Econ 122: Fall 2010
Determination of interest rates:
Supply and demand for money and other assets
1
Information items
• We will have special TF Friday presentations on finance,
math, and financial reform later in course.
• Problem 1 will be posted today.
• Readings on money are chapter 19 not 18.
• Sections this week. If you are Wed pm, go to Thurs pm or
other.
• Sections:
Wed 4-4:50 is in WLH 112
Wed 5-5:50 is in WLH 209
Thurs 4-4:50 is in WLH 203
Thurs 5-5:50 is in WLH 002
Thurs 7-7:50 is in WLH 112
Thurs 8-8:50 is in WLH 007
• Notes on readings [on the board]
2
Federal Reserve Districts
3
3. FOMC Minutes August 10, 2010
The information reviewed at the August 10 meeting indicated that the pace of
the economic recovery slowed in recent months …. The economy was
operating farther below its potential than they had thought and the pace of
recovery had slowed in recent months…
Many said they expected underlying inflation to stay below levels they judged
most consistent with the dual mandate to promote maximum employment
and price stability. Participants viewed the risk of deflation as quite small,
but a number judged that the risk of further disinflation had increased
somewhat despite the stability of longer-run inflation expectations.
The Committee determined it would be appropriate to maintain the target
range of 0 to 1/4 percent for the federal funds rate…. [It] Reiterated the
expectation that economic conditions were likely to warrant exceptionally
low levels of the federal funds rate for an extended period.
[Additionally and unconventionally, the Fed will] maintain the total face
value of domestic securities held in the System Open Market Account at
approximately $2 trillion by reinvesting principal payments from agency
debt and agency mortgage-backed securities in longer-term Treasury
securities.
Voting: 10 to 1 in favor.
4
Administration (cont.)
4. Actual mechanism:
•
•
•
•
•
Open market operations are arranged by the Domestic Trading Desk
at the Federal Reserve Bank of New York (“the Desk”)
Every morning, staff decided if an OMO is needed to keep rate near
target.
Fed contacts the “primary dealers” (e.g., Goldman Sachs, BNP Paribas,
Morgan Stanley, etc.) and asks them to make offers
Fed generally makes temporary purchases (“repos” = purchase and
forward sale, or the reverse) at 10:30 each day, but generally does not
enter more than once per day.
Because the Fed intervenes only daily, the FF rate can deviate from the
target.
5. Then supply and demand
for reserves take over
5
Recent history of Fed Funds rate: 2007-2010
6
Recent history of Fed Funds rate: 2008
7
General equilibrium of assets
Have multiple assets of interest rates or yields
General theory:
- short term nominal rates determined by Fed
- long term safe rates determined by expected future short
rates.
- risky rates = safe rates + risk premium
- real interest rate = nominal interest rate - inflation
8
Note on theory of the term structure
Many businesses and households borrow risky long-term
(mortgages, bonds, etc.).
These differ from the federal funds rate in two respects:
- term structure (discuss now)
- risk premium (postpone)
The elementary theory of the term structure is the
“expectations theory.”
It says that long rates are determined by expected future
short rates.
Two period example (where rt,T is rate from period t to T):
(*)
(1+r0,2)2 = (1+r0,1) [1+E(r1,2)]
With risk neutrality and other conditions, (*) determines
term structure. (Finance people find many deviations, but
good first approximation.)
9
Recent term structure interest rates (Treasury)
4.5
Yield to maturity (% per year)
4
Expectations theory
says that short
rates are expected
to rise in coming
years.
3.5
3
2.5
2
1.5
9/18/2009
1
9/17/2008
0.5
0
0
5
10
15
20
25
30
Note that this can
explain why Fed
makes statement
about future rates
(look back at Fed
statement.)
Term or maturity of bond
10
Yield to maturity (% per year)
Older term structure interest rates (Treasury)
20
9/18/2009
9/17/2008
18
9/19/2006
May-81
In period of very
tight money (198182) short rates
were very high, and
people expected
them to fall.
16
14
12
10
8
6
4
2
0
0
5
10
15
20
25
30
Term or maturity of bond
11
Example
Short rates:
1 year T-bond =
0.41 % per year
2 year T-bond =
1.03 % per year
Implicit expected future rate from 1 to 2 is:
(1+r0,2)2 = (1+r0,1) [1+E(r1,2)]
(1+.0103)2 = (1+ .0041) [1+E(r1,2)]
This implies:
E(r1,2) = 1.65 % per year
[Again, finance specialists point to deviations from this simple
theory.]
12
But the major story to remember is the following:
12
Federal funds rate
3 month T bill
10 year T bond
Baa bond rate
10
8
6
4
2
0
88
90
92
94
96
98
00
02
04
06
08
10
13
The demand for money
14
Mechanics of OMO: The Fed buys a security…
Fed
Commercial banks and primary dealers
Assets
Bonds
Liabilities
1000
Bank borrowings
0
Cu
Assets
900
Reserves (bank
deposits)
100
Liabilities
Reserves (bank
deposits)
100
Investments
1000
Checkable
deposits
Equity
1000
100
15
… and this increases reserves …
Fed
Commercial banks and primary dealers
Assets
Bonds
Liabilities
1000
+10
Bank borrowings
0
Cu
Assets
900
Reserves (bank
deposits)
100
+10
Liabilities
Reserves (bank
deposits)
100
+10
Investments
Checkable
deposits
1000
-10
Equity
1000
100
1. Fed buys bond.
2. Dealer deposits funds in bank.
3. This creates a credit in the account of the bank at the Fed and
voilà! the Fed has created reserves. (red)
16
… and normally this increases investments and M
Fed
Commercial banks and primary dealers
Assets
Bonds
Liabilities
1000
+10
Bank borrowings
0
Cu
Assets
900
Reserves (bank
deposits)
100
+10
Reserves (bank
deposits)
100
+10
Liabilities
Checkable
deposits
Investments
1000
+100 -10
1. Fed buys bond.
2. Dealer deposits funds in bank.
3. This creates a credit in the account of the bank at the Fed and
voilà! the Fed has created reserves. (red)
4. In normal times, the bank lends out the excess, and this leads
to money creation (blue). Today, this just increases reserves.
Equity
1000
+100
100
17
Actual and required reserves
1,400
1,200
Reserves
Required reserves
1,000
800
600
400
200
0
90
92
94
96
98
00
02
04
06
08
10
18
… but today it just increases excess reserves
Fed
Commercial banks and primary dealers
Assets
Bonds
Liabilities
1000
+10
Bank borrowings
0
Cu
Assets
900
Reserves (bank
deposits)
100
+10
Liabilities
Reserves (bank
deposits)
100
+10
Investments
1000
-10
Checkable
deposits
Equity
1000
100
1. Fed buys assess backed mortgage (from bank for simplicity)
2. Bank is glad to unload it, and just holds excess reserves.
3. No impact on the money supply or on federal funds rate. A (very
small) impact on mortgage interest rates.
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Now let’s move on to money demand
Recall that monetary policy operates on the market for
reserves.
The demand for reserves is a derived demand – derived from
the demand for money.
We need therefore to understand the foundations of the
demand for money, and particularly why it depends
upon the interest rate.
20
Balance Sheet of Household
Assets
Cu
D
Bh (net)
E
Cu = currency
Bh = household bonds (net of
Liabilities
NW = household net
worth
E = equity
NW =HH net worth
debts and mortgages)
D = checkable deposits
21
Real Wealth of US Households
Balance sheet of households
Total assets
2,007
2,009
Change
29,577
24,847
-4,730
Tangible assets
24,851
20,026
-4,825
Real estate
22,305
18,272
-4,033
7,284
7,760
476
7,284
7,760
476
212
300
88
3,834
4,327
493
10,532
6,266
-4,266
5,017
3,741
-1,276
13,865
10,656
-3,208
1,371
1,379
8
Financial assets
Deposits and currency
Checkable deposits and currency
Credit market instruments (ex. equities)
Corporate equities
Mutual fund share holdings
Pension fund reserves
Proprietors' equity
Misc
…
Total financial liabilities
14,379
14,068
-311
Home mortgages
10,585
10,402
-183
Consumer credit
2,517
2,476
-41
53,140
-14,505
Misc.
Net worth (market value)
…
67,645
Source: Federal Reserve, Flow of Funds, Table B.100; in 2009 $.
22
Simplification for macro
• Let k = number of “independent assets.” In macro, we generally
use k = 2 (money and bonds).
• Further assume no inflation, so inflation = п =0 and r = i.
• Assume that nominal interest rate on money = 0.
• We then substitute in the wealth identity to get:
1
M (t )/ P (t )  D [0, r (t ), W (t ) / P (t ) , Y (t )]
W (t )  B (t )  M (t )
• In short run, W(t) is fixed, so this reduces to the demand for
money equation:
M (t )/ P (t )  D [r (t ), Y(t ) ]  D[ i (t ), Y (t )]
• This is the canonical equation used in macroeconomics.
23
Fisher Theory of Transactions Demand for Money
• The transactions demand is a specific case of an inventory
demand theory (think shoe store)
• Used in advanced macro in “cash-in-advance models”
• Simple example:
earn Y at beginning (example is per year; more generally
would be per payment period of say month)
spend evenly at rate of Y per period
constant price level
money has yield of 0
no opportunity to move from money to other assets.
In this case, we see that the average money holdings:
M* = Y/2
This leads to “monetarist” theory of M. Friedman; money
demand insensitive to interest rates and “only money
matters.”







24
Y
Average
money
balance
M = Y/2
0
1
25
What’s wrong with this theory?
26
Opportunity cost of money balances
7
Interest rates (percent per year)
3-month Treasury bills
6
5
4
Implicit
cost of
holding
money
3
2
1
0
Interest rate on money (M1)
96
97
98
99
00
01
02
03
04
05
06
07
Source: Treasury interest rate from Federal Reserve; interest rate on checking accounts
27
from Informa Research Services, Inc.
More general demand for money
What happens if we have other assets?
• If have bonds as well as money, then can move some of money
to bonds to earn interest.
• Yale train to New York in 1950s; “repos” today for wholesale
• This leads to more general theories in which the demand for
money is interest-elastic
Baumol-Tobin model.
• This is an explicit model of how income, interest rates, and other
factors determine how often we move money to bonds.
• Typical methodology of macroeconomics.
• We will cover briefly and do more carefully in section (see
Mankiw, pp. 559-562)
28
Baumol-Tobin model
Problem with Fisher model: Assumes only one asset (M)
Must recognize that there are other assets that you can
purchase depending upon costs and benefits
Say that can move back and forth into and out of bonds (M
and B)
Bonds yield iB > iM = 0.
Go to bank at beginning of period and deposit half in bonds;
then go in mid-period to move to money so that you can
buy your pizzas.
For one trip, have only half the money and the other half is
earning interest.
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Y
Average
money
balances are
triangles
labeled
“Money”
Money
For 2 trips to
the bank, have
M* = Y/4
For N trips to
the bank, have
M* = Y/2N
Bonds
Money
0
1
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Money and finance: The finale
Irving Fisher, Yale
(1867-1947)
Milton Friedman, Chicago
(1912-2006)
James Tobin, Yale
(1918-2002)
31
Daily life in macroeconomics
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Info items
Federico will do a special session on finance this Friday, here at
11:35.
Reading is from a free online textbook on Corporate Finance,
available at the course website.
33
Optimizing money balances (special case of optimal inventory):
Total cost = C(N) = Forgone Interest +
Cost of trips
=
iY/(2N)
+
FN
Maximizing to determine optimal number of trips (N*):
dC/dN = 0 = - iY/(2N*2) + F
N* = (iY/2F)½
Optimal average money holding are
M* = Y/(2N*) = (YF/2i)½
This is the famous “square root inventory rule” for money holdings
What are elasticities of M w.r.t. Y and i (EM,Y and EM,i )? [E =½ ]
This is the crux of the debate between monetarists and Keynesians:
• Is the interest elasticity EM,i = 0 or < 0?
• If = 0, monetarist; if < 0 then Keynesian
• Huge debate in 1960s and 1970s; pretty much settled now.
34
Empirical test of money demand equation:
Is money demand interest elastic (1975-2009)?
16
Short term interest rate
14
12
10
8
6
4
2
0
800
1,000
1,200
1,400
1,600
1,800
Real money demand
35
Econometric estimate of money demand equation
Dependent Variable: ln(Real M1)
Method: Least Squares
Sample (adjusted): 1959Q2 2009Q2
Coefficient
ln(3 mo Tbill)
ln(real GDP)
Constant, AR1, …
-0.040
0.34
t-Statistic
Prob.
-7.0
3.2
0.0000
0.0016
Standard error regression = 0.033
******************************************************************************************
Elasticities have correct sign and are statistically significant but interest
rate coefficient is small.
• Why is EM,i so small? Wrong model? Behavioral economics?
Corner solution?
36
i
Short term
interest rate
DM
SM
S’M
i*
i*’
DM
Money balances
M*
M*’
37
Monetary policy helpless: the liquidity trap
• In depressions or deep recessions, when i close to zero, have
highly elastic demand for money and reserves
– US 1930s, Japan 1990s and 2000s, US 2010!
• Monetary policy therefore ineffective (note what happens when
M supply shifts from S to S’’’ in figure on next page).
• The Fed has “run out of bullets,” or at least conventional
bullets, and must turn to “unconventional instruments”
• This is the nightmare of central banks!
38
The supply and demand for bank reserves, 1950-2010
S
9
S’’
8
S’’’
Federal funds rate
7
6
S’
5
4
3
2
1
0
0
400
800
Bank reserves
1,200
39
Portfolio Theories
More general theories
• This goes back to our general equilibrium model above; multiple
assets (money, bonds, stocks, foreign assets,...)
• Portfolio theory considers how to allocate wealth among assets
• Yale’s management of endowment
• Individual’s management of 401(k) account
Standard analysis examines
• preferences (like life-cycle model + preference toward risk)
• asset risks and returns
• Many good courses at Yale and B. Schools
This leads to the modern theory of finance.
• You can get a preview on Friday from Federico (same time, same
station; free reading online)
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