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Money and Interest Rates 1
Money and Interest Rates
MBA 774
Macroeconomics
Class Notes – Part 2
Money and Interest Rates 2
What is Money? Medium of exchange
Allows transactions not based on barter Avoids the need for a “double coincidence of wants”
Unit of account Common measure of value for goods, services, and
contracts
Store of value Allows for transfer of wealth through time Most liquid of all assets
Money and Interest Rates 3
Types of Money
Pure Commodity Scarce commodity is agreed on as “money” For example: gold, silver, cattle, cigarettes
Commodity Standard Certificates representing claims on a commodity are
issued and used instead of the commodity itself For example: the US was once on a “gold standard”
Fiat Money Money established by government decree Fiat money has no intrinsic value
Money and Interest Rates 4
US Measures of Money Currency = Bills and coins outside U.S. Treasury, Federal
Reserve Banks and the vaults of depository institutions
M1 = Currency plus travelers’ checks, demand deposits, other checkable deposits
M2 = M1 plus savings deposits, small-denomination time deposits, retail money market mutual funds, and overnight repurchase agreements
M3 = M2 plus large-denomination time deposits, institutional money funds, and Eurodollars
L = M3 plus other liquid securities such as savings bonds and short-term Treasury securities
Money and Interest Rates 5
US Money Supply Statistics
Measure USD Billions % of M3 1-yr %Chg
Currency 653 7.3% 5.6%
M1 1,288 14.5% 8.1%
M2 6,109 68.6% 7.2%
M3 8,900 100.0% 6.8%Source: Federal Reserve Statistical Release H.6
Money and Interest Rates 6
The US Federal Reserve Federal Reserve System is the US “central bank”
Foreign counterparts include the European Central Bank (ECB), The Bank of England, and the Bank of Japan
Founded in 1913 by congress, “to provide the nation with a safer, more flexible, and more stable monetary and financial system.”
Primary functions are Monetary policy Banking supervision and regulation Providing certain services (e.g., check clearing)
Money and Interest Rates 7
The US Federal Reserve (2)
The “System” is composed of 12 regional banks and a Board of Governors in Washington, DC Governors, the Chairman and Vice-Chairman are
appointed by the President and confirmed by the Senate
Monetary policy is overseen by the “Federal Open Market Committee” or FOMC which includes Board of Governors Fed Bank of NY President 4 other regional bank presidents on a rotating basis
Money and Interest Rates 8
Monetary Policy (1) About every six weeks the FOMC meets to
determine monetary policy for the US In practice, this means determining the target for
the “Federal Funds Rate” which is an inter-bank overnight interest rate
Fed decreases (increases) the Fed Funds rate by buying (selling) government securities which increases (decreases) the available money supply The Federal Reserve Bank of NY makes these
purchases or sales on the open market--hence the name Federal Open Market Committee.
Money and Interest Rates 9
Monetary Policy (2)
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%7/
4/19
907/
4/19
917/
4/19
927/
4/19
937/
4/19
947/
4/19
957/
4/19
967/
4/19
977/
4/19
987/
4/19
997/
4/20
007/
4/20
017/
4/20
027/
4/20
037/
4/20
047/
4/20
057/
4/20
06
Fed Funds Target
Fed Funds Actual
Money and Interest Rates 10
The Fed’s Actions around 9/11
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
9/5/
01
9/7/
01
9/9/
01
9/11
/01
9/13
/01
9/15
/01
9/17
/01
9/19
/01
9/21
/01
9/23
/01
9/25
/01
9/27
/01
Fed Funds Actual
Fed Funds Target
Stock Markets Re-open
Money and Interest Rates 11
Monetary Policy (3) The official objectives of US monetary policy are,
“economic growth in line with the economy's potential to expand, a high level of employment, stable prices (that is, stability in the purchasing power of the dollar), and moderate long-term interest rates.”
Conceptually, the Fed will raise (the real) interest rate if GDP is greater than “Potential GDP” and vice-versa
Money and Interest Rates 12
Aside: Real vs. Nominal Rates
It is often said that the interest rate is the “cost of money.” Is this true?
Ultimately, we use money to obtain consumption goods
Think of the interest rate in terms of trading some real amount of consumption in one time period for some real amount of consumption in another time period Note however, borrowing and lending contracts are
stated in nominal terms.
Money and Interest Rates 13
Aside: Real vs. Nominal Rates
The real rate of interest (R*) can be defined as approximately,
Real Interest Rate =
Nominal Interest Rate - Anticipated Inflation
Currently, what is R* in the U.S.? Japan?
Money and Interest Rates 14
Monetary Policy (4) Potential GDP is the rate of economic activity that
leads to stable prices and employment
Intuitively it is the amount of output that is generated by utilizing all available resources at there highest sustainable level.
Algebraically, we can think of it as
PotGDP = (aggregate hours available for work) x
(average output per hour)
Money and Interest Rates 15
Monetary Policy (5) Economists often discuss the Potential GDP
Growth Rate which is approximately
PotGDP Growth = Labor Force Growth Rate
+ Productivity Growth Rate
We can calculate PotGDP Growth with this formula for the last 50 years
Money and Interest Rates 16
Historical Potential GDP
-2.0%
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%19
50
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
Productivity Growth
Labor Force Growth
Money and Interest Rates 17
Better Estimates of PotGDP
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%19
50
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
PotGDP-Congressional Budget Office Estimates
PotGDP-( 5yr- Moving Average from Previous Graph)
Money and Interest Rates 18
Monetary Policy and the GDP Gap
Monetary Policy Regime Change
Note: GDP Gap = (Actual GDP - PotGDP) / PotGDP
-10.0%
-5.0%
0.0%
5.0%
10.0%
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
Real Fed Funds
GDP-Gap
Monetary Policy Regime Change
Money and Interest Rates 19
NAIRU Another way of thinking about potential output is
the equilibrium rate of unemployment or NAIRU (Non-accelerating Inflation Rate of Unemployment)
NAIRU is the rate of unemployment below which there will be inflationary pressures
The exact level of NAIRU is an issue of debate. Most economists believe it is somewhere between 4%
and 6% in the US and Japan. Probably higher in Europe (7-8%).
Money and Interest Rates 20
Monetary Policy and NAIRU
-5.0%
0.0%
5.0%
10.0%
Real Fed Funds
U-NAIRU
Monetary Policy Regime Change
Note: U-NAIRU is actual unemployment minus NAIRU and is sometimes called the employment gap.
Money and Interest Rates 21
Other Mechanisms for Monetary Policy
The Fed also has two other ways of controlling monetary policy The discount rate Reserve requirements
Reserve requirements (rr) directly affect the level of money via the “money multiplier” (1/rr) Example, if the reserve requirement is 20% of deposits
then the money multiplier is 1/0.2 = 5
Money and Interest Rates 22
Fractional Reserve Banking The Fed buys a $1,000 (market value) treasury
bond from a bond dealer The dealer deposits the $1,000 proceeds into its
bank, FirstBank Money supply increases by $1,000
FirstBank only has to keep $200 as reserves and loans the $800 balance:
FirstBanks Balance Sheet
Assets Liabilities
Reserves $200 Deposits $1,000
Loans $800
Money and Interest Rates 23
Fractional Reserve Banking (2)
Assume FirstBank made an $800 computer loan to a student. Money supply increases to $1,800
The student buys a computer at BestBuy which deposits the $800 at its bank, SecondBank
SecondBank also loans out all but 20% SecondBank Balance Sheet
Assets Liabilities
Reserves $160 Deposits $800
Loans $640 Now money supply = 1,000 + 800 + 640 = 2,440
Money and Interest Rates 24
Fractional Reserve Banking (3) This practice of keeping 20% reserves and loaning
out the rest continues indefinitely
However, the ultimate increase in the money supply (MS) is finite and equal to
MS = D / rr
MS = $1,000 / 0.2
MS = $5,000
where D is the original increase in money by the Fed[ Mathgeeks note, its a converging geometric sequence:
1+x+x2+x3+... = 1/(1-x) where x = (1-rr) ]
Money and Interest Rates 25
Fed Reserve Requirements Requirement
Type of Deposit % of Deposits Effective Date
Net transaction accounts $0 million-$6.6 million 0 12/25/03
$6.6 million-$45.4 million 3 12/25/03
More than $45.4 million 10 12/25/03
Nonpersonal time deposits 0 12/27/90
Eurocurrency liabilities 0 12/27/90Required reserves must be held in the form of deposits with Federal Reserve Banks or vault cash. Nonmember institutions may maintain reserve balances with a Federal Reserve Bank indirectly, on a pass-through basis, with certain approved institutions. Under the Monetary Control Act of 1980, depository institutions include commercial banks, savings banks, savings and loan associations, credit unions, agencies and branches of foreign banks, and Edge Act corporations.
See also: http://www.federalreserve.gov/monetarypolicy/0693lead.pdf
Money and Interest Rates 26
Interest Rates There are lots of important USD interest rates
Federal funds rate Discount rate Prime rate Commercial paper rate LIBOR and Eurodollar (similar for other currencies) T-bill, T-note, T-bond rate Swap rates Corporate bond rates Overnight repurchase rate or “Repo” rate
Rates depend on credit risk, liquidity, and maturity
Money and Interest Rates 27
Government Issues
Thru5/06
-5
0
5
10
15
2019
34
1939
1944
1949
1954
1959
1964
1969
1974
1979
1984
1989
1994
1999
2004
3-month T-Bill
20-year T-Bond
Term Spread
Money and Interest Rates 28
Corporate Bonds
Thru5/06
0
5
10
15
2019
34
1939
1944
1949
1954
1959
1964
1969
1974
1979
1984
1989
1994
1999
2004
Moody's AAA Corp
Moody's Baa Corp
Baa Credit Spread (over Treasuries)
Money and Interest Rates 29
A Model of the Money Market More detail about what affects interest rates
For now consider “money” to be M1
Also we assume that the money supply is controlled by the central bank (e.g., the US Federal Reserve)
Specifically, the central bank fixes the amount of money in the aggregate economy (MS) at a level it desires regardless of other factors
Money and Interest Rates 30
Individual Money Demand Individuals’ demand for money is based on
The expected (real) return on money: Money (M1) pays little or no interest => higher interest rates will lead to less demand for money
The riskiness of the return The risk of holding money comes from variation in the price
level. Why?
Liquidity The primary value associated with money is derived from
liquidity Since a primary use of money is as a medium of exchange, this
implies an increase in the value of individual transactions increases the demand for money
Money and Interest Rates 31
Aggregate Money Demand
Aggregate money demand is the sum of demand for money by all households and firms in the economy
In aggregate we can say the determinants of the aggregate demand for money are The interest rate The price level (think CPI) Real national income (or GNP or GDP)
Money and Interest Rates 32
Aggregate Money Demand Define aggregate money demand as
MD = P * L(R,Y) or
MD / P = L(R,Y)where,
MD = Aggregate money demand P = Price level R = Interest rate Y = Real national income (or GNP or GDP)
and,
L decreases as R increases
L increases as Y increases
Money and Interest Rates 33
Aggregate Money Demand
L(R,Y)
Interest Rate (R)
Aggregate Real Money (M/P)
L(R,Y1)
Interest Rate (R)
L(R,Y2)
Increase in Y
Aggregate Real Money (M/P)
Money and Interest Rates 34
Equilibrium in the Money Market In equilibrium, MS = MD = P*L(R,Y)
Aggregate Real Money Demand L(R,Y)
Interest Rate (R)
Real Money Supply
R1
MS/P
2
3
1
R2
R3
Q2 Q3 Aggregate Real Money (M/P)
Money and Interest Rates 35
Increase in Money Supply Suppose the money supply increases from M1/P to M2/P
Aggregate Real Money Demand L(R,Y)
Interest Rate (R)
Real Money Supply Increases
R1
M1/P
2
1
R2
M2/PAggregate Real Money (M/P)
Money and Interest Rates 36
Increase in GDP Suppose real income (GDP) increases from Y1 to Y2
L(R,Y2)
Interest Rate (R)
Real Money Supply
R1
MS/P
2
1’1
R2
Q1’
L(R,Y1)
Aggregate Real Money (M/P)
Money and Interest Rates 37
Determining the Real Interest Rate
The interest rate is the price of future consumption in terms of consumption today
Consider an individual with the following attributes Two-period time horizon (today and 1 future date) Only cares about one nonstorable commodity, say beer Endowment of concave production technology to produce
beer equals T(X) Convex preferences for present and future consumption No opportunities to save across time periods Rational (implying she maximizes intertemporal utility) Knows the future with certainty
Money and Interest Rates 38
Intertemporal Preferences
Consumption Today (t=0)
Future Consumption
(t=1)
U3
U2
U1
U1 > U2 > U3
Money and Interest Rates 39
Intertemporal Production Possibilities Frontier
Consumption Today (t=0)
Future Consumption
(t=1)
20
18
T(X)
10
13
Money and Interest Rates 40
Optimal Consumption Without Savings
Consumption Today (t=0)
Future Consumption
(t=1)
U*
C*1 = X*
1
=14
C*0 = X*
0 =9
Money and Interest Rates 41
Optimal Consumption Without Savings
Optimal level of production comes at tangency point of production function and indifference curves (this is the highest level of utility possible)
Because there is no ability to borrow or lend, production = consumption in both periods so
C*0 = X*
0 and C*1 = X*
1
Money and Interest Rates 42
Savings: Borrowing and Lending
Consumption Today (t=0)
Future Consumption (t=1)
C’0
C’1 = C’0 (1+R)
C1 = C0 (1+R)
C’’1 = C’’0 (1+R)
C0 C’’0
Slope of Savings Lines = -(1+R)
Money and Interest Rates 43
Optimal Production With Savings
Consumption Today (t=0)
Future Consumption
(t=1)
U*
14
9
U**
U** > U*
C**1 = 17
X**1 = 8
X**1 = 16 C**
0 = 8
Money and Interest Rates 44
Optimal Production With Savings If we allow savings across time periods our individual
will: Choose the production levels at t=0,1 that maximizes total
wealth at time 0 (W0) defined as
W**0 = X**
0 + X**1 / (1+R)
Then chose the level of consumption in each period:
(C**0 , C**
1)
that maximizes total utility given the level of total wealth
Note that production and consumption are unbundled:
C**0 X**
0 and C**1 X**
1
Money and Interest Rates 45
Optimal Production With Savings
In this example, our individual is a lender
This is because C**0 X**
0
In effect, our individual takes the amount not consumed (X**
0 - C**0) and puts it in the bank to earn
interest at a rate of R
If our individual had different preferences, she might prefer to be a borrower
Money and Interest Rates 46
Optimal Production With Borrowing
Consumption Today (t=0)
Future Consumption
(t=1)
U*
C*1 = X*
1
C*0
=X*0
U** U** > U*
C**1
X**1
X**0 C**
0
Money and Interest Rates 47
Change in the Interest Rate
Consumption Today (t=0)
Future Consumption
(t=1)
ULUH
UH > UL
CH1
XH1
XL0<XH
0CH0<CL
0
-(1+RL)
-(1+RH)
XL1
CL1
LendingHLendingL
Interest Rate Declines from RH to RL
Money and Interest Rates 48
Why Are We Doing This?!? First, what have we established so far?
The ability to lend or borrow increases utility The ability to lend or borrow uncouples production and
consumption Individuals can be either borrowers or lenders depending
on their intertemporal preferences Changes in interest rates effect the demand for
borrowing and lending But our goal was to figure out where interest rates
came from. How do these results help us?
Money and Interest Rates 49
Equilibrium Interest Rate Now consider an economy with two individuals with
different intertemporal preferences one will be a lender and one will be a borrower
Lender will be supplier of funds and borrower will be demander of funds
The interest rate in the economy will be set so that the supply of funds equals the demand for funds
Money and Interest Rates 50
Equilibrium Interest Rate
Consumption Today (t=0)
Future Consumption
(t=1)
UB*
UL*
BorrowerCB1
X1
X0 CB0 CL
0
CL1
Lender
Money and Interest Rates 51
Aggregate Economy
Borrowing / Lending
Interest Rate
R*
Supply = Demand
Desired Lending(Supply of Funds)
Desired Borrowing(Demand for Funds)