Supply and Demand for the Monetary Base: How the Fed Currently Determines Interest Rates

Before October 3, 2008, the interest rate the Fed paid on excess reserves was zero, because it was only on that date that the Fed received authority to pay a nonzero rate on excess reserves. Since for market equilibrium, it is the amount of interest paid on the last dollar of reservers that matters most, I will simplify by calling the interest rate on excess reservers simply the interest on reserves (IOR). As you can see from the top graph, during that period when the Fed was limited to an IOR of zero, the federal funds rate and the 3-month Treasury bill rate, while tracking each other, were often very different from the IOR.

The second graph shows that, more recently, the federal funds rate and the 3-month Treasury bill rate have not only tracked each other, but also move together with the IOR. What is going on? Let me lay out a very simple model of supply and demand for the monetary base to explain this.

“The monetary base” means the same thing as “high-powered money” and the same thing as “narrow money.” The monetary base is equal to reserves + paper currency and coins. Paper currency and coins stored in bank vaults counts as part of the monetary base, but only once: it must be counted either as reserves or as paper currency, but not both.

The Fed (or other central bank) is in complete control of the monetary base because the only thing that adds to the monetary base is when the Fed buys things; and other than the rare cases in which someone literally sets fire to paper currency, or destroys a coin, the only thing that reduces the monetary base is when the Fed sells things. (If paper currency or coins were permanently lost, it would probably still be counted as part of the monetary base, but in economic effects, this permanent loss of paper currency or coins would be like a reduction in the monetary base. On the other hand, when paper currency wears out, that is not a reduction in the monetary base, because people can take worn-out paper currency to the cash window of the central bank and get new paper currency in exchange.)

The Fed mostly buys assets, but it does some amount of buying goods and services. (For example, it pays salaries to its staff.) The main asset it buys are 3-month Treasury bills. (If the Fed buys any other asset besides 3-month Treasury bills or a derivative of 3-month Treasury bills it is called Quantitative Easing, or QE for short.) Similarly, the main thing the Fed sells is 3-month Treasury bills; it controls the amount of 3-month Treasury bills that it sells.

Because the Fed completely controls the quantity of the monetary base, I draw the supply curve for the monetary base as vertical:

From here on, I when I write “paper currency” I mean “paper currency and coins.” While the Fed controls the total quantity of the monetary base, given current paper currency policy the division of the monetary base between paper currency and reserves is totally up to the private sector. In “An Underappreciated Power of a Central Bank: Determining the Relative Prices between the Various Forms of Money Under Its Jurisdiction” I write about the “cash window” that in the US exists at each regional Federal Reserve Bank. Under current paper currency policy, commercial banks can freely exchange reserves in their reserve accounts for the same face value of paper currency or exchange paper currency for reserves in their reserve accounts equal to the face value of the paper currency that is deposited.

Because the monetary base consists of paper currency plus reserves, the demand for the monetary base comes from the demand for paper currency and the demand for reserves. A certain amount of paper currency and coins has relatively high value—which I measure as an annual rate of return on the vertical axis—for (a) convenience in transactions, (b) tax evasion and (c) other illegal activities. A certain amount of reserves has a relative high value—again measured as an annual rate of return—for (1) supporting required reserves and (2) providing excess reserves that banks feel they need for safety purposes. But at some point, the monetary base would be so large that just keeping the dollars as reserves earning the IOR is a better option than (a), (b), (c), (1) or (2). After that point, the value of an extra dollar of monetary base is simply the IOR. (I am abstracting from the situation in which massive paper currency storage is an attractive option—that is, when the official paper currency interest rate, which is traditionally set by policy to zero, minus storage costs, is an attractive return relative to the marginal value of monetary base for (a), (b), (c), (1) or (2). I have written a lot about how the Fed or other central bank should deal with the possibility of massive paper currency storage. See the links collected in “How and Why to Eliminate the Zero Lower Bound: A Reader’s Guide.”)

Putting everything together, at a large enough value of the monetary base, the demand for monetary base curve should be flat at the height of the IOR. Left of that point, the demand for monetary base curve should be higher. And the smaller the quantity of the monetary base the further up the value (=implicit rate of return) of a dollar of monetary base should be. That means that on the left side of the graph the demand for monetary base curve is downward-sloping, while on the right side of the graph, the demand for monetary base curve is flat at the height of the IOR.

To give the intuition in a slightly different way for why the demand for monetary base curve is downward sloping to the left, but flat to the right, the first few dollars of monetary base are very valuable. But at some point all of this higher rate of return is exhausted; the monetary base is large enough that banks and others see the value of the last dollar as only the ability of that dollar to earn the interest on reserves.

One subtle but useful point is that the demand for monetary base curve is really the vertical maximum over two curves that are determined separately. There is a downward sloping curve for the marginal value of a dollar in monetary base for uses (a), (b), (c), (1) or (2). Then there is a curve that is flat at the height of the IOR. Whichever is higher at any given quantity of monetary base rules the day. But these two pieces of the demand for monetary base curve move separately, “hiding” the part of the other curve that is underneath.

What do we learn from equilibrium between the supply and demand for the monetary base? The vertical level of equilibrium is the marginal value or rate of return of a dollar of monetary base. The federal funds rate is the rate at which commercial banks lend reserves to one another, so the federal funds rate should measure the marginal value or rate of return of a dollar of monetary base. And term structure relationships force a close alignment between the federal funds rate and the 3-month Treasury bill rate. These rates in turn affect many other interest rates in the economy. The Fed can control many interest rates in the economy in the short run by changing the height of the equilibrium of the supply and demand for the monetary base. Hence, I have labeled the vertical axis with the letter i, standing for the nominal interest rate (and in particular, a very short-term, very safe rate).

Historically, the Fed used to keep the monetary base small, so that the supply of monetary base intersected the demand curve for the monetary base at the downward-sloping part to the left. But since the 2008 Financial Crisis, the Fed increased the monetary base enough that the supply of the monetary base intersects the demand curve for the monetary base on the flat part to the right, like this:

At that point, the IOR was quite low, .25% per year. But recently, the Fed has increased the IOR, so that the current situation is like this:

(Notice how some of the downward-sloping part got hidden by the higher IOR.)

The striking thing from these last two graphs is the theory’s implication that when the monetary base us large enough, the IOR basically determines the level of other safe, short-term rates such as the federal funds rate and the 3-month Treasury bill rate. In the real world, things are complicated by the fact that only banks, and then only some banks, are allowed to have reserve accounts. So other financial firms that want to take advantage of the IOR have to go through banks that are allowed to have reserve accounts. Those banks take a cut, leaving the rest as a somewhat lower federal funds rate (which is closely tied by a term-structure relationship to the 3-month Treasury bill rate).

Recently (2019), in my interpretation of Fed news, the Fed has begun to make noises that it intends to keep the monetary base large enough that the supply of the monetary base continues to intersect the demand curve for the monetary base on the flat part to the right. That will keep the rate of return for monetary base very close to the interest on reserves (IOR), implying that the federal funds rate at which banks lend reserves to each other, the 3-month Treasury bill rate and the repo rate at which banks lend Treasury bills to one another will stay close to the interest rate on reserves (IOR). If those key interest rates (the federal funds rate is the Fed's target rate in the US) stay close to the interest on reserves (IOR), then one can view the interest on reserves (IOR) is the central tool for determining short-run safe rates. But the IOR is the central tool for determining short-run safe rates only in the context of the monetary base being kept large enough that the supply of the monetary base is to the right of the downward-sloping part of the demand for monetary base curve. 

Here is the key passage behind that interpretation, from the unabridged version of Nick Timiraos’s March 2019 article “Fed Keeps Rates Unchanged, Signals No More Increases Likely This Year”:

On the asset-portfolio front, the Fed has been shrinking its $4 trillion in holdings since October 2017. While the runoff has slowly removed stimulus from the economy, officials have said the decision to end that runoff is being driven primarily by technical factors to make sure the central bank can smoothly implement its monetary policy decisions.

Any time the Fed buys “holdings” it adds to the monetary base, and anytime it sells “holdings” it reduces the monetary base. I interpret the phrase “technical factors to make sure the central bank can smoothly implement its monetary policy decisions” to mean that the Fed likes being on the flat part of the monetary base demand curve. (Let me mention that in my view, among current reporters on the Fed, Nick Timiraos is the best in the business.) Thus, it seems that an equilibrium in which the monetary base is large enough that the IOR is the key determinant of the level of short-term safe rates could be the new normal.

Besides the convenience and reliability of nailing down short-term safe rates with the IOR, which the Fed gets when it keeps the monetary base large, there is one other benefit to keeping the monetary base—and particularly reserves—large. At the 2016 Jackson Hole conference that I was luck enough to be invited to, Jeremy Stein presented his paper coauthored with Robin Greenwood and Samuel Hanson: “The Federal Reserve’s Balance Sheet as a Financial-Stability Tool.” This paper argues, in effect, that if the Fed or some other arm of the government doesn’t provide enough short-term safe assets, that the demand for such assets will be high enough that private firms will create assets that pretend to be short-term safe assets, but aren’t—at least not in the same way reserves are. When the pretense unravels, people freak out, which can create or contribute to a financial crisis. For example, in the Financial Crisis that intensified toward the end of 2008, when it became clear that money market mutual fund shares that pretended to always be worth a dollar were actually worth less than a dollar, people freaked out. (This was called “breaking the buck.”) I was very impressed with this argument, and I suspect that, with some delay, other Fed officials were impressed with it as well. Jeremy Stein was himself on the Federal Reserve Board for a short time, and I’ll bet was well-respected by his colleagues. I wrote about Jeremy in my column “Meet the Fed's New Intellectual Powerhouse.” (Unfortunately, Jeremy stepped down from the Federal Reserve Board soon after I wrote this.)

What I have written above is what I now teach my students in my intermediate macro class about how the Fed determines interest rates operationally. It should be in macro textbooks, but for the most part isn’t yet.

Update, April 5, 2019: On the Facebook page for this post, Roc Armenter wrote: check the “normalization plans and principles” update of january 2019 for something more than “making noises”...

For other aspects of what I teach my students in my intermediate macro class, see “On Teaching and Learning Macroeconomics.” Also, don’t miss last week’s post, “The Costs of Inflation.” On the division of the monetary base into paper currency and reserves, some of you might be interested in the very heavy-duty post, “The Supply and Demand for Paper Currency When Interest Rates Are Negative.”