# Money and Banking, v. 2.0

by Robert E. Wright

## 15.5 The M2 Money Multiplier

### Learning Objectives

1. Why is the M2 multiplier almost always larger than the M1 multiplier?
2. Why are the required reserve ratio, the excess reserve ratio, and the currency ratio in the denominator of the m1 and m2 money multipliers?
3. Why are the currency, time deposit, and money market mutual fund ratios in the numerator of the m2 money multiplier?

Note that m1 is the M1 money multiplier. With a little bit more work, one can also calculate the M2 money multiplier (m2). We want to do this because M2 is a more accurate measure of the money supply than M1, as it is usually a better indicator of changes in prices, interest rates, inflation, and, ultimately, aggregate output. (And hence whether you and your family live in a nice place with a 3D HDTV, three big refrigerators, etc., or if you live in “a van down by the river.”)

Recall from Chapter 3 "Money" that M2 = C + D + T + MMF, where T = time and savings deposits and MMF = money market funds, money market deposit accounts, and overnight loans. We account for the extra types of deposits in the same way as we accounted for currency and excess reserves, by expressing them as ratios against checkable deposits:

(T/D) = time deposit ratio

(MMF/D) = money market ratio

which leads to the following equation:

$m 2 = 1 + ( C / D ) + ( T / D ) + ( M M F / D ) / [ r r + ( E R / D ) + ( C / D ) ]$

Once you calculate m2, multiply it by the change in MB to calculate the change in the MS, specifically in M2, just as you did in Exercise 2. Notice that the denominator of the m2 equation is the same as the m1 equation but that we have added the time and money market ratios to the numerator. So M2 is alwaysM2 would equal m1 iff T = 0 and MMF = 0, which is highly unlikely. Note: if means if and only if. > m1, ceteris paribus, which makes sense when you recall that M2 is composed of M1 plus other forms of money. To verify this, recall that we calculated m1 as 2.6316 when

Required reserves (rr) = .2

Currency in circulation = $100 million Deposits =$400 million

Excess reserves = $10 million We’ll now add time deposits of$900 million and money market funds of \$800 million and calculate M2:

$m 2 = 1 + ( C / D ) + ( T / D ) + ( M M F / D ) / [ r r + ( E R / D ) + ( C / D ) ]$ $m 2 = 1 + ( 100 / 400 ) + ( 900 / 400 ) + ( 800 / 400 ) / [ .2 + ( 10 / 400 ) + ( 100 / 400 ) ]$ $m 2 = 1 + .25 + 2.25 + 2 / ( .2 + .005 + .25 )$ $m 2 = 5.5 / .455 = 12.0879$

This is quite a bit higher than m1 because time deposits and money market funds are not subject to reserve requirements, so they can expand more than checkable deposits because there is less drag on them during the multiple expansion process.

Practice calculating the M2 money multiplier on your own in the exercise.

### Exercise

1. Calculate the M2 money multiplier using the following formula: M2 = 1 + (C/D) + (T/D) + (MMF/D)/[rr + (ER/D) + (C/D)].

Currency Deposits Excess Reserves Required Reserve Ratio Time Deposits Money Market Funds Answer: M2
100 100 10 0.1 1,000 1,000 18.33
100 100 10 0.2 1,000 100 10
100 100 10 0.2 100 1,000 10
1,000 100 10 0.2 1,000 1,000 3.01
1,000 100 50 0.2 1,000 1,000 2.90
100 1,000 50 0.2 1,000 1,000 8.86
100 1,000 0 1 1,000 1,000 2.82
100 1 10 0.1 1,000 1,000 19.08

### Key Takeaways

• Because M1 is part of M2, M2 is always > M1 (except in the rare case where time deposits and money market funds = 0, in which case M1 = M2).
• That fact is reflected in the inclusion of the time deposit and money market fund ratios in the numerator of the M2 multiplier equation.
• Moreover, no reserves are required for time and money market funds, so they will have more multiple expansion than checkable deposits will.
• The required reserve ratio, the excess reserve ratio, and the currency ratio appear in the denominator of the m1 and M2 money multipliers because all three slow the multiple deposit creation process. The higher the reserve ratios (required and excess), the smaller the sum available to make loans from a given deposit. The more cash, the smaller the deposit.
• The currency, time deposit, and money market mutual fund ratios are in the numerator of the M2 money multiplier because M2 is composed of currency, checkable deposits, time deposits, and money market mutual funds.