Interest on holding money vs interest on lending/borrowing money

Prerequisite: intermediate macro.

I reckon some people might be getting those two things muddled. The difference matters. Actually, the difference is the only thing that matters. It's the spread between those two interest rates, not the levels of those two interest rates, that matters for Aggregate Demand.

Simplify massively. There are two rates of interest. There is the rate of interest you get paid for holding money. Call it Rm. And there is the rate of interest you pay/get paid for borrowing/lending money. Call it Rb. Those are two conceptually very different interest rates. Rm is the rate of interest you get paid for the media of exchange in your pocket or chequing account. Rb is the rate of interest you get paid for the bonds or non-media of exchange IOUs you own.

[Update: I have a new post that adds a picture to this one.]

For example, take the very simplest textbook ISLM model. There appears to be only one rate of interest in that model, the one on the vertical axis. There are in fact two rates of interest in that model. The one on the vertical axis is Rb. The other rate of interest, Rm, is implicitly or explicitly assumed to be fixed at 0%. We know that because, as all the textbooks say, "the rate of interest is the opportunity cost of holding money". That statement only makes sense if we assume Rm=0%. Because the opportunity cost of holding money, rather than lending it, is Rb-Rm. So the rate of interest on the vertical axis must be Rb.

If we assumed that Rm were not fixed exogenously at 0%, and if we instead assumed that Rm followed Rb up and down, so that the spread between them Rb-Rm were a constant, then the LM curve would be vertical for a given Ms. Because there would be only one level of Y at which Md=Ms, if Md=L(Y,Rb-Rm). Where L_Y>0 and L_R<0. Which would give us a very different version of the textbook ISLM model. Because shifts in the IS curve would have no effect on Aggregate Demand.

Start in textbook ISLM equilibrium. Now suppose there is an exogenous increase in expected inflation. It rises from 0% to 2%. We stick a 2% vertical wedge between the IS and LM curves, with the top of the wedge on the LM curve, and the bottom of the wedge on the IS curve. Because saving and investment depend on the real interest rate, and the demand for money depends on the nominal interest rate, and nominal - real = inflation. That 2% expected inflation wedge shifts the Aggregate Demand curve to the right.

But another way to say exactly the same thing is to say that when expected inflation rises from 0% to 2%, the real rate of interest on holding money drops from 0% to minus 2%. And that fall in the real rate of interest on holding money is what shifts the AD curve to the right.

You could get exactly the same rightward shift in the AD curve, holding expected inflation constant, by assuming the nominal interest on holding money drops from 0% to minus 2%.

Aggregate Demand does not depend on the level of interest rates. Aggregate Demand depends on the spread between Rb and Rm. If that Rb-Rm spread is constant, so the opportunity cost of holding money is constant, the LM curve is vertical for a given M, and shifts in the IS curve have no effect whatsoever on AD. And shifts in the LM curve, caused by changing M, cause the AD curve to shift by exactly the same amount, regardless of whether the IS curve slopes down, up, or sideways. It simply does not matter what happens to the level of interest rates, if the spread between Rb and Rm is held constant.

Monetary policy works by changing Ms, and also by changing Rm to change the Rb-Rm spread.

[The interest rate in New Keynesian models is actually Rm. There are no bonds, so there is no Rb. Everyone has a chequing account at the central bank, which can have a positive or negative balance, but the net aggregate balance is fixed at zero, and if agents are identical each agent chooses to hold a zero balance in equilibrium.]

Comments

[David Andolfatto]

Nick,

"You could get exactly the same rightward shift in the AD curve, holding expected inflation constant, by assuming the nominal interest on holding money drops from 0% to minus 2%."

Did you mean "leftward?"

Consider standard textbook experiment: tighten monetary policy (by lowering M). Since we usually assume Rm = 0, effect is to raise Rb. This is contractionary, since higher (Rb-Rm) reduces AD (movement along IS curve).

But we might alternatively have assumed Rb=0 and let Rm vary. Same experiment (monetary tightening) means a *decline* in Rm. The increase in (Rb-Rm) is again contractionary.

Lowering the central bank deposit rate here corresponds to a *tightening* of monetary policy (and is contractionary).

Is this what you were trying to say?

Incidentally, I have a fully worked out OLG model that links demand (investment demand) to Rb - Rm, see equation (9) here: https://research.stlouisfed.org/publications/review/2015-09-08/a-model-of-u-s-monetary-policy-before-and-after-the-great-recession.pdf

[Nick Rowe]

David: I'm holding M constant, and lowering Rm. So there's an excess supply of money at existing Y and Rb, which increases AD. It's a loosening of monetary policy. In your experiment you are reducing M, which is rather different.

I think of the central bank as having two instruments: M and Rm. (Plus of course announcements about future M and Rm.)

[David Andolfatto]

Can you display what you mean using IS-LM diagram? Would be helpful for me. Thx. :)

[Bill Woolsey]

I am sure you know you are heading into my favorite place--pure inside money.

Anyway, you start off with a quantity of money instrument and all interest rates floating. There is no liquidity effect because the interest rate on money and the interest rates on bonds move together.

But then I cannot see how you are doing anything else but switching around and making the nominal (or real?) interest rate exogenous, controlled by the central bank setting an interest rate on money. Doesn't that require a horizontal LM curve?

[Nick Rowe]

David: I will have a go at it. (If my daughter had not taught me how to use Paint, though I'm still struggling, I would be in trouble.)

Bill: "I am sure you know you are heading into my favorite place--pure inside money."

Yep! Rm on central bank money can be treated as an exogenous policy variable. Rm on inside commercial bank money must be treated as endogenous. If an IS shock causes Rb to change, Rm will almost certainly change too, and if it changes by the same amount, the spread stays the same, so we get the vertical LM curve.

"But then I cannot see how you are doing anything else but switching around and making the nominal (or real?) interest rate exogenous, controlled by the central bank setting an interest rate on money. Doesn't that require a horizontal LM curve?"

Take the case of a pure outside money economy. Central bank money is the only money. Everyone has a chequing account at the central bank, so there are no adminsitrative difficulties of paying interest on money. The central bank has two instruments: the quantity of money M; the interest paid on money Rm. Holding both M and Rm constant, and holding expected inflation constant at 0%, and with Rb on the vertical axis, we get a standard upward-sloping LM under standard assumptions. An increase in Rb increases Rb-Rm which increases the opportunity cost of holding money, which reduces Md, and an increase in Y would increase Md, so LM slopes up. Now if the central bank increases Rm by 1%, holding M constant, the LM curve shifts vertically up by 1%, so it intersects IS at lower Y, so AD shifts left.

OK, I will draw the pictures, for a new post.

[Max]

A central bank that could costlessly set Rm would probably choose to hold Rb-Rm constant (and >0) rather than having it flop around randomly, which serves no purpose.

[Nick Rowe]

Max: I think that makes sense. And then it would adjust M, if needed to offset velocity shocks, to keep the vertical LM curve in the right place.

[Frank Restly]

Nick,

"Simplify massively. There are two rates of interest. There is the rate of interest you get paid for holding money. Call it Rm. And there is the rate of interest you pay/get paid for borrowing/lending money. Call it Rb."

Effectively a move to a negative Rm on money that you hold increases the net interest that you pay (Rb - Rm) on an existing loan - yes? You could achieve the same effect if all borrowers paid a floating interest rate on long term loans.

"Aggregate Demand does not depend on the level of interest rates. Aggregate Demand depends on the spread between Rb and Rm."

I am not sure that is always the case. Taking on a floating rate long term loan entails more risk for the borrower. And so, how would risk appetite affect the demand for credit?

[Nick Rowe]

Frank: stop babbling. You don't have the prerequisite.

[AARIZAM]

Nick, I would like to learn something here so Im going to state the following expecting you to correct me. Note: I might be totally, I mean totally lost here. If there is only one period and there is no risk of default, then rm should be equal to rb due to arbitrage considerations. Now lets supposed that there are two periods but no risk of default and no term premium, so rb_t should be equal roughly to 0.5*(rm_t+rm_t+1), where rm_t+1 is the rate of interest you will get paid for holding money in the second period, due to arbitrage considerations again/rational expectations. Finally, the spread that matters today would be equal to 0.5*(rm_t+1-rm_t).What happens if the central bank is expeceted to set the future rate (rm_t+1) equal to the present rate rm,t?

[Nick Rowe]

AARIZAM: People hold some of their wealth in the form of money even when other assets are known to give much higher rates of return. People will hold some money even when it's depreciating at a very high rate, like in a hyperinflation. Because money is the medium of exchange; you buy everything else with money.

You are (implicitly) assuming a world of zero transactions costs, where all assets are perfectly and instantly liquid. We wouldn't use money in a world like that. I would swap my apples for your bananas; it would be a barter economy.

[AARIZAM]

Thanks for your answer. Nick, I was seeing rm as a money market mutual fund rate. Those funds deliver a yield roughly equal to the centrals bank short term rate and you can get back your money in 24 hours. What happens if everybody holds their money market mutual fund shares? Now is it true what I said in my previous post?

[Nick Rowe]

AARIZAM: The words "money market" are banned on this blog ;-). In a monetary economy, as opposed to a barter economy, every single market is a money market. The apple market is a money market, because that is where money gets traded for apples. When you say "money market" what you really mean is "the market where money gets traded for short-term IOUs". We should instead call that "the short-term IOU market".

Sorry to be pedantic, but it is precisely this conceptual distinction that confuses discussion between finance people (like you?) and money/macro people (like me). Finance people do not understand how very special money is.

Back to your question: the "money market mutual fund rate" is (one example of) Rb. It's not Rm. There are many different Rb rates, because some assets are more liquid than others.

[AARIZAM]

Nick thanks so much again. I almost fell from my chair since you discovered I’m finance guy. I really want to learn something here. But again I might be totally, I mean totally lost here. So let’s see if I have learned something. If a mutual fund that buys short term IOUs that yield a rate pretty similar to the central bank policy rate becomes instantaneously liquid (you can have back your money whenever you want) and the policy rate goes pretty high exogenously; everyone will want to buy shares of this mutual fund, so there will be an excess of demand for money in all markets, in the market for bananas and for apples, which will decrease the price level till nobody wants to sell their products for money to buy those mutual fund shares? Or as the price level falls, because inflation expectation rises, the attractiveness of the mutual fund decreases. Sorry if Iam a lost cause.