money and interest rates1 mba 774 macroeconomics class notes – part 2

Money and Interest Rates 1

Money and Interest Rates

MBA 774

Macroeconomics

Class Notes – Part 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


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


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


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


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)


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


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.


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


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


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


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.


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?


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)


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


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


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)


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



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%).


Monetary Policy and NAIRU

-5.0%

0.0%

5.0%

10.0%

Real Fed Funds

U-NAIRU


Note: U-NAIRU is actual unemployment minus NAIRU and is sometimes called the employment gap.


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


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


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


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) ]


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


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

http://www.federalreserve.gov/releases/h15/update/


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


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)


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


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


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)


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


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



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)


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)


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)



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


Intertemporal Preferences

Consumption Today (t=0)

Future Consumption

(t=1)

U3

U2

U1

U1 > U2 > U3


Intertemporal Production Possibilities Frontier


Future Consumption

(t=1)

20

18

T(X)

10

13


Optimal Consumption Without Savings


Future Consumption

(t=1)

U*

C*1 = X*

1

=14

C*0 = X*

0 =9


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


Savings: Borrowing and Lending


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)


Optimal Production With Savings


Future Consumption

(t=1)

U*

14

9

U**

U** > U*

C**1 = 17

X**1 = 8

X**1 = 16 C**

0 = 8


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


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


Optimal Production With Borrowing


Future Consumption

(t=1)

U*

C*1 = X*

1

C*0

=X*0

U** U** > U*

C**1

X**1

X**0 C**

0


Change in the Interest Rate


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


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?


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


Equilibrium Interest Rate


Future Consumption

(t=1)

UB*

UL*

BorrowerCB1

X1

X0 CB0 CL

0

CL1

Lender


Aggregate Economy

Borrowing / Lending

Interest Rate

R*

Supply = Demand

Desired Lending(Supply of Funds)

Desired Borrowing(Demand for Funds)

money and interest rates1 mba 774 macroeconomics class notes – part 2

Documents

federal funds rate

cost of money

institutional money

federal reserve banks

clearingthe us federal

bank of england

government decreefiat

bank of japanfounded