Download Lecture 7. Classical monetary theory

EC3115 :: L.7 : Classical monetary theory
Almaty, KZ :: 23 October 2015
EC3115 Monetary Economics
Lecture 7: Classical monetary theory
Anuar D. Ushbayev
International School of Economics
Kazakh-British Technical University
https://anuarushbayev.wordpress.com/teaching/ec3115-2015/
Tengri Partners | Merchant Banking & Private Equity
a.ushbayev@tengripartners.com – www.tengripartners.com
Almaty, Kazakhstan, 23 October 2015
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Relevant reading
Book treatment
F. Mishkin. (2013). The Economics of Money, Banking and Financial Markets, 10th edition, Pearson Education, Chapter 20.
J. Handa. (2009). Monetary Economics, 2nd edition, Chapter 18.
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The quantity theory of money
Section 1
The quantity theory of money
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The quantity theory of money
“[The quantity theory of money] is fundamental. Its correspondence
with fact is not open to question. Nevertheless it is often misstated and
misrepresented.”
– John Maynard Keynes, (1924), Tract on Monetary Reform.
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The quantity theory of money
History of the QTM
Initially developed by, among others, John Stuart Mill, who expanded on
the ideas of David Hume. The more relevant mathematical formulation
was later given by the American economist Irving Fisher in 19111 .
The idea goes that in a monetary economy in which non-monetary
transactions are insignificant, one may write:
M · Vtransactions =
pT q
|{z}
P
= i ( pi ·qi )
where M is the average total amount of money in circulation over a period,
Vtransactions is the transactions velocity of money, and p and q are vectors of
prices and quantities of all transactions.
1
I. Fisher. (1911). The Purchasing Power of Money. Its Determination and Relation to Credit,
Interest and Crises. New York: Macmillan.
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The quantity theory of money
In a simplification, the above reduces to what is called the equation of
exchange:
M · Vtransactions = Ptransactions · T
where now Ptransactions is the price level over a period and T is the index of
the real value of all transactions.
With the development of national income and product accounts this has
been refomulated:
M ·V = P·Y
where V is the velocity of money in final expenditures and Y is an index of
real value of final expenditures.
The equation of exchange thus states that the quantity of money
multiplied by the number of times that this money is spent in a given year
must equal nominal income (the total nominal amount spent on goods
and services in that year).
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The quantity theory of money
The Cambridge approach
From Alfred Marshall and Arthur Pigou, Keynes had inherited an alternative
version of the above statement of relationship between goods, prices and
money, which focused more on money demand, rather than supply:
Md = k · P · Y
The Cambridge economists argued that a certain portion of the money
supply will not be used for transactions and will be held in cash balances
instead. This cash portion of nominal income is denoted k in the above
Cambridge cash balances equation.
When the economy is at equilibrium (M d = M ), and assuming that in the
short-run both Y and k are fixed, we see that the above can be rearranged
to give
where
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1
k
1
= P·Y
k
is equivalent to V from the equation of exchange.
M·
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The quantity theory of money
The quantity theory of money
Now the above formulaic results can begin to be used for theorizing about
the price level dynamics. Rearranging the equation of exchange and adding
a subscript for the time variable we get:
Pt =
M t · Vt
Yt
Log-linearization:
ln Pt = ln M t + ln Vt − ln Yt
Differentiating w.r.t. time:
1
·
dPt
=
1
Pt dt
Mt
or, in growth rates notation:
·
dM t
dt
+
1
Vt
·
dVt
dt
−
1
Yt
·
dYt
dt
%∆Pt = %∆M t + %∆Vt − %∆Yt
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The quantity theory of money
Further, assuming short-run exogeneity of both velocity and real output,
we get:
:−0%∆Y
:0
%∆Pt = %∆M t + %∆V
t
t
Which is equivalent to saying:
%∆Pt = %∆M t
| {z } | {z }
π
m
i.e. the growth rate of the price level – the inflation rate – is equal to the
rate of growth of the money supply.
If, on the other hand you assume only the stability of the velocity of
money, the growth rate relation becomes:
%∆Pt = %∆M t − %∆Yt
| {z }
π
i.e. the inflation rate is equal to the rate of growth of the money supply
minus the rate of growth of real output.
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The quantity theory of money
H0 : π = %∆M – No support from the data at annual frequency
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The quantity theory of money
H1 : π = %∆M − %∆Y – ditto.
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The quantity theory of money
Since... velocity is not constant either
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The quantity theory of money
...but is positively related to the interest rate
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The classical dichotomy and Walrasian analysis
Section 2
The classical dichotomy and Walrasian analysis
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The classical dichotomy and Walrasian analysis
The classical view
Real variables – measured in physical units: quantities and relative
prices, e.g.:
real output: quantity of output produced
real wage: output earned per hour of work
real interest rate: output earned in the future by lending one unit of
output today
Nominal variables – measured in monetary units, e.g.:
nominal wage: units of money earned per hour of work
nominal interest rate: units of money earned in future by lending one
unit of money today
the price level: the amount of money units needed to buy a
representative basket of goods
⇒ ∆ in the price level is merely a ∆ in the units of measurement.
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The classical dichotomy and Walrasian analysis
Classical dichotomy: in the classical model nominal and real variables
are separable and therefore nominal variables do not affect real
variables.
Neutrality of money: changes in the the stock of money do not affect
real variables.
Wages and prices are completely flexible.
Only real variables (preferences, factor supply, technology) determine
real outcomes (quantities of output and relative prices).
Monetary variables determine only monetary outcomes (value of
output and absolute prices), from the equation of exchange.
Demand and supply functions for goods are therefore notional and
possess homogeneity of degree zero in all prices.
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The classical dichotomy and Walrasian analysis
Say’s law
Attributed to Jean-Baptiste Say in the first quarter of the 19th century,
considered to be one of the underpinnings of the classical
(pre-Keynesian) macroeconomic model.
Usual statement: “Supply creates its own demand”.
Original idea considered a pure exchange economy (and thus was
meant to refer exclusively to commodities) with N goods.
More precise statement: “Aggregate supply of commodities creates its
own aggregate demand”.
Formally (since Say was not explicit on the role of prices) expressed as:
N
N
X
X
pi Di ≡
pi Si
i=1
i=1
i.e. there is no excess demand for any and all commodities
irrespective of the price level:
N
N
X
X
pi EiD ≡ 0
pi Di − Si ≡
i=1
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The classical dichotomy and Walrasian analysis
Original logic of causation from supply to demand:
the supply of commodities creates income which the recipients must
spend on commodities, so that any increase in the aggregate supply
of commodities creates a corresponding increase in the aggregate
demand for them.
Obviously falls apart once financial assets are allowed to exist:
increase in income could be partly or wholly used to increase money
balances or e.g. bond holdings, so that the increase in the aggregate
supply of commodities would cause a less than equal increase in their
aggregate demand.
conversely, an increase in commodity demand can be induced by
running down money or bond holdings, so that the increase in the
aggregate demand for commodities will come about without a
corresponding prior increase in their supply.
⇒ Hence, the causal argument behind Say’s law is invalid in modern
monetary economies.
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The classical dichotomy and Walrasian analysis
Original logic of identity of supply and demand for all goods:
“A product is no sooner created, than it, from that instant, affords a
market for other products to the full extent of its own value.”2
Failures of validity are rather obvious:
Say’s law asserts that the aggregate demand for commodities always
equals their aggregate supply, irrespective of the price level – i.e.
money is neutral in the short-run – which is contrary to all modern
econometric studies, economic intuition and modeling.
If Say’s law is correct generally, then it should also be true for the
labour market – i.e. widespread involuntary unemployment (caused
by inadequate demand) cannot occur – which is markedly untrue in
recessions.
Say’s central notion concerning money was that if one has money, it is
irrational to hoard it – i.e. there is no precautionary, speculative or
finance motive to hold money – which is markedly untrue given the
rise of the role of financial assets in modernity.
2
J.-B. Say. (1834 [1803]). A Treatise on Political Economy. [English translation]. Philadelphia:
Grigg & Elliott.
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The classical dichotomy and Walrasian analysis
Walras’ law
Due to Leon Walras, fundamental to macroeconomic analysis,
underlies IS-LM.
Considers at first a monetary exchange economy with N + 1 goods,
the extra good being money.:
for any economy, over any given period of time, the sum of the market
values of all the goods demanded must equal the sum of the market
values of all the goods supplied.
Expressed mathematically as:
N
+1
N
+1
X
X
pi Si
pi Di ≡
i=1
i=1
i.e. the sum of nominal demands for all goods identically equals the
sum of the nominal supplies of all goods:
N
+1
+1
X
NX
pi Di − Si ≡
pi EiD ≡ 0
i=1
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The classical dichotomy and Walrasian analysis
Implication of above:
p j E jD = −
N
+1
X
pi EiD
i=1,i6= j
This means that if
EiD = 0 ∀ i = 1, ..., N then END+1 = 0
i.e. if there exists equilibrium in N markets, then there would also be
equilibrium in the (N + 1)th market.
In the absence of financial assets, Say’s law can be reformulated in the
Walrasian setting to be:
“If and only if the excess demand for money is zero, then Walras’ law
implies Say’s law for other goods”:
D
Emoney
+
N
X
pi EiD = 0
i=1
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The classical dichotomy and Walrasian analysis
The demand for good i will depend on the relative prices and also on
income.


1
pN PN +1 
 p1
Di = f i 
, ...,
,
,Y
pN +1
pN +1 PN +1
Using money as the numeraire good, its price in terms of itself is 1, of
course.
And hence, without so far giving more structure to the functional form
of the supply function for good i, the excess demand for good i will
take the form:
p1
pN
E Di = f i
, ...,
, Y − Si
pN +1
pN +1
Demand curves are functions of relative prices and are homogeneous
of degree zero in all relative prices.
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The classical dichotomy and Walrasian analysis
Demand functions here are based on the axiom of substitutability of
commodities – which gives rise to relative prices
Money and commodities are not substitutable in this sense and thus
money can have no effect on the quantities demanded for
commodity goods.
Monetary prices are arbitrary scale-transformations of the relative
prices, deriving from the arbitrary monetary value assigned to the real
numeraire.
On this basis, money is “neutral” in the determination of equilibrium
prices and constitutes a mere “veil” that can simply be ignored in
determining the equilibrium level of production and employment.
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The classical dichotomy and Walrasian analysis
Note that in this world money has no store of value function, but is
simply a medium of exchange a currency of the Marshallian type,
serving no other purpose than to make the exchange process fluid,
and the demand for it is thus exclusively transactions-driven.
We have, however, already seen that Keynesian analysis has
subsequently shown that the demand for money in reality has more
components, than pure transactions-driven demand.
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The classical dichotomy and Walrasian analysis
Pigou and real balance effects
All of the above was so far cautioned with the words “in equilibrium”.
When critiqued, classical economists maintained that, while disequilibrium
obviously exists, any such state of disequilibrium will incorporate certain
“market forces” that will bring the economy back into equilibirum.
Among such forces were the two classical attempts to relax the dichotomy
while retaining the neutrality of money:
Pigou effect
∂ real consumption
| ∂ financial
{z assets }
+
×
∂ financial assets
|
∂{zP
−
<0
}
A disequilibrium with deficient demand for commodities will cause a fall
in their prices. Since wealth includes financial assets, the fall in price
level will increase wealth, which, in turn, will increase consumption and
aggregate demand, bringing the economy back to equilibrium.
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The classical dichotomy and Walrasian analysis
Patinkin’s real balance effect
∂ real consumption
|
∂ (M /P)
{z
+
}
×
∂ (M /P)
| ∂{zP }
<0
−
A price level fall due to a demand deficiency will increase the real value
of money holdings and thereby increase the household’s wealth. This
will lead to an increase in consumption and therefore in aggregate
demand, bringing the economy back to equilibrium.
Neither effect is significant empirically.
Pigou himself had later described the Pigou effect as a mere toy, based on
extremely improbably assumptions.
Rather, in reality, he said, the deflationary fall in prices would be
accompanied by bankruptcies among firms and a fall in the physical capital
stock in production. This would cause a decrease in real wealth, a rise in
unemployment and a fall in aggregate demand.
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The classical dichotomy and Walrasian analysis
More specific groupings
Since in equilibrium Walras’ law holds for all markets, then it does not
matter how we group the markets.
E.g. we can have a 4-good economy consisting of the markets for
commodities (c), money (m), bonds and equities (b), and labour (n).
EcD + EmD + E bD + EnD ≡ 0
Note that a useful feature of the Walras’ law is that market clearing for the
(N+1)th market is guaranteed once the other N markets clear.
This means that in general equilibrium analysis, we can exclude explicit
treatment of one chosen market. It of course continues to exist and to
function but its treatment becomes implicit. Solutions and equilibrium
values of real variables and prices will be identical irrespective of which
market is omitted from the explicit analysis.
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The classical dichotomy and Walrasian analysis
One of the major points of debate between the classical and the Keynesian
schools concerns the issue of whether the labor markets will or will not
clear over a reasonably short period (nevermind continuously) – at the
same time not clearing continuously in the commodities, money and
financial markets.
i.e. whether the following is true:
Dn = Sn ∗
n=n (full employment)
=⇒ EcD + EmD + E bD ≡ 0
In fact, however, in economies with developed financial markets, the most
plausible assumption would be that the money and bonds markets adjust
the fastest to clear any disequilibrium.
At the same time, the labor markets are the slowest to adjust since they are
characterized by long-term contracts.
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The classical dichotomy and Walrasian analysis
While Walras’ law holds in the general equilibrium states of the economy,
its implications for the dynamic analysis of prices, wages and interest rates
(i.e. in disequilibrium) are not always valid.
E.g. let’s consider the following.
The money and bond markets are so efficient in the modern
financially developed economies that they adjust continuously while
the financial markets are open – i.e. they can be regarded as
continuously in equilibrium for analytical purposes.
EmD = E bD = 0
This means that
EcD = −EnD
Hence, the must be a positive excess demand for commodities
whenever there is excess supply of labour.
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The classical dichotomy and Walrasian analysis
However, the real experience of economic recessions show that they
are usually described by the combination:
EnD < 0 – positive unemployment (i.e. negative excess demand for
labour), and
EcD < 0 – shortage of demand for products of businesses.
That is excess supply for labour and excess supply of commodities
occur simultaneously in recessions.
Similarly, during an economic boom (positive demand shock):
EcD > 0 – an excess demand for commodities can trigger
EnD > 0 – an response from businesses in the form of increased output
and employment.
This casts doubt either on the validity of Walras’ law itself in
disequilibrium or on the validity of the assumptions of continuous
equilibrium in money and financial markets (EmD = E bD = 0).
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The classical dichotomy and Walrasian analysis
What does this have to do with (monetary) policy?
In disequilibrium, where the Walras’ law is violated, a shock that
produces an aggregate demand deficiency of goods can be (and
usually is) accompanied by an excess supply (unemployment) of labor.
The free market mechanisms that should supposedly bring the
economy back to equilibrium are of questionable validity, and, even if
they were to be functional, would take a (really) long time.
The Keynesian (and logical humanitarian) argument is that such
demand-deficient situations should prompt a response from the
government and the central bank.
In fact, such responses to demand deficiency are, for example,
embodied in the Taylor-type rules of monetary policy formulation.
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A simple general equilibrium model
Section 3
A simple general equilibrium model
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A simple general equilibrium model
Fiat money cannot be valued by market participants in a Walrasian
setting, because here the value of something that is intrinsically
worthless is also zero – the imaginary Walrasian auctioneer is “too
efficient” to permit an equilibrium where fiat money has non-zero
value.
Thus, when incorporating money in general equilibrium, an ad hoc
assumption is traditionally made such that an individual agent’s utility
depends on the level of real money balances.
A justification, due to Don Patinkin, is that even if households plan to
balance their budgets so that planned purchases are equal in value to
planned sales, it may be convenient to buy and sell goods at different
times. The more money they hold, the greater the extent to which
they can purchase goods ahead of making sales. Money holdings
stand as a proxy for the more convenient sequence of transactions
they make possible.
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A simple general equilibrium model
Assume a household’s utility depends on the quantity of goods
consumed, X , and on real money balances, M /P.
Denote the household’s initial endowments of goods by X 0 and of
nominal money balances by M0 .
The budget constraint faced by the household in nominal terms then
can be written:
P X + M ≤ P X 0 + M0
i.e. the household can only afford to buy goods and accumulate
nominal money balances to the value of his initial endowments of
goods and money.
Dividing both sides of this budget constraint by the price level gives
the budget constraint in real terms:
X+
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M
P
≤ X0 +
M0
P
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A simple general equilibrium model
Further assume a standard quasi concave Cobb-Douglas form of the
utility function:
 ‹1
M 2
1
U=X2
P
In order to maximize this utility we write down the Lagrangian:
L=X
1
2

M
P
‹1
2

+ λ X0 +
M0
P
−X −
M
‹
P
and thus the first order conditions are:


€ Š1 ‹
1

− 12 M 2
 dL
X
−λ=0
=
dX
2
P
 € Š 1‹
−
1

 €dLM Š = 12 X 2 MP 2 − λ = 0
d
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A simple general equilibrium model
Rearranging both sides for λ and equating gives:

 € Š 1‹
€ Š1 ‹
−2
1
1
1
− 12 M 2
X
X 2 MP
=
2
P
2
1
X−2
€ Š1
M
P
2
1
=X2
€ Š− 1
M
P
2
which is solved by:
X=
M
P
Plugging this back into the budget constraint produces the optimal
solution:
(
M
X
M
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=
=
X0+
0
P
2
P X 0 +M0
2
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A simple general equilibrium model
If we now assume that the economy is populated by nidentical
households we can write the market clearing condition (by equating
total demand to total supply) for the goods market as:
!
M
X 0 + P0
n
= nX 0
2
Solving for the price level gives:
P=
M0
X0
Note, that we could have alternative first written the market clearing condition for the
money market as:
‹

P X 0 + M0
n
= nM0
2
and solving for the price level would also give:
M0
P=
X0
which is consistent with Walras’ law.
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A simple general equilibrium model
We observe that in this economy, money is neutral.
Real output per household is fixed at X 0 as it depends on endowments.
From the solution of the price level, a change in the money supply will only lead to a
proportional increase in prices.
Real money balances and production of goods do not change.
An increase in money, M0 , will shift the demand function for good X outwards, but this
simply causes the price level to increase:
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