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The necessary condition to set the value of the BMO dollar is that the bank has enough assets to buy back all its demand deposits at par. Without this, any attempt to maintain convertibility will cause a bank run.

Convertibility can take many forms. It can be instant or delayed, certain or uncertain, at the bank's option or at the customer's option, in real units or in nominal units, etc. You are talking about suspending just ONE kind of convertibility (into BOC dollars), and of course as long as other channels of convertibility remain open, the loss of that one channel is irrelevant. For example, my BMO bank might have issued 1 BMO dollar in exchange for 1 BOC dollar, which I keep in my vault. Then I lend $99 BMO into existence, leaving me with $100 checking account BMO dollars on the liability side of my balance sheet, while my assets consist of $1 BOC plus $99BMO of loans. As loans are repaid and re-issued that $99 will grow and shrink without me ever having to pay out that last $1 BOC. I could stay in business for 1000 years and only pay out that $1 BOC on my last day in business.

Almost makes you think the same is true of every central bank, doesn't it?

Mike: suppose the central bank wants to target the price of gold, but it has a taboo against handling gold. But it has no taboo against handling silver. So it makes central bank money directly convertible into silver, and adjusts the silver exchange rate so as to keep the market gold exchange rate (almost exactly) fixed. No problem. That's the third instrument. It's a little bit more indirect that direct convertibility, but it should work almost as well. **It is not an interest rate instrument**.

Nick,

Are we grouping together loan sales and deposits as basically the same thing? With loan sales, the lending bank removes credit risk from the asset side of it's balance sheet by selling the loans that it makes off to a third party (could be depositors, could be mutual fund / insurance company / other third party investors). With interest on deposits, that is not necessarily true - credit risk is often shared by the depositor and the lending bank.

Also, implicitly a beta bank is free to turn away business either in the form of additional deposits or additional borrowers.

"If it is sufficient for the Bank of Canada, why wouldn't it also be sufficient for the BMO?"

To make this a meaningful comparison, I think you need to suppose some kind of stickiness in the exchange rate between BMO money and BoC money.

First shot at it:

The BMO dollar in effect becomes a foreign currency relative to the Canadian dollar.

So there’s going to be a floating FX rate for the BMO dollar. It’s a market rate. BMO can try to target parity on that rate, without guaranteeing conversion, using interest rates (as it would if it guaranteed conversion):

Since BMO (still) competes with Canadian dollar banks for business (I think you have actually stated that), it can gain or lose business for both deposits and loans depending on how it sets its interest rates. If the BMO dollar is under pressure, it can “tighten” by increasing both loan and deposit rates, which should tend to attract net foreign currency (Canadian dollar) inflows – because it will tend to gain deposits and lose lending business.

This assumes it will “convert” natural Canadian dollar inflows into BMO dollar liabilities while increase Canadian dollar reserves as a result.

And presumably the conversion rate for those deposit liabilities as they are created reinforces the parity targeting.

The opposite effect occurs when it “eases” its interest rates.

It’s still a commercial bank with an equity position, so it needs to manage its interest margins and profitability accordingly. And even while it is targeting parity, it will have FX risk on its Canadian dollar reserves.

Given its small size relative to the residual Canadian banking system, there will still probably be lots of undesirable market volatility in the exchange rate it’s trying to target - requiring aggressive interest rate management. It's a hot money bank.

So maybe. But it could be a very wild ride, with a rather uncertain outcome.

Frank: "Are we grouping together loan sales and deposits as basically the same thing?"

No. Red herring.

Nick E: Fair point. If prices are sticky in the short run, or if expected future prices are sticky in the short run, that will matter. But in the long run, if both actual and expected prices (and inflation rates) can adjust, there shouldn't be any difference.

JKH: I was fully with you up to this point:

"This assumes it will “convert” natural Canadian dollar inflows into BMO dollar liabilities while increase Canadian dollar reserves as a result.

And presumably the conversion rate for those deposit liabilities as they are created reinforces the parity targeting."

at which you lost me. What determines the market conversion rate? (We could imagine some third party (clearing house??) that converts between BMO dollars and BoC dollars, at a market rate.)

To make it simpler, we don't need to assume BMO maximises profits. Let's just assume it tries to keep the exchange rate constant, without directly intervening in the market.

I'm a beta bank.

If I set the interest rates I lend and borrow at too low then the qty of my dollars expands and its value will tend to fall below 1:1 with aloha money. If people know and trust that i will keep my money 1:1 with alpha money they will know I will eventually have to adjust the interest rates I set so will not be too worried about a short term deviation. But if people don't know this (or don't trust me) they may think I plan to expand my money beyond what is sustainable at 1:1. I will have to raise interest rates to compensate for this concern, and this could easily end badly for me with my currency becoming worthless.

So I think you would need something like the third instrument tying the value of my currency to some externally measurable thing to make interest rates guaranteed to enable me to pin the value of my money.

I think perhaps when a CB sets a target (inflation or NGDP) but people are not convinced it really is committed to meet it then (and it actually does miss it) this may lead to interest rates becoming inefficient as means for hitting the target because the "third instrument" has broken at the point people lose faith in the commitment.

I would say that an important difference between the BOC money and the BMO money is the fact that governments only accept BOC money in their contracts and for tax payments. This raises the intrinsic convenience value of holding at least a minimum of BOC money which enables you to settle government transactions. This fact, along with network effects stemming from it, helps underpin a minimum of demand for BOC liquidity.

This minimal amount of intrinsic convenience value may act as an anchor that allows interest rates to be tied to something intrinsically valuable instead of circularly to something measured with the measuring instrument we are trying to adjust through those rates.

The advantage of BOC money over BMO money may not be that great when too much excess idle reserves are held and BOC money is accumulated beyond the amount needed for transaction convenience. Then most of money’s value becomes more like a guess of what (and when) other people are going to be willing to trade for it. Without some other non-circular anchor, interest rates might not be enough to control the value of money. If a shock causes people and banks to suddenly start to want to spend the excess reserves, we might see spikes in inflation that are difficult to control for the issuing bank.

There is also minimal amount of adaptive expectations stickiness. People may collectively assume (possibly falsely, but it doesn't matter for this to work ) that there is something real and somewhat stable causing money's value to be at a certain level and they assume that future money value will not go too far outside previous levels. This might be enough for interest rates to have some traction with both BOC and BMO money, that is until a shock happens that is large enough to overpower the effect of these assumptions (and at the same time maybe falsify the assumptions).

If BMO is constrained to make a profit, then it can't dictate the minimum size of its balance sheet. If the demand for BMO dollars falls, it has to buy them back, otherwise the value would fall.

If BMO could call upon an unlimited external subsidy, then adjusting interest rates would suffice - if necessary, by paying more on BMO dollars than receiving on loans.

Nick,

Starting from the premise that the BMO dollar is in effect a foreign currency relative to the Canadian dollar, there needs to be an exchange mechanism at some point in order for BMO dollar interest rates to have an effect on the BMO/Canadian dollar exchange rate.

That means for starters that there must be an exchange mechanism at the point where an increase in BMO dollar interest rates attracts a "capital inflow" of Canadian dollars into BMO deposits.

I've assumed as the starting point that BMO traders will set the rate on that conversion, although they are instructed to target that rate at parity. Then there is a 1:1 conversion of Canadian dollars into BMO dollars at the point of deposit, and BMO's Canadian dollar reserves increase.

At that point, one can assume that the market for BMO/Canadian dollar exchange will start to develop. It may start with one trader outside BMO and then progress to an institutional foreign exchange market of some sort - the same as for any currency in varying degrees.

That market allows speculation on the durability of the fixed exchange rate targeted by BMO, volatility in flows, etc. It improves market liquidity in that foreign exchange.

I think you have to assume the development of institutional mechanisms of some sort for that exchange rate - because otherwise BMO dollar interest rates will have no traction on the "external value" (i.e. relative to the Canadian dollar) of the BMO dollar.

MF said: "I'm a beta bank.

If I set the interest rates I lend and borrow at too low then the qty of my dollars expands and its value will tend to fall below 1:1 with aloha money. If people know and trust that i will keep my money 1:1 with alpha money they will know I will eventually have to adjust the interest rates I set so will not be too worried about a short term deviation. But if people don't know this (or don't trust me) they may think I plan to expand my money beyond what is sustainable at 1:1. I will have to raise interest rates to compensate for this concern, and this could easily end badly for me with my currency becoming worthless."

Assume your demand deposit "dollars" expand so they tend to fall below 1 to 1. Assume your bank is solvent. Assume there is a bank run on your bank. Will central bank "crisis lending" thru a discount loan happen to keep the exchange rate 1 to 1? I am going to say yes.

"Here's my question: but is it necessary? In other words, if you dropped that third instrument, and dropped any pretence that you might restore convertibility in future, so you dropped that third instrument permanently, would you still be able to control the value of the BMO dollar by using interest rate instruments alone?"

That's a great question.

One problem I have trouble wrapping my head around is what happens if there is a sudden across-the-board collapse in the demand for BMO dollars. Everyone wants to get rid of them. It seems paradoxical to me that BMO would be able to stabilize the value of the BMO dollar in the face of a demand shock by jacking up interest rates. After all, to pay that higher interest rate BMO has to create ever more BMO dollars. But how can you solve for a collapse in demand by increasing the supply? It's like getting in a race with your shadow.

So if this was an exam question, my answer would be no, you'd still need the third instrument. BMO dollars would collapse under certain scenarios, and the knowledge that this could happen would prevent them ever getting off the ground in the first place. But I wouldn't feel too confident with my answer and can be convinced otherwise.

JP,

"One problem I have trouble wrapping my head around is what happens if there is a sudden across-the-board collapse in the demand for BMO dollars. It seems paradoxical to me that BMO would be able to stabilize the value of the BMO dollar in the face of a demand shock by jacking up interest rates. After all, to pay that higher interest rate BMO has to create ever more BMO dollars."

Presumably the BMO is paying interest on deposits from interest it receives on loans. So I don't agree with your conclusion that the BMO must create more BMO dollars to pay the higher interest rate. BMO dollars could circulate more quickly through the economy to accommodate both higher interest rates on loans and deposits.

Faced with an across the board collapse in the demand for BMO dollars, the bank could try to shrink the supply of BMO dollars to try to stabilize their value. The BMO can do this by selling off loans that it currently holds for BMO dollars, increasing the spread between the interest rate it receives on loans versus the interest rate it pays on deposits or some combination of the two.

Finally, if their was a sudden collapse in the demand for BMO dollars, presumably existing loans would be paid off more quickly than the BMO anticipated. And so, the BMO could see an influx of BMO dollars that eventually equalizes the supply and demand for BMO dollars to a new lower level.

Good points. So then the answer to Nick's question is that it is possible control the value of BMO dollars with interest rates alone?

Benoit: "I would say that an important difference between the BOC money and the BMO money is the fact that governments only accept BOC money in their contracts and for tax payments."

Leaving aside the question of why that fact should matter, is it even true? I always pay my (federal and provincial) income taxes with a cheque drawn on my Bank of Montreal account. I'm not even sure if I can pay my income taxes with Bank of Canada currency. (Plus, unless it has changed recently, the federal government has a chequing account at all the (main) commercial banks, as well as at the Bank of Canada.)

JP: "After all, to pay that higher interest rate BMO has to create ever more BMO dollars. But how can you solve for a collapse in demand by increasing the supply? It's like getting in a race with your shadow."

Remember this old post?

Suppose BMO could increase the interest rate paid on deposits, while at the same time holding the stock of deposits constant. Then it would be able to get around your point. But what I have just done there is implicitly given it a third instrument: direct control over the quantity of deposits. It has to do reverse-QE (an open market sale of bonds/loans) tp offset the higher interest rate paid on deposits, to stop the stock of deposits growing.

Frank: "Presumably the BMO is paying interest on deposits from interest it receives on loans. So I don't agree with your conclusion that the BMO must create more BMO dollars to pay the higher interest rate."

No. For a given interest rate on loans, an increase in the interest rate paid on deposits will increase the growth rate of deposits by an equal amount, *relative to the rate of growth that would otherwise have occurred*.

"Faced with an across the board collapse in the demand for BMO dollars, the bank could try to shrink the supply of BMO dollars to try to stabilize their value. The BMO can do this by selling off loans that it currently holds for BMO dollars,..."

That is correct and important (if we ignore the rest of your sentence that follows). But what you are implicitly doing there (see my comment immediately above) is giving BMO a third instrument -- direct control over the quantity of deposits (and loans) -- so that the quantity of deposits (and loans) is no longer demand-determined at the interest rates set by BMO. (Notice we have just demolished the whole of the "Banking School" approach to monetary policy.)

My answer to my own question:

No. Controlling those two interest rate instruments is not sufficient. BMO needs a third instrument. That third instrument could be directly convertibility at an exchange rate set by BMO, or it could be direct control over the quantity of deposits, by Open Market Operations (buying or selling loans in the secondary market for BMO dollars).

By implication, this means that BoC cannot control the value of the BMO dollar just by setting two interest rates and letting the stock of BMO dollars be demand-determined at those interest rates. It needs OMO as well (or direct convertibility of BoC dollars into some other good at an exchange rate set by BoC).

If there is a spontaneous fall in demand for BMO deposits, BMO raises the interest rate on loans and deposits. This should increase demand for deposits, but at the same time encourage repayment of loans which reduces the supply. (We have to assume here BMO loans are only made and repaid in BMO deposits.)

For this to work, it is critical that there is some degree of stickiness in the exchange rate between BMO deposits and BoC money, so that the BMO can actually influence the rate of return on BMO deposits (and cost of BMO loans) when expressed in terms of BoC money. With a completely flexible exchange rate, any change in the own rate on BMO instruments will be completely offset by an expected appreciation rate.

(btw, my feeling that this is possible in theory is not an indication that I think that interest rate manipulation is an efficient way of managing inflation.)

Nick E: so, if the exchange rate is sticky in the short run, but perfectly flexible in the long run, it won't work?

There is no Omega point to pin everything down. An expected eventual return to convertibility at a fixed exchange rate provides an Omega point.

I'm not sure what "perfectly flexible in the long run" even means here.

If you have a starting exchange rate, a rule for how the exchange rate changes under stickiness and a rule for how BMO adjusts its rate, that should give you enough to extrapolate the exchange rate out to eternity. It's only when you do away with the rule for how the exchange rate changes, that you need an omega point.

I think it would be a matter of getting incentives for the bank right. Interest rate control alone could not be enough because the economic incentive would always be to set the conversion rate to 0 and thus transfer wealth from depositors to stock holders of the bank. A higher interest rate means you would promise to deliver more in the future of something potentially (or likely or surely) worth nothing. If the bank or the senior officials would be punished enough in someway when they set the conversion rate unfairly low, then the system could possibly work.

Bit off topic this, but the lending on of deposit money should be banned for the simple reason that that activity is fraudulent. That is it involves promising to repay depositors $X for every $X deposited, but that’s plain incompatible with lending on the money because there is no such thing as a totally safe set of loans.

I.e. the above promise is as ridiculous as promising those who invest in the stock exchange that they'll get their money back.

QED.

Makroint: BMO may or may not have an incentive to try to keep the exchange rate constant. (It has an incentive to devalue its liabilities, just like any borrower, but also has an incentive to create a reputation to get prospective depositors to believe it will not do this, just like any borrower.) But for this question, let's just assume it does have an incentive to keep its exchange rate stable. Are the two interest rate instruments sufficient to enable it to hit this exchange rate target (at least approximately)?

@Nick, unrelated but:

http://www.wsj.com/articles/alternative-currencies-flourish-in-greece-as-euros-are-harder-to-come-by-1439458241

Maybe I do not get it?

If BMO has enough assets I think it can always defend the value of its liabilities (just like Mike said)? If it can charge enough spread between assets (loans) and liabilities (demand deposits) considering all costs (like loan defaults and liquidity) it can always defend the value of the demand deposits.

To see this consider that it is announced that BMO dollar will be banned after a year. So everybody runs to BMO which then sells its _real_ assets (loans) and acquire BOC dollars to fulfill the parity. Thus it can defend the value using its assets even if the demand is demolished.

The level of the interest rate is due to the profit maximization - too high and too few loans will be made, too low and too few deposits are attracted. I do not see how the level of interest rates can be used to defend the parity? If BMO sky rockets interest on demand deposits (and loans to keep the spread constant) the rational investor doesn't buy more BMO dollars as the price decline will net out the higher interest rate.

BOC case is difficult and not sure how much can be extrapolated from the BMO case. IMO it is difficult mostly because of the nature of its assets. They are not mainly held at BOC (like future taxation), have interest rate sensitivities and feedback loops with monetary policy.

But if there would be just one bank for the whole economy the issues seems clearer: the interest rate needs to be set to maximize the quantity of money by using the interest rate tool only (then the Central Bank needs to grant loans too - but I guess there is a way to privatize this bit without private dollars).

BJH: Thanks for the tip! Good find!

Jussi: "So everybody runs to BMO which then sells its _real_ assets (loans) and acquire BOC dollars to fulfill the parity."

What does it mean to say "everybody runs to BMO", if BMO does not promise to convert BMO dollars to BoC dollars at par on demand? What are they running to do? What do they expect to get from BMO?

I think there's a fundamental difference between exact, precise convertibility and a target, even if the latter is inflexible.

Convertibility is a simultaneous guarantee that the market will clear and that the clearing price will be precisely what is specified. It binds the issuing bank to buying (or selling) as much of its currency as is necessary to ensure the market clears, both now and in the future.

The bank's other policy tools are then subservient to this goal, such that they are designed to control the flow of demand in the future. If we also couple this with a no-Ponzi condition, then the bank needs to always have real assets sufficient to cover its liabilities, so this interest-rate control is limited.

A convertible currency cannot experience a liquidity crisis. One with only an open-market target can, where a sparse market can't clear at the current price and either won't match buyers and sellers or will have a drastic (if temporary) shift in price away from the peg.

Think about the problem from the other direction: if we can only observe their actions, how can we tell that BMO is a beta bank and that the Bank of Canada is an alpha bank, and what would that look like for a central bank with a gold standard?

Off-topic.

I was just reviewing some old posts.

I found the one about Min that I had not finished reading.

I apologize for commenting since then. I did not see it.

I wish I had. I had another point to make on that old one.

Wouldn't a truly omniscient CB be able to hit any target or peg it wanted to just via a single instrument (a single interest rate that it either lends or borrows at) ?

Its because CBs are not omniscient (and actually are subject to quite a high degree of human error) that means that they need further tools (like OMO of some sort or another) to adjust the money supply directly for when the screw the interest rate up and things get out of control.

I wish the Royal Canadian mint would go rogue and let people buy loonies for a quarter. Then there wouldn't be anymore quarters in circulation and gumball machine companies would go out of business. I hate gumball machines.

MF: it would be very hard to hit a target *exactly* without direct convertibility (or a crystal ball). But let's set that aside. All I'm looking for here is whether BMO could keep its exchange rate *approximately* constant, using only interest rate instruments.

Nick: "What does it mean to say "everybody runs to BMO", if BMO does not promise to convert BMO dollars to BoC dollars at par on demand? What are they running to do? What do they expect to get from BMO?"

I assumed that in your example the demand deposits are legal claims on bank's assets? So yes, they might run for BOC dollars or any medium there is left circulating. So the bank's assets "determines the value of the BMO dollar, in terms of Bank of Canada dollars.".

"would you still be able to control the value of the BMO dollar by using interest rate instruments alone?"

I would say interest rate instruments are set by market forces due to profit maximization and thus not relevant. The spread (loan rate - depo rate) can be lowered in order to try to attract more demand deposits but in theory that should only make deposits less valuable (just like stock dividends). So I vote mainly no.

I mean (where is edit?!) ultimately "runners" have claim only on assets but those can be valued in BOC dollars.

> All I'm looking for here is whether BMO could keep its exchange rate *approximately* constant, using only interest rate instruments.

Approximately constant? Yes, but this isn't interesting.

Look at GICs or corporate bonds, which have a well-known value on the secondary market based on interest rates, even if that market might be illiquid at the moment. These instruments may be convertible in the future, but convertibility is suspended for their term.

We get from there to a full floating instrument by extending that term to infinity, or far enough in the future that nobody currently alive will be able to convert.

However, in practice this runs into two significant and interrelated problems:

*) The value is based not just on the current interest rate, but also on the expected future path of interest rates, and
*) The issuing authority has limited backing.

These conditions can be contradictory, if a stable value involves baking in an expected future path of interest rates that would lead to insolvency.

As a clearer example, imagine I try to set up a "US Canadian Bank," which exists in the United States but deals in dollars that are ostensibly Canadian dollars. This exchange happens on the open market in terms of physical paper, where BoC plastic is exchanged for whatever I issue.

That means that I'm committed to essentially following the Bank of Canada path on interest rates to prevent an imbalance. But what if the BoC decides to deflate the currency, redenominating every paper note via law?

I'm not sovereign; I can't simply redenominate my own liabilities like that. If I must use interest rates, I have to greatly decrease the number my notes in circulation, which means I must offer a vast *positive* interest rate. But that in turn means that I have to mark up the balances of my clients' accounts to "pay" interest, but that increases the my M1-equivalent. So I am forced to offer an ever-increasing spiral of positive rates to keep my MB-equivalent from increasing. Very quickly, I would lose credibility.

Nick,

"All I'm looking for here is whether BMO could keep its exchange rate *approximately* constant, using only interest rate instruments."

Yes, but it would need to make all floating rate loans.

If the BOM can charge more interest on loans than it pays out on deposits, then the BOM can offset any rise in demand for loaned funds. Therefor, it can stabilize the amount of it's BOM dollars in circulation.

For instance - Period #1
Total Loans = $1000
Total Deposits = $1000
Loan Interest Rate = 10%
Deposit Interest Rate = 10%

And so the BOM is paying out in deposit interest whatever interest it is receiving on loans. Now suppose the supply of loans and deposits increases by 25%.

Period #2
Total Loans = $1250
Total Deposits = $1250

The BOM wants to alter interest rates to shrink the supply of deposits and so it raises the loan rate to 30% keeping the deposit interest rate the same. The BOM now captures a 20% spread on all loans and destroys the profits. In the first year, the BOM pays out $125 (10% of $1250) in deposit interest but receives $375 (30% of $1250)in loan interest capturing $250 of profit and returning deposits back to the original $1000 amount.

@JKH: "If the BMO dollar is under pressure, it can “tighten” by increasing both loan and deposit rates, which should tend to attract net foreign currency (Canadian dollar) inflows – because it will tend to gain deposits and lose lending business."

I think this is fair description but "tightening" IMO would not work. What happens (in the end) is that BMO deposits (liabilities) are issued to pay the BOC dollar (assets). This is just a fair exchange. Nothing else is changed but as said lending business is lost and the respective BMO dollars disappear. So I do not see how BMO dollars would be boosted by the exchange. But if the rates are kept elevated the bank will soon disappear.

Majro: "Look at GICs or corporate bonds, which have a well-known value on the secondary market based on interest rates, even if that market might be illiquid at the moment. These instruments may be convertible in the future, but convertibility is suspended for their term."

The issuer of corporate bonds has a third instrument. It controls the quantity of bonds issued. If a beta bank sets only an interest rate on loans, it is the market that decides on the quantity of loans and deposits it will create.

I'm confused by the starting premise. If BMO deposits are not convertible into BoC dollars, what are they? How would I acquire them, and why would I want to?

nive: ask the exact same questions for Bank of Canada dollars!

BMO dollars are bits of paper, with numbers printed on them. Sorry, I mean numbers on a ledger, with your name on top. Sorry, I mean numbers on a computer somewhere.

BMO gives them to you when you give BMO your signed IOU, promising to pay them back, with interest, a few years later.

Funny thing is, you want them because other people want them too. Which means you can buy and sell things with them. And they are very convenient for buying and selling things.

Then you are not considering the operation of a bank. You are considering a different currency, and asking how, say, the SNB could maintain a fixed conversion rate of the Swiss franc vs the euro.

nive: in the olden days, the BMO did in fact issue a paper currency (it was convertible into gold), just like the other Canadian commercial banks. Did the Bank of Canada issue a "different" currency, back in the days when the Bank of Canada dollar was convertible at a fixed exchange rate into the US Fed's dollar?

And does it matter if the money is paper or electronic?

BMO today issues a different money, only it's electronic not paper, and it has a fixed exchange rate to the Bank of Canada money.

Nick, given that Frank Restly's points are ruled out since they give BMO a third instrument, then I agree with your answer at @05:41. Controlling interest rates is not enough. (I had originally though the third instrument referred only to direct convertibility but you've also included control over the quantity of deposits in that category)

But I think you're going too far to say you've demolished the whole Banking School approach. Banking school theorists (at least the good ones) always assumed some sort of convertibility.

Also, you say that the Bank of Canada "does not use that third instrument." But the BoC can do open market operations and control the quantity of deposits. According to your definition, that gives it the vital third instrument necessary to determine the value of Bank of Canada deposits.

BMO are not able to appreciate its deposits (or its dollars attached to deposits) by higher interest rate assuming rational investors or long term because:

1. BMO set its interest rate on deposits over market deposit rate
2. Naive investors buy more BMO deposits, the demand drives value of BMO deposits up

Now two possibilities

3a. BMO spread (loan rate - deposit rate) takes hit and loan/deposit quantity stays the same
3b. BMO has some percentage of sticky borrowers it can charge premium coupons

3a. BMO is not sustainable, it needs to pay higher deposit rate it cannot afford long term and its liabilities will take the hit. BMO deposits will depreciate.

3b. If its running cost are only variable I think this is sustainable. But the quantity of loans/deposits goes down. The bank is smaller, it has only higher values assets (premium loans with higher than market coupon) left and thus all its liabilities are valued higher.

And the appreciation in 3b doesn't rely directly on hiked interest rate on deposits but its consequences: better managed asset side (higher coupons) and smaller size (only higher coupons).

JP: "But I think you're going too far to say you've demolished the whole Banking School approach. Banking school theorists (at least the good ones) always assumed some sort of convertibility."

True. I'm not sure if they understood the importance of convertibility to the rest of their system though. Banking school are foxes; currency school are hedgehogs; I think that's still true today.

"According to your definition, that gives it the vital third instrument necessary to determine the value of Bank of Canada deposits."

True. But somehow that third instrument is missing from Neo-Wicksellian analysis.

Nick, is "beta" and "alpha" banks the same thing as "pyramid of IOUs" in the MMT primer?
http://neweconomicperspectives.org/2011/09/mmp-blog-15-clearing-and-pyramid-of.html

I'm sorry I still don't get it - at all. And I have now read even the comments many times.

After reading this multiple times it looks to me that this post based on assumption of some money demand specifically for single name commercial (e.g. BMO) deposits/dollars? Why there is such demand or is this just assumed? How there can be such demand?

I think the assumption, if made, contradicts with the the general idea that commercial banking is highly competitive and different bank deposits can be used interchangeable as medium of exchange - which IMO means there is zero demand for single name dollars even if there is demand for the aggregate. E.g. When BMO sells the loan book, some other bank will get that business, the whole economy is not affected?

Nick: "or it could be direct control over the quantity of deposits"

If there is nothing special in BMO dollars I cannot see how "direct control over the quantity of deposits" matters at all? Lets say BMO sells half of its loan book back to its customers (and competing bank gets the loans). The related BMO deposits are then destroyed. So both side of the balance sheets are shrank by 50 % (assuming away the bank's equity). What is the deposit worth of this half-sized bank relative to the full-sized bank? Why half-bank's deposits would be worth more (assuming away the effects from lower leverage)?

> Funny thing is, you want them because other people want them too. Which means you can buy and sell things with them. And they are very convenient for buying and selling things.

From this perspective: BMO cannot wholly control its exchange rate through interest rates alone.

Consider what you ask not from a control point of view but an equilibrium point of view: for any value of (demand for BMO dollars, amount of BMO dollars in circulation), is there a set of deposit/loan interest rates such that the market-clearing price of 1$BMO is 1$CAD?

The answer here is trivially "no." If there is no demand for BMO dollars, then no path of interest rates will set a nonzero value.

We can only get a positive value if BMO itself can set a floor on demand. This can be done through interest rates on loans if and only if BMO is a government that can enforce payment. If there is 1$BMO in circulation from a 1$BMO loan and BMO sets a billion-percent interest rate, then that creates demand for BMO dollars.

This is the chartalist argument, since in this context the BMO interest rate is nothing but a tax on the unfortunate person who took out a loan.

However, one distinguishing feature of a subnational bank (leaving aside alpha/beta for the moment) is that can't enforce payment in this way, and debtors can default on their obligations. This limits BMO's ability to generate demand -- if we take this argument literally then a court would value the BMO-paper debt in terms of its current near-zero exchange rate.

"Funny thing is, you want them because other people want them too."

People want deposits in aggregate but it (usually) doesn't matter who issues them. IMO deposit value derives from the assets held by the bank. Having value they can be used as medium of exchange. Money IMO cannot be truly fiat (yet Bitcoins still seem to have value). If that is not true why do we have bank runs?

Bob: from a quick skim, I think it's related.

Here's an old post: http://worthwhile.typepad.com/worthwhile_canadian_initi/2014/03/alpha-banks-beta-banks-fixed-exchange-rates-market-shares-and-the-money-multiplier.html

What about the euro? It is only issued by the national central banks yet it is one, homogenous currency. Are there 15 alpha euros that are magically identical or does the euro actually not exist? Or are target 2 liabilities the actual alpha euro?

Also, according to your account, it would make perfect sense to have a system with one commercial bank and one central bank. My tin foil hat tells me that's patently absurd. But then maybe it needs some adjusting....

I'll side with Jussi here and say it's the underlying assets that determine the value of a currency and the corresponding debts that creates demand for it. So in a system with several commercial banks the value of the currency is in effect the average if all their respective liabilities. And it's the regulating authorities' duty to impliment lending standards are and make sure lending volumes are conducive to policy objectives.

I don't see what's so special about (3). Interest rates are exactly like exchange rates, except that they give the relative price of a Dollar Today and a Dollar Tomorrow, rather than the relative price of a Dollar Today and a Euro Today.

If you can anchor the value of the Dollar Today by fixing it at a certain relative price with the Euro Today, why can't you anchor the value of the Dollar Today by fixing it at a certain relative price with the Dollar Tomorrow?

The obvious response is that you need some way to fix the Dollar Tomorrow. The obvious counter-response is that you can fix the Dollar Tomorrow the same way, by setting its price relative to the Dollar Two Days from Now. The obvious counter-counter-response is that if you continue this indefinitely, you still need something to be pinning down the value of the Dollar at Infinity.

The counter-counter-counter-response is that as long as the value of the Dollar Tomorrow is going to be above zero, it doesn't matter that much what is pinning down the Dollar Tomorrow -- so you don't have to worry about how determinacy of the Dollar One Hundred Years from Now is going to be achieved, or anything like that. Whatever value the Dollar Tomorrow is expected to have, you simply take that value into account and then set the relative price of the Dollar Today and Dollar Tomorrow in order to give the Dollar Today the value you'd like it to have.

Sticky prices and inflation inertia complicate this procedure in some ways, but make it simpler in others. The end result is a monetary policy that looks pretty much like the one we see in practice. If the real value of the Dollar Tomorrow is expected to be 10% lower than the real value of the Dollar Today, you set the relative price of the Dollar Today and Dollar Tomorrow to be 1.15 (i.e. you set an interest rate of 15%), in an effort to bid up the value of the Dollar Today and stem the inflation. This is the Taylor Rule.

(Then you get a debate between Mike Woodford and John Cochrane about whether this policy will really increase the value of the Dollar Today, or whether it will decrease the expected value of the Dollar Tomorrow. Without getting into the specifics, it's safe to say that central bankers count on the former, and have been successful in the process.)

So yes, I do think that the BMO dollars could in principle be maintained in value with just interest rates, not any kind of additional instrument... I suppose I'm an unrepentant neo-Wicksellian!

@Nick, but you're not talking about what they actually did in the old days, which was to issue notes that were convertible into assets like gold, nor what they do today, which is issue deposits convertible into BoC dollars.

You're talking about notes that are backed by nothing. Only central banks have ever engaged in this operation, as far as I know. Introducing commercial banks into this picture confuses rather than clarifies. If we consider central banks that have or had currency pegs, we can actually look at their real world experience and see what instruments they used to achieve their peg.

I don't believe there have been any examples of central banks successfully maintaining a peg using only interest rate policy?

@Matt, that process does not actually work in the currency markets. Spot and forward exchange rates are determined in terms of each other by relative interest rates, but the spot exchange rate is not determined in absolute terms by interest rates.

@Matt, though your point does bring up something interesting. If the central bank is only targeting the rate of inflation, not the price level, then interest rate policy may be sufficient.

Example, suppose the nominal interest rate in the currency is 5%. 100 apples go for $100 today, the interest rate in applies is also 5%, i.e. 100 apples today can be swapped for 105 apples tomorrow, but we expect inflation, so that those 105 apples can be swapped for $110 tomorrow. This implies that the interest rate in the currency is too low and if it were increased to 10%, you could ward off the expected inflation. As long as the nominal rate on the currency is set equal to the real interest rate, expected inflation will be 0%. This does not, however, rule out unexpected shocks to the price level, which with this policy would be permanent. If the central bank wishes to maintain a stable price level, rather than a stable rate of expected inflation, interest rate policy will not be enough.

Something's a bit fishy with what I just said.

Right, my original scenario is arbitrageable. Should have started with nominal interest rate = 10% and real = 5%, which forces the 105 apples to go for $110 tomorrow, producing inflation.

This scenario of course still falls apart if we have sticky prices and the nominal interest rate can affect the real interest rate.

Ah Matt R.! You are good at this.

"I don't see what's so special about (3). Interest rates are exactly like exchange rates, except that they give the relative price of a Dollar Today and a Dollar Tomorrow, rather than the relative price of a Dollar Today and a Euro Today."

Well they have different units, for starters. Exchange rates have $ in the units, and interest rates are just 1/years.

"If the real value of the Dollar Tomorrow is expected to be 10% lower than the real value of the Dollar Today, you set the relative price of the Dollar Today and Dollar Tomorrow to be 1.15 (i.e. you set an interest rate of 15%), in an effort to bid up the value of the Dollar Today and stem the inflation."

Suppose we have an inflation targeting central bank. That means a random walk in the value of the dollar. For every 1% change in the value today, the infinite horizon expected value would also change by 1%. There is no long-run Omega point to pin it all down. (Though even a price level path target seems to me to assume the conclusion.)

"Without getting into the specifics, it's safe to say that central bankers count on the former, and have been successful in the process."

Yep. That's important. We mustn't forget that empirical fact. But do we understand why it works. Is it some anachronistic way in which people form expectations, that they learned under the gold standard? Or is it Open Market Operations, and not interest rates, that are really pinning down the price level (i.e. "they've been doing QE all along, and interest rates are just a sideshow."?)

"Well they have different units, for starters. Exchange rates have $ in the units, and interest rates are just 1/years."

Well, it depends on how you specify the units! My gimmick here is to say that "Dollar Today" and "Dollar Tomorrow" are different currencies in exactly the same way that a dollar and euro at any one point in time are different currencies. That isn't how most people think -- because the existence of pieces of paper worth $1 or $5 or $20 (without reference to time), as well as our contracting and accounting conventions, make them view the dollar as a persistent unit, so that an "interest rate" is a pure rate with units 1/time.

But imagine a cashless world where the central bank pays overnight interest on reserves. If it pays 10% on balances held overnight from April 22 to April 23, it might as well be converting a unit called "April 22 dollars" into a unit called "April 23 dollars" at a 1:1.1 ratio. (And for all anyone would know, maybe this would be the actual implementation in the central bank's computer system - the April 22 dollar ledger is frozen and saved, and then a new April 23 dollar ledger is created with initial positions at 1.1 times the old ones.)

"Suppose we have an inflation targeting central bank. That means a random walk in the value of the dollar. For every 1% change in the value today, the infinite horizon expected value would also change by 1%. There is no long-run Omega point to pin it all down."

The flippant but partly correct answer (which was my "counter-counter-counter-response" earlier) is that as long as it works, you don't really care what is pinning it down. Some wild mix of psychology and projection could be determining the public's expectations of the value of the Dollar Tomorrow; taking that as given, you'd set an exchange rate with the Dollar Today in order to push the Dollar Today toward the value you seek.

The potential problem with this, as you’ve identified, is that the value of the Dollar Tomorrow depends partly on the Dollar Today - so you can’t use the Dollar Tomorrow as some kind of totally independent target. (This is a difference with exchange rate targeting, although there are sometimes glimmers of this behavior with exchange rates too; if I’m a huge country and I conduct my monetary policy by manipulating my exchange rate with the euro, the ECB might take my decisions into account.)

Of course, if you have any way of predicting how the Dollar Tomorrow’s value reacts to your Today/Tomorrow exchange rate policy, you can take that into account. Practically, when you tighten policy by making a Dollar Today worth more relative to a Dollar Tomorrow, the value of the Dollar Tomorrow will probably also go up, increasing the value of a Dollar Today even further and making your life easier. But even if Cochrane is partly right and tightening policy actually decreases the value of a Dollar Tomorrow, that still could be okay, as long as we tighten further in response, and the (policy reaction, Dollar Tomorrow reaction) spiral doesn’t diverge.

To ensure that it doesn’t diverge, you basically have to constrain the expected value of the Dollar Tomorrow within reasonable limits - and if we try to do that using the same policy, we have to think about the Dollar Two Days from Now and the Dollar Three Days from Now and so on. Inevitably, we arrive at the question of long-run determinacy… (and I understand your complaint about how “a price level path target seems to me to assume the conclusion!”).

My answer to the problem of long-run determinacy with interest on reserves is that it’s not really as hard as it initially looks… and that a lot of the legendary trouble with determinacy is just modeling artifact.

Suppose that I live in a (continuous-time) world with a constant real GDP growth rate g=.02 and real interest rate r=.06. Now consider the following progression. First, I define a “dollar” to be a perpetual security that pays out a tiny share X of aggregate GDP as dividend, where X declines at a constant rate of .04. Here, there’s no doubt that the dollar’s value is determinate, as a matter of simple asset pricing: its value should be X/(.06+.04-.02) = 12.5*X times GDP, and its real value will fall at a rate of .04-.02=.02 (i.e. a 2% rate of inflation).

Next, I decide to implement the same payout not as a “dividend”, but as “interest on reserves”, where the dollar is now an accounting entry on the ledger of the central bank. On the equilibrium path, where the dollar has the 12.5*X times GDP value, I pay interest at a rate of .08, giving the desired X times GDP payout. Off the equilibrium path, where the dollar has too high or low a value, I adjust my rate of interest inversely in response (so if the price level is twice the target, then I pay interest at a rate of .04). I replicate the same payout as before, always hitting X times GDP, and the dollar’s value is pinned down at the same value as before.

Next, assuming that I live in a world where the interest and price elasticities of money demand are -1 and 1, I implement this interest rate rule not via interest on reserves but instead via a money supply target, where the money supply increases at a constant rate of .04. Everything remains the same.

What’s funny to me is that I think most people would think that the price level was obviously determinate in the case where we view the dollar as a security paying out a certain fraction of GDP, probably determinate in the case where we achieve the same payout for dollar-holders via a money supply target, and dubiously determinate in the case where we achieve the same payout with explicit interest on reserves. But they’re all isomorphic to each other, both on and off-equilibrium -- it’s really hard to make the claim that one should work while the other doesn’t!

And it follows that achieving determinacy with an interest rate rule shouldn’t really be that hard; after all, mimicking the payout of a GDP security is only one rather contrived way to pin down the value of the dollar, and presumably there are a number of other policies that would achieve the same effect.

I am sweeping something under the rug here, through my pseudo-continuous time formulation. In the traditional discrete time model, the problem with interest rate rules is that expectations can always move against them; however aggressive you set your interest rate rule to be, there’s some expectation-formation rule where expected inflation moves even more, offsetting the intended effect. But this difficulty is really an artifact of how the model is specified; it assumes that the interest rate policy can’t incorporate expected inflation, when of course it can if really necessary; and by doing so, it can set the expected real payout from interest on reserves to be whatever it likes.

(Alas, I realize that my metaphors here are hopelessly jumbled. I started by saying (1) that interest on reserves was a lot like the exchange rate as an instrument, and can similarly be used to control the price level; then I ended by saying (2) that interest on reserves could be used to replicate the real payout stream of a security. (1) and (2) are very different points, and the best I can say is that they are both useful ways of thinking about interest rate policy. (1) is probably useful for the practical, day-to-day stuff, where “What If the World Collapses and the Dollar Tomorrow is Worth Nothing?” is not so much of a concern; (2) is useful for thinking about how, very much off-equilibrium, the central bank can always be sure that the dollar stays worth something.)

Matt: again great comments, which I'm digesting.

"(This is a difference with exchange rate targeting, although there are sometimes glimmers of this behavior with exchange rates too; if I’m a huge country and I conduct my monetary policy by manipulating my exchange rate with the euro, the ECB might take my decisions into account.)"

In my terminology, that's where both central banks try to play beta to the other's alpha.

I'm still thinking through your thought-experiment. I haven't grasped it yet.

Oliver: "So in a system with several commercial banks the value of the currency is in effect the average if all their respective liabilities."

That is part but IMO through the Central Banking and government actions the assets not held by the banking sector matters too. That way all the assets within the currency area matters (assuming strong enough tax ability). Thinking in these terms can IMO nicely explain all the extreme cases (Japan, Weimar, Zimbabwe, etc).

@Matt, doesn't your suggestion only work when the dividend is actually a share of real GDP? i.e. it is not just interest rate policy now, you've made the dollar convertible into real GDP. With interest rate policy, the dollar pays out dividends that are denominated in dollars, not in real GDP.

My question would be this: let's suppose you have a security very similar to what you describe, except the dividends are paid in additional units of the security, not in hard currency/GDP. i.e. let's suppose BoC deposits offer an interest rate of 5%, now and forever. I issue a security X -- if you own 1 X, you are entitled to 5% multiplied by the exchange rate in X/BoC dollar, paid in additional units of X, each year. This is apparently worth the same as one BoC dollar, by your calculation.

What stops some random dude like me from issuing these securities, which cost me nothing to create, and collecting BoC dollars in return?

I was recently rebalancing my portfolio and had need to rebalance some bank account assets. Now my bank imposes a daily limit on this, annoying. That got me thinking how great it would be if I could just buy and sell these bank assets (which have guaranteed par, insured, and pay interest) as I can trade stocks. But I cannot. There are money market funds which I can do this with, but these aren't insured. And deposit insurance is structured on the premise that the assets are not tradable...

The key difference between bmo and boc is that the latter has traded liabilities and the former does not. If you cannot trade, you need to offer at par. Something needs to determine the value, either that's a legal prescription or it is market determined.

@jon, that does not seem correct. Your bank may impose daily withdrawal limits on ATM transactions, online banking or debit cards, to combat fraud, but in the wholesale market, bank deposits are freely traded, and even for retail, your bank will certainly permit you to withdraw your entire checking account balance if you actually go to your branch with some proof of identity. Further, this ability to trade is not what gives the deposits value. Stocks to take your other example, have value because they represent claims of ownership of a company, which has assets and profits (hopefully!), not because they can be traded easily. The key difference between BMO and the BoC today is that it is BMO that offers to exchange its deposits for BoC dollars at par, not the BoC.

I don't think it's possible to really understand the dynamics of fiat currency by comparing it to privately issued securities.

Nivedita you can take loonies out of the bank but you cannot trade bank script anymore.

"I don't think it's possible to really understand the dynamics of fiat currency by comparing it to privately issued securities."

Yet historically deposits were exactly that, privately issued securities people started to use as money. What was the critical step after this is not a way "to really understand the dynamics of fiat currency" (or what made it fiat?)?

@Jon, not sure what you mean by bank script, but you can trade bank certificates of deposit in your brokerage account, and banks trade overnight deposits among themselves each day. The price set by that market is what the overnight interest rate is.

@Jussi, no, both historically and today, bank deposits are privately issued securities that represent claims on the bank. Historically they used to be denominated most commonly in gold, today they are denominated in central bank currency, but they always represent claims on the assets of the bank, and the assets of the bank are always either real assets (its buildings, ownership shares in companies, gold etc), or someone else's liabilities.

Modern central bank currency does not really represent a claim on anything. For example, the Bank of Canada's balance sheet consists of approximately 100bn of assets against 100bn of liabilities. The 100bn of assets are Government of Canada securities that promise to pay out in Bank of Canada liabilities -- essentially, the assets of the Bank of Canada consist of its own liabilities. A private bank that tried this sort of thing would never get off the ground.

Should also have said about the BoC, that's even leaving aside the fact that unlike a private bank, the BoC doesn't even offer to redeem your deposits for the assets that it does have.

"bank deposits are privately issued securities that represent claims on the bank"

nivedita: That was exactly my point! Thus I'm saying one should look the asset side when determining the value of the liability side.

Nick is IMO stating that backing view (asset view) is not useful but without giving any reasoning. He views money as truly fiat (ie. not a claim on anything). But his story is IMO not believable without explaining at what point of time and why money started to be fiat? I haven't seen him trying to address this.

nivedita: "Modern central bank currency does not really represent a claim on anything. For example, the Bank of Canada's balance sheet consists of approximately 100bn of assets against 100bn of liabilities."

This is why we should consider the consolidated balance sheet. It has mainly currency and government debt on liability side. And Assets are mainly related to sovereign power to tax. That is why hyperinflation can happen either if taxation is compromised when the state collapses or if its liability side (foreign debt) runs amok.

"BoC doesn't even offer to redeem your deposits for the assets that it does have"

You mean bank cannot redeem their reserve accounts? But the base money is not used as medium of exchange - so it is not the money Nick is talking about.

Nick seems to suggest every single bank has some demand to its deposits. I find it implausible. If some bank tries manipulate the price of their deposits based on imaginary demand people just switch their deposits to an other bank. So there is no such thing than demand on single name deposits. Bank losing deposits has to find the way to fund itself in market terms. In that sense the whole banking sector is interlinked in a way that deposits are just a homogenous product 99,99% of time. And if that is not the case the Central Bank is usually the one who gives in.

@Jussi, right with that view fiat money is backed by the power of taxation. That makes it even more obvious that it is futile to try to understand it by looking at private banks, since the power of taxation resides only with the state.

I am somewhat more ambivalent -- for private money (i.e. private bank deposits), I think the asset-backed view makes sense. Private banks are subject to competition, and why would you want to use the money of a bank that doesn't back its deposits when you can use other banks that do.

For central bank currency I am less certain that its value derives purely from taxation power of the government. But it is certainly a reasonable argument, and I have nothing better to offer.

Re "BoC doesn't offer to redeem", I had meant that when you have private bank deposits, you can redeem them for assets of the bank, i.e. the bank will give you some of its assets (BoC dollars) in exchange for your deposits. You cannot ask the BoC to give you Canadian government bonds in exchange for currency. Now that I think about it a bit more, though, this doesn't really make sense, the BoC will certainly sell you the assets on its balance sheet.

@Jussi, right with that view fiat money is backed by the power of taxation. That makes it even more obvious that it is futile to try to understand it by looking at private banks, since the power of taxation resides only with the state.

Yes, I think this is quite true. That is why I was puzzled why Nick was trying to go this avenue. Plus as said demand for a commercial bank deposit is qualitatively different than demand for monetary aggregate.

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