Most simple macro models have just one (nominal) interest rate. I want to complicate it, just a little, by talking about two (nominal) interest rates:
1. There is the rate of interest you get paid if you hold money. Call it Rm.
2. There is the rate of interest you get paid if you lend money. Call it Rb.
For a paper money, Rm is nearly always fixed at 0%, simply because of the practical difficulties of paying interest on paper currency. But for an electronic medium of exchange, there are no practical difficulties, and Rm can be positive or negative. For example, chequing accounts sometimes pay positive interest (or reduce your fees if you hold a large balance). And commercial banks may get paid interest on the electronic money they hold in their accounts at the central bank. But Rb is generally not the same as Rm. Rb is nearly always greater than Rm (otherwise people would simply hold money rather than lending it). Except for the constraint that Rb cannot be less than Rm, the two interest rates don't have to move together.
Now for my simple question:
If you believe that "Central banks control monetary policy by setting the rate of interest" which of those two interest rates do you have in mind? Is it Rm, or Rb?
Old Keynesian ISLM models assume that the rate of interest is the opportunity cost of holding money, so they implicitly assume Rm=0%, so "the interest rate" means Rb.
But in simple New Keynesian models, all money is electronic money and the central bank sets the rate of interest on electronic money, so "the interest rate" means Rm.
That's an important conceptual difference between those two "Keynesian" models.
We can imagine a world where all central bank money is electronic money, and the central bank can alter both the quantity of money and the interest rate paid on that money, and can make Rm and Rb move by different amounts, or even in different directions, if it wants to.
To my monetarist mind, an increase in Rm increases the demand for money, and that causes an excess demand for money, just like a reduction in the supply of money causes an excess demand for money. An excess demand for money, or an excess supply of money, has macroeconomic consequences. Any change in Rb is just one symptom of those macroeconomic consequences. We would get roughly the same macroeconomic consequences even if Rb was fixed by law, or if lending money at interest was tabu.
Worthwhile Canadian Initiative 
“We can imagine a world where all central bank money is electronic money, and the central bank can alter both the quantity of money and the interest rate paid on that money …”
Suppose that, in such a world, the central bank doesn’t do OMOs. The quantity of money doesn’t change, except for changes arising from the interest rate paid on money. (Interest on money is “payment in kind,” so interest on money affects the quantity of money.) In this world, the interest rate on money is equivalent to the growth rate of the money supply. Over time, the higher the interest rate on money, the larger the quantity of money.
In such a world, is raising the interest rate on money deflationary, or inflationary?
(For simplicity, assume that central bank money is the only form of money; there are no commercial banks; everyone has an account at the central bank.)
M.R. “In such a world, is raising the interest rate on money deflationary, or inflationary?”
Good question. Assume all prices perfectly flexible. Assume initially Rm=0% and inflation = 0%. Now, unexpectedly, the CB increases Rm to 10%, and increases the growth rate of M by that same 10% (all new money is paid as interest). The price level does not jump (it normally would jump, if new money was just helicoptered in). But the inflation rate now jumps to 10%. The real interest rate on money stays the same, so real money balances stay the same.
“The real interest rate on money stays the same, so real money balances stay the same.”
That sounds right to me under the assumption of perfectly flexible prices.
What if prices are sticky? CB unexpectedly increases Rm to 10%. So that’s also the growth rate of M in my scenario.
Real money balances are now growing, so this should encourage spending. At the same time, money has become a more attractive asset, which discourages spending.
What’s the right way to think about this?
M.R. Hmmm. Dunno. My brain has stopped working.
M.R.,
Imagine that the level of reserves is $25M in a $1.8T economy. The central bank controls the policy rate by setting Rm. At Rm=5%, there is $1.25M of new money introduced into the economy every year. Apart from the fact that the central bank buys back the $1.25M via OMOs every year, that economy is Canada. So unless you think that $1.25M of OMOs is the critical
difference, there you have the empirical answer to your question. Other than maybe Steve Williamson and Ed Prescott, I don’t think there are very many people who believe that if the Bank of Canada raises IOR to 10% inflation will go up. The Bank of Canada certainly doesn’t believe it. Like Tony Yates says Chris Sims got a Nobel prize for empirically settling this stuff. And apart from empirical evidence, it strains credulity to imagine that anyone cares about the quantity of about $25M of reserves.
Like Nick points out in his newest post, it just doesn’t matter whether M is positive, negative or even zero.
Anon, try as I might, I didn’t understand Nick’s most recent post …
I’m not sure the Canada comparison is apt. We were imagining a very different, stripped-down institutional environment.
My point was just that, in the stripped-down setting we were discussing, and assuming no OMOs, Rm is the growth rate of the money supply.
So higher Rm means higher money growth. Higher money growth should mean higher inflation. I gather you disagree?
M.R.: I now think, that if inflation is sticky/inertial, that the initial effect will be a decline in inflation, followed by an eventual rise in inflation. But I’m not sure. Because if inflation fails to rise by the full 10% immediately, the demand for money will initially increase, so inflation falls.
I am beginning to wonder about stability.
M.R.,
I think the gist of your question is, even if inflation deviates a bit from equilibrium, will it be driven back to equilibrium by the 10% rate of money growth. I think the answer is well-known to be no. The only way to get an asymptotic 10% inflation rate is with a 10% inflation targeting Taylor rule as well as an expectation of an asymptotically bounded inflation rate. You need both. In your case, you don’t have a Taylor rule. This has been known for a long time, but is extensively discussed in Benhabib, Schmitt-Grohe, and Uribe (2001) The Perils of Taylor Rules. Friedman’s k% rule isn’t stable. The problem is that any downward deviation in inflation from equilibrium raises the real rate which causes a further reduction in inflation and consumption.
There are GE models where the quantity of money matters more, but the intertemporal equilibrium doesn’t distinguish much between money and government debt (the central bank can arbitrarily transform either one into the other at all points in the future) and you need to consider the backing (or not) by future taxes (Ricardian equivalence) rather than just liquidity demand. I.e. a large quantity of total bonds+money may have non-Ricardian inflationary effects which overwhelm the deflationary consumption depressing Euler equation effects. This will happen if the rate of production of bonds+money is faster than a sustainable bubble. I.e. there are limits to the power of government to transport your consumption from the present into the future.
This directly contradicts the monetarist view where only the quantity of money matters for the price level. Woodford has written a fair bit about fiscal dominance and the fiscal theory of the price level. In these models any increase in money needs to be seen versus the larger context of the total quantity of money and debt, so your money base expanding interest payments would look very small compared to outstanding debt levels in modern economies.
Nick: Interesting answer, I see what you’re saying.
Anon:
To be clear, I didn’t say that only the quantity of money matters for the price level.
What I did say — and I don’t think it is very controversial — is that we usually think that, ceteris paribus, higher money growth means higher inflation.
The gist of my question was to ask whether this latter proposition depends upon the institutional setting, and on the way in which the change in money happens.
Nick’s post said this: “To my monetarist mind, an increase in Rm increases the demand for money, and that causes an excess demand for money, just like a reduction in the supply of money causes an excess demand for money.”
My point is just that, in the institutional setting we were imagining, and assuming no OMOs, an increase in Rm is equivalent to an increase in money growth. Yet Nick is equating the effects of an increase in Rm to those of a reduction in the supply of money. There is a tension here that’s worth thinking about.
I get the sense that you don’t think the quantity of money has any bearing on the price level?
M.R.
“I get the sense that you don’t think the quantity of money has any bearing on the price level?”
Like I said, it depends. In the case of a non-Ricardian fiscal policy, it is the total government liabilities, bonds+money, that will determine the price level. Money is typically a very small fraction of that, and anyways, can be freely converted to bonds. In the case of a Ricardian policy, the transversality condition (the governments asymptotic budget constraint) means that debt and money will all be paid off via taxes in the limit. In this case there is no connection to the price level. Finally, you might be able to make the classical monetarist argument for the price level if money wasn’t created by buying bonds. Since it’s created by buying bonds, the real balance is not net wealth to the private sector sustained by liquidity preference alone (at least not in a Ricardian economy).
So all in all, I’d tend to agree with that statement. I’m not saying that you couldn’t construct economies in which M decides the price level. I’m just saying that real world economies look nothing like those economies, and in the real world, as well as in realistic model economies, the quantity is basically irrelevant.
To be even clearer, here’s what I believe:
For a Ricardian fiscal policy (the usual assumption): Contingent on the path of the real rate the path of the quantity of money is irrelevant.
For a non-Ricardian fiscal policy: The asymptotically unpaid portion of the governments liabilities (bonds+money) is linked to the asymptotic price level via the asymptotic demand for the real balance (liquidity preference).
“What I did say — and I don’t think it is very controversial — is that we usually think that, ceteris paribus, higher money growth means higher inflation.”
Who’s we? I’m sure it’s uncontroversial among the general public.
Anon:
“in the real world … the quantity [of money] is basically irrelevant [to the price level].”
Hmm… I will take the other side of that one. But you get credit for internal consistency!
“Who’s we?”
Fair question. I suppose everything is controversial. My guess is that most (all?) current Fed board members would agree with the statement that “ceteris paribus, higher money growth means higher inflation.”
M.R.
“My guess is that most (all?) current Fed board members would agree with the statement that “ceteris paribus, higher money growth means higher inflation.””
In non-diverging equilibrium, yes. I also agree that for a stabilized economy, the growth of the money supply will tend to be around the nominal short rate (actually around the nominal growth rate, but whatever). But we were talking about your thought experiment, which was a control problem that involved suddenly raising the rate paid on money and keeping it there. Ask those same Fed members what would happen if we suddenly raise IOR to 10% and don’t do any further OMOs (In fact, we would have to stop QE). I won’t venture to guess what some of the dinosaurs (Plosser, Fisher) might answer, but I am pretty sure I can guess the answers of experts like Evans, Bullard and Kocherlakota. The fact is, there is no way a policy rate hike to 10% wouldn’t tank both inflation and the US economy at the same time. The fact that those 10% would produce an additional $400Bn of reserves next year is irrelevant (there’s already over $3T out there, up a factor of 1000 over the past 6 years, and it’s growing by over $700Bn/year).
“Yes your mortgage rate just went up by 10%, but don’t worry. There will be yet another $1000 per person sitting on reserve at the NY Fed by the end of next year.”
If the existing stock of money is non-zero, and if increasing both the growth rate of M and Rm by 10% has zero effect on inflation, then the real stock of money M/P will become infinitely large.
Nick,
I agree. So will the real value of government debt. The effects of both appear together as total government liabilities, and how that quantity effects the equilibrium depends on fiscal policy (Ricardian or not?). So you can’t use some non-Ricardian argument to save some version of the exchange equation. Instead you end up with the price level determined via the FTPL. But you are right, I think, that a large quantity of government liabilities can save you from an out of control deflation spiral (assuming that’s what you were implying). There are lots of tricky complications here, so I think it’s better just to refer to Benhabib et al or Woodford’s chapter on Self-Fulfilling Inflations and Deflations.
Barro-Ricardian Equivalence says that paying new bonds as interest on old bonds makes no difference to either nominal or real variables, and if you assume that money and bonds are perfect substitutes, not just at the margin but everywhere, then you will get the same result with money, in M.R.’s thought-experiment. You are assuming Rm=Rb always. But if you drop that assumption, and allow Rm < Rb, then the real stock of money will matter.
By the way, just for my curiosity, because it’s strange arguing with an anonymous person: I don’t need to know your name, but my guess is you are a recent PhD from a top Canadian or US school. That’s the image I have in mind. Is my guess roughly right? (You don’t need to answer.)
Nick,
I have posted a new comment at Scott’s blog, trying to persuade Scott that changing Rm-Rb is not a fiscal policy.
Nick, sorry to drag you back to this post (if you’re even willing to come back here), but can you please elaborate a bit on what you meant by this last sentence:
“We would get roughly the same macroeconomic consequences even if Rb was fixed by law, or if lending money at interest was tabu.”
What kind of “law” are you talking about? Lending money tabu? You mean like under Islamic law or something?
Thanks.
We were having a discussion of it here, and it was confusing:
http://pragcap.com/a-new-operating-framework-for-the-federal-reserve/comment-page-1#comment-167092
… upon further reflection, I think I got what you mean, but you still might take a look at the link to clear up any misconceptions that John or I may have (you’ll probably be aghast at my sloppy [dead wrong?] summary of MM thought there).
Tom: looks to me like you got it right.
Yep, something like Islamic Law, only with no loopholes. People would evade that law, of course, but it’s just a thought-experiment.
The other guy (John) on PragCap says that Rb is a vector/matrix, since Rb varies by term/risk/etc. He’s right of course. All models simplify.
Vaidas: I will take a look a little later. Off skating on the world’s largest skating rink.
Thanks Nick!! Appreciate it.