# Additional Factors That Determine the Money Supply

So far we have been assuming that the Fed has accurate control over the monetary base. However, whereas the amount of open market purchases or sales is completely controlled by the Fed's placing orders with dealers in bond markets, the central bank cannot unilaterally determine, and therefore cannot perfectly predict, the amount of borrowing by banks from the Fed. The Federal Reserve sets the discount rate (interest rate on discount loans), and then banks make decisions about whether to borrow. The amount of discount loans, though influenced by the Fed's setting of the discount rate, is not completely controlled by the Fed; banks' decisions play a role, too.

Therefore, we might want to split the monetary base into two components: one that the Fed can control completely and another that is less tightly controlled. The less tightly controlled component is the amount of the base that is created by discount loans from the Fed. The remainder of the base (called the nonborrowed monetary base) is under the Fed's control, because it results primarily from open market operations.5 The nonborrowed monetary base is formally defined as the monetary base minus discount loans from the Fed:

where

MBn = nonborrowed monetary base MB = monetary base DL = discount loans from the Fed

The reason for distinguishing the nonborrowed monetary base MBn from the monetary base MB is that the nonborrowed monetary base, which is tied to open market operations, is directly under the control of the Fed, whereas the monetary base, which is also influenced by discount loans from the Fed, is not.

To complete the money supply model, we use MB = MBn + DL and rewrite the money supply model as:

where the money multiplier m is defined as in Equation 4. Thus in addition to the effects on the money supply of the required reserve ratio, currency ratio, and excess reserves ratio, the expanded model stipulates that the money supply is also affected by changes in MBn and DL. Because the money multiplier is positive, Equation 5 immediately tells us that the money supply is positively related to both the nonbor-rowed monetary base and discount loans. However, it is still worth developing the intuition for these results.

Changes in the Nonborrowed Monetary Base MB„

### Changes in Discount Loans DL from the Fed

As shown in Chapter 15, the Fed's open market purchases increase the nonborrowed monetary base, and its open market sales decrease it. Holding all other variables constant, an increase in MBn arising from an open market purchase increases the amount of the monetary base that is available to support currency and deposits, so the money supply will increase. Similarly, an open market sale that decreases MBn shrinks the amount of the monetary base available to support currency and deposits, thereby causing the money supply to decrease.

We have the following result: The money supply is positively related to the non-borrowed monetary base MBn.

With the nonborrowed monetary base MBn unchanged, more discount loans from the Fed provide additional reserves (and hence higher MB) to the banking system, and these are used to support more currency and deposits. As a result, the increase in DL will lead to a rise in the money supply. If banks reduce the level of their discount loans, with all other variables held constant, the amount of MB available to support currency and deposits will decline, causing the money supply to decline.

5Actually, there are other items on the Fed's balance sheet (discussed in the appendix on the web site) that affect the magnitude of the nonborrowed monetary base. Since their effects on the nonborrowed base relative to open market operations are both small and predictable, these other items do not present the Fed with difficulties in controlling the nonborrowed base.