Chapter 11 The Central Bank Balance Sheet and the Money Supply Process

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1 Chapter 11 The Central Bank Balance Sheet Problems and Solutions 1. In an effort to diversify, the Central Bank of China has decided to exchange some of its dollar reserves for euros. Follow the impact of this move on the U.S. banking system's balance sheet, the Federal Reserve's balance sheet, and the European Central Bank s balance sheet. What is the impact on the U.S. and Chinese monetary bases? The decision by a foreign central bank to sell dollars moves them into the U.S. commercial banking system, increasing U.S. commercial bank reserves and thus the U.S. monetary base. The balances sheets of the various central banks are unaffected, as is the Chinese monetary base. 2. The Fed buys $100,000 worth of U.S. Treasury bonds in an open market purchase. Assume that the reserve requirement is 10 percent, the banking system as a whole holds no excess reserves, and that the nonbank public is holding all the currency it wants. Show the impact of this injection of reserves, assuming that some banks in the system choose to purchase securities rather than to make loans with the increase in reserves. When the Fed purchases the bonds, the value of securities on the balance sheet of the U.S. banking system falls by $100,000 and bank reserves rise by $100,000. Banks will use some of the excess reserves to purchase securities and will then use the remainder of the excess reserves to make loans. Let s assume banks buy $30,000 in securities; securities rise by $30,000 and reserves fall by $30,000, leaving banks with $70,000 in excess reserves. Banks then extend $70,000 in loans; loans rise by $70,000 and reserves fall by $70,000. Then the deposit expansion multiplier comes into effect. People who have been lent money will use it to purchase goods and services. The people who sold them the goods and services will deposit the money in their accounts; banks will then lend out 90 percent of the value of their deposits. This process continues. If banks don t hold excess reserves and if individuals deposit all of their money into checking accounts, then the value of deposits eventually rises $700,000 above the level it was at before the Fed purchased the bonds. 3. Follow the impact of a $100 cash withdrawal through the entire banking system, assuming that the reserve requirement is 10 percent and that banks have no desire to hold excess reserves.

2 Deposits fall by $100 and reserves fall by $100. The bank (Bank A) needs to increase its reserves by $90 in order to meet the required reserve ratio. To raise the $90, Bank A will sell $90 of securities to someone. The deposit account of the person who purchased the securities will fall by $90, as will the reserve balance of his bank, Bank B. Bank B now needs to increase its reserves by $81 in order to meet the reserve requirements so it will sell $81 of securities. This continues until deposits contract by $100/0.1 = $ Compute the impact on the money multiplier of an increase in desired currency holdings from 10 percent to 15 percent of deposits when the reserve requirement is 10 percent of deposits, and banks desired excess reserves are 3 percent of deposits When desired currency holdings = 10% of deposits, m = = When desired currency holdings = 15% of deposits, m = = Consider an open market purchase by the Fed of $3 billion of Treasury bonds. Show the impact of the purchase on the bank from which the Fed bought the securities. Then, using the assumptions in problem 4, compute the impact on M1. The bank s securities fall by $3 billion and reserves rise by $3 billion. Assuming that the required reserve ratio is 10 percent, the bank does not want to hold extra reserves, and the public does not wish to hold currency, the value of deposits will rise by $30 billion. 6. Recall that the definition of M2 is currency plus demand deposits plus time deposits. Assume that there is no reserve requirement on time deposits, but that individuals hold time deposits in a constant ratio to demand deposits called the time-deposit-to-demand-deposit ratio, or {TD/D}. Derive the M2 money multiplier and discuss its properties. M2 = C + T + D = D[C/ T/ 1] o MB = C + R = =[{C/D}+ r {ER/D}]D o 1 D = {C/D} + r xmb {ER/D}

3 M 2 = m 2 = { C / D} + ( T / D) + 1 xmb {C/D} + r {ER/D} { C / D} + ( T / D) + 1 {C/D} + r {ER/D} The M2 money multiplier increases when the time-deposit-to-demand-deposit ratio increases, or when the currency-to-deposit ratio, required reserve-to-deposit ratio, or excess reserve-to-deposit ratio decreases. 7. From the web site of either the Federal Reserve Board or the Federal Reserve Bank of St. Louis, collect monthly data on the monetary base, M1, and M2 over the past decade, seasonally adjusted and adjusted for changes in the reserve requirement. Compute the M1 and M2 money multipliers and plot them. Discuss the patterns you find. M1 Money Multiplier 3 M1/Monetary Base M2 Money Multiplier 9 M2/Monetary Base The M1 money multiplier has been falling. The M2 multiplier is more volatile.

4 8. List the factors that you suspect may have caused the Federal Reserve to lose control of the quantity of money in the economy. Explain your reasoning. Financial and technological innovations have had an impact on the various components of the money multiplier. The increasing variability and unpredictability of the money multiplier has weakened the link between the monetary base and the money supply. Some factors that have contributed to the changing value of the money multiplier include the introduction of ATM machines, rising use of credit cards, and increased availability of relatively liquid financial instruments, such as money market mutual funds; all of these have reduced the currency-to-deposit ratio. The practice of sweeping balances from checking accounts into savings accounts each weekend has rendered the reserve requirement irrelevant. 9. In fall 1999, people in the financial community were making their final plans for the beginning of the year Everyone was concerned about the Y2K problem the fear that old computers would stop working because they used only 2 digits to record the year, so that the year 2000 would be represented as 00 (the same as 1900). The primary concern was that the public would panic and remove significant amounts of cash from banks. What would you expect banks to do in anticipation of this problem? What was the appropriate response by the Fed? Can you figure out from the Fed s balance sheet at the time what was done? Banks increased their reserves, especially currency, in order to be able to meet the anticipated withdrawal demands of their depositors. By looking at the weekly balance sheet at we see that the size of the monetary base went from $576.3 billion on December 1, 1999 to $644.6 billion on December 29, 1999, and then back down to $571.1 billion on January 27, From this we can infer that the Fed injected roughly $75 billion in reserves on a temporary basis to ensure that there was sufficient liquidity in the banking system. 10. The U.S. Treasury maintains accounts at commercial banks. What would be the consequences if the Treasury shifted funds from one of those banks to the Fed? The balance sheet for the bank would reflect a decrease in reserves and a decrease in deposits. The decrease in reserves would also appear on the Fed s balance sheet; however, it would be balanced by an increase in the government s account. The consequences would be a decline in the quantity of money. 11. Suppose the Fed buys $1 billion in Japanese yen, paying in dollars. What is the impact on the monetary base? What would the Fed need to do to keep the monetary base from changing following the purchase?

5 On the Fed s balance sheet, currency and foreign reserves would both rise by $1 billion; the monetary base would increase by $1 billion. If the Fed wished to keep its balance sheet from changing (performing what is called a sterilized intervention ) it could then sell $1 billion in securities. 12. Suppose the Fed purchases $1 billion in securities from First Bank. What is the impact on First Bank s balance sheet? First Bank s securities would fall by $1 billion and the bank s reserves would rise by $1 billion. 13. The Fed occasionally considers paying interest on reserves, following the example of central banks in a number of other countries. What impact would such a change have on excess reserve holdings and the money multiplier? If the Fed paid interest on reserves, banks would be more willing to hold reserves and the excess reserve-to-deposit ratio would increase. This would decrease the money multiplier. 14. In 1937, the Fed s policymakers noticed the high level of excess reserves in the banking system and became concerned about the potential for the banking system to expand the quantity of money and spark inflation. As a result, the Fed raised the reserve requirement. Why were banks holding excess reserves in 1937? What do you think the banking system s response was to the increase in required reserves? What do you think happened to the quantity of money outstanding? Banks were holding excess reserves because they were concerned about facing illiquidity in the event of a bank run. When the Fed increased the required reserve ratio, banks simply increased the levels of their reserves even further. This reduced the quantity of money. 15. Footnote 19 mentions that the central bank of China raised the reserve requirement on deposits in the summer of Describe the likely impact of this action on the quantity of money in the Chinese economy. Banks increased their reserves, which reduced the quantity of money in the economy.