This post covers the same ground as my previous post, but it's written for a different audience. It's written for those people who approach monetary policy from a banking/finance perspective.
Suppose you are running a commercial bank. Let's call it "BMO". And let's simplify massively. On the asset side of your balance sheet you have "loans". On the liability side of your balance sheet you have demand deposits. Let's call those demand deposits "BMO dollars", because that's what they are.
Again simplifying massively, you have three instruments, or control levers:
1. You set the interest rate on loans. Yes, you have to watch the competition when you set it, but you set it. (And you also care about risk, term to maturity, liquidity, etc., but let's abstract from those things.)
2. You set the interest rate on deposits. Yes, you have to watch the competition when you set it, and you might set it at 0%, or even negative, but you set it. (And you also set fees for cheques, and paying bills, etc., but let's abstract from those things.)
3. You set the exchange rate at which you promise to convert BMO dollars into Bank of Canada dollars. And you fix that exchange rate permanently at one, of course.
It's very easy to forget that third instrument, because it's just so natural that it goes without saying. Of course you promise to convert BMO dollars into Bank of Canada dollars at par. That's what "demand deposit" means. And as long as your promise is credible, the market value of a BMO dollar will stay at one Bank of Canada dollar. That third instrument is sufficient to determine the value of the BMO dollar, in terms of Bank of Canada dollars.
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?
Because the Bank of Canada tries to target the value of the Bank of Canada dollar in terms of the CPI basket of goods, but does not use that third instrument. You cannot walk up to the Bank of Canada and demand it redeem your $100 note in CPI baskets of goods as specified by the inflation target. The Bank of Canada targets a 2% crawling peg exchange rate between the Bank of Canada dollar and the CPI basket of goods, without using that third instrument of direct convertibility. The BMO has a stock of Bank of Canada dollars behind the counter. The Bank of Canada does not have a stock of CPI baskets of goods behind the counter.
The Bank of Canada tries to control the value of the Bank of Canada dollar using interest rate instruments only. It sets (1) the interest rate on loans, and (2) the interest rate on deposits. Is that sufficient? If it is sufficient for the Bank of Canada, why wouldn't it also be sufficient for the BMO?
I can't help but recall the old joke about economists: interest rate control seems to have worked in practice, but does it work in theory? But maybe, just maybe, theory is trying to tell us something important about what happens in practice at the Zero Lower Bound, when interest rate instruments hit their limits.
[Update: my answer is "no". BMO would need a third instrument. That third instrument could be convertibility into something at some exchange rate it sets, or it could be direct control over the quantity of deposits, by buying or selling loans for BMO dollars in the secondary market (Open Market Operations). Setting two interest rates, and letting the quantities of loans and deposits be demand-determined at those interest rates, is not sufficient to control the value of the BMO dollar.]
Worthwhile Canadian Initiative 
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) = 12.5X 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 12.5X 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.