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The Federal Reserve and
Open Market Operations
What is the Federal Reserve System?
The Federal Reserve:
•Creates money (widely accepted means of payment: specifically the U.S. dollar),
•Serves as the bank of the U.S. government,
•Serves as the “banker’s bank” by moving funds among commercial banks via checks, electronic
payments and currency.
Prices in $/unit: where $ come from?
•This lecture emphasizes the Federal Reserve’s role in creating the money supply.
•Throughout this course, prices have been expressed in units of money
• And so far we have taken it as given as a medium of exchange.
•Since it plays such a fundamental role in micro and macro economic activities, it is worth
exploring money creation in some detail.
The U.S. money supplies
•There are several categories of assets that function as money:
• Currency, i.e., paper and coin,
• Reserves held by banks at the Federal Reserve (hereafter “the Fed”),
• For transactions with other banks and with the Fed.
• Checkable deposits,
• Savings deposits, money market funds, and small-time deposits.
•Currency, reserves, and checkable deposits are more liquid forms of money.
• They can be used as a payment easily and without harming their value.
The U.S. money supplies (continued)
•The categories of money on the previous slide are the basis for economists’ informal definitions
of the money supply.
• The monetary base (MB): currency and reserves held by banks at the Fed.
• The portion the Fed can directly control, i.e., by buying assets with newly minted currency or by increasing banks’ reserves. More
on this later.
• M1: currency and checkable deposits.
• M2: M1, plus savings deposits, money market mutual funds, and small-time deposits.
•For a given base, M1 and M2 can vary depending on the propensity of banks to lend their
reserves and households’ preferences over liquidity of their assets, consumption, and saving.
Fractional reserve banking
•M2 is much larger than MB and M1 because banks multiply the money supply beyond the level
of their deposits.
•Specifically they keep a fraction of their deposits as reserves and loan out the rest.
• The Fed requires them to do this, but it is also sensible to have reserves to meet depositors’ demands
for liquidity.
The reserve ratio
•Use the notation RR for the reserve ratio, i.e., the ratio of reserves to deposits.
• 0 < 𝑅𝑅𝑅𝑅 < 1 fraction of deposits are held as reserves, and the remaining (1 − 𝑅𝑅𝑅𝑅) fraction is turned
into loans.
•The loans are eventually deposited in the account of someone who sold something to the
• RR fraction of this is held as reserves, and
• the rest is (again) turned into more loans.
The money multiplier
•It can be shown that this multiplies the original amount of deposits by the factor,
𝑀𝑀𝑀𝑀 monetary base
•MM is called the money multiplier.
•Since RR is less than 1, the inverse is greater than 1.
•If the reserve ratio is small, that means a large fraction of each deposit is turned into loans and
then used to increase the volume of money in M2.
•The money multiplier also applies to changes in the base that result from actions of the Federal
• Examples. See next slide.
Cowen and Tabarrok, Facts and Tools #5
Practice with money multipliers. Think of the “money supply” (MS) as equal to either M1 or M2.
a. RR = 5%; Change in reserves = $10 billion: MM = ? ; Change in MS = ?
= 20. Change in MS = 20 ∗ $10 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = $200 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
b. RR = ?; Change in reserves = -$1,000; MM = 5 ; Change in MS = ?
= 5. Change in MS = 5 ∗ −$1,000 = $5000
c. RR = 100%; Change in reserves = $10 billion; MM = ? ; Change in MS = ?
ANS: MM = = 1. Change in MS = 1 ∗ $10 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = $10 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏. Some monetarists and
other monetary reformers have supported a mandatory 100% reserve requirement, in order to
give the Fed better control over aggregate demand.
How the Fed controls the money supply
The Fed changes the monetary base by performing one or more of the following:
•Open market operations,
•Discount rate lending,
•Paying interest on reserves held by banks at the Fed.
Open market operations
•The challenge for the Fed is not how to create money.
• They have employees with knowledge of the printing press, both in the literal sense (printing more
currency) and the figurative sense (adding electronically to reserves).
•The question is how to “inject” it into the economy where it can be used.
•Instead of handing it out on a street corner, the Fed simply makes transactions with money, i.e.,
it buys (increase $ supply) or sells (decrease $ supply) durable and portable assets: government
•If the Fed wants to expand the money supply, it purchases U.S. Treasury bills from whoever is
willing to sell them, mostly banks.
•The seller gets money that they spend or loan out, ultimately multiplying its way through the
banking system as some form of M2.
•The Fed gets more government debts (a.k.a. “T-bills”, “Treasury securities”, or “Treasuries”).
Open market operations and interest
•The choice of using Treasury securities to execute monetary policy has a side effect.
•When a large entity like the Fed buys or sells bonds, it affects their price:
Buying bonds→increase in demand →price of bonds goes up
Selling bonds→decrease in demand →price of bonds goes down.
Open market operations and interest
rates (continued)
•And recall that the price of a bond and its implied interest rate are inversely related. So,
Buying bonds→interest rate goes down→quantity loanable funds demanded increases
Selling bonds→interest rate goes up →quantity loanable funds demanded decreases.
•This gives you an idea why monetary expansion relates to economic expansion: increasing the
money supply increases the supply and therefore the quantity demanded of loanable funds.
The Federal Funds rate
•The Fed changes the money supply using the Federal Funds rate as a target.
• The nearly riskless short-term rate banks pay for loans for terms of 1 day (“overnight”) from other
• Because the Fed can easily affect banks’ assets and liabilities via open market operations, and this rate is
sensitive to banks’ balance sheets.
•Other interest rates in the economy are affected by many additional factors including
expectations, risk, and terms of the loans (which we will not discuss here).
• They’re also affected by the Federal Funds rate, though, because agents look to it as a “baseline”
indicator of monetary policy.
Other functions of the Fed
•The Fed also affects the money supply by making loans.
• After all it is still a bank.
•Banks usually do not have to use this option to obtain credit, but they occasionally have to use
the “discount window” in the event of insolvency or illiquidity.
Illiquidity vs. insolvency
•Insolvency: when a bank’s assets’ values fall below its deposits’, preventing the bank from
meeting its depositors’ demands.
•Illiquidity: when a banks’ assets are structured with too few liquid assets to meet depositors’
demands, though the total value still exceeds that of the deposits.
•Illiquidity in the eyes of the depositor can be mistaken for insolvency, leading fear to destroy a
perfectly solvent bank.
• FDIC insurance is valuable in allaying these fears and preventing “runs”.
Other functions of the Fed (continued)
•When these problems occur, the Fed serves as the lender of last resort to restore liquidity
immediately or refund depositors at an insolvent bank.
• The Fed’s discount lending temporarily increases the money supply but subsequently decreases it when
they are repaid.
•And like other banks, the Fed (as of 2008) pays interest on the reserves banks deposit.
• This interest also adds to the money supply, albeit trivially compared to the other tools of monetary
Cowen and Tabarrok, Thinking and
Problem Solving #5
You are a bank regulator working for the Federal Reserve. It is your job to see whether banks
are solvent or insolvent, liquid or illiquid. Fit each bank below into one of the following four
Liquid and solvent (best)
Illiquid but solvent (probably needs short-term loans from other banks or from the Fed)
Liquid but insolvent (should be shut down immediately: could fool people for a while if not for
your good efforts)
Illiquid and insolvent (should be shut down immediately)
Cowen and Tabarrok, Thinking and
Problem Solving #5
a. Bank of DelMarVa
Short-term assets
$10 million
Total assets
$40 million
ANS: liquid but insolvent
Short-term liabilities
$6 million
Total liabilities
$50 million
b. Bank of Escondido
Short-term assets
$6 million
Total assets
$50 million
ANS: illiquid but solvent
Short-term liabilities
$10 million
Total liabilities
$40 million
Cowen and Tabarrok, Thinking and
Problem Solving #5
c. Bank of Previa
Short-term assets
$12 million
Total assets
$50 million
ANS: liquid and solvent
d. Bank of Cambia
Short-term assets
$8 million
Total assets
$30 million
ANS: illiquid and insolvent
Short-term liabilities
$10 million
Total liabilities
$40 million
Short-term liabilities
$10 million
Total liabilities
$40 million
The Fed and systemic risk
•In the recent financial crisis, the Fed did (had to?) exceed its traditional role in the banking
• It guaranteed loans to JPMorgan when it purchased (investment bank) Bear Stearns in March 2008, on
the justification that banks owned a lot of Bear’s debt and they would become insolvent if Bear’s failure
depressed the values of the creditor banks’ assets.
• Similar reasoning led the Fed to secure a loan to and ownership in (insurance company) AIG in the
autumn of 2008.
•These interventions attempted to eliminate systemic risks to the banking system.
• Systemic risk: the possibility of one institution’s failure having a domino effect on other institutions.
• A problem because such a financial crisis would devastate the loanable funds market and the whole
Moral hazard
•The removal or amelioration of systemic
risks, however, spares institutions from
punishment for risky decisions.
•Punishment, e.g., bankruptcy, is the price
banks pay for leveraging their assets heavily
and buying risky assets.
•When the Fed tries to curtail systemic risk,
this price goes down, and banks react by
taking (“demanding”) more risk.
• The same way individuals may take fewer
precautions as a result of having insurance for
their health, home, and car.
•This phenomenon of altering behavior in
response to insurance against bad outcomes
is called moral hazard.
•The dual forces of systemic risk and moral hazard
have led to an expansion of the role of the Fed in
the U.S. economy.
• Along with the exigencies of financial crisis abatement
and the subsequent recession and recovery.
•Add to all of this the diverse objectives agents want
the Fed to pursue and one begins to understand the
textbook authors’ Big Idea #10: “Central Banking is
a Hard Job”.
•The role of the Fed is actively evolving right now in
the wake of the “Great Recession”.
•For the first time in a while it has a new Chair (first
Chairwoman), too! Janet Yellen is the first woman
to fulfill this role, replacing Ben Bernanke.
Who controls the Fed?
•Directly, the Board of Governors.
• 7 members appointed by the President and confirmed by the Senate for 14 year terms.
•The chairperson of the Fed is appointed by the president from among the members of the board
for 4 year terms.
•The structure divides the U.S. into 12 regions with a Federal Reserve bank in each.
•Each is a non-profit bank with nine directors.
•Presidents of the regional banks participate on the FOMC (Federal Open Market Committee),
the most important policy making body of the Fed.
The 12 regional Feds
Independence of the Fed
•The structure of the Fed makes it one of the most independent agencies in the U.S. government.
•The independence of the Fed is controversial. Depending on who you talk to,
• The Fed has too much power not to be controlled by democratically elected politicians, or
• Without this independence, politicians including the President could order the Fed to boost the money
supply just before an election.
•Most economists are in the 2nd “camp” and defend the independence of the Fed.
•The Federal Reserve is the government’s bank, the banker’s bank, and has the power to:
• Create money.
• Influence aggregate demand.
•The Fed controls the money supply by buying and selling government bonds in open market
• Buying and selling bonds changes bank reserves which changes the money supply through a multiplier
process of rippling loans and deposits.
• When the Fed buys bonds, the interest rate falls and investment and consumption are stimulated.
•For day to day operations, the Fed focuses its attention on the Federal Funds rate.
•The Fed serves as a “lender of last resort” for banks and for major financial institutions.
•Preventing “systemic risk” is one of the Fed’s most important jobs.
The money multiplier and reserve ratio
The goal is to show that with a reserve ratio of RR and a base of $B, the supply of money (M) is equal
𝑀𝑀 =
•The money supply is the sum of all the deposits that flow from the base, beginning with the base
𝑀𝑀 = 𝐵𝐵 ∗ 𝑅𝑅𝑅𝑅 + 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 +. . . ⇔ 𝑀𝑀 = 𝐵𝐵+. . .
• Fractional reserve banking dictates that a fraction is turned into loans, adding to the money supply when they
reach the account of the seller of goods and services bought by the lender.
𝑀𝑀 = 𝐵𝐵 + 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 +. . .
•This is where it gets a little tricky. From the loans originated by the 1st bank, another fraction is held
as reserves, with the remaining fraction being turned into more loans, i.e., repeating the first step but
with only a fraction of a fraction of the base adding to the money supply.
𝑀𝑀 = 𝐵𝐵 ∗ 𝑅𝑅𝑅𝑅 + 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 + 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 2 +. . .
The money multiplier and reserve ratio
•Fractional reserve banking produces a sequence of loans, each of which is a fraction smaller
than the preceding one, à la,
𝑀𝑀 = 𝐵𝐵 + 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 + 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 2 + 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 3 + . . . +𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 ∞ .
•By a clever manipulation of this sequence, one can derive the money multiplier. Begin by
multiplying both sides of the sequence by (1 − 𝑅𝑅𝑅𝑅).
𝑀𝑀 1 − 𝑅𝑅𝑅𝑅 = (1 − 𝑅𝑅𝑅𝑅) 𝐵𝐵 + 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 + 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 2 +. 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 3 + . . . +𝐵𝐵 1 − 𝑅𝑅𝑅𝑅
⇔ 𝑀𝑀 1 − 𝑅𝑅𝑅𝑅 = 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 + 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 2 +. 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 3 + . . . +𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 ∞ .
The money multiplier and reserve ratio
•Then subtract the second sequence from the first sequence.
𝑀𝑀 − 𝑀𝑀 1 − 𝑅𝑅𝑅𝑅 = 𝑀𝑀 ∗ 𝑅𝑅𝑅𝑅
= 𝐵𝐵 + 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 + 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 2 +. 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 3 + . . . +𝐵𝐵 1 − 𝑅𝑅𝑅𝑅
− 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 + 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 2 +. 𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 3 + . . . +𝐵𝐵 1 − 𝑅𝑅𝑅𝑅 ∞
•Looking at it carefully, almost all of the terms in this sequence cancel out because there is a
positive in the first sequence canceled by a negative in the second. The only exception is the first
term in the first series (B). So,
𝑀𝑀 ∗ 𝑅𝑅𝑅𝑅 = 𝐵𝐵 or 𝑀𝑀 = 𝐵𝐵 ∗
is the money multiplier.
Objectives of monetary policy
•Monetary policy and the effect of changing the money supply is not just an academic exercise. It
is done with the following purposes in mind:
High employment,
Real economic growth,
Price stability,
Interest rate stability,
Stability of financial markets,
Stability in foreign exchange markets.
•Discussing the numerous challenges in simultaneously pursuing these objectives forms the
content of a course in Money and Banking, e.g., ECON 380.
• The interested student is also directed to Chapter 33 in Cowen and Tabarrok’s text.