Helpful Hint The Money Multiplier

Transcription

1 Helpful Hint The Money Multiplier This helpful hint examines the basics of the seemingly magical process of deposit or money creation. In class, we called this process the money multiplier. As with many magician's tricks, however, the magic disappears upon close examination. Our method of examination will be to look closely at changes in bank balance sheets. The secret to following this balance sheet analysis is remembering that for every change we make to an entry in the balance sheet, there must be an offsetting change to some other entry in that balance sheet. Balance sheets must balance. We will consider three cases. First, Mr. Hoard, who has been keeping $10,000 in cash under his mattress, deposits the $10,000 into his checking account. Second, the Federal Reserve buys $10,000 worth of bonds from a member of the public who then deposits the money into her checking account. Third, the Federal Reserve buys $10,000 worth of bonds from a bank and credits the bank's account at the Fed for the full amount. Note: Cases 2 and 3 are examples of an open market operations (OMOs) and lead to the same increase in the money supply. Case 1 is not an OMO; only the Fed conducts OMOs. Rather, Case 1 is an example of how fractional reserve banking creates a money multiplier. Case 1: Mr. Hoard takes $10,000 out of his mattress and deposits it in a bank. Mr. Hoard has just deposited $10,000 into his checking account at Bank 1. The changes in Bank 1's balance sheet are as follows: Balance Sheet #1: Reserves + $10,000 Checking Deposits + $10,000 Let's suppose that the reserve requirement is 20%; that is, a bank is required to hold 20% of the money deposited with it in checking accounts as reserves (in the form of cash or deposits with the Fed.) Let's further suppose that banks do not hold any more reserves than they are required to; that is, they do not hold any excess reserves. Clearly, Balance Sheet #1 does not tell us the whole story. Bank 1 will loan out $8,000 and keep $2,000 on reserve to meet its reserve requirement. These actions are summarized in Balance Sheet #2.

2 Balance Sheet #2: Reserves + $10,000 Checking Deposits + $10,000 Reserves - $8,000 Loans + $8,000 Total + $10,000 Total + $10,000 The deposit creation process does not stop here. We assume that all the funds that are loaned out find their way back into checking accounts. A simple case is where the person who has received the loan from Bank 1 deposits the funds into her checking account at Bank 2. This allows Bank 2 to make extra loans equal to $6,400 (80% of $8,000). These transactions are summarized in Balance Sheet #3 for Bank 2: Balance Sheet #3: Reserves + $8,000 Checking Deposits + $8,000 Reserves - $6,400 Loans + $6,400 Total + $8,000 Total + $8,000 The "chain reaction" has begun. The recipient of the $6,400 will deposit it in a third bank, and so... the deposit creation process continues. What will be the total increase in deposits? ) Deposits = $10,000 + $8,000 + $6,400 + $5, = $10,000 + (80% of $10,000) + (80% of 80% of $10,000) = $10,000 ( ) = $10,000/(1-.8) = $10,000/.2 = 50,000

3 The money multiplier is equal to 1/R, where R is the reserve ratio. What is the increase in the money supply? The increase in deposits is equal to the initial deposit by Mr. Hoard multiplied by the money multiplier. We must not forget, however, that the currency outside banks has been reduced by $10,000: Mr. Hoard no longer has $10,000 under his mattress. The total increase in the money supply is $50,000 minus $10,000, which is $40,000. Important Points: 1. ) Deposits = 1/R x initial deposit = 5 x $10, Our definition of money includes "cash held by the public" and "bank deposits." It does not include cash reserves that are assets of banks. 3. Therefore, ) Money = ) Deposits + ) Cash held by public = $50, $10, We have assumed that banks hold no excess reserves. If, instead, banks held a fraction E of deposits as excess reserves, the money multiplier would have been 1/(R+E) instead of 1/R. 5. Note that the money-multiplier/deposit-creation process does not create new wealth (i.e., nobody's net worth has changed.) It does, however, create liquidity.

4 Case 2: An OMO where the Fed buys bonds from the public. The second case we consider is one in which the initial cash injection into the banking system is brought about by an open market operation (OMO) in which the Fed buys $10,000 worth of bonds from a member of the public. The person who receives the $10,000 from the Fed then deposits it into her checking account. Balance Sheet #4 records the changes in the balance sheet of the bank that receives the deposit. Balance Sheet #4: Reserves + $10,000 Deposits + $10,000 From here the deposit creation process is exactly the same as in Case 1. What is the total increase in the money supply in this case? The answer is the full $50,000 because the Fed was able to print money to buy the bonds. That is, nobody reduced their "cash held by the public" to start the deposit creation process. ) Money = ) Deposits + ) Cash held by public = $50, = $50,000. Case 3: OMO where Fed buys bonds directly from banks. The final case we consider is one in which the Fed buys bonds worth $10,000 from a bank and credits the bank's account at the Fed with $10,000. Balance Sheet #5 records the changes in the bank's balance sheet. Balance Sheet #5: Bonds - $10,000 Reserves (Deposits with the Fed) + $10,000 From the bank's perspective deposits with the Fed are just as good as having cash reserves. Since no checking deposit has been created, the bank's required reserves have not changed, and the bank is thus able to increase its loans by the full $10,000. This loan will eventually be deposited in a bank. These transactions are shown below in Balance Sheet #6 (for the first bank) and Balance Sheet #7 (for the second bank.)

5 Balance Sheet #6: Reserves - $10,000 Loans + $10,000 Balance Sheet #7: Reserves + $10,000 Deposits + $10,000 From here, the $10,000 in deposits will be magically "multiplied" into $50,000 worth of deposits as in Cases 1 and 2, and there is a $50,000 increase in the money supply. ) M S = ) Deposits + ) Cash held by public = $50, = $50,000 The key point is that it does not matter whether the Fed buys bonds from the public or from banks. The ultimate change in the money supply/deposits is exactly the same.