The demand for money
1
What is money?
1. Means of exchange (pay bills)
2. Unit of account (what are units in balance sheets)
2
Money and finance: The superstars of all time
Irving Fisher, Yale
(1867-1947)
Milton Friedman, Chicago
(1912-2006)
James Tobin, Yale
(1918-2002)
3
Equations of short-run interest determination
Demand for R:
Bank regulation: reserve requirement on checking deposits (D).
(1’) R = hD
In normal times (not now!)
The demand for checking deposits (Dd) is determined by output and
interest rate:
(2) Dd = M(i, Y)
This leads to the demand for reserves by banks in normal times:
(3) Rd = h M(i, Y)
Supply of R:
Fed supplies non-borrowed reserves (NBR) by open-market operations
(OMO). We omit bank borrowings as usually tiny.
(4) Rs = NBR
Which yields equilibrium of the market for reserves
(5) h M(i, Y) = NBR + BR(d)
4
5
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
6
Real Wealth of US Households (corrected from class)
Balance sheet of households
2007
2009
Total assets
29,366
24,847
Tangible assets
24,674
20,026
Real estate
22,146
18,272
Financial assets
52,071
42,361
Deposits and currency
7,232
7,760
Checkable deposits and currency
210
300
Credit market instruments (ex. equities)
3,806
4,327
Corporate equities
10,457
6,266
Mutual fund share holdings
4,981
3,741
Pension fund reserves
13,765
10,656
Proprietors' equity
1,361
1,379
Misc
…
Total financial liabilities
14,276
14,068
Home mortgages
10,509
10,402
Consumer credit
2,499
2,476
Misc.
…
Net worth (market value)
67,161
53,140
Source: Federal Reserve, flow of funds, Table B.100
Change
-4,519
-4,648
-3,874
-9,710
528
90
520
-4,191
-1,240
-3,109
18
-208
-108
-23
-14,021
Source: Federal Reserve, Flow of Funds, Table B.100; in 2009 $.
7
Simplification for macro
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In macro, we assume 2 assets (money and bonds).
Further assume no inflation, so inflation = п =0 and r = i.
Assume that nominal interest rate on money = 0.
In short run, wealth 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.
8
i
Md
Interest rate
on bonds (i)
Md
Demand for transactions deposits
9
Cash in advance (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 Milton Friedman;
money demand insensitive to interest rates and “only
money matters.”
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10
Y
Average
money
balance
M = Y/2
0
1
11
What’s wrong with this theory?
12
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.
• See next slide for example.
• 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.
• Not in textbook. I have a little note, and this will be covered in
section.
13
Example of how companies keep M = 0.
14
Baumol-Tobin model
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
16
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 “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.
17
Is money demand interest elastic (1975-2012)?
16
3 month Treasury bill rate
14
12
10
8
6
4
2
0
4
5
6
7
8
9
10
Real money demand
18
Econometric estimate of money demand equation
Dependent Variable: ln(Real M1)
Method: Least Squares
Sample (adjusted): 1959Q2 2011Q2
Coefficient
ln(3 mo Tbill)
ln(real GDP)
Constant
-0.040
0.31
t-Statistic
Prob.
-5.0
10
0.0000
0.0016
Standard error regression = 0.085
******************************************************************************************
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?
19
i
DM
SM
SM
Equilibrium
in the
money
market
i*
i*
DM
Money balances
M*
M*
20
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 2008 to at least 2015!
• Conventional monetary policy is therefore ineffective (note
what happens when M supply shifts from S’’ to S’’’ in figure on
next page).
• The Fed must turn to “unconventional instruments”
• This is the nightmare scenario for the economy and explains (in
part) why the recovery has been so slow.
21
The supply and demand for bank reserves, 1950-2012
S
9
S’’
8
S’’’
Federal funds rate
7
6
S’
5
4
3
2
1
0
0
400
800
Bank reserves
1,200
22
Overview of Supply and Demand for Money
Starts with short-run interest rate (federal funds rate)
• Supply of reserves determined by central bank (Fed, ECB, …)
• Demand for transactions money (M1) depends upon interest rate;
• Equilibrium of supply and demand for reserves → short-term
nominal risk-free interest rate.
Then to other assets and rates:
Short rates + expectations → long risk-free rate by term structure
theory
Risky rates = risk-free rate + risk premiums
Real rate = nominal rate – inflation (Fisher effect)
23
Daily life in macroeconomics
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