Download The Microfoundations of Money, Part 2

Lecture 3
The Microfoundations of Money Part 2
• Dissatisfaction with ad hoc formulation and
MIUF approach
• OLG - a theory of monetary exchange under
Laissez Faire
• Critical evaluation of OLG - purely a store
of value
• Intergenerational contracts
• Legal restrictions
• Another look at MIUF and CIA
Fiat money economy
•
•
•
•
Must satisfy two conditions
1) Inconvertibility
2) Intrinsic uselessness
According to Wallace if the 2 conditions are
taken seriously, then for a monetary theory
to develop there are 3 options
Fiat Money Theory
• 1.
Abandon
the
conditions
of
inconvertibility and intrinsic uselessness
• 2. Impose legal restrictions to give money
value
• 3. Model the notion that fiat money
facilitates exchange
Overlapping Generations
Model (OLG)
The Young have endowment of 1 unit of labour and consumption preference
of c~t and ct*1 when old.
The old has no endowment but have consumption of ct*
Output is storable but depreciates at the rate , so  
1
1 
Let kt = the amount of output stored in period t
mt = the quantity of real money held by the young at end period t
y = f(n) = f(1)
The young maximise
u  u( c~t , ct*1 )
The old have no endowments but receive a lump sum real value money
transfer of vt, so that output can be purchased to the amount;
 Pt 1 

 Pt 
vt + mt-1
per capita consumption of the old at time t is;
 Pt 1 

ct* = kt-1 + vt + mt-1
 Pt 
The young chooses,c~t , ct*1 , kt, and mt that maximises;
u  u( c~t , ct*1 )
c~  k  m  y
t
t
t
t
 P 
ct*1  k t  vt 1  mt  t 
 Pt 1 
Let
M t  (1   ) M t 1
  1
The interior solution for a monetary equilibrium occurs when kt = 0
A condition of equilibrium is  <  which demonstrates the ‘tenuousness of
equilibrium’.
An example
~ *
U  U (Ct , Ct 1 )
~ M
Ct 
 yt
Pt
C
*
t 1
M
~
  ( yt  Ct ) 
Pt 1
1

1 
Consumption of the existing
old
M
~
C   ( yt 1  Ct 1 ) 
Pt
*
t
Autarky-no trade (M=0)
C*t+1
Y
Y
Ct
Monetary equilibrium (M0
but no saving)
~ M
Ct 
 yt
Pt
Ct*1 

M
~
  y t  Ct
Pt 1



 Pt 
~

  Ct*1   yt  Ct
 Pt 1 
P  P 
~
~
Ct  Ct*1  t 1     t 1  yt  Ct  yt
 Pt   Pt 
~
max Ct  yt  Ct*1  0
M
Pt


 P 
~
max Ct*1  yt  t   Ct  0  yt
 Pt 1 
Monetary equilibrium (M0)
C*t+1
Y(P/Pt+1)
Y
Y
Ct
• Notice that with no
inflation Pt+1 = Pt and Y >
γY
• If inflation increases Pt+1 >
Pt then the upper budget
line swings down.
• When Pt/Pt+1 = γ, the
young are indifferent
between storing their
output and receiving
money from the old.
Critique
• Ignores medium of exchange function
• does not explain, why store of value
function is not dominated by contracts
• But Wallace says that medium of exchange
occurs inter-generationally
• McCallum says that an economy with a
medium of exchange is more efficient than
one without
Store of Value
• Any monetary model must face the
following problems
• 1. Possible dominance of money by
contracts
• 2. Segniorage
• 3. Terminal value of money
Money in the Indirect
Utility Function (MIIUF)
Utility function
c = consumption, l = leisure
u = u(ct, lt, ct+1, lt+1)
lt = 1-nt-st
nt = amount of labour time expended in work
st = amount of labour time expended in search
say
st = (mt)
‘ < 0
this leads to the composite function
u = u~ (ct, nt, mt, ct+1, nt+1,mt+1)
which resembles the MIUF approach. Note that unlike the simple MIUF
approach where,
u
  as m  0
m
In the indirect utility approach if m = 0, this simply implies that the
holding costs of money are too high. Similarly it allows satiation to be
reached with finite m if    0 . Giving money a framework such as this
does not imply that money is ‘intrinsically useless’.
Cash - in - Advance
• The cash in advance constraint is intended
as a formal representation of the
transactions demand for money. Baumol
(1952) for example makes the implicit
assumption that money is required for
transactions and add a cost of ‘going to the
bank’.
C-I-A continued
Households are assumed to maximise a discounted expected utility function;

E   t 1 U(c t )
t 1
where 0 <  < 1
subject to
 m  m t 1 
ct   t
  b t  b t 1  y t  rt b t 1
Pt


where {yt}, is an endowment of income, {Pt}is the price of goods in terms of
money, {bt} is a vector of the real value of other assets, {rt}is the vector of
returns paid on the other assets, {ct} is consumption at time t.
The cash-in-advance constraint is
m 
c t   t 1 
 Pt 
C-I-A
• One of the criticisms of this model is that it
implies a demand for money that is
insensitive to the rate of interest and also
has a unit income elasticity of demand for
money.
Townsend’s Spatial
Separation Model
• There are an infinity of infinitely lived
agents
• In each period household ‘i’ has an
endowment ‘m’ but because of spatial
separation is physically able to contact only
adjacent households {i-1} and {i+1}.
• Tastes of household {I} are such that it
desires goods from {i} and {i+1}.
Turnpike Model
• Household {i+1} desires goods from itself
{i+1} and {i+2}.
• Households cannot make bilateral IOU
arrangements because there is nothing that
household {i-1} can offer {i} and nothing
that {i} can offer {i+1}
• So barter is impossible
Monetary existence
Goods
0
M
1
2
Why is it that money and
default-free interest bearing
securities co-exist
• Suppose government issues risk-free small
denomination bearer bills.
• If the bills co-existed with cash, would they
sell at a discount or at par?
• If sold at a discount, consider at a date close
to maturity everyone would prefer bills to
cash.
• By repeated argument that means no one
will ever hold cash.
Co-existence
• If bills co-exist then they must always sell
at par - i.e. no interest.
• But since we know that bills sell at a
discount, co-existence occurs because:
• bills are non-negotiable
• large denominations
• represents a legal restriction
• The different yields on cash and bills is a
LR
Legal Restrictions Theory of
Money
• Prediction of legal restrictions theory:
• non-interest bearing paper currency should
not co-exist with risk-free small
denomination interest-bearing securities in
the absence of legal restrictions.
Historical evidence
• Makinen & Woodward - JPE (1986) provide evidence to show that small
denomination French government issued
bearer bonds in pre-revolution France,
failed to circulate as a medium of exchange
• White JMCB (1987) - free banking period
1716-1844 (Scotland) paper money
circulated with interest-bearing promissory
notes, redeemable on demand.
Question?
• Economists continue to ask the question:
• A monetary economy clearly works ‘in
practice’
• But does it work ‘in theory’
• The answers are not entirely satisfactory