Download Lecture 7 - Money, Prices and Inflation

Intermediate Macroeconomics
Lecture 7 - Money, Prices and Inflation
Zsófia L. Bárány
Sciences Po
2011 October 19
Chapter 10
Functions and types of money
Functions of money:
1. medium of exchange
2. unit of account
3. store of value
Types of money:
I commodity money
I
I
I
historically
has intrinsic value
fiat money
I
I
I
in nearly all contemporary money systems
does not have intrinsic value
usually: paper currency issued by the government
Monetary policy
I
monetary policy is control over the money supply
I
central bank (CB) determines monetary policy
I
when the CB wants to increase the money supply, it buys
government bonds
→ bonds enters the CB
→ money leaves the CB ⇒ quantity of money held by the
public expands
I
when the CB wants to decrease the money supply, it sells
government bonds
→ bonds leave the CB
→ money enteres the CB ⇒ quantity of money held by the
public falls
Monetary aggregates
1. M0: total currency in circulation - most closely resembles our
theoretical construct
2. MB: monetary base / high-powered money - total currency in
circulation + notes and coins deposited at banks and other
depository institutions (including bank reserves)
3. M1 - currency held by the public + all checkable deposits
4. M2 - M1 + savings deposits, small-time deposits, retail
money-market mutual funds
5. M3 - M2 + large-time deposits, institutional money-market
funds, short-term repurchase agreements and other larger
liquid assets
M2 already goes beyond ”money as a medium of exchange”
⇒ we need to use a narrower definition of money
The demand for money I.
Main assumption:
I
the interest paid on money is zero
I
bonds and capital ownership pay a positive return
Remember the household budget constraint:
P · C + ∆M + P · ∆K + ∆B = π + w · L + i(B + p · K )
I
the household receives & spends income in the form of money
I
unless the inflow and outflow of income perfectly coincide, the
hh needs to hold a positive money balance
Trade-off
B + P · K bear interest ⇔ money facilitates exchange
Money demand: the average holding of money that results from
the household’s optimal strategy for money management
The demand for money and the interest rate
I
a higher interest rate, i ⇒
I
higher gains from increasing the holdings of interest-bearing
assets, B + P · K
I
⇒ greater incentive to reduce average holdings of money, M
I
that is, with a higher i, households are more willing to incur
transaction costs in order to reduce
I
prediction: an increase in i reduces the nominal demand for
money, M d
I
if the price level, P is fixed, a higher i also reduces the real
d
demand for money, MP
The demand for money and the price level
I
suppose the price level, P, doubles
I
now assume that the nominal wage, w , and the nominal
rental rate of capital, R, also double
I
the real wage,
I
⇒ the real income of the household stays the same as well:
π
w
R
B
P + P L + ( P − δ)( P + K )
I
in real terms the households budget constraint did not change
I
the trade-off between money and interest bearing assets did
not change
I
⇒ the real demand for money,
I
⇒ the household’s nominal demand for money, M d would
double
w
P,
and the real rental rate,
Md
P
R
P,
stay the same
is unchanged
The demand for money and the real GDP
I
Economies of scale in cash management: at higher
incomes households hold less money in proportion to their
income
I
higher real income shifts the trade-off between interest income
and transaction costs
I
the transaction costs change less than proportional to the
income
I
prediction: when real income increases, nominal money
demand, M d , increases as well, but less than proportionally
I
if P, the price level is unchanged, then the real money
d
demand, MP , also increases, but less than proportionally
The demand for money II.
Based on the previous analysis, the money-demand function is
defined as:
M d = P · L(Y , i)
equivalently
Md
= L(|{z}
Y , |{z}
i )
P
+
−
where L(·, ·) is increasing in its first argument, and decreasing in
its second argument
Market clearing on the money market I.
the nominal quantity of money supplied =
the nominal quantity of money demanded
M s = M d = P · L(Y , i)
I
M s is constant
I
for a given real quantity of money demanded, L(Y , i), M d is
proportional to P, the price level
I
⇒ M d is an upward sloping function of P
I
P adjusts to ensure that the money market clears
Intuition: suppose M s > M d , hh have more money than they want
to hold ⇒ try to spend the excess money on goods ⇒ the price
level increases
Market clearing on the money market II.
We are taking as given Y and i.
Market clearing and general equilibrium
Three markets: money, labour, capital
Ms = Md
Ls = Ld
(κK )s = (κK )d
three nominal prices - P, w , and R - adjust rapidly to ensure that
the three equilibrium conditions hold simultaneously
this situation is referred to as general equilibrium
A change in the nominal quantity of money I.
I
assume that M s increases from M to 2M
I
suppose that the money demand line, M d does not shift
I
in this case the equilibrium price level, P ∗ has to double
A change in the nominal quantity of money II.
Effect on the labour market
I
the technology level, A did not change
I w = A · FL ((κK )d , Ld ) = MPL
P
I ⇒ Ld unchanged, w stays the same and
P
I w , the nominal wage rate has to double,
Ls stays the same
as P is twice as high
Effect on the capital market
I
the technology level, A did not change
I R
P
= A · FK ((κK )d , Ld ) = MPK
R
P
stays the same and κK s stays the same
I
⇒ κK d unchanged,
I
R, the nominal rental rate has to double, as P is twice as high
I
the interest rate, i =
R
Pκ
− δ(κ) is also unchanged
A change in the nominal quantity of money III.
Effect on the real GDP
I
the technology level, A did not change
I
labour input, L, did not change
I
capital services, κK , did not change
I
⇒ Y = A · F (κK , L) does not change
In general equilibrium, a one-time increase in the nominal quantity
of money supplied, M s , does not affect the real GDP.
Neutrality of money: in the long run, an increase or decrease in
the nominal quantity of money supplied, M s , influences nominal
variables but not real ones.
A change in the demand for money I.
I
I
the technology for making financial transactions improves
for example: increased use of credit cards or ATM machines
decreases the real demand for money to e
L(Y , i):
e
L(Y , i) < L(Y , i)
I
the nominal demand for money becomes: M d = P · e
L(Y , i)
I
a decrease in the real demand for money is similar to an
increase in the nominal quantity of money supplied
in the sense that people have excess money that they want to
spend
I
⇒ P ∗ increases
I
however, this change is not fully neutral, as if affects real
variables
A change in the demand for money II.
The cyclical behaviour of the price level I.
Consider a recession, where real GDP, Y , falls
I
the decline in Y reduces the real quantity of money demanded
I
in a recession, the interest rate, i, tends to fall as well
I
the decrease in i raises the real quantity of money demanded
the overall effect depends on:
I
I
I
the magnitude of the decreases in Y and i
the sensitivity of L(Y , i) to Y and i
I
estimates indicate that L(Y , i) declines in a recession, as i
falls by a little, and L(Y , i) is not very sensitive to i
I
⇒ we assume that L(Y , i) falls in a recession
I
given that the nominal quantity of money supplied, M s , is
constant
I
P increases in a recession ⇒ P is counter-cyclical
The cyclical behaviour of the price level II.
The cyclical behaviour of the price level III.
I
the result that P is counter-cyclical might seem
counterintuitive:
one might think, that in a recession, since income is low,
which leads to low consumer demand, which reduces P
I
however, in our equilibrium business cycle model, the
underlying shocks come from the supply side, not the demand
side
I
a low technology level, A - the source of a recession in the
model - means that goods and services are in low supply
I
looking at it this way, it makes sense that P would tend to be
high in a recession
Price-level targeting and endogenous money supply
I
price-level targeting: the monetary authority seeks to attain
a specified price level: P = P
I
it typically has to adjust the nominal quantity of money
supplied, M s , in response to changes in the nominal quantity
demanded, M d
I
P ·L(Y , i)
M s = |{z}
I
M s has to vary in line with L(Y , i), to keep the price level at P
fixed
Price-level targeting: M s = P · L(Y , i)
Trend growth of money
I
if L(Y , i) is growing at a constant rate, then M s must grow at
this same rate
I
most important factor in this trend growth is long run
economic growth, i.e. the upward trend in GDP
I
in most countries the money supply has an upward trend
The cyclical behaviour of money
I
L(Y , i), the real quantity of money demanded is high in
booms and low in recessions
I
⇒ M s has to follow this cyclical pattern in order to keep the
price level at P
I
M s should be pro-cyclical
I
data: M s is weakly pro-cyclical
Seasonal variation of money
Chapter 11
Data on inflation and money growth I.
I
inflation rates and money growth rates for 82 countries from
1960 to 2000 (Table 11.1)
I
price level measured by the consumer price index (CPI)
I
the inflation rate was greater than zero for all countries from
1960 to 2000
I
the growth rate of nominal currency was greater than zero for
all countries from 1960 to 2000
I
there is a broad cross-sectional range for the inflation rates
and the growth rates of money
Data on inflation and money growth II.
I
the median inflation rate from 1960 to 2000 was 8.3% per
year, with 30 countries exceeding 10%
I
for the growth rate of nominal currency, the median was
11.6% per year, with 50 above 10%
I
in most countries, the growth rate of nominal currency, M s ,
exceeded the growth rate of prices
I
a country that has a high inflation rate in one period it is
likely to have a high inflation rate in another period
I
there is a strong positive association between the inflation
rate and the growth rate of nominal currency
The inflation rate and the growth rate of money
”Inflation is always and everywhere a monetary phenomenon, in
the sense that it cannot occur without a more rapid increase in the
quantity of money than in output.”
Milton Friedman
Actual and expected inflation I.
Inflation is the percentage change in the price level from one year
to the next:
P2 − P1
∆P1
π1 =
=
P1
P1
I
in the data, inflation is typically positive, so P2 > P1
I
however, it can be that P2 < P1 , this is called deflation
P2 can be expressed as:
P2 = (1 + π1 )P1
Actual and expected inflation II.
When households make choices, they have to form expectations
about the future price levels, or equivalently expectations about
inflation.
The expected inflation, π1e usually differs from the actual inflation
rate, i.e. the forecast error, the unexpected inflation will usually
be different from zero:
π1e − π1 6= 0
Households try to minimise the forecast error, therefore, they use
available information on past inflation and other variables to avoid
systematic mistakes.
Expectations formed this way are called rational expectations.
Inflation and interest rates I.
I
the dollar value of assets held as bonds rises over the year by
the factor 1 + i1
I
the interest rate, i1 , is the dollar or nominal interest rate,
because i1 determines the change over time in the nominal
value of assets held as bonds
I
suppose that i1 = 0.05, if the household holds $1000 of bonds
in year 1, then in year 2 they will be have
$1000 + $1000 · 0.05 = $1050
I
however, the price level might have changed between the two
years, and in this case $1050 buys a different amount of goods
in year 2 than it would have bought in year 1
Inflation and interest rates II.
I
to account for this, we have to calculate the real value of the
assets held by the household in year 1 and in year 2
I
suppose that π1 = 0.01
I
and let us normalise the price level in year 1, P1 = 100
note: this is without loss of generality, as we care about the
change in price level, not the absolute value
I
in this case P2 = (1 + π1 )P1 = 1.01 · 100 = 101
I
the nominal value of assets in year 1 is $1000, the real value
1000
1
of this is B
P1 = 100 = 10
I
the nominal value of assets in year 2 is $1050, the real value
1050
2
of this is B
P2 = 101 = 10.4
I
the real interest rate is then
B2
P2
1
= (1 + r1 ) B
P1 ⇔ r2 = 0.04
Inflation and interest rates III.
the nominal value of assets evolves according to:
B2 = B1 (1 + i1 )
the price level evolves according to:
P2 = P1 (1 + π1 )
the real value of assets then evolves according to:
B2
B1 (1 + i1 )
B1 1 + i1
=
=
P2
P2
P1 1 + π1
the real interest rate is then:
1 + r1 =
1 + i1
1 + π1
Inflation and interest rates IV.
The real interest rate is the rate at which assets held as bonds
change in real value
1 + i1
1 + r1 =
1 + π1
By rearranging:
(1 + r1 )(1 + π1 ) = 1 + i1 ⇔ 1 + r1 + π1 + r1 π1 = 1 + i1
Arranging for r1 :
r1 = i1 − π1 − r1 π1
Since the cross-term r1 π1 is very small, we can approximate
r1 ≈ i1 − π1
Expected inflation and expected real interest rate
I
households care about real consumption ⇒
I
it is the real interest rate, r1 , rather than the nominal rate, i1 ,
that matters for intertemporal substitution
I
the real interest rate depends on the inflation rate, which is
unknown ex ante
I
the expected inflation rate, π1e , determines the expected real
interest rate, r1e
r1e = i1 − π1e
I
the expected real interest rate on money is:
expected real interest rate on money =
nominal interest on money − π1e = −π1e
Measuring expected inflation
Three methods:
1. ask a sample of people about their expectations
problem: sample might not be representative
also maybe the behaviour of people is more revealing than
how they answer questions
2. use the hypothesis of rational expectations:
the expectations correspond to optimal forecasts, given the
available information
→ use statistical techniques to gauge these optimal forecasts
challenge: what information hhs have when forming
expectations
3. use market data to infer expectations of inflation
main source: indexed bonds
Measuring expected inflation - Method 1
Measuring expected real interest rates - Method 1
Measuring expected inflation - Method 3
Indexed government bonds: these bonds guarantee the real
interest rate over the maturity of each issue
Measuring expected real interest rates - Method 3
The nominal US Treasury bonds give us the nominal interest rate,
subtracting from this the real interest rate that the indexed US
Treasury bonds give (Figure 11.4), we get the expected inflation:
Inflation in the equilibrium business cycle model
Goals:
I
to see how inflation affects our conclusions about the
determination of real variables:
real GDP, consumption and investment, quantities of labor
and capital services, the real wage rate, and the real rental
price
I
to understand the causes of inflation
Method:
I
assume: fully anticipated inflation, i.e.:
πte = πt
I
allow for money growth
The government prints money
I
and gives it to the people as transfer payments
I
these payments are lump-sum: the amount received is
independent of how much the household consumes and works,
how much money the household holds, etc
⇒ we do not have to analyse how people adjust their
behaviour to attract more transfers
We have to consider in what ways inflation affects the real
variables in the equilibrium business cycle model.
Effect on household’s decisions I.
1. Intertemporal substitution:
I
the expected real interest rate, rte , has
intertemporal-substitution effects on consumption and labour
supply
I
for given it , a change in πt changes the
intertemporal-substitution effects
2. Decision between bonds and capital:
I
the real return on these two assets have to be the same in
equilibrium
I
before: πt = 0 ⇒ it =
I
the return on capital is in real terms ⇒
rt = RP κ − δ(κ)
R
Pκ
− δ(κ)
Effect on household’s decisions II.
3. Demand for money:
I
interest rate on money: −πt ↔ interest on assets: it − πt
I
it is the difference between the two that affects money
demand: −πt − (it − πt ) = −it
I
the demand for money depends on the nominal interest rate
⇒ money demand: M d = P · L(Y , i)
Note:
I
it is the real interest rate that affects the intertemporal
substitution
I
it is the nominal interest rate that influences the real
demand for money
A change in inflation and the capital market
I
does not shift the demand curve for capital services
as inflation does not affect the marginal product of capital, as
long as the labour input is unchanged
⇒ the (κK )d curve is unchanged
I
does not shift the supply curve of capital services
as the total amount of capital K is fixed in the short run &
for any real rental price the optimal κ stays the same
⇒ the (κK )s curve is unchanged
I
as both curves stay the same, the market clearing capital
∗
services, κK ∗ , and real rental price RP stay the same
A change in inflation and the labour market
I
does not shift the demand curve for labour
as inflation does not affect the marginal product of labour, as
long as the capital input is unchanged
⇒ the Ld curve is unchanged
I
the labour supply curve, Ls would shift, if a change in π would
have income effects
we assume that this income effect is small enough to ignore
I
as both curves stay the same, the market clearing real wage
∗
∗
rate, w
P , and labour input, L do not change
Why would the inflation have income effects?
I
as we have seen, it is the nominal interest rate, it , that affects
the real demand for money
I
through this, the inflation influences the real money demand,
M
P and the transaction costs associated with money
management
I
normally these income effects are minor
I
⇒ we can ignore the income effect as a reasonable
approximation
A change in inflation and the real GDP
I
ignoring income effects we find that
labour and capital input, L and κK , and real wages and real
R
rental rates, w
P and P , stay the same
I
moreover, the technology level, A, is fixed
I
Y = A · F (κK , L) ⇒ real GDP is unchanged
I
the real interest rate is unchanged: r =
I
the division of Y between C and I is also unchanged,
since the intertemporal substitution is unaffected
and we continue to ignore income effects
R
Pκ
− δ(κ)
⇒ The neutrality of money also holds for the entire path of
money growth, as an approximation.
Money growth and the inflation rate
The growth rate of money:
−Mt
t
µt = Mt+1
= ∆M
Mt
Mt
⇒ Mt+1 = (1 + µt ) · Mt
The inflation rate:
Pt+1 −Pt
t
πt = ∆P
Pt =
Pt
⇒ Pt+1 = (1 + πt ) · Pt
Before we showed that when the supply of money increased by a
fixed factor, the price level also increased by the same factor.
By analogy, we make the conjecture that when the growth rate of
money is constant, µt = µ, then the inflation rate is constant and
equal to the growth rate of money: πt = µ.
We will now show, that µt = πt = µ is an equilibrium.
1.
Mt
Pt ,
the real supply of money is constant ⇒
2. L(Yt , it ), the real demand for money, has to be constant and
equal to the real money supplied
3. we showed before that the real GDP, Y is constant (as an
approximation), hence all we need is that i is constant:
i = r + π = r + µ is constant, as the real interest rate, r is
constant (as an approximation)
t
4. final step: L(Y , i) = M
Pt for all t ≥ 1
enough to show for t = 1, since both quantities are constant
the price level, P1 adjusts in equilibrium such that the real
demand for money equals the real quantity of money supplied:
M1
1
L(Y , i) = M
P1 ⇔ P1 = L(Y ,i)
A shift in the money growth rate I.
Suppose that the monetary authority raises the money growth rate
from µ to µ0 in year T
A shift in the money growth rate II.
I
the red line shows that the nominal quantity of money, Mt ,
grows at the constant rate µ before year T
I
the blue line shows that the price level, Pt , grows at the same
rate as money, µ, before year T
I
after year T , Mt grows along the brown line at the higher rate
µ0
I
after year T , Pt grows along the green line at the same rate
as money, µ0
I
the price level, Pt , jumps upward during year T
I
t
this jump reduces real money balances, M
Pt , from the level
prevailing before year T to that prevailing after year T
A shift in the money growth rate III.
Why is there a jump in the price level?
I
the real interest rate does not change
I
but the inflation rate jumps from µ to µ0
I
⇒ the nominal interest rate increases:
from i = r + µ to i 0 = r + µ0
I
an increase in the nominal interest rate reduces the real
demand for money:
L(Y , i) > L(Y , i 0 )
I
⇒ the price level, Pt , has to increase during year T
to equate the real quantity of money demanded to the real
quantity of money supplied:
MT = PT · L(Y , i 0 )
|{z}
|{z} | {z }
constant
↑
↓
A shift in the money growth rate IV.
I
the jump in the price level in year T can be interpreted as
an inflation rate that it temporarily higher than µ0
⇒ the real money balances drop in year T
I
in the case depicted in Figure 11.9 the temporarily higher
inflation is for a very short time, only for an instant
I
more general result:
t
there is a period of transition, during which M
Pt decreases,
because the higher nominal interest rate reduces the real
quantity of money demanded
during the transition the inflation rate exceeds the growth rate
of money, i.e. πt > µt
Trend growth in the demand for money I.
I
assume that L(Y , i) is growing at a constant rate, γ
→ i.e. due to long-term growth in real GDP, as in the Solow
model
I
assume that the quantity of money supplied, Mt , grows at a
constant rate µ
I
if the inflation rate is πt , then
the growth rate of the real money supply is ≈ µ − πt
I
equilibrium requires that
I
⇒
I
⇒ πt = π = µ − γ ⇒ of γ > 0, then π < µ
intuition: the rising money demand reduces the prices, as
shown before for a one-time increase in L(Y , i)
Mt
Pt
Mt
Pt
= L(Y , i)
must grow at rate γ, thus µ − πt = γ
Trend growth in the demand for money II.
prediction: a higher growth rate of real money demand implies a
higher difference between money growth and inflation
Government motives for printing money
I
I
why do governments print (too much) money?
they get to spend it first
three ways to finance government spending:
1. levy taxes
2. borrow money from the public (or from world markets)
3. print money
I
printing money is like levying an inflation tax:
increasing M leads to increases in P
⇒ real value of money held by the public declines
⇒ the purchasing power is transferred from holders of money
to the government
Government revenue from printing money
The nominal revenue is
Mt+1 − Mt = ∆Mt
The real revenue is
µt Mt
Mt
∆Mt
Pt+1 = Pt+1 ≈ µt Pt
If the government increases µt , it has two opposing effects on the
real revenue:
I
higher µ → more revenue
I
higher µ → higher π, higher i → lower money demand →
lower money supply → less revenue