff like cups of coffee and pints of beer.

TKG: No it's the other way around. The central bank would need to target lower inflation to increase the size of M/NGDP.

Dan: it probably looks like that. IIRC, US social security(?) was designed according to Samuelson 58.

[The Keystone Garter]

I thought the Central Bank was Mr Ponzi. I thought he was targetting the GDP growth rate minus 0.1%. If the central makes GDP growth the only factor in setting the interbank overnight interest rate, it will be hyperinflationary. Whoever Mr Ponzi is, he is hyperinflationary. In a recession, he is hyperdeflationary.

An added tanget about land: The USA subscribes to inferior suburbia becuase of the idiosyncracies of Thomas Jefferson. Someone probably threw out garbage on him while he was on his way to a date or something. They have an inferior myth to the rest of the world and too much market forces ideology is preventing them from correcting this error and having liveable cities. So urban land would be a better store of wealth here.

[The Keystone Garter]

...it is calculus. A given interest rate will induce a given "natural" rate of GDP growth. As you allude to this morning, interest rates and inflation tend to run inversely. If anyone basis interest rates upon GDP growth, in a naturally growing economy, the rates will run away to infinity. In a market of alternative investments, it isn't just overnight bank lenders that get the Ponzi rate, it is every chequing account holder. Maybe the savings account holders too. Different levels of Mr Ponzi's have different levels of public trust and different insurance capabilities. Jeffereson may have been a good editor, but I wouldn't trust anything that guy wrote.