If new money is always paid as interest on old money

...will an increase in the rate of interest paid for holding money be deflationary (because it increases the demand for money), or inflationary (because it increases the growth rate in the supply of money)?

This question crops up from time to time, in comments here and on other blogs, so I thought I would lay out a simple answer. Mostly as a "teaching" post, but also because it raises an interesting question about interest on reserves and central banks' communications strategy.

The answer is: an increase in the rate of interest paid for holding money will increase the equilibrium inflation rate; but it will not cause an additional one-time jump up or down in the equilibrium price level. (Yep, you gotta keep your head clear on the distinction between levels and rates of change over time.)

Here's my simple model: assume perfectly flexible prices and rational expectations. Let the demand function for money be:

1. M = P.L(R-p) where L' > 0, R is the nominal interest rate paid on holding money, P is the price level, p is the (expected) inflation rate, and so (R-p) is the real rate of return on holding money.

This is a very standard money demand function, except I have suppressed real income, and the real interest rate on other assets, which would normally appear as additional arguments in the demand function. I am holding them constant.

And let the supply function for money be:

2. m = R.M where M is the stock of money, and m is the growth rate of the stock of money.

This supply function embodies my assumption that all new money is always paid as interest on existing money. The central bank sets R.

Start with the case where R=0, so m=0. The central bank pays no interest on its monetary liabilities, and so holds the stock of money constant over time. The equilibrium (strictly speaking one equilibrium) is p=0. There is zero inflation.

Now suppose the central bank suddenly and unexpectedly announces that it will immediately start paying 1% interest on holding money, and so the stock of money will be growing at 1% per year too. The (strictly a) new equilibrium is that M/P stays the same, and the inflation rate is now 1%. There is no initial jump in the price level (either up or down), but the price level starts rising at 1% per year.

You can see that that new equilibrium satisfies both equations.

Here is the intuition:

1. Announcing an increase in interest on money, but no change in the money supply growth rate, would cause a one-time increase in the demand for money, so M/P increases, and so cause a one time decrease in the price level, but no subsequent change in the inflation rate.

2. Announcing an increase in the money supply growth rate, but no change in the interest rate paid on money, would cause an increase in expected inflation, which would cause a one-time decrease in the demand for money, so M/P decreases, and so cause a one-time increase in the price level, on top of the increased subsequent rate of inflation.

3. If you put 1 and 2 together, the two one-time jumps in the price level exactly cancel out, leaving only the increased subsequent rate of inflation.

OK. All that was very standard money/macro. The sort of keyboard exercise that bright upper year undergrads should be able to tackle.

But here's the kicker: what happens in the real world when central banks increase the rate of interest they pay on reserves? Do people interpret that as implying an increase in the growth rate of central bank money? Because if they do interpret it that way, an increase in the rate of interest they pay on reserves will increase expected and actual inflation.

There is nothing to say they must interpret it that way, because there is nothing to stop central banks using open market operations to offset any changes in the total stock of base money that arise from paying higher interest on existing base money. But there is nothing to say they mustn't interpret it that way either. What are people holding constant in their expectations? M, or OMO? What is the central bank communicating when it changes the rate of interest it pays on reserves?

God only knows. But this is a daft way to run monetary policy.

[Thanks to commenter MR, for raising this question long ago.]

[P.S. The question here is not the same as the "Neo-Fisherite" (Irving rolls in his grave) sign-wars kerfuffle, which was about the nominal rate of interest on other assets.]

Comments

[Adam P]

Nick,

The Fed won't be creating new money to pay the interest, they'll pay it out of their current income or a claim on their own future income (a future reduction in their remits back to the treasury will retire the claim).

The Fed can't create money and just give it away, they can only lend it (against collateral) or use it to buy an asset, even if the asset is their own debt (they'd book a deferred asset).

Interest on reserves does not result in a permanent increase in the money supply.

[JP Koning]

On the interpretation of an increase in the rate of interest that a central bank pays on reserves, what Adam said. A central bank needs to earn back the dollars it creates so that it can pay interest.

[Nick Rowe]

Adam (hi!) and JP: let Rb be interest on bonds, and Rm be interest on central bank money. Assume the central bank has assets=liabilities. Ignore other costs. So each year the central bank pays to the government seigniorage equal to S=(Rb-Rm)M. Provided S > 0, the central can set Rm whererever it likes, and simply adjust the transfers of seigniorage to the government.

Plus, can't the central bank give money to charity? Or would doing so violate some accounting identity? So much the worse for accounting identities! What if a central bank overpays a visiting economic consultant? Or goes out and buys supplies at an above-market price?

This is accounting mumbo-jumbo. A central bank owns a printing press. The accountants can tell whatever faked-up story they like, by inventing assets and liabilities, to make the books balance. But it doesn't change the facts.

[Market Fiscalist]

Assume the CB increases interest rates. This will have 2 opposite effects. The CB will payout more interest which will increase the money supply. The CB will probably have to sell new bonds for existing money to maintain this new rate and this will reduce the money supply.

I assume that the latter effect outweighs the former effect in terms of how they affect nominal variables like NGDP or inflation otherwise monetary policy would work in the opposite way to the way it seems to work in practice.

Is this a correct understanding ?

[Nick Rowe]

MF: there is no correct understanding. There is only the understanding that people have, and what understanding central banks communicate, and how central banks actually behave.

Most of us implicitly assume M is constant when R changes. We don't even recognise that may be a problematic assumption. I have come across more than one non-economist who implicitly made the opposite assumption. (One earlier this morning). God only knows what assumption market traders are making!

[Majromax]

@Nick:

> But here's the kicker: what happens in the real world when central banks increase the rate of interest they pay on reserves? Do people interpret that as implying an increase in the growth rate of central bank money? Because if they do interpret it that way, an increase in the rate of interest they pay on reserves will increase expected and actual inflation.

We can also ask the Central Bank what it's doing. At least in the case of the US, it appears that money creation acts independently of any sort of interest on reserves, so IOR should be independent of the equilibrium inflation rate.

We can infer the maximum possible amount of IOR money creation (US) by looking at the US Fed Funds Rate multiplied by the total excess+required reserves, and compare that to the changes of MB. For the periods where it's in FRED, we can also look at excess reserves * interest paid on excess reserves, which should be more accurate (but the latter series is discontinued).

Outside of a period in the early 2000s, the IOR-estimate is totally visually uncorrelated with the year-over-year change in MB. In fact, I'm surprised at just how constant "reserves * funds rate" actually is over time. Of course, the Fed's IOR policies have also changed over this time period, so the lines are probably best considered as a counterfactual.

[Nick Rowe]

Majromax; good answer.

But notice what your answer implies: it means we cannot tell whether raising interest on reserves should be considered a tightening or a loosening of monetary policy without first looking at a graph like yours. Interest rate (on reserves) policy is not monetary policy. We can't even get the sign right, without more info.

[Majromax]

> But notice what your answer implies: it means we cannot tell whether raising interest on reserves should be considered a tightening or a loosening of monetary policy without first looking at a graph like yours.

Indeed. I was really surprised to see that fall out of this graph, since previously I was solidly a member of the "raising IOR is tightening" camp.

I suppose that this just reinforces that over time spans of a few years, distributional and "micro" effects are still very much relevant.

[louis]

We know the Fed is targeting inflation.
We know that the Fed sees IOR as a tool to manage inflation as a complement to allowing its balance sheet to shrink as QE unwinds. As the economy recovers, the Fed may find M is too large for maintaining a stable price level. It could shrink M via OMOs, but increasing R seems like a valid way of increasing the size of M consistent with the targeted price level (your point 1 above) and so reducing the actual amount of OMO the Fed needs to do.

If the markets interpret IOR as the Fed looking to increase its inflation target, the markets are getting it wrong. If it sees inflation rising, the Fed will resort to OMO to shrink M. IOR is a tool, not a goal, and communications from the Fed make it clear that the inflation target is unchanged.

[Nick Rowe]

louis: OK. Suppose the Bank of Canada communicates clearly that it has a 2% inflation target, and suppose that target is 100% credible, and nobody believes it will ever change.

If the BoC increases the deposit rate (IOR), people would then interpret that as tightening monetary policy, in response to a positive demand shock, to keep inflation on target, and so must be assuming that it does not mean that money growth will rise.

But couldn't they equally interpret it as loosening monetary policy, in response to a negative demand shock, to keep inflation on target, and so must be assuming that it does mean that money growth will rise?

In other words, it doesn't matter what the Bank of Canada does with the deposit rate (IOR), because there is always an interpretation and implied assumption about money growth that is consistent with any facts?

(Not sure if I explained that clearly.)

[Miami vice]

What happens if you subsidize deposit taking?

Debit reward cards.

[Nick Rowe]

Miami vice: I don't follow. Here we are talking about "subsidising" (paying interest on) the holding of central bank deposits.

[Miami vice]

What happens to a bank's cb reserves if they are able to attract deposits?

What happens to a bank's cb reserves and income from debit transactions and ior if individuals use cash?

[Matt McOsker]

Majormax - I may not get the entire gist, but what I have always found interesting is that the FFR and inflation match each other pretty closely. Always find it odd not sure if the tail is wagging the dog or the other way around. So I always wonder that the FFR will equal the inflation rate, unless some endogenous factor beyond the immediate control of the fed enters the picture like a natural resource shock. So if IOER goes to 4% the price inflation rate would follow it up. But maybe need to look more closely at real rates.

http://research.stlouisfed.org/fred2/graph/fredgraph.png?g=Hhx

[Nick Rowe]

Matt: be very careful there about reverse causality. It is absolutely standard practice for central banks to increase their interest rate target if they expect inflation to rise, and want to bring it back down. Plus, the standard Fisher effect says the same thing: increases in expected inflation cause increases in equilibrium nominal interest rates. Plus, you are talking about the Federal funds Rate, which is not the same as Interest On Reserves.

[JP Koning]

If people did have such contradictory interpretations of the effect of changes in interest-on-reserves on the price level, then how is it that the Bank of Canada was able to hit its 2% inflation target over the last 20 years?

I don't believe that a central bank can create new reserves by donating... but it can donate out of the income it earns, or the already-created reserves that flow back to it. This has nothing to do with accountants and accounting identities. It's a procedural thing, a rule or convention.

[Nick Rowe]

JP: "If people did have such contradictory interpretations of the effect of changes in interest-on-reserves on the price level, then how is it that the Bank of Canada was able to hit its 2% inflation target over the last 20 years?"

1. Hey! That's *my* line! That's the argument *I* use, against crazy econobloggers who get the sign wrong, or who think the magnitude is zero!

2. Dunno. I'm still thinking about this. But I think there's a difference between a channel system, like the BoC has, and a floor system, which I think is what I have here.

"I don't believe that a central bank can create new reserves by donating..."

Whatever happened to "the stroke of the pen/keyboard"? Where's the MMT guys when you need them? Or, where's JKH? BMO has $100 on deposit at the BoC, and the BoC just crosses out "$100", and writes "$101" instead. Done. And then donates $1 less to the GoC (again by stroke of the pen).

[CMA]

"The answer is: an increase in the rate of interest paid for holding money will increase the equilibrium inflation rate; but it will not cause an additional one-time jump up or down in the equilibrium price level."

what if the higher rate causes an influx into money holdings which decreases V? Would this cause a one time jump down in equilibrium price level?

"...will an increase in the rate of interest paid for holding money be deflationary (because it increases the demand for money), or inflationary (because it increases the growth rate in the supply of money)?"

Both? Wont the equilibrium inflation rate increase due to higher interest pmts with a jump down in equilibrium price level in short term if higher interest paid causes people to demand more money? There is like a short term shock when the rate goes up which causes people to demand more money in short run creating deflation but becuase the of the higher interest payments the equilibrium inflation rate is higher.

[Max]

Nick: "So each year the central bank pays to the government seigniorage equal to S=(Rb-Rm)M. Provided S > 0, the central can set Rm whererever it likes, and simply adjust the transfers of seigniorage to the government."

Right. The CB is paying out its income. Money out = money in, no matter what Rm is.

So my answer would be: increasing Rm increases M (not the growth rate), with no effect on inflation or the price level. S may go up or down, depending on whether Rb-Rm is above or below the profit maximizing level.

[Jussi]

Lets say IOR is -50% annually. Given M is halved during the year (no OMOs). Everybody has 50c left and the price level is down by half. That is clear by now - thanks to Nick's post and explanations.

Now I cannot figure out how the OMO actually changes everything, isn't it only a kind of swap?

Lets say I got $50 in deposits and $50 in Tbills. I think we can assume the rate of interest R is -50% because the IOR will cap the market rates. So my deposit is $25 and my Tbills are worth $25 after a year. The CB OMO desk buys my bills, so I got $50 in my bank account again (M is unchanged) but my net worth is down from $100 to $50 in nominal terms, isn't it? What is the price level - what determines my propensity to consume?

Sure, if the -50 % IOR money is donated and thus given back, that will do it, I think.

[Adam P]

Max,

increasing Rm changes neither the money supply nor it's growth rate.

If Rm=0 then the fed earns S = Rb*M and remits it to the treasury. The treasury either spends the money or reduces taxes. In all cases the money is still part of the money supply, getting back into circulation via the treasury.

Now suppose the fed sets Rm >0, thus remitting S = (Rb - Rm)*M back to the treasury. As you say S may or may not be a smaller number than before but it's no matter. The part of Rb paid out as interest goes dirctly back into the money supply and the rest goes back into the money supply via the treasury as before.

Only OMO's change M, changing Rm doesn't. (I'm viewing the booking of a "deferred asset" as an OMO here, the fed issues a debt instrument and then "buys" it).

[Max]

Adam, what I meant was that increasing Rm increases equilibrium M. If M didn't increase then the CB would have made a mistake.

[Nick Rowe]

Max: this, I think, is Adam P's point:

The central bank is earning net interest equal to (Rb-Rm)M. And if the central bank simply sat on its earnings, that would mean the money supply would be falling by that same (Rb-Rm)M. So we would have m= -(Rb-Rm)M. But if the central bank simply returns those earnings to the government, by giving money to the government, and money held by the government counts as part of the money supply, it's a wash. m=0 regardless of Rm and Rb. The government takes its earnings from the central bank, and buys bonds, so that money goes straight back into circulation. The government, rather than the central bank, is doing the "OMO".

To get my little model to work, we need to consolidate the central bank and government's balance sheets, and define an "OMO" as a purchase of bonds *either* by the central bank *or* by the government.

[Jussi]

Thought experiment:

Assume: both islands have the same output, similar populace and no loss in production due to public ownership.

First island (private owners, M is low): people own assets and only a small fraction of the wealth is kept as currency.

Second island (communism, M is high yet volatile): the state owns everything but gives out currency to its people. The amount of currency is decided and announced to be always distributed to reflect peoples net worth on the first island.

What are the price levels?

Lets say there is a revolution on the first island and the CB agrees to buy all the assets. Is the price of the last asset the same than on the second island if the same asset is privatized there simultaneously?

I think the both island need to have similar price levels to start with; even if the amount of the currencies are different (why?). If true the last asset needs to have the same price as everything is now identical, right? But then the asset purchasing program doesn't change the price level, does it?

Okay, where did I go wrong?

[Majromax]

@Jussi:
> Lets say I got $50 in deposits and $50 in Tbills.

Define $50 in TBills.

If you exchanged $50 of cash for TBills, then you did so in the expectation of profit -- that at mature you will have more than if you had kept the $50 in cash. The central bank's OMO is then *not* purchasing the TBill from you today for $50, but instead $51 or somesuch.

Owning the bond means that you are committed to not consuming money now in exchange for more consumption later. The open market operation is the central bank's way of saying "well, what if we gave you a bit more now then?"

[Jussi]

I do not see how TBills an TBonds are that different, from macro point of view only the maturity sets them apart. Imagine a short bond tail instead.

If IOR is -50% I think it is safe to assume that TBills will trade close enough that level to almost cut to half the net worth in the example. Yes this is pretty extreme example but maybe it helps me (us?) to understand the idea more clearly. The theory should work notwithstanding the rate? (The example was originally inspired by JP's comment at praqcap.com, where Nick kindly weigh in)

Does the bond purchase really mean that? Knowing I'll get the money in the future does not courage my credit card usage?

[JP Koning]

"Hey! That's *my* line! That's the argument *I* use, against crazy econobloggers who get the sign wrong, or who think the magnitude is zero!"

Heh heh, yep. It worked pretty effectively for you against Stephen Williamson so I've decided to steal it from you ;)

[Miami vice]

"Does paying interest on excess balances constitute a change in monetary policy?
No. The stance of monetary policy continues to be set by the target for the overnight federal funds rate established by the FOMC. Paying interest on excess balances just makes it easier for the Desk to implement the target federal funds rate chosen by the FOMC."

" Is paying interest on excess balances inflationary?
No. The payment of interest on excess balances will permit the Desk to keep the federal funds rate closer to the target even as the Federal Reserve provides the necessary liquidity to support financial stability through its liquidity facilities. The federal funds rate target is set at the level that is appropriate in light of the Federal Reserve’s objectives of maximum employment and price stability."

http://www.newyorkfed.org/markets/ior_faq.html

[Majromax]

> If IOR is -50% I think it is safe to assume that TBills will trade close enough that level to almost cut to half the net worth in the example.

It depends on what the real interest rate is, which we can't uniquely determine from your scenario.

Remember that OMO operations act not just on the quantity of money, but also to adjust the real interest rate. It's that change in real interest rate that affects the spending patterns of (New-Keynsian) agents who have freedom to time-shift consumption.

Also, for you to be the one to sell to the central bank with the OMO, we also have to presuppose that you were the marginal holder of TBills -- the next most easily convinced to sell. Presumably, you had some better use for the cash in mind but didn't have the right price for the bill.

[Jussi]

That's why I said 'close enough'. Lets say I got interest rate of -48 %. As said I don't think this matters from the macro point of view. Or do you imply that the real rate would for some reason be substantial here?

Yes, the rate channel is there but that is not a part of the Nick's idea where M dictates alone the price level.

[Too Much Fed]

"But here's the kicker: what happens in the real world when central banks increase the rate of interest they pay on reserves?"

I mostly agree with Adam P. and JP.

Out here in the real world, interest payments are transfers of existing currency and/or existing demand deposits. I believe the collection of interest payments increases equity and "IOR" payments would decrease equity.

[Too Much Fed]

Nick said: "Whatever happened to "the stroke of the pen/keyboard"? Where's the MMT guys when you need them? Or, where's JKH? BMO has $100 on deposit at the BoC, and the BoC just crosses out "$100", and writes "$101" instead. Done. And then donates $1 less to the GoC (again by stroke of the pen)."

I believe JKH would say that is a decrease in equity in both cases. It is just a matter of who gets the "donation". The MMT people would talk about how the gov't runs a deficit ...