Transcript Money Demand (Handa, Chapter 2)
Money Demand
(Handa, Chapter 2)
Monetary Theory and Policy Graduate Seminar ECON 6411 Fall 2008
1
First Lessons
Hicks (1967),
Critical Essays in Monetary Theory
, Oxford University Press.
Uses the model of a medieval market fair Claims to have constructed a system with money as a medium of exchange, but not as a store of value.
Problem:
Money
is
a store of value for the market period.
2
First and Second Principles
A First Principle of Monetary Theory is:
Money is a store of value. There are things that act as stores of value that are not money, but there are no forms of money that are not stores of value.
A Second Principle of Monetary Theory is:
A crucial difference between barter and monetary exchanges is that in a monetary economy exchanges are nonsynchronized— the buying and the selling may occur at different times and in different places.
3
Uncertainty
• • If the value of money varies over time (inflation), then this nonsynchronization of exchanges amounts to
risk
.
The need for money occurs because of time and nonsychronization. Add uncertainty, and you have potentially costly risk.
4
Equations of Exchange
I. Fisher Equation
M=
money
, T=
real number of transactions
, V T =
circular velocity of transactions
MV MT
P T T
II. Income-type Model/Commodities Approach
M=
money
, y=
real income
, V Y =
circular velocity of income
MV My
P y y
III. Cambridge Cash-Balances Equation
k
= cash balances “constant”
M
kP y y
5
Equations of Exchange (2)
IV. Disaggregation among components
D=
demand deposits
, V dy =
velocity of demand deposits
C=
currency in hands of public
, V cy =
velocity of currency
P y
average price of output
DV Dy
CV Cy
P y y
V. Cambridge Cash-Balances Equation
B =
Monetary Base
k
= cash balances “constant”
BV By
P y y
6
More on Quantity Theory
This really results from the system:
M M M s d s
M
0
d M kPY
Exogeneity of Money Equilibrium Condition (ex post) Money Demand Relation Therefore, the crude quantity theory is
a theory of equilibrium absolute price levels.
Note:
Not all quantity theorists assume exogeneity.
7
Neoclassical Model and the Quantity Theory
We begin with the “crude”, “old”, or “basic” quantity theory:
An exogenous change in the stock of money eventually results in a proportionate change in the absolute price level.
The Quantity Theory operates best in a Marshallian-type neoclassical model.
8
Marshallian Model
P LRAS
nominal wages
w/P
w 2 w 1 P 2 P 1 AD 1
Y
AD 2
r Y* N s S N d N Y=F(N,K) r* I S*,I* S,I
Marshallian Model in Equations
(1)
N s
N s
(
w
) (2) (3) (4) (5)
N d
N d
(
I N s
(
w P
)
I
(
r
)
S
S
(
r
)
N w P
)
d
(
w P
)
I
(
r
)
S
(
r
)
N
*, (
w P
) *
I
*,
S
*,
r
* (6) (7) (8) (9) (10)
Y C
F Y
* (
N
*,
S
*
K
*)
C
Y C
* (
r
*) (
P w P
) *
M
P
0 *
kY
*
w
*
P
*
C
* 10
Fisher (1911)
• • • Fisher used the disaggregated model.
Argued that the velocities are the “average rate of turnover” and depends upon: – – – – – – Individual agent habits Population density (demographics) Commercial customs Rapidity of transport Other technical conditions But NOT on the quantity of money or the price level. That is, velocity is EXOGENOUS.
Fisher does not assume velocity is constant.
11
Fisher (1911) -- II
• • • Fisher also argues that the real volume of trade or transactions is independent of the quantity of money,
except during transition periods
.
– This has been challenged by Keynesians. This is less likely to be true if the economy is not continuously at equilibrium.
Production is the result of capital, physical capabilities and technique—none of which depend on the quantity of money.
– This assumes that the labor market always clears and full employment always ensues. It relies on the notion that full employment is independent of money and prices.
Therefore, if the quantity of money is expanded, prices will rise. That is, prices will vary directly as
M
varies.
12
Assumptions
(1) Money supply is exogenous. (2)
k
and
Y
do not change substantially from one period to the next. (Are they constant? Stable? Is the velocity function stable?)
Some argue that y is constant, based on the idea that the economy is
always at full employment.
Some argue that y is constant because this is a long run theory and Say’s Law does not allow for long-run deviations from full
employment.
Some argue that k is relative constant because it is related to the slowly evolving payments system.
Some argue that k is simply exogenous—it is not related to any of the other variables.
13
Fisher’s Direct Transmission Mechanism
• • Fisher assumes that the individual’s money holdings are doubled.
“Prices being unchanged, he now has double the amount of money and deposits which his convenience has now taught him to keep on hand. He will then try to get rid of the surplus money and deposits by buying goods. But, as somebody else must be found to take the money off his hands, its mere transfer will not diminish the amount in the community. It will simply increase somebody else’s surplus. Everybody will want to exchange this relatively useless extra money for goods, and the desire to do so must surely drive up the price of goods.” 14
Indirect Transmission Mechanism
• • Presented here only for contrast! This is NOT Fisher’s view!
According to the indirect mechanism, money supply increases affect interest rates which then induce changes in investment, which is a component of aggregate demand. Aggregate demand increases, driving the AD curve to the right along an upward-sloping AS curve. Prices rise.
15
Cash Balances Approach
• • • • • This is a theory of money demand.
Pigou argues that agents choose to allocate resources to a portfolio of assets, based upon convenience and security.
The issue is the proportion allocated to money.
k = k(r) –
where r refers to the attractiveness of “rival” uses of resources. As
r
increases,
k
falls.
There is a discussion regarding the provision of security against unexpected demands due to sudden need or rise in prices.
16
Knut Wicksell
• Defended the quantity theory as the appropriate aggregate theory for the determination of the price level.
– The alternative theory is called the “full cost pricing theory” or the “mark-up price theory”. Under this theory, the firms price according to the cost of production plus a normal rate of profit. In aggregate, this forms the price level.
17
Knut Wicksell (2)
• Wicksell analyzed a “pure credit economy” which was short run with a fixed capital stock. – – The public does not hold currency All transactions are paid for by checks drawn on demand accounts in banks.
– – – – Banks hold no reserves, so lend all deposits.
Banks can lend without limit without risking insolvency.
The market rate of interest is the rate charged by the banks.
Banks are willing to lend any amount that firms want at the market rate of interest. – – The
normal rate of interest
is the rate equates saving and investment.
The
natural rate of interest
is the marginal productivity of investment in firms, the internal rate of return on firms’ investment.
– He presented this in the context of a model of disaggregated output (capital goods industries vs. consumer goods industries). In many ways he was a precursor of Keynes’ analysis.
18
Keynes
• • Keynes identifies motives for holding money: – Transactions demand – – Precautionary demand Speculative demand – Finance demand We will discuss Keynesian theory more fully later in the course.
19
Portfolio Approach
Agents allocate demand wealth across assets, of which money is one:
M t d
f
(
r t M
,
r t B
,
r t A
,...,
w t
) This leads the money demand relations like:
W t
M t
B t
20
Friedman’s Restatement of the Quantity Theory
• • • • Source: Studies in the Quantity Theory of Money, pp. 1-21.
Quantity theory is a theory of money demand.
Money is one of a variety of assets, a store of wealth or value.
– Money is a factor in the production function; it is a capital good.
The demand for money, like any other asset, depends upon: – – – Total wealth W Price of and return on this and competing assets Tastes and preferences – Intertemporal rates of substitution 21
More Elements
• • Wealth relates to all sources of income or consumable services: – – – So that
Y = Wr W = Y/r
Where
W
= total wealth,
Y
= total income,
r =
the rate of interest Agents allocate their wealth across assets so as to maximize utility subject to costs and returns.
22
More Elements
• • • • •
B
= bonds
E =
claims to stated pro-rata shares of firms
G =
physical non-human goods
H =
human capital
P =
price level 23
The Model
• Assume that the bonds are perpetuities, so that the market price of the bond is:
P B
1
r B
if the price is constant. If capital appreciation can occur, the nominal return is:
r b
( 0 )
r b
( 0 )
d
1
r b
(
t
)
dt
r b
( 0 )
r b r b
2 ( 0 ) (
t
)
dr b
(
t
)
dt
24
The Model (2)
• • Which is approximated at
t=0
r b
1
r b dr b dt
Rate of return on equities
r e
1
dP
1
dr e P dt r e dt
Rate of return on physical goods 1
dP P dt
25
The Model (3)
• Let
w
be the ratio of nonhuman to human wealth. •
u
is a portmonteau variable, which accounts for all the other variables that might affect tastes and preferences.
•
M
Money demand is:
f
P
,
r b
1
r b dr b dt
,
r e
1
P dP
dt
1
r e dr e dt
1 ,
P dP
;
dt w
,
Y r
;
u
26
Model (4)
• • • Equivalently, we can write:
M
f
P
,
R B
,
R E
,
R K
,
w
,
Y r
,
u
Arbitrage will lead
R
B
= R
E
, or
r b
1
r b dr b dt
r e
1
P dP dt
1
r e dr e dt
Assuming the rates move together,
r b
r e
1
P dP dt
(
I = r +
) 27
Model (5)
• • Assume
f(
)
is homogeneous of degree one in
P
and
Y.
f
(
P
,
r b
,
r e
, 1
P dP
;
dt w
;
Y
;
u
)
f
f
(
P
,
r b
, (
P
,
r b
,
r e r e
1 , ,
P
;
dP dt w
;
Y
;
w
;
Y
;
u
) ;
u
) 1
P M
Y f
(
r b
,
r e
, ,
w
,
P Y
,
u
) 28
Model (6)
• This implies that:
Y
v
(
r b
,
r e
, ,
w
,
Y P
,
u
)
M
• Note that this moves away from money as a transactions medium, and toward money as a portfolio asset.
29
Conclusions
1.
2.
3.
4.
Money demand and velocity are highly stable.
v
is not a constant, but rather a well-defined function of a few specific variables.
Friedman regards money demand as playing the key role in the determination of the whole economy.
This amounts to a defense against the attacks of Keynes that money demand and velocity are unstable.
Money supply and demand are independent.
30
Conclusions (2)
5.
6.
Implies there is not reason to assume that money demand is infinitely elastic at some small, positive, interest rate, and therefore no support for a liquidity trap.
Argues that
Y
, as he has defined it, is
permanent income
, and does not vary as rapidly as
measured income
. 31
Transmission Mechanisms
• Direct Transmission Channel – Increases in the money supply causes undesired money balances which are directly spent on commodities, increasing aggregate expenditure and income.
• Indirect Transmission Channel – (Keynes Effect) Increases in the money supply lowers the interest rate which increases aggregate expenditure (think IS-LM) by increasing investment and triggering the multiplier.
• The Lending Channel – The availability of money causes banks to change their lending practices, raising or lowering barriers to borrowing that may involve more than interest rates.
32
Walrasian-Type Model
There are
n
goods:
x
1 ,
x
2 ,...,
x n
In a
barter economy,
there are
n-
1 relative prices (exchange ratios) for each good:
p p
2 1 ,
p p
3 1 ,...,
p
1
p n
.
prices are: 1
p
1
p n
1 ,
p
2
p n
1 ,...,
p n p n
1 33
Numeraire & Absolute Price Level
We define
money
as the
numeraire
good, and set
p n
1 so that money prices are: 1
p
1 ,
p
2
p n
The
Absolute Price Level
is a weighted average of the money prices of the individual goods:
n p
i
.
p i i
1 We may define the relative prices as:
p
1 ,
p p
2 ,...,
p p n p
which is essentially the prices in
real
terms.
34
Neoclassical Model and the Quantity Theory
The Quantity Theory operates best in a Marshallian-type neoclassical model.
Problem :
Link between money and the goods market
Problem :
inconsistencies between the quantity theory and Walrasian General Equilibrium Theory • Highlighted by Patinkin (1965) 35
Walrasian General Equilibrium
Excess Demand
x i XD
x i D
x i S
= individual x i = a good, the ith good If there are
Or individuals, then in aggregate:
1
x i XD
1
x i D
1
x i S
x i XD
x i D
x i S is
Aggregate Excess Demand
.
36
Walras’ Law
The sum of the excess demand and supplies over all markets must identically equal zero. Equivalently,
i n
1 1
p i x i XD
0 .
Note: If there is an excess demand across the
n
goods markets, then there must be an off-setting excess supply in the
(n+1)th
market (for example in the money market).
x n
1 ( )
p n
1
x XD n
1
p n
1
x XS n
.
1
p
1 37
Walras’ Law (2)
Derivation:
Walras’ Law can be derived from the budget constraint. The budget constraint essentially tells us that
no
individual can, through market trading, obtain a greater value of goods and money (assets) than the initial endowment.
Homogeneity Postulate
(typical assumption): The demands and excess demands in the
n
goods markets will
not
change in response to a change in the absolute price level.
Note: A homogeneous function
x = f
(
y
,
z
) is said to be homogeneous of degree with respect to
y
if and only if it has the property that:
x
f
(
y
,
z
).
38
Walras’ Law (3)
Note that homogeneity of degree one implies:
x
f
(
y
, ,
z
) which means that changes in
y
result in proportionate changes in
x
. Homogeneity of degree zero implies that changes in
y
result in
no
change in
x
.
Basic Elements of a Basic Walrasian GE Model
1. Walras’ Law 2. Excess demand equations Excess demand equations are homogeneous of degree zero in money prices and the absolute price level; i.e., the excess demand equations obey the homogeneity postulate.
39
Walrasian GE and the Quantity Theory
Relative vs. Absolute Price levels
The Quantity Theory determines the absolute price level, but not relative prices.
The Walrasian GE Model determines relative prices but not the absolute price level.
QUESTION:
Can we marry the two together?
This amounts to integrating microeconomic price theory with macroeconomic monetary theory.
Can we add some form of the Equation of Exchange to the Walrasian Model?
Answer: No.
Patinkin demonstrates that such a model produces an invalid dichotomy.
40
WGE & Quantity Theory (2)
The model has
n
goods markets equilibrium equations, which we assume are homogeneous of degree zero.
x i XD
f i
p p
1 ,...,
p p i
,...,
p p n
,
i n
1
p p i x i S
x i S
0 .
It also has an equation to define the absolute price level:
i n
1
i p i p
1 Add money demand:
M D = kpy
41
WGE & Quantity Theory (3)
Subtract
M S
from both sides: (1)
M XD
kpy
M S
0 at equilibrium.
M
(2)
M XD
( 1 )
i n
1
p i x i XD
because M is the
n+
1th good.
Unfortunately, this gives two excess demand functions for money, and they are mutually inconsistent outside equilibrium: (1) is nonhomogeneous to any degree.
(2) is homogeneous of degree one in prices .
42
Notes
Say’s Law
As a whole, S=D. Or equivalently,
i n
1
p i x i XD
0 .
• Walras’ Law includes the money market; Say’s Law is real sector only.
• Walras’ Law: If there is a glut of goods, it is accompanied by an excess demand for money.
43
Patinkin’s Solution
Patinkin decides that only reasonable approach is to abandon the homogeneity postulate (and Says’ Law).
Patinkin adds real balances throughout:
x i XD
f i
p
1 ,...,
p p i
,...,
p p n p
,
i n
1
p i p x i S
M S p
x i S
,
i
1 ,...,
n
thus demands and excess demands depend upon real
money balances!
44
Assume:
x XD
M S p
0 .
Unfortunately, this makes demands and excess demands a function of the absolute price level. To maintain consistency throughout, we write the money demand and money excess demand functions so as to incorporate real balances:
M D
pf n
1
y
,
M p S
M XD
pf n
1
y
,
M p S
M S
Money does prove neutral in this model.
45