The Market for Reserves and the Federal Funds Rate

In Chapter 15, we saw how open market operations and discount lending affect the balance sheet of the Fed and the amount of reserves. The market for reserves is where the federal funds rate is determined, and this is why we turn to a supply-and-demand analysis of this market to analyze how all three tools of monetary policy affect the federal funds rate.

Supply and The analysis of the market for reserves proceeds in a similar fashion to the analysis of

Demand in the the bond market we conducted in Chapter 5. We derive a demand and supply curve

Market for for reserves. Then the market equilibrium in which the quantity of reserves

Reserves demanded equals the quantity of reserves supplied determines the federal funds rate, the interest rate charged on the loans of these reserves.

Demand Curve. To derive the demand curve for reserves, we need to ask what happens to the quantity of reserves demanded, holding everything else constant, as the federal funds rate changes. Recall from Chapter 16 that the amount of reserves can be split up into two components: (1) required reserves, which equal the required reserve ratio times the amount of deposits on which reserves are required, and (2) excess reserves, the additional reserves banks choose to hold. Therefore, the quantity of reserves demanded equals required reserves plus the quantity of excess reserves demanded. Excess reserves are insurance against deposit outflows, and the cost of holding these excess reserves is their opportunity cost, the interest rate that could have been earned on lending these reserves out, which is equivalent to the federal funds rate. Thus as the federal funds rate decreases, the opportunity cost of holding excess reserves falls and, holding everything else constant, including the quantity of required reserves, the quantity of reserves demanded rises. Consequently, the demand curve for reserves, Rd, slopes downward in Figure 1.

Supply Curve. The supply of reserves, Rs, can be broken up into two components: the amount of reserves that are supplied by the Fed's open market operations, called non-borrowed reserves (Rn), and the amount of reserves borrowed from the Fed, called discount loans (DL). The primary cost of borrowing discount loans from the Fed is

FIGURE 1 Equilibrium in the Market for Reserves

Equilibrium occurs at the intersection of the supply curve Rs and the demand curve Rd at point 1 and an interest rate of i **.

FIGURE 1 Equilibrium in the Market for Reserves

Equilibrium occurs at the intersection of the supply curve Rs and the demand curve Rd at point 1 and an interest rate of i **.

Fed Funds Rate Supply And Demand

Rn Quantity of

Reserves, R

Rn Quantity of

Reserves, R

www.federalreserve.gov /fomc/fundsrate.htm

This site lists historical federal funds rates and also discusses Federal Reserve targets.

the interest rate the Fed charges on these loans, the discount rate (id). Because borrowing federal funds is a substitute for taking out discount loans from the Fed, if the federal funds rate iff is below the discount rate id, then banks will not borrow from the Fed and discount loans will be zero because borrowing in the federal funds market is cheaper. Thus, as long as iff remains below id, the supply of reserves will just equal the amount of nonborrowed reserves supplied by the Fed, Rn, and so the supply curve will be vertical as shown in Figure 1. However, as the federal funds rate begins to rise above the discount rate, banks would want to keep borrowing more and more at id and then lending out the proceeds in the federal funds market at the higher rate, iff. The result is that the supply curve becomes flat (infinitely elastic) at id, as shown in Figure 1.

Market Equilibrium. Market equilibrium occurs where the quantity of reserves demanded equals the quantity supplied, Rs = Rd. Equilibrium therefore occurs at the intersection of the demand curve Rd and the supply curve Rs at point 1, with an equilibrium federal funds rate of if When the federal funds rate is above the equilibrium rate at iff, there are more reserves supplied than demanded (excess supply) and so the federal funds rate falls to iff as shown by the downward arrow. On the other hand, when the federal funds rate is below the equilibrium rate at if, there are more reserves demanded than supplied (excess demand) and so the federal funds rate rises as shown by the upward arrow. (Note that Figure 1 is drawn so that id is above i* because the Federal Reserve now keeps the discount rate substantially above the target for the federal funds rate.)

How Changes in the Tools of Monetary Policy Affect the Federal Funds Rate

Now that we understand how the federal funds rate is determined, we can examine how changes in the three tools of monetary policy—open market operations, discount lending, and reserve requirements—affect the market for reserves and the equilibrium federal funds rate.

Open Market Operations. We have already seen that an open market purchase leads to a greater quantity of reserves supplied; this is true at any given federal funds rate because of the higher amount of nonborrowed reserves, which rises from Rn to Rf. An open market purchase therefore shifts the supply curve to the right from R1 to Rf and moves the equilibrium from point 1 to point 2, lowering the federal funds rate from ijf to iff (see Figure 2).1 The same reasoning implies that an open market sale decreases the quantity of reserves supplied, shifts the supply curve to the left and causes the federal funds rate to rise.

The result is that an open market purchase causes the federal funds rate to fall, whereas an open market sale causes the federal funds rate to rise.

Discount Lending. The effect of a discount rate change depends on whether the demand curve intersects the supply curve in its vertical section versus its flat section. Panel a of Figure 3 shows what happens if the intersection occurs at the vertical section of the supply curve so there is no discount lending. In this case, when the discount rate

1We come to the same conclusion using the money supply framework in Chapter 16, along with the liquidity preference framework in Chapter 5. An open market purchase raises reserves and the money supply, and then the liquidity preference framework shows that interest rates fall.

FIGURE 2 Response to an Open Market Operation

An open market purchase increases nonborrowed reserves and hence the reserves supplied, and shifts the supply curve from Rj to R2. The equilibrium moves from point 1 to point 2, lowering the fto ijj.

federal funds rate from i i to i2

Reserves, R

Reserves Curve

Reserves, R Reserves, R

(a) No discount lending (b) Some discount lending

FIGURE 3 Response to a Change in the Discount Rate

In panel a when the discount rate is lowered by the Fed from i j to ij, the vertical section of the supply curve just shortens, as in Rj, so that the equilibrium federal funds rate remains unchanged at if. In panel b when the discount rate is lowered by the Fed from ij to ij, the horizontal section of the supply curve Rj falls, and the equilibrium federal funds rate falls from f to f.

www.frbdiscountwlndow.org/

Information on the operation of the discount window and data on current and historical interest rates.

www.federalreserve.gov /monetarypolicv /reservereq.htm

Historical data and discussion about reserve requirements.

is lowered by the Fed from ij to ij, the vertical section of the supply curve where there is no discount lending just shortens, as in Rj, while the intersection of the supply and demand curve remains at the same point. Thus, in this case there is no change in the equilibrium federal funds rate, which remains at if. Because this is the typical situation—since the Fed now usually keeps the discount rate above its target for the federal funds rate—the conclusion is that most changes in the discount rate have no effect on the federal funds rate.

However, if the demand curve intersects the supply curve on its flat section, so there is some discount lending, as in panel b of Figure 3, changes in the discount rate do affect the federal funds rate. In this case, initially discount lending is positive and the equilibrium federal funds rate equals the discount rate, ij = ij. When the discount rate is lowered by the Fed from i j to i2, the horizontal section of the supply curve R2 falls, moving the equilibrium from point j to point 2, and the equilibrium federal funds rate falls from ij to ij (= i2) in panel b.

Reserve Requirements. When the required reserve ratio increases, required reserves increase and hence the quantity of reserves demanded increases for any given interest rate. Thus a rise in the required reserve ratio shifts the demand curve to the right from Rj to Rj in Figure 4, moves the equilibrium from point 1 to point 2, and in turn raises the federal funds rate from i j to i j.

The result is that when the Fed raises reserve requirements, the federal funds rate rises.2

FIGURE 4 Response to a Change in Required Reserves

When the Fed raises reserve requirements, required reserves increase, which increases the demand for reserves. The demand curve shifts from Rj to Rj, the equilibrium moves from point 1 to point 2, and the federal fund rate rises from ij to i j.

FIGURE 4 Response to a Change in Required Reserves

When the Fed raises reserve requirements, required reserves increase, which increases the demand for reserves. The demand curve shifts from Rj to Rj, the equilibrium moves from point 1 to point 2, and the federal fund rate rises from ij to i j.

Rn Quantity of

Reserves, R

Rn Quantity of

Reserves, R

2Because an increase in the required reserve ratio means that the same amount of reserves is able to support a smaller amount of deposits, a rise in the required reserve ratio leads to a decline in the money supply. Using the liquidity preference framework, the fall in the money supply results in a rise in interest rates, yielding the same conclusion in the text that raising reserve requirements leads to higher interest rates.

Similarly, a decline in the required reserve ratio lowers the quantity of reserves demanded, shifts the demand curve to the left, and causes the federal funds rate to fall. When the Fed decreases reserve requirements, it leads to a fall in the federal funds rate.

Now that we understand how the three tools of monetary policy—open market operations, discount lending, and reserve requirements—can be used by the Fed to manipulate the money supply and interest rates, we will look at each of them in turn to see how the Fed wields them in practice and how relatively useful each tool is.

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