If you look at the balance sheet of a central bank, you will see it has liabilities (mostly currency) and assets (normally mostly government bonds/bills). Why do central banks have assets? Do they need them?
The wrong answer is that central banks need assets to "back" the value of the currency, and that paper currency would be worthless otherwise. The right answer is: since the government gets all the profits from a central bank anyway, there's no point in giving the government the assets; that owning assets lets the bank reverse course and reduce the money supply if it ever needs to; and it stops the accountants freaking out.
Let's deal with the wrong answer first. According to the "backing" theory of the value of money, the value of a central bank's currency is equal to and determined by the value of the central bank's assets backing the currency. (This is different from the fiscal theory of the price level, which says that the value of currency plus bonds is equal to and determined by the present value of primary fiscal surpluses.)
The backing theory sounds good. How can intrinsically worthless paper money have value? Because it is backed by valuable assets. It's just like shares in a mutual fund, which have value equal to and determined by the value of the assets in the fund.
Here are three arguments against the backing theory of money:
1. The assets of central banks are normally nearly all nominal assets, denominated in the same currency as the liabilities. Suppose the price level were to double magically overnight, and the real value of currency halved. The real value of the bonds held by the central bank would also halve. So a magical doubling of the price level would not violate the equality between the value of the currency and the value of the assets backing it. The backing theory leaves the price level indeterminate. It could only pin down the price level if the assets were real assets. If (say) 10% of the bank's assets were real (gold reserves, plus the building), then a 1% loss of its real assets (the building burns down) would cause a 10% jump in the price level.
2. Suppose a mutual fund held bonds, but all the interest on the bonds (minus the administrative expenses of running the fund) were handed over to some third party, and not to the owners of shares in the mutual fund. Who would want to own shares in that mutual fund? The net present value of the dividends paid to the shareholders would be zero, so the shares would be worth zero too. But this is exactly what central banks do. Every year central banks earn profits from the interest on the bonds they own, minus administrative expenses, and hand the whole of that profit to the government, not to the holders of currency.
3. We don't need "backing" to explain why money has value. People want to hold a stock of money because money is a medium of exchange, and holding a stock of the medium of exchange makes shopping easier. This creates a (stock) demand for money. Provided the central bank restricts the supply of money, the intersection of demand and supply curves creates a positive equilibrium value of money (a finite price level). Now you could argue that if paper money were worthless it could not function as a medium of exchange, so you need to assume paper money has value in order to explain the value it has, so the demand and supply theory of the value of money begs the question.
There is some truth in this criticism of standard theories of the value of money. There are indeed two equilibria: the normal one, where paper money has value, and a weird one, where it is worthless. But Ludwig von Mises, for example, addressed this problem in 1912 with his Regression Theory of Money. Historically, money needed to be commodity money, or have commodity backing, in order to get started. But once it does get started, as a social institution, the demand for a medium of exchange supplements the industrial demand for the commodity, and the commodity backing can eventually be withdrawn as custom keeps us out of the weird equilibrium. (When Cambodia reintroduced paper money, after the fall of the Kymer Rouge, it could not create paper money ex nihilo, but initially made it convertible into rice, IIRC.)
A Ponzi scheme is a financial institution with liabilities and no assets backing those liabilities. Paper money can operate just like a Ponzi scheme, but with one important difference. Mr Ponzi promised his clients high rates of interest and/or capital gains. They would not have held his liabilities unless they believed him. The Bank of Canada promises zero interest, zero nominal capital gains, and a minus 2% real rate of interest on people who hold its paper money. Mr Ponzi could not deliver on his promise, even if he hadn't spent the assets. The Bank of Canada can deliver on its promise, even if it gave away all its assets, provided the (real) demand for its paper money does not fall over time more quickly than 2% per year. (If the real demand for money were falling at 2% per year, a constant nominal supply of money would yield 2% annual inflation).
The Bank of Canada does not need assets, because the long run growth in the (real) demand for its paper exceeds the real interest rate at which people are willing to hold its paper. If Mr Ponzi could have met the same test, he wouldn't have needed assets either. People are willing to hold paper money, even at very negative real rates of return (Zimbabwe), because doing so makes shopping easier.
The only reason that the value of a central bank's liabilities are roughly equal to the value of its assets is that whenever the difference between them (its net worth) gets too big, the bank hands its profits over to the government. If central banks choose to keep assets equal in value to their liabilities, and only hand over their annual profits to the government, then saying the value of their assets determines the value of their liabilities gets causality reversed. It is the value of their liabilities that determines the value of their assets.
So why do central banks hold any assets at all? Three reasons (funny how 3 is a magic number):
1. It makes no difference to the owners of the central bank (the government) whether the central bank keeps the bonds and hands the interest over to the government each year, or whether the central bank gives the bonds to the government. The government gets the interest either way; it just passes through another pair of hands. It's a wash.
2. Normally the real demand for paper money grows at about 3% per year (roughly the same as GDP growth rate), but sometimes it rises faster than this (like last year), and sometimes it falls (like next year?). If the demand for money falls, the central bank needs to reduce the supply of money to prevent inflation, and it reduces the supply of money by selling assets. If it had given away all its assets it wouldn't be able to do this.
3. Accountants like double-entry bookkeeping and balance sheets and stuff so they can keep track of things. They like to record assets on one side, and liabilities on the other side, to make sure that everything adds up, to check that everything's been properly recorded. So they like to list currency as a liability of central banks (even though it isn't, because there's no promise to redeem it, or pay interest on it), and assets on the other side. An accountant would freak out if he recorded currency as a liability and couldn't find an equivalent value of assets. He would say that the central bank is a Ponzi scheme. Which of course it is. And it's just not worth the hassle of trying to explain to accountants that some Ponzi schemes are sustainable, really.
Everything your write is true.. but...
If monetary authority is committed to a nominal target other than than the quantity of the monetary instrument it issues directly--like nominal expenditure, the CPI, the price of gold, or even some broad measure of the quantity of money, then it is obligated to reduce the quantity of monetary instruments it issues. It is this committment that makes them into liabilities more or less. If the quantity of the monetary instruments issued by the monetary authority is the only variable considered--perhaps a rule controlling its growth rate, or irresponsible efforts to purchase resources for the government, then they aren't liabilities to anyone.
As someone who strongly favors a growth path for nominal expenditure, the idea that central bank monetary instruments are liabilities is natural.
The monetary instruments issued by the monetary authority isn't the same thing as the quantity of money. There is a long tradition of treating the demand for money as being a constant fraction of real income. This leads to thinking in terms of "k" or even velocity. In my view, really we are assuming (and have lots of evidence) that money is a normal good. And that it is exactly of the cusp between a necessity and luxury.
While that may be true of "money," why would it be true of the particular monetary instruments created by the monetary authority. In particular, if there is a move towards a currency less economy, the demand for currency could fall significantly. Of course, the use of central bank clearing balances would continue to play a role in a currency-less payments system. Should financial innovation in cleargins be limited to protect some proportionality (loose or tight) betweeen the real demand for those instruments and real income?
In my view, no. And so, treating the monetary authority as a bank, with assets and liabilities, and focusing on controlling the quantity of those liabilities to stabilize their value is a key.
Again, I have no criticism really of your analysis. It is all correct in my view. I just wanted to add these two emphasisis that I consider important.
Posted by: Bill Woolsey | October 31, 2009 at 11:55 AM
Bill:
I fully agree with your second point. I was sloppy. Whenever I said "demand for money" I should have said "demand for central bank money".
On the first point, I think you are right in practice. I wasn't thinking about a convertible currency when I wrote it. If you have direct convertibility into gold, it would be very hard to implement in practice without significant gold reserves. But let me try to weasel out in principle. Redefine "inflation" as "inflation in the price of gold". Then if there's a sudden fall in the demand for base money, the central bank will need assets (such as gold) in order to reduce the money supply and prevent "inflation". Which is what I wrote (almost).
OK, that was very weaselly of me. You are right. I should have made my point in more general language, in terms of a reduction in the demand for money relative to the supply needed to keep the target at the target level (whether it be CPI inflation or the price of gold).
By the way, I would appreciate your thoughts on my "Why is a bank a central bank" post. Do you think I'm wrong too?
Posted by: Nick Rowe | October 31, 2009 at 12:21 PM
Bill: I re-read your first point, and see I misunderstood you. OK. I now think I see your point. If the central bank might be obliged to buy them back in order to fulfill its obligation to hit its target, then they are liabilities in that sense.
Posted by: Nick Rowe | October 31, 2009 at 12:27 PM
Don't forget the special case of "credit easing" (not so special now), where the central bank holds assets issued by the private sector.
Posted by: original anon | October 31, 2009 at 12:43 PM
Other than credit easing, the only reason for the central bank to hold assets is to make loans to member banks as required.
Apart from that, what are currently assets can be handled through internal transfer of funds (transfer priced) from the central bank to the government.
The central bank could issue its own wholesale liabilities as required for market intervention. More generally, it could undertake any required monetary operations (except for member bank loans and credit easing) entirely through liability management, including issuance and redemption.
Posted by: original anon | October 31, 2009 at 12:55 PM
Nick:
Once you admit that owning assets lets the central bank reverse course and buy back its money, you should ask what would happen if the bank lost 20% of its assets. The value of the currency unit would fall by 20%, as people would realize that the bank is now capable of buying back only 80% of the money it issued at the old par value. If you think this is right, call yourself a backing theorist and turn in your quantity theorist badge.
Starting with your first 3 numbered arguments against the backing theory:
1) The fact that most of the bank's assets are denominated in the bank's own currency is not an argument against the backing theory. It is a STATEMENT of the backing theory. Let a bank (central or private) issue 100 currency units ('dollars'), while it holds assets of 100 ounces of silver plus bonds worth $200 (bonds denominated in dollars). Let E=the exchange value of the dollar (oz./$). Setting assets (100 oz. plus bonds worth 200E oz.) equal to liabilities (300 dollars worth E oz. each) yields 100+200E=300E, or E=1 oz./$. In this case a loss of 3 oz. of gold, which amounts to a 1% loss of assets, changes the equation to 97+200E=300E, or E=.97 oz/$--a 3% inflation. There is nothing indeterminate about the value of the dollar. The case is analogous to a firm that buys call options on its own stock. Those calls will act as backing for the stock, but the stock will become more volatile as a result.
2) Think of the fed's profits this way: Suppose some foreign private competitive bank issues 100 notes ('shekels') costlessly, while holding $100 of US bonds as assets. Each shekel will initially be worth $1. The bonds yield $5 in interest every year, which the bank keeps. Rival banks will see that they can get a piece of this free lunch by issuing 100 of their own shekel notes and promising that their notes will be redeemable for $1.01 each after 1 year. Those banks will have a $4 profit at the end of the year. Rival banks will continue this bidding war until every shekel note bears 5% interest, and notes yield zero profit. If it cost $3 per year to issue and circulate those shekels, the same process would lead the shekels to bear 2% interest. If cost of issue =5%, the shekels will bear no interest.
Return to the costless case and suppose that all banks are required to donate their profits to local hobos each year. Now each shekel will always be worth $1. If the shekel ever fell to $.99, the bank would eagerly use $99 of its bonds to buy back all 100 of its shekels, for a profit of $1. If the bank lost all of its assets, the shekels would fall to zero, since the bank is incapable of buying them back.
You had made it sound like the fact that the fed pays its profits to the treasury is tantamount to the fed having no assets. That is not the case.
Of course, the Fed can be thought of as just a branch of the government. This does makes things wash, as you say. We can either say that the dollar is backed by the Fed's bonds, which are backed by 'taxes receivable', or we can say that the dollars are backed directly by taxes receivable.
3) You're right. The supply and demand theory of money begs important questions. The backing theory begs no questions at all. It says that paper money has value for the same reason that any financial security has value. The quantity theory of money asks us to believe that paper money, alone among all financial securities, has value because people want it, and people want it because it has value.
About your 3 reasons for central banks to hold assets:
1) Yes; it's a wash. As I said above, we can either think of money backed by bonds, which are backed by taxes, or as money backed directly by taxes. The main thing is that someone, bank or government, has to have assets, or the money will have no value.
2) Yes; assets are necessary to buy back the bank's money. And my question about a 20% loss of assets takes it one step farther. Once you admit this, you should stop being so sure that the backing theory is wrong.
3) Accountants aren't as dumb as all that. Assets matter and liabilities matter, and that's why accounting as a profession has survived for centuries. The dollar is truly a liability of the Fed. Suppose, for example, that some great new form of money led us all to stop using paper dollars. At that point the fed would (or should, at least) use its assets to buy back all of the paper money it has issued, and at that point people will realize that the accountants were right all along.
Now I'll repeat 3 points of my own, which I don't think any quantity theorist can answer (intelligently, anyway):
1) Name a bank, central or otherwise, that has ever issued notes (of positive value) without holding assets against them.
2) Since a money-issuing bank (called bank A) gets a free lunch in your zero-asset world, what prevents other banks from issuing rival notes, getting a piece of that free lunch, reducing the demand for A's notes, and ultimately driving their value to zero?
3) If A's notes have no backing, what happens when private banks issue derivative moneys, each of which is convertible into A's notes (or something of equivalent value). Those banks can even operate offshore, where there is no reserve requirement. As the offshore bank issues 1 unit of derivative money, it puts itself in a short position in A's notes, at the same time that it reduces the demand for (and value of) A's notes. The offshore bank profits as A's notes fall to zero value.
(Anyone interested in a fuller explanation of the backing theory, aka the Real Bills Doctrine, can click on my name above. There is also a video podcast of me explaining it to my macro principles class here:
http://www.oid.ucla.edu/webcasts/courses/2009-2010/2009fall/econ2-1
I gave an introduction in the lecture on 10/6/09, and a more extended discussion started on 10/29 and will continue until the class ends in 4 weeks.)
Posted by: Mike Sproul | October 31, 2009 at 02:49 PM
Original anon@12.43: Agreed.
@12.55: Agreed, up to the limit of the present value of the bank's seigniorage (which is a very wide limit indeed, and so barely counts as a limit in any normal circumstances).
Mike: I didn't think it would take you long ;)
0. If the bank lost 20% of its assets (in a fire), the value of its money would be unaffected, unless people thought it would ever need to redeem more than 80% of its money. The value of its assets matter only insofar as it might affect the expected future money supply. All quantity theorists (except those who argue that velocity is independent of the opportunity cost of holding money) accept that the expected future money supply affects the current value of money. I keep my quantity theorist's badge!
1. (I think you have a typo here. I think you meant to say that the bank issues 300 currency units, not 100. Let me know if I'm right about the typo, and I will edit your comment.) Assuming I'm right about the typo: I agree with your math, and agree that's an implication of the BT, but I argue that it's empirically extremely implausible. As the proportion of real assets goes to zero, the "multiplier" effect of a fall in real assets on the price level goes to infinity (and the price level becomes indeterminate at the limit). Do we see that volatility? If backing theorists really believed their theory, they would check to see if the Fed had fire insurance before deciding whether to hold bonds in their pension plans.
By the way, what happens if the real price of silver changes? What happens to the CPI? If the real price of silver doubles, I think it means the CPI must halve. Is my math right? Because it does not seem empirically plausible that a doubling of the real value of gold would halve the CPI, even for a central bank that held tiny real gold reserves, with all other reserves as nominal bonds. Not sure if my math is right.
2. If banks were truly competitive, with free entry and a zero profit equilibrium, then the backing theory would be correct. You could not run a sustainable ponzi scheme. There would be no seigniorage profits from central banking. Money would not be net wealth, as Pecek and Saving showed in the 1960's. But central banks have a de jure or de facto monopoly on issuing currency, and people continue to hold currency even at Zimbabwean negative real rates of return. It is seigniorage that makes backing irrelevant.
3. The quantity theory does indeed beg one important question, because there are two equilibria (the "Hahn Problem"?). But Ludwig von Mises provided a satisfactory answer to that problem 100 years ago.
B1. Assume no bonds for simplicity, consolidate the central bank and the government, and also ignore government spending for simplicity, so the backing theory states that the value of money is backed by taxes. The real value of the stock of base money equals the real present value of taxes. But what rate of interest do you use in that PV calculation? If you do the math, you will find it must be the real rate of return on holding money. But that is typically a negative rate of interest. Start with a 2 year problem, and keep on adding one year, and you will find that the PV formula never converges. The "bubble" term does not converge to zero in the limit as you approach an infinite horizon. It goes to minus infinity instead. In other words, if you own a printing press, and people are willing to hold your money even at negative real rates of interest, you can print money every year, give it out as transfers (negative taxes) and go on like that forever (as long as you stay within the revenue maximising rate of inflation).
B2. Quantity theorist recognise that the future demand and supply of money also affects the present price level. Assets matter if they affect expected future money supply.
B3. Same as B2.
C1: I think that's a good argument. I don't know of any banks in the normal sense of the word. But I think my arguments can also explain why central banks hold assets. Though I would admit to feeling more comfortable if I had one historical example of a central bank with negative net worth. Yap stones and cowrie shells is the closest i can come. Sure, they are both real commodities (but even paper is a "real" thing too). My point is that both Yap stones and cowrie shells (the Yap stones especially) look totally useless except as money. Even if they did have some value apart from their use as money, that "industrial value" would be a small proportion of their value as money. Again, von Mises addressed this back in 1912. (Probably others did too).
C2. It's normally only true for central banks, by the way. Central banks have a de facto monopoly (or considerable local monopoly power). Some people say this is due to legal tender laws. Others (I lean more this way) say this is due to a QWERTY equilibrium, where nobody wants to switch to a competing currency unless everyone else switches too. Whatever the reason, central banks do have monopoly power, and do earn super-normal profits year after year.
C3. Canadian Tire money is a good example. It's of dubious legality, but is tolerated by the Bank of Canada, but doesn't circulate. It doesn't pay interest because perhaps of technical difficulties. And if it paid interest by appreciating it would mess up as a unit of account. I tried to address this question in an old post comparing Canadian Tire with California scrip. No good answer. Legal restrictions? Custom (QWERTY)? Some variant of Gresham's Law? Dunno. But whatever the reason, central banks earn supernormal profits, and have always done so, and keep on rolling.
Good arguments going on two posts now!
Posted by: Nick Rowe | October 31, 2009 at 04:13 PM
Great topic!
I think you're being a bit flippant about accounting though. And there is a promise to redeem central bank notes! Section 16.4 of the Federal Reserve Act specifies that notes are a "first and paramount lien" on the Fed's assets. Section 24 of the Bank of Canada Act says that "The Bank has the sole right to issue notes and those notes shall be a first charge on the assets of the Bank." The promise to redeem may not be immediate, but it indeed exists. Assets are necessary to make good on this promise.
I never liked the Regression Theorem. It depends on naive backwards expectations, whereas people are forward looking too. Is there any other theory one can substitute for it?
Anyways, I'm stepping out of this one. Want to watch the great Nick Rowe quantity theory vs. Mike Sproul backing theory debate.
Posted by: JP Koning | October 31, 2009 at 04:26 PM
Nick: @12.55: Agreed, up to the limit of the present value of the bank's seigniorage (which is a very wide limit indeed, and so barely counts as a limit in any normal circumstances).
And later
If banks were truly competitive, with free entry and a zero profit equilibrium, then the backing theory would be correct. You could not run a sustainable ponzi scheme. There would be no seigniorage profits from central banking
What happens as seigniorage approaches 0, say with digital currency?
Posted by: edeast | October 31, 2009 at 04:40 PM
I know I said I'd pipe down, but the topic of Yap stones came up.
Nick, here is a great article on Yap Stones by Dror Goldberg: http://www.appropriate-economics.org/materials/famous_myths_of_fiat_money.pdf
It appeared in the Journal of Money, Credit and Banking.
The article points out that modern theorists caricature Yap money as worthless, without exploring the "laws, customs, religion, and trade relations" that gave Yap stones their intrinsic non-monetary value. He goes on to detail these non-monetary features, including various religious and social traditions. Anyways, I don't think you can use Yap stones as an example of "totally useless" fiat money, nor say that any non-monetary value was a small proportion of total value. Unless you are from Yap and haven't told us?
Posted by: JP Koning | October 31, 2009 at 04:53 PM
Nick:
0) How far would you press that 20% loss of assets argument? What if the bank lost 99% of its assets? 100%? If we were talking about private, competitive money-issuing banks, I think you'd agree that a 20% loss of assets would cause the currency to lose 20% of its value. Why claim that central banks immune to this? Especially if those central banks are in countries that are small, weak, and close together, with currencies crossing borders without much trouble?
1) (The $100 was a typo. It should have been $300.) What you called the 'multiplier' is what I call 'inflationary feedback'. I didn't use 'multiplier' because it's overused, and always incorrectly. You're right that the value of money becomes indeterminate when all the bank's assets are denominated in the bank's own money, so real banks must hold some real assets. If you doubt that this is plausible, just think of my example of a firm that buys calls on its own stock. If that firm loses assets, its stock will lose value. But then the calls will fall too, which makes the stock fall more, etc.
One reason we don't see that volatility is that everyone believes that the government stands behind the central bank, so even if the bank lost some assets, the government would bail it out. This muddies up the equations. But if we were talking about a private competitive bank with no chance of a bailout, the effect would be just what the math implies. I'd give the same answer to your question about a doubling of the price of silver. If we were talking about the no-bailout case, then the CPI would double. But if the central bank is just a branch of the government, there would be little or no effect on the CPI.
3) Can you cite the relevant chapter and verse in Mises' Theory of Money and Credit? It's online at mises.org. I doubt very much that he gave a satisfactory answer.
B1) Here's simpler example: A landowner collects rents of 50 oz. of silver per year. The market interest rate, which is beyond his control, is 5%. His land is therefore worth 1000 oz. When he buys groceries, he pays with his own 1-ounce IOU's, which he accepts in payment of rent. His IOU's circulate as money, because lots of people rent from him. He is just like a government, except he collects rent instead of taxes. He could issue those IOU's through a separate set of books called a central bank, but he might as well consolidate his bank with his other assets.
Note that there is no problem determining the appropriate rate of interest, and that non-convergence problem you mentioned never happens. The landowner could issue 400 IOU's and spend them on candy. This would reduce his net worth to 600 oz, but each IOU would still be worth 1 oz. He could then issue another 600 IOU's, spend them wastefully, and reduce his net worth to zero, but still no inflation. He has just burned up his net worth. If he then issued another 2000 IOU's and spent them wastefully, his IOU's would fall to 1/3 ounce. But if those 2000 IOU's were instead spent on land worth 2000 oz, he would then have 3000 oz of land backing 3000 IOU's, and there would be no inflation. Or he could buy the land by issuing a 2000 oz. bond. Then he could sell the 2000 oz. bond to his personal central bank, which would purchase the bond with 2000 newly-printed IOU's. Same result.
The landowner's IOU's might actually bear negative interest, but only if the cost of issuing them was greater than 5%/year. If those notes were a source of profit to the landowner, rival banks would offer notes that paid better interest.
B1 and B2: Why try to use a supply and demand model to explain the value of money, when the simple accounting relation: assets=liabilities explains it? I suppose you could say that the price of GE stock is determined by peoples' expectation of the future supply and demand of GE stock, but that just leads you to a tautological explanation of stock prices. That's why stock market analysts use accounting, not supply and demand models, to value stock.
C1) There's another story of some sailors in WWII who used Monopoly money to buy some food from natives. Years later they returned and found the monopoly money still circulating on the island. This can be explained by the natives' ignorance. The backing theory does not deny that usefulness as money can give value to a commodity. For example, before paper money, part of silver's value resulted from monetary demand for it. As paper and credit money was introduced, the value of silver fell to its 'use value'. This one-time fall in the value of silver is a case where a bank issuing money on real-bills principles would still cause inflation. But once silver has fallen to its use value, additional paper money can't make silver fall any lower, and the real bills rule will be fully correct.
C2) The Bank of England had a monopoly of note issue within London since 1694. Its pounds were convertible into gold at about 4 pounds/oz. The Bank had to have assets worth 100 ounces of gold (fractional reserves) for every 400 pounds it issued. Otherwise a bank run would have happened. On Feb 26, 1797, the Bank suspended convertibility. The value of the pound was unaffected. It was during this period (1797-1821) that people got the idea that since the pound was inconvertible, it must be unbacked. But where were the super-normal profits? If inconvertible money can have value in excess of the assets backing it, why did the value of the Bank's money continue to equal the value of the bank's assets? My answer is that people, then as now, confused 'inconvertible' with 'unbacked'. Convertibility was restored in 1821, a 24-year suspension. Would you have said that the pound was unbacked from 1797-1821? Or would you have said that it was backed but physically inconvertible into gold? Would you say that the dollar suddenly became unbacked in 1933? Or just inconvertible? What about a competitive note-issuing bank that closes every weekend? Do its notes suddenly become unbacked every Friday night, or just backed but inconvertible?
C3: Same answer as C2 about supernormal profits.
Posted by: Mike Sproul | October 31, 2009 at 06:40 PM
Mike: the link to von Mises Human Action version of the Regression Theory of Money is in my main post. It's probably a simpler treatment than the 1912 original. Halloween in full swing here. I will return later, maybe tomorrow, to consider the rest of your response.
P.s. liked your argument with David Laidler (both sides).
Posted by: Nick Rowe | October 31, 2009 at 07:04 PM
I think that "worthless paper money" can have value without the price level being determinate. If the central bank's assets are nominal in nature, that presumably means that they generate a certain nominal income, in which case the obligor must obtain central bank money to meet their commitment. For example, if the central bank supplied currency by buying interest-bearing debt, when that debt matures, there is a net shortage of currency outside the central bank, and the obligor must then either default or sell whatever the central bank demands to obtain the money it requires to discharge its obligation.
Posted by: RebelEconomist | October 31, 2009 at 07:12 PM
Nick (and everyone):
By reading your recent posts (and comments), I've got a feeling that you may be interested in the argument of the following people.
http://bilbo.economicoutlook.net/blog/?p=381
http://bilbo.economicoutlook.net/blog/?p=1075
http://www.nakedcapitalism.com/2009/10/all-debt-is-not-created-equal-government-debt-is-not-the-same-as-private-debt.html
http://neweconomicperspectives.blogspot.com/2009/08/money-as-public-monopoly.html
Their argument is peculiar in that it is the government spending, not the central bank, that creates and provides money to people. Central bank seems to play a rather minor role in their argument. I'd like to know what you think about their assertion. (Although I know Scott Sumner already had some skirmish with one of these people over negative rate... cf) http://neweconomicperspectives.blogspot.com/2009/07/why-negative-nominal-interest-rates_14.html)
Posted by: himaginary | October 31, 2009 at 11:53 PM
himaginary,
Chartalism seems far fetched to me. I agree that ultimately most governments can direct the central bank, and would recapitalise the central bank if it went bust, but I have no reason to believe that governments routinely conduct their fiscal policy with these extreme scenarios in mind, which seems to be the key tenet of Modern Monetary Theory, as its adherents grandly name it. In normal conditions in the developed economies, the government regards the base money supply as a given, set by the central bank. In many countries, the central bank does not buy much if any government debt to distribute and back its base money (they buy secured bank debt - repo - instead), and even the government debt is managed by a specialist agency that is semi-detached from fiscal policy. But I must admit to being instinctively hostile to the fervour of some of the disciples of MMT and the long and tedious blog posts that they expect the curious to read.
Posted by: RebelEconomist | November 01, 2009 at 05:22 PM
Mike: reading through your second comment, a thought suddenly came to me. Suppose a firm had a legal monopoly on the right to produce apples. How would we value its assets? We ought to include that monopoly right as one of the assets, not just the land and machinery. The share price of the firm would certainly reflect it. Now suppose that monopoly right right to produce apples could not be sold. We would want to make a distinction between the value of the firm as a going concern (the PV of its profits, which would include the value of the monopoly), and the break-up value of the firm (which would exclude the monopoly). The same thing would presumably apply to a financial institution that had a monopoly on issuing mutual funds. And the same thing would presumably apply to a monopoly issuer of currency. You can't just look at the value of the assets on the books, which might represent the break-up value of the firm, but don't represent its value as a going concern.
Now suppose the apple monopolist gave to charity all the profits it didn't need to keep the share price at some target. We would need to subtract the present value of charitable donations in calculating the share price. But the PV of charitable donations is endogenous wrt to price of shares. The value of assets (= book assets + PV monopoly profits - PV charitable donations) cannot determine the price of shares, because part of the asset value (the charitable donation) is endogenous wrt the share price.
Now, it doesn't need to be a legal monopoly. It could be a monopoly based on network externalities, or whatever.
0). As long as the PV of the central bank's monopoly profits are big enough, if it lost 20% of its book assets it could make up the loss by reducing its charitable donations to government, and the price of its currency would not be affected.
B1) Suppose B is initial government debt, with a real interest rate r, and the economy has a real growth rate g, and S is the initial real primary surplus and grows at rate g. Ignore money. We can write the long run government budget constraint as:
B = PV(Surpluses) = S/(r-g) + limit as t goes to inf of B(1+g)^t/(i+r)^t.
As long as r exceeds g, the second term goes to zero in the limit, and it simplifies to B = S/(r-g). The value of government debt equals the PV of primary surpluses.
Now suppose the government uses money finance of deficits. Ignore bonds for simplicity. Let M/P be real stock of currency, and r the real rate of interest on currency.
M/P = PV(Surpluses) = S/(r-g) + limit as t goes to inf of M/P(1+g)^t/(i+r)^t.
Trouble is, r is typically negative on money, and is also almost always less than g. So the second term does not converge to zero. It usually goes to plus infinity.
JP: "I never liked the Regression Theorem. It depends on naive backwards expectations, whereas people are forward looking too. Is there any other theory one can substitute for it?"
I'm unhappy with the backwards expectation bit too. But in the real world, I can't help noticing that conventions do seem to work based on naive backward looking expectations nearly all the time. But let me throw a bone to the "backing" theory: if there were a single ounce of gold backing all the paper money in Canada, that would be enough to rule out the zero value of money equilibrium.
Posted by: Nick Rowe | November 01, 2009 at 10:08 PM
Let's do some back of the envelope calculations.
Suppose a central bank has $100 of currency liabilities and $100 in bonds as assets. Suppose the economy grows at 2% per year, and the real demand for currency grows at 2% too. Suppose the bank targets 2% inflation, so it can issue $4 of new currency each year. Suppose its admin costs are 1%, so its net seigniorage profits are $3. If interest rates are 5% nominal, 3% real, then the present value of its net seigniorage profits are the present value of $3 growing at 2% per year in real terms discounted at 3% real = $3/(3%-2%) = $300. In other words, the asset value of its stream of supernormal (monopoly) profits is much bigger than the value of the assets on the books.
Posted by: Nick Rowe | November 01, 2009 at 11:01 PM
Nick:
It's late and I just got home, and it's a long day at work tomorrow. Before I address the hard stuff, am I right in thinking that you would agree that the backing theory is correct in the economist's usual model of perfectly competitive, zero-profit, money-issuing banks? Would you then agree that the BT becomes more correct even for central banks as those banks' currencies come to compete with each other?
Posted by: Mike Sproul | November 01, 2009 at 11:30 PM
Mike: "It's late and I just got home, and it's a long day at work tomorrow."
No rush. I sympathise. I delay too long in responding to comments myself. Take your time.
"Before I address the hard stuff, am I right in thinking that you would agree that the backing theory is correct in the economist's usual model of perfectly competitive, zero-profit, money-issuing banks?"
Yes.
"Would you then agree that the BT becomes more correct even for central banks as those banks' currencies come to compete with each other?"
I'm still trying to get my head around that one. Part of me is saying "yes"; the two theories ought to converge in the limit. But I can't quite see it clearly enough yet.
Posted by: Nick Rowe | November 02, 2009 at 12:15 AM
Yes, they do converge in the limit.
Assume zero growth in real currency demand. Assume no admin costs. Assume 5% real interest on bonds. At zero inflation, no assets are needed. At 1% deflation (a 1% real return on currency), the central bank must retire 1% of the money stock each year, and it will need 20% (=1%/5%) of its assets to do this. At 2% deflation it will need 40% of its assets...and as competition increases, and the required deflation rate needed to meet the competition approaches 5%, it will need all its reserves.
Percentage of reserves needed to preserve the existence of the equilibrium in which paper currency has value (assuming zero admin costs) = (real interest rate on currency minus growth rate of real demand for currency)/real interest rate on bonds. It's a negative percentage under current parameter values.
Posted by: Nick Rowe | November 02, 2009 at 12:29 AM
"But let me throw a bone to the "backing" theory: if there were a single ounce of gold backing all the paper money in Canada, that would be enough to rule out the zero value of money equilibrium."
Nick, by this do you mean to say that backing in general is enough rule out the zero value of money equilibrium, or do you mean that there is something special about gold backing in particular?
Posted by: JP Koning | November 02, 2009 at 04:29 PM
JP: I mean that backing with some real asset is enough to rule out the zero value of money equilibrium. It doesn't have to be gold, it could be real estate. The BoC building would do it. But it must be real; nominal bonds (promising to pay Loonies) wouldn't work.
I hadn't realised this before. Learn something new, every post, from the comments. More than one thing, usually.
Posted by: Nick Rowe | November 02, 2009 at 06:16 PM
himaginary: I skimmed through the first link you posted. As far as I can see, the author just defines "fiscal policy" as being money-financed (and he ignores the stock-flow distinction, because an increased money-financed deficit changes the rate of increase of the stock of money, not the level of the stock of money, except over time). And he assumes unemployed resources in a demand-constrained economy with a fixed price level. That's how he gets his result that fiscal deficits cause interest rates to fall.
Nothing unorthodox about it, except his definition of fiscal policy.
Posted by: Nick Rowe | November 02, 2009 at 09:46 PM
RebelEconomist and Nick:
Thank you for responding to my comment. I didn't know this school is called Chartalism - or Neo-Chartalism to be exact, according to Wikipedia.
http://en.wikipedia.org/wiki/Chartalism#Modern_Proponents
The reason I recalled their argument is that they deem government debt as only a tool of monetary operation. Here is what Bill Mitchell says (from first link of my previous post):
"Government debt-issuance is a monetary policy consideration rather than being intrinsic to fiscal policy"
This statement seemed to resonate with No.2 of above reasons for central banks to hold assets.
Nick@11:01 PM:
"In other words, the asset value of its stream of supernormal (monopoly) profits is much bigger than the value of the assets on the books."
This discrepancy between asset and book value makes money look like equity rather than liability of the central bank. In this line of thinking, money issuance can be deemed as capital increase at market price, and corresponding increase of government debt as the asset procured by it. (Conversely, retiring the part of money stock can be thought as share buyback.) Thinking along finance theory, it follows that monetizing government debt this way wouldn't do real harm, unless it undermines the overall growth prospect of the country (including accelerating inflation) or exceeds the asset value.
In this sense, too, I suppose that your monetary theory may have some common ground with Neo-Chartalism. The monopoly profit here may correspond to what they call tax-collecting power.
Posted by: himaginary | November 02, 2009 at 11:21 PM
himaginary,
Before the financial crisis, the stock of base money in most developed economies was of the order of single figure percentages of GDP, say three times a typical fiscal deficit. I have not read the posts you give in detail, because, as I said, these people seem incapable of putting their arguments objectively and concisely, but just this simple consideration of scale suggests that such a policy would be highly inflationary.
I used to work in a central bank, and I never heard of chartalism or the idea that governments issue bonds for monetary control until I left. That's how much impact it has on practical monetary policy. But then they would probably dismiss me as part of some conspiracy or complacent elite.
Posted by: RebelEconomist | November 03, 2009 at 04:13 AM
I read the Wikipwedia entry. Some of it is quite orthodox, just re-framed so it sounds unorthodox. It is absolutely orthodox, for example, to say that governments get revenue from seigniorage - money creation. The unorthodox part is the (usually implicit) assumption of fixed prices, plus maybe the (to my mind daft) belief that money would disappear if governments required us to pay taxes in goods, rather than money.
You can think of governments financing deficits by printing money, then the central bank retiring that money, if it wants, by selling bonds. Or you can think of governments financing deficits by issuing bonds, then the central bank retiring those bonds, if it wants, by printing money. It makes absolutely no difference.
A mixture of Abba Lerner and Knapp. But I'm not sure if they read Knapp correctly (I sympathise, since it's a horrible book to read). There's maybe less in Knapp than they read into him. I'm not sure that Knapp ever understood the distinction between the real and nominal value of money. This might be what caused the German hyperinflation.
The big difference between money and shares is that people want to hold money, even at a negative real rate of return, because money makes shopping easier.
Posted by: Nick Rowe | November 03, 2009 at 06:42 AM
"But it must be real; nominal bonds (promising to pay Loonies) wouldn't work."
What about paper claims to gold (like a gold ETF), or paper claims to real estate? Would you consider those real enough to serve as backing for money? What about bills of exchange (short term debt) specifically secured by a firm's inventories? Say the firm makes trucks and its inventories are half finished trucks and valuable parts.
Posted by: JP Koning | November 03, 2009 at 09:10 AM
JP: the paper claims to a fixed physical amount of gold or real estate would do it, because their nominal value if the price level doubled. Bills of exchange that promise to pay a given quantity of dollars, even if secured by real assets, wouldn't do it (OK, they might just do it, if the risk of default were large, so that a doubling of the price level had a significant affect on the nominal value of those bills, because the trucks would be worth more relative to the face value of the bill).
Posted by: Nick Rowe | November 03, 2009 at 09:37 AM
"OK, they might just do it, if the risk of default were large, so that a doubling of the price level had a significant affect on the nominal value of those bills, because the trucks would be worth more relative to the face value of the bill"
If you can see how the above bills have real backing and might do the trick of ruling out the zero value of money equilibrium, then its not a far stretch that bonds can do same.
Secured bonds, or asset-backed bonds, are backed by a specific asset of a corporation or government, such as real estate or equipment. Unsecured bonds are simply claims on the remaining real assets. Bonds are more than just promises to pay a certain coupon; all debt has some sort of real backing at its core, either through its claim (in case of default) to a specific real asset or to the rest of an entity's real assets. There's no reason that bond backing, like gold backing, can't prevent the zero value of money problem.
Posted by: JP Koning | November 03, 2009 at 11:14 AM
JP: "There's no reason that bond backing, like gold backing, can't prevent the zero value of money problem."
If money became worthless in real terms, bonds promising to pay that money would become worthless too, in real terms, even if they were secured by real assets.
Bonds promising to pay a physical quantity of gold, or trucks, would not become worthless.
Posted by: Nick Rowe | November 03, 2009 at 11:34 AM
"If money became worthless in real terms, bonds promising to pay that money would become worthless too, in real terms, even if they were secured by real assets."
You're trying to keep me trapped in the zero-value of money problem by assuming the zero-value of money to begin with. I can't get out of that one!
No currency has ever fallen in one day. Prior to worthlessness, bond issuers will have increased rates, attached an inflation adjustment, or issued bonds payable in several currencies. All these protect from exchange rate risk, while the bond's backing protects from firm-specific risk.
Alternatively`; once money is worthless, it ceases to exit. Bond issuers will be unable to meet their promise to pay, and will either have to renegotiate with holders to pay in a real currency, or go into default and forfeit their assets to the bondholders.
You seem to be saying that the promise of money payment is all that drives bond value. What happens if a firm announces it will stop paying money to bondholders? The bond's value won't fall to 0, since the bondholders can go to court to pursue the firm's assets. Real backing exists and is essential to bond valuation, and it prevents the zero-value problem as good as gold does.
Posted by: JP Koning | November 03, 2009 at 01:07 PM
If money were worthless, nominal bonds would never default, because the issuers of the bonds would just pick up worthless paper for free and use it to pay off the bondholders, as promised. Much better than losing the trucks.
Posted by: Nick Rowe | November 03, 2009 at 01:22 PM
Let's back up: we're trying to figure out what causes the zero-value of money problem. I'm saying it is backing (could be bonds) that prevents the zero value problem, lack of backing causes it. For the last 2 posts you arrive at the zero-value of money by assuming the zero-value of money to begin with. That's circular reasoning.
Do you think that a firm's renunciation of interest and principal payments will result in bonds with zero value?
Posted by: JP Koning | November 03, 2009 at 02:37 PM
JP: "For the last 2 posts you arrive at the zero-value of money by assuming the zero-value of money to begin with. That's circular reasoning."
Yep. It is circular. But that's OK.
Suppose you want to check whether P=$4 is an equilibrium. This is how you do it. First you assume P=$4, then figure out quantity demanded and quantity supplied when P=$4. If quantity demanded and supplied are equal, then you have proven that P=$4 is an equilibrium. (But you haven't proven it is the only equilibrium.) If quantity supplied and demanded are not equal at P=$4, then you have proven that P=$4 is not an equilibrium.
Posted by: Nick Rowe | November 03, 2009 at 04:16 PM
JP: "Do you think that a firm's renunciation of interest and principal payments will result in bonds with zero value?" Yes, unless: the courts can force them to pay; the bonds are unusually attractive to hang on your wall; or they are already in use as media of exchange.
Posted by: Nick Rowe | November 03, 2009 at 04:18 PM
Nick:
00) “The value of assets (= book assets + PV monopoly profits - PV charitable donations) cannot determine the price of shares, because part of the asset value (the charitable donation) is endogenous wrt the share price”
This sounds like the inflationary feedback problem, where the value of the bonds depended on the value of the money. But the price level was determinate in that case. I think in this case if S=share price, n=number of shares, and d=charity donations as a proportion of share price, the equation would be
Book assets+ PV monopoly profits –dS=nS, and this yields a value for S.
0) “if it lost 20% of its book assets it could make up the loss by reducing its charitable donations to government, and the price of its currency would not be affected.”
I agree. If the bank has some source of wealth to make up for a loss of assets, then the value of the currency needn’t fall.
B1) I’m still scratching my head on this one. I’ll let it go for now.
I’ve listed what I think are key points below. This is important enough that I’ll start a new numbering system:
I. No bank has ever issued notes without holding assets against them. This point certainly favors the BT over the QT. I would add that no bank has ever kept notes in circulation while holding assets worth 20% less than the notes. If it did, speculators would attack the currency. If the currency were convertible, the attack would take the form of a bank run, and speculators would walk away with all the bank’s assets. If the currency were inconvertible, the attack would take the form of large short positions in the currency, which would drive the currency down while yielding profits to the attackers. Your claim that the bank can maintain the currency’s value by holding assets worth only 20% ignores the possibility of attack. Only when assets are worth at least 100% as much as the currency is the bank immune.
II. Convertibility: Every text I know of starts by saying “The dollar is inconvertible, therefore it is unbacked. So how can an unbacked currency have value? Because it is limited in supply and people demand it.”
My answer is that ‘inconvertible’ does not equal ‘unbacked’. Every time a bank closes for the weekend, its money becomes inconvertible, but the money is still backed by the bank’s assets. So what if the weekend suspension of convertibility is extended to 76 years, as long as the bank’s assets are still there in the vault?
Furthermore, there are many kinds of convertibility. The dollar is not physically convertible, meaning that the Fed will not buy back its dollars with gold. But the dollar has always been financially convertible, meaning that the Fed always stands ready to buy back its dollars with its bonds. Financial convertibility can make physical convertibility irrelevant. Some day the Fed might sell its gold for dollars. That’s physical convertibility, but at the Fed’s option rather than the customers’.
Convertibility can be instant or delayed, certain or uncertain, at the Fed’s option or at the customer’s option, etc. In 1933 the Fed suspended just one kind of convertibility: instant physical convertibility at the customer’s option. The other forms of convertibility remain in effect, so lack of physical convertibility does not imply lack of backing.
III. Do you still think the dollar is not the Fed’s liability? JP Koning and I have both argued this, and I’m hoping you might be weakening. I’d think you’d agree that if the currency were convertible, then it would be a true liability of the issuing bank. But given the many forms of convertibility I mentioned above, and given my earlier argument that the Fed might someday use its assets to buy back all the paper dollars, it seems to me that the dollar is a true liability of the Fed.
IV. The Fed’s monopoly power. We agree that the backing theory is right for perfectly competitive banks. So a belief in the quantity theory is left hanging on the Fed’s monopoly power, and that’s not much to hang a theory on. There’s a range of central banks in the world, and their currencies compete with each other to varying degrees, so you’d have to say that the backing theory has varying degrees of correctness for these banks.
Personally, I question whether monopoly power is even relevant. The Bank of England had a monopoly of note issue within London since 1694. What was a B of E paper pound trading for on the street? Exactly one pound in coin. There were competitive country banks that also issued paper pounds outside London. Their paper pounds also traded for one pound coin. Where’s the monopoly premium in the B of E’s notes? There isn’t one. The only thing monopoly gives to the Bank is the ability to lend notes at maybe 6% when the market interest rate is 5%. That matters, I know, but I don’t think it matters much.
V. The quantity theory implies weird things: a) Legitimate bankers have the same impact on the price level as counterfeiters. b) When dollars get spent in Mexico and stay there, the dollar appreciates and the peso depreciates, and the US gets a free lunch at Mexico’s expense. c) People accept dollars because other people accept them. d) Most quantity theorists think that more base money causes inflation, but they’re split on whether derivative moneys cause inflation. e) It doesn’t matter how many dollars we have. If there are twice as many, each will be worth half as much, so the business of the country gets done regardless of the amount of money. f) MV=Py is a tautology. It’s just as true of GE stock as it is of money, but at least economists understand that it’s meaningless when applied to GE stock.
Posted by: Mike Sproul | November 03, 2009 at 10:07 PM
"2. Normally the real demand for paper money grows at about 3% per year (roughly the same as GDP growth rate), but sometimes it rises faster than this (like last year), and sometimes it falls (like next year?)."
By paper money I am going to assume you mean currency. So, if currency has been growing by 3% per year and currency denominated debt has been growing about 8% to 9% a year (since about 1975), does that scenario eventually lead to problems?
Posted by: Too Much Fed | November 04, 2009 at 12:00 AM
"Yep. It is circular. But that's OK. Suppose you want to check whether P=$4 is an equilibrium..."
Gulp, equilibrium. I prefer to understand money from an evolutionary perspective. Walrasian reasoning (I've read my Laidler) can't grasp money, because if you posit a Walrasian auctioneer you don't need a monetary system to begin with. So that's probably why I accuse you of circular reasoning here - temporal cause and effect is my bread and butter. But let me give it a try.
Hypothesis: An equilibrium in which money is valueless can be prevented if a currency has real backing. If backing is bonds, then the expectation that courts can and will make good on a bond issue's covenant and deliver a bond-issuing firm's remaining real assets to bondholders, ensures a monetary equilibrium.
Proof: Assume for the sake of argument that people did expect money to be worthless despite the bond backing. And that because of this, as you say, the bonds themselves are worthless.
Arbitrageurs would take people's bonds off them for a tiny fee and hold them. (Since money is worthless, they might have to perform some tiny service for the bond, or maybe barter a coffee bean for the bond). Why would they do this? Because there is a possibility that while they hold those bonds the issuing firm goes bankrupt or winds itself up, the real assets being returned to creditors as per the bond covenant. Thus, due to arbitrage, the bonds' value rise above nothing. Other arbitrageurs, seeing that the bonds now have some value, and realizing that the issued money is a claim on said bonds, now offer to take people's valueless money from them for a pittance (say a coffee bean).
But now that money has some slight purchasing power, a feedback loop begins. The bonds no longer promise to pay a monthly payment of worthless money, but a monthly payment of money worth slightly more than 0. The bonds' price is quickly bid up: their value no longer depends solely on the possibility of the bondholder receiving real assets from a judge upon windup, but also an actual monthly money payment. As a result money claims to those bonds get bid up. As a result bonds get bid up. Money gets bid up.
So the real assets that back bonds and are enshrined in all bond covenants can guarantee a non-zero value of bond-backed money. I call it the Progression theorem ;) What do you think?
Posted by: JP Koning | November 04, 2009 at 12:06 AM
original anon said: "Don't forget the special case of "credit easing" (not so special now), where the central bank holds assets issued by the private sector."
Bingo! Those treasuries are there to BAILOUT the fed's banking buddies in case they ever get into trouble producing too much currency denominated debt, preferably on the lower and middle class.
Is that the REAL reason greenspan was worried about gov't surpluses back in around 2000? That reason would be he and the fed do/did NOT want gov't debt to be zero.
Posted by: Too Much Fed | November 04, 2009 at 12:06 AM
Nick said: "Suppose a central bank has $100 of currency liabilities and $100 in bonds as assets. Suppose the economy grows at 2% per year, and the real demand for currency grows at 2% too. Suppose the bank targets 2% inflation, so it can issue $4 of new currency each year."
Maybe I don't get this, but what happens to the extra $2 of new currency?
Also, what happens if the extra $2 is currency denominated debt instead of currency?
Posted by: Too Much Fed | November 04, 2009 at 12:21 AM
Nick@Nov 01-11:01 can be formulized as:
PV of net seigniorage profits = sum of (g+p-c)*Y0*{(1+g)^(t-1)}/{(1+r-p)^t}
where g is real growth rate, p is inflation rate, c is admin cost, Y0 is initial GDP, r is return on money.
Here, economy is assumed to grow like Yt=Y0*(1+g)^t.
Nick assumed r=5%, but I think that should be 0%, as it is money, not bond. So PV of net seigniorage profit is plus infinity as long as economy achieves positive growth and positive inflation (g>0,p>0; normal case).
Even in deflation case (p<0), PV goes to infinity as long as nominal growth is positive (g+p>0).
However, if nominal growth is zero or negative (g+p<=0), we have trouble. In that case, PV becomes less than minus value of current GDP:
PV = -Y0 + c*Y0/(p+g)
This may suggest the importance of NGDP growth, as Scott Sumner always asserts.
Posted by: himaginary | November 05, 2009 at 10:29 AM
Correction of my previous comment: Y0 should be regareded as current size of CB asset, not GDP.
So if nominal growth is negative, value of current asset becomes c*Y0/(p+g), or admin cost divided by that negative growth. Queerly, the larger the absolute value of the negative growth is, the smaller its negative impact becomes. That's because admin cost is assumed to grow at that growth rate, too.
Posted by: himaginary | November 05, 2009 at 06:48 PM