Download Money, prices and exchange rates in the long run

Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected])
Money, prices and exchange rates in the long run
Index:
Money, prices and exchange rates in the long run.........................................................1
15.1 Introduction........................................................................................2
15.2 Model setup........................................................................................2
15.2.1 The real side...............................................................................................2
15.2.2 Money supply.............................................................................................3
15.2.3 Money demand...........................................................................................4
15.2.4 The Fisher effect ........................................................................................4
Box 1: Money demand during the Bolivian hyperinflation ...................................5
15.2.5 Equilibrium in the money market ..............................................................6
15.3 The money market equilibrium in the long run .................................7
15.3.1 What happens when M increases? (once-and-for-all) ...............................7
15.3.2 What happens when the money demand falls? ..........................................9
15.3.3 Open economy considerations .................................................................11
Nominal anchors ..........................................................................................12
15.3.4 Tying down the price level ......................................................................13
15.3.5 Alternative Nominal Anchors ..................................................................14
15.3.6 The long run dilemma..............................................................................15
Box 2: Exchange rate regimes .............................................................................15
15.3.7 Exchange rate targeting............................................................................16
15.3.8 Money targeting .......................................................................................18
15.3.9 Inflation targeting.....................................................................................19
15.3.10Two-country considerations.....................................................................22
15.3.11Foreign reserves as an insurance for price stability .................................23
15.3.12No one size fits all....................................................................................24
15.4 Inflation............................................................................................25
15.4.1 Baseline case: equilibrium with inflation ................................................25
15.4.2 Unexpected increase in the rate of money growth...................................28
15.4.3 Wealth effects ..........................................................................................29
15.4.4 Money based stabilization........................................................................30
15.4.5 Exchange rate based stabilization ............................................................31
Box. The end of Bolivian hyperinflation ............................................................33
15.5 Currency crisis .................................................................................33
15.5.1 Sterilized credit expansion.......................................................................34
15.5.2 The speculative attack..............................................................................35
15.5.3 The timing of the currency collapse.........................................................37
15.5.4 Fiscal sustainability and monetary stability.............................................39
15.6 Review questions and exercises.......................................................40
Review questions .................................................................................................40
Exercises ..............................................................................................................40
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15.1
Introduction
In this note, we analyse the behaviour of money, prices and exchange rates in the long
run. By long run we mean a time horizon that is large enough for prices to fully adjust to their
equilibrium levels. Thus, in the long run, the economy will be producing at full employment,
and the classical dichotomy will hold: real variables, such as the real interest rate and output
are determined on the real side of the economy, while money only determines nominal
variables, such as the price level and the nominal interest rate.
In Section 14.2, we describe the main assumptions of our model. In Section 14.3 we
briefly review the equilibrium in the money market and its adjustment to once-and-for-all
changes in money supply and demand. In Section 14.4 we discuss the alternative avenues a
central bank may follow to pursue the goal of price stability. In Section 14.5, we adjust the
model to the context of inflation, and we examine the challenges posed by inflation
stabilization. Finally, in Section 14.6, we review the so-called first generation model of
currency crisis.
15.2 Model setup
15.2.1 The real side
This note focuses on the nominal side of the economy. Hence, rather than modelling
the real side, we just take relative prices and full employment output as given. In our analysis,
the key relative prices will be the real interest rate (the price of current consumption in terms
of future consumption) and the real exchange rate (the price of foreign goods in terms of
domestic goods). We assume that the real exchange rate is always at its equilibrium level
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(assumed constant), and that the real interest rate is determined abroad (we are in a small
open economy)1. Hence:
Q  Qn
r  r*
eP* ~

P
(1)
(2)
(3)
15.2.2 Money supply
Assume that the money multiplier is equal to one, so that money supply and base
money are the same. Also abstract from changes in the net worth of the central bank. The
central bank balance sheet results as follows:
M  eBc*  BC
(4)
The ratio:
  eBc* M
(5)
is labelled “backing ratio”. It gives the proportion of base money that the central bank could
potentially buy back, using gold and reserves, at the current exchange rate, e.
When the backing ratio is equal to zero, the central bank has no hard currency at all.
In this case, it will not be able to intervene in the foreign exchange market to influence the
nominal exchange rate. When the backing ratio is equal to one, the central bank could – at
least theoretically – buy back the entire monetary base with foreign currency at the current
exchange rate. Some countries engaged in fixed exchange rate regimes commit themselves
1
When the equilibrium real exchange rate is not constant (say, because the home country is catching up
~ ~
in terms of productivity), then the real interest rate parity condition takes the form: r  r *    . In what
follows, we get rid of this unecessary complication, assuming that the equilibrium real exhange rate is constant
over time.


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with a backing ratio equal to one, to signal full convertibility of their currencies. These hard
peg regimes are called “currency board”.
15.2.3 Money demand
The money demand is assumed to depend positively on real income (transactions
motive), and negatively on long-term bond yields (the opportunity cost of holding money):
  
m d  m Q , i 


(6)
When the nominal interest rate increases, people will optimally decide to hold less
money per unit of transactions, allocating a higher fraction of their wealth to interest-bearing
bonds. In other words, money velocity – defined as the ratio between output and real money
balances - increases.
In what follows, we will often refer to a particular case of (6), in which money
velocity (V) is independent of real income2:
md 
.
Q
 k (i )Q ,
V (i )
(6a)
When figuring out how an equilibrium looks like, we will often appeal to the idea that
in the long run (that is, after all variables have adjusted to their equilibrium levels) the
nominal interest rate shall be constant over time. In that case, money velocity will be
constant, too.
15.2.4 The Fisher effect
2
More generally, money velocity is likely to depend on the nominal interest rate, income, as also on
third factors, like technological progress, and macroeconomic uncertainty not reflected in bond-yields. For
instance, financial innovations (credit cards, internet banking) influence the velocity of money, because they
allow people to make more transactions out of a given quantity of money holdings.
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When borrowers and lenders decide the nominal interest rate in financial contracts,
they have an eye on expected inflation. This is because they are concerned with real returns.
Thus, for instance, when expected inflation increases, agents will set a higher nominal
interest rate, in order to achieve the desired real return3.
This behavior implies a positive relationship between expected inflation and the
nominal interest rate:
i  r e
,
(7)
where  e is the expected inflation rate. This equation shows that the nominal interest rate can
change for two reasons: because the real interest rate changes, or because expected inflation
changes. The one-to-one relation between expected inflation and the nominal interest rate is
called the Fisher effect4.
An implication of the Fisher effect is that money demand (6) becomes a negative
function of expected inflation. Box 1 illustrates this.
Box 1: Money demand during the Bolivian hyperinflation
During the 1980s Bolivia was hit by an hyperinflation that reached annual rates of
24,000 percent during the peak years of 1984 and 1985 (and 60,000 percent along MayAugust of 1985).
According to the money demand theory sketched out above, one would expect money
velocity to reach very high levels during this episode. Why? Because with a higher inflation,
3
Note that there is a distinction between ex ante and ex post real returns. Individuals set nominal
interest rates in financial contracts to achieve a desired (ex-ante) real interest rate, given the expected inflation.
Because the actual inflation rate may differ from the expected one, the materialized (ex post) real interest rate
will in general differ from the desired one. Unexpected inflation leads to unplanned transfers of income between
borrowers and lenders.
A similar equation for the foreign economy implies i *  r *   *e . Then, the equality of real interest
rates at home and abroad (equation 2) implies i  i *   e   *e , that is, nominal interest rates at home and
abroad shall differ by the expected inflation differential.
4
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the cost of holding money should have shoot up, driving the demand for real money balances
to a record low or, which is the same, money velocity to a record high.
Figure 1 confirms that this was indeed the case. The figure displays the quarterly
inflation and money velocity in Bolivia along 1980-1994. As shown in the figure, during the
hyperinflation episode, money velocity increased sharply relative to the previous levels. This
means that the demand for money fell drastically per unit of output.
Figure 1: Money velocity and Inflation in Bolivia, 1980-1994
2.4 Money Velocity
Quarterly Inflation (%) 500
400
2.0
300
1.6
200
1.2
100
0.8
0
0.4
1980 1982 1984 1986 1988 1990 1992 1994
Money Velocity
Inflation
Source: International Financial Statistics, IMF
15.2.5 Equilibrium in the money market
Given the money supply, M, and real money demand, m, the money market
equilibrium is obtained by a price level, P, that satisfies the following equality:
M
 m d Q, i 
P
(8)
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In the long run, the economy is at full employment, the nominal interest rate is
determined by the Fisher effect, and the real interest rate is determined abroad5. Hence, the
long run version of (8) is:

M
 md Q n , r *   e
P
15.3

(8a)
The money market equilibrium in the long run
We now examine what happens to the nominal side of this economy in face of
changes in money supply or demand. These changes are thought to be once-and-for all, and
not anticipated by economic agents. That is: nobody anticipated these changes before they
occurred, and after these changes occurred, nobody expects them to be repeated. This is
obviously a simplifying assumption but is what we need to make the point.
15.3.1 What happens when M increases? (once-and-for-all)
Suppose that the central bank unexpectedly decided to expand the money supply,
once-and-for all. What will be the impact on prices and on the nominal interest rate?
To answer this question, we refer to Figure 2. The figure describes the time path of
the main variables in the model. First notice that a once-and-for-all increase in money supply
will not come along with a higher expected inflation: since prices are fully flexible, all the
required adjustment in prices will take place at the exact timing of the shock, with no further
changes. That is, inflation will be extremely high during one second, and will return to zero
immediately after the shock. Hence, by the Fisher equation (7), after the shock the nominal
interest rate will remain equal to the real interest rate (just like before the shock).
5
We are ignoring productivity changes that cause the real exchange rate to change in the long run.
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On the other hand, we know that the economy will not deviate from full employment
(prices are flexible). Hence, the right hand side of equation (8a) will be unaffected by the
one-and-for-all monetary expansion: with a constant output and a constant interest rate, the
demand for money will not change.
If the right hand side of equation (8a) remains unchanged, the value in the left-hand
side of equation (8a) has to remain unchanged too. Thus, any change in the numerator
(money supply) has to be matched by a proportional increase in the denominator (price level).
This example illustrates the classical neutrality of money, which in modern economics
is though to hold only in the long-run: in a context where prices are flexible, any monetary
expansion will be fully matched by a proportional increase in the price level, without any
impact on the real variables, such as the real interest rate and output6.
Figure 2: Once-and-for-all monetary expansion
6
Note that this model solves in a different manner than the Keynesian (short-run) model. The
Keynesian model assumes that prices are sticky in the short run: thus, from (8), any increase in M can only be
accommodated by a decline in the nominal interest rate or by an increase in output. In the Keynesian model,
prices and money are exogenous, while output and the nominal interest rate are endogenous; in this model,
money supply, output and the real interest rate are exogenous, while prices are endogenous.
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Figure 3 describes the money market equilibrium (8a) before and after the shock. The
new equilibrium occurs exactly in the same point as the equilibrium before, because the real
money demand did not move at all. All in all, the only effect of the monetary expansion was a
proportional increase in the price level.
What is the intuition for the monetary expansion to come along with a higher price
level? To answer this, note that the price level, P, corresponds to the amount of money one
needs to buy one unit of output. Conversely, 1/P, is the amount of output one is able to buy
with one unit of money. This relative price, 1/P, is no more than the purchasing power
(value) of money. Thus, when the money supply M expands ahead of money demand (m), a
natural implication is that its value, 1/P, decreases7.
Figure 3: Adjustment in the money market to a (once-and-for-all) monetary expansion
15.3.2 What happens when the money demand falls?
7
Note that the jump in the price level comes along with a capital loss for those holding domestic
money. Thus, if people anticipated the monetary shift, they would have tried to get rid of money before the
money supply actually increased. This, in turn, would have caused an earlier increase in the price level. We will
turn to this discussion later on in this note.
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Consider now the effects of a money demand contraction. This can occur, for
instance, when full employment output declines or when money velocity increases, say
because people fear future inflation. In any case, there will be a lower demand for money for
transaction purposes, and this will affect the price level.
This case is illustrated in Figure 4. In the figure, the fall in money demand creates a
momentary excess supply of money (distance between point 0 and point 1).
The equilibrium in money market could either be restored by an increase in the
interest rate (point 1’) or by an increase in price level that brings the real money supply to
(M/P)1. Since the nominal interest rate is tied to the real interest rate through the Fisher effect
and expected inflation is zero (again, the shock is once-and-for-all), the only way of restoring
the money market equilibrium is through the increase in the price level. Thus, the equilibrium
moves from 0 to 1.
The intuition is similar to that above: because the demand for money declined while
money supply remained unchanged, the purchasing power of money (1/P) eroded.
Figure 4: Adjustment in the money market equilibrium to a once-and-for-all fall in money
demand.
Figure 5: Adjustment to a once and for all fall in money demand
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15.3.3 Open economy considerations
We have stated that any expansion of money supply ahead of money demand
translates in to a fall in the purchasing power of money, so that the price level increases. In an
open economy, however, prices are constrained by foreign competition. Thus, the exchange
rate has to increase as well.
To examine what will happen in the external dimension, remember that in the long
run, the equilibrium real exchange rate has to be met. Hence, domestic prices, foreign prices
and the nominal exchange rate are tied together, obeying to (3).
With such restriction in mind, the adjustment will be as follows: first, any excess
supply of money (either caused by a monetary expansion or by a fall in money demand)
cannot be accommodated in the market for domestic goods, because output is given. Thus,
there will be a higher demand for assets. This will not deliver a lower real interest rate,
because in a small open economy the real interest rate is determined abroad (eq. 2). Hence,
the only possible counterpart of the excess supply of money is an excess demand for foreign
bonds. Then, because purchases of foreign bonds need to be settled in foreign currency, this
means people will demand foreign currency. This, in turn, will translate into an excess
demand for foreign currency in the foreign exchange market and a nominal depreciation of
the domestic currency. Finally, because equation (3) implies that, all else equal, a nominal
exchange rate depreciation has to be matched by an increase in domestic prices, the final
result is the increase in the price level.
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All in all, a once-and-for-all monetary expansion comes along with proportional
increases in the price level and in the nominal exchange rate. The nominal interest rate and
prices increase proportionally, because the real exchange rate is given.
Note that, just like the inverse of the price level, 1/P, measures the domestic value of
money, the inverse of the nominal exchange rate, 1/e , measures the external value of money.
In general, the value of money (domestic or external) has to decrease when money supply
expands ahead of money demand.
Figure: Inflation, money growth and exchange rate depreciation in Angola, 1984-2008.
Nominal anchors
The most important goal of monetary policy is to preserve “price stability”, which
central bankers define as low and stable inflation. Preserving the value of money (both
internally and externally) is essential for people to trust it and use it in the three basic
functions (store of value, means of payment, unit of account).
Sometimes, policymakers are tempted to engage in excessive money printing. This
can happen because policymakers want to achieve temporary output expansions (say, before
elections), or because they need to finance government deficits, or to rescue bankrupt banks.
Inflation, however, is bad news. When inflation is high and variable, economic planning
becomes more difficult, inhibiting investment. Savers shift the denomination of their nominal
assets towards foreign currencies, and may store value in the form of precious metals or of
low productivity real assets. High inflation comes along with higher costs of transacting,
lower saving rates, lower investment and thereby slower economic growth. Inflation also
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comes along with undesirable transfers of income from the public in general to the central
bank and (when unexpected) between debtors and creditors.
In order to avoid high and variable inflation, societies impose constraints on central
bankers’ choices. These constraints belong to the general class of institutions. The institution
that governs a country’ monetary policy and the communication of the central bank with the
public is called the “monetary regime”. A monetary regime envisaging price stability shall
include the adoption of an implicit or explicit nominal anchor, that is, a nominal variable such
as the exchange rate, the money supply, or a price index, to tie down the rekationship
between money and prices.
15.3.4 Tying down the price level
In a World with fiat currencies, a key question that arises is what determines the
purchasing power of money. Why should 5 pesos be a fair price for one pizza, and not for one
bicycle? After all, money is just a piece of paper, without any intrinsic value…
Saying that 5 pesos is the right price for a pizza but not for a bicycle is just a matter of
convention. Note however that once a society gets convinced that 5 pesos is the price of a
pizza, then all the other prices – including that of the bicycle - should be well determined.
As an example, suppose that the fair price of pizzas in terms of pencils was 5 (that is,
given the costs of production and relative demands, one pizza should be priced the same as
five pencils). Further assume that, by similar reasons, one bicycle should cost the same as 500
pencils. Given this, you would conclude that one bicycle should cost the same as 100 pizzas.
Otherwise, arbitrage opportunities would arise. This example illustrates an important property
of general equilibrium: in a world with N goods, you can only set N-1 relative prices
independently. Once N-1 independent relative prices are set, then the price of the Nth good
will become automatically determined.
In the example above we only referred to goods with intrinsic value. The relative
prices of these goods is determined in real side of the economy, by production costs and
relative demands. Now, let’s add a fiat currency (say pesos) to our economy. Since a peso
bill has no intrinsic value, its “fair” price cannot be assessed by real-side considerations.
Hence, some convention needs to be adopted. Thus, for instance, if you establish that one
peso shall be traded for one pizza, than the bicycle will cost 100 pesos and the pencil will
cost 20 cents. If you established instead that one peso is the price for one pencil, then the
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pizza will cost 5 pesos and the bicycle 500. Whether you adopt one standard or the other is a
matter of convention. But in no way you would be able to set one peso to value one pizza and
one bicycle at the same time. That would be violating the N-1 rule, opening the window for
arbitrage opportunities. Tying down the price level is the role of nominal anchors.
15.3.5 Alternative Nominal Anchors
In order to pin down expectations of agents regarding the value (purchasing power) of
money, central banks need to commit with some rule regarding the behaviour of a nominal
variable. Adherence to such a rule will help promote price stability. But adherence to such a
rule will also imply the subordination of the central bank’ actions to that goal.
In the past, a widely adopted nominal anchor among central banks was the price of
gold. By tying the value of a currency to that of gold – say, announcing that one ounce of
gold should cost 35 pesos – a central bank will provide an anchor for all other prices in terms
of the domestic currency. Of course for this anchor to be credible, the central bank would
need to subordinate the monetary policy to that goal: standing ready to buy or sell any
amount of gold for pesos at the announced price. Thus, the central bank will be unable to
choose the amount of pesos in circulation each moment in time.
The main problem of adopting gold as nominal anchor is that gold has an intrinsic
value. Moreover, gold has an intrinsic value that is highly unstable relative to other goods. By
tying the value of a currency to that of gold, a central banker has to accept that the overall
price level may move dramatically up or down, depending on what happens to the demand
and supply of gold. Episodes of inflations and of deflation caused by gold discoveries or by
gold scarcities where common during the Gold Standard period (1870-1930). The recognition
that these swings in the price level have little to do with price stability, led to the
abandonment of gold as nominal anchor by all central banks.
In today’s world, three categories of nominal anchors are privileged by central banks:
money targeting (committing with a given path for money supply), exchange rate targeting
(committing with given path of the exchange rate), and inflation targeting (committing with a
given path for the consumer price index). A fourth option is to adopt an “implicit” nominal
anchor: a variable that the central bank targets internally, but without announcing it explicitly
to the public.
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In any case, by choosing any of these nominal anchors, the central bank imposes a
constraint on its actions.
15.3.6 The long run dilemma
To illustrate the long term policy dilemma of monetary authorities, consider again our
key relationships, (3) and (8a). Solving these equations together, one obtains:
M P*m
 ~
e

(9)
This equation summarises the long run dilemma that underlies the choice of a
monetary regime in the long run: the central bank can try to influence M or e, but not both at
the same time. Targeting the money supply implies giving up setting objectives for the
exchange rate, and targeting the exchange rate implies giving up setting quantitative goals for
the money supply. This is no more than a corollary of the N-1 rule sketched out above.
Box 2: Exchange rate regimes
An exchange rate regime is a set of rules that govern the central bank intervention in
the foreign exchange rate market.
a. In a fixed exchange rate regime, the central bank commits to maintain a preannounced exchange rate, and stands ready to buy or sell any amount of foreign
currency for domestic currency at the pre-announced exchange rate8. According to
(9), when the central bank targets the exchange rate, it has to abdicate from
influencing the money supply.
8
Of course, a central bank without foreign reserves may still announce an “official exchange rate”.
However, if it has no foreign currency to enforce the announced rate in the market, this will not be a true peg.
When the central bank announces an official exchange rate but it does not stand ready to sell any amount of
foreign currency at the announced rate, the currency is said to be “non-convertible”. In these cases, an excess
demand for foreign currency appears in the official market, creating the conditions for the emergence of a black
market exchange rate.
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b. In a flexible exchange rate regime, the central bank refrains from intervening in
the forex market, so it keeps the ability to influence the money supply.
A problem with flexible exchange rates is that in the short term the nominal exchange
rate can deviate quite significantly from the fundamental relationship (3). This may be a
problem, especially for small open economies, as it gives rise to undesirable swings in
competitiveness. Because of this, a pure floating regime has never been well accepted in
emerging economies.
In practice, pure floating regimes are hard to find. Most central banks allowing their
currencies to float end up intervening in the foreign exchange market, from times to time.
The motivation can be either to smooth fluctuations in the nominal exchange rate, to prevent
drastic overvaluations and undervaluation of their currencies, or simply to build up foreign
reserves. When the Central Bank keeps an eye on the exchange rate, the regime is said to be a
managed float (or dirty float). This is more common in emerging economies9.
15.3.7 Exchange rate targeting
Exchange rate targeting can be implemented in a strict manner, by setting a constant
exchange rate against a single currency or against a basket of currencies (fixed exchange rate
regime), or in other modalities. This includes, for instance, allowing the nominal exchange
rate to vary inside a narrow band (target zone), or to devalue at a constant rate (crawling peg).
Although these different modalities differ in detail, they share a common feature: as long as
the central bank is committed to drive the exchange rate in a given direction, it cannot, at the
same time, set independent targets for the money supply.
9
The USD and the Euro are closer to the pure float case. But even these two currencies were object of
rare but massive interventions – coordinated by the largest World’ central banks – designed to correct extreme
misalignments. The most notable cases were the Plaza Agreement and the Louvre Accord (to rescue to USD)
and a coordinated intervention to contain the depreciation of the euro following a summit of the G7 in Prague
(September 2000).
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In the following, let’s consider the simpler case, in which the domestic currency is
pegged to another currency, via a time invariant exchange rate e  e . In this case, the
domestic price level will be determined as follows:
e P*
P ~

(3a)
Substituting (3a) in the money market equilibrium condition (8a), the money supply
becomes endogenously determined:
M
e P *m
~

(9a)
Equation (9a) shows that the money supply shall be allowed to vary, in order to
accommodate price developments abroad, changes in the demand for domestic money, and
changes in the equilibrium real exchange rate: under fixed exchange rates, the monetary
policy needs to be subordinated to the aim of keeping the nominal exchange rate at the
announced level, and this means adjusting the money supply passively whenever a key
exogenous variable changes.
As an example, suppose that the demand for domestic money increases for transaction
purposes: given the money supply, this will cause an excess demand for domestic money. To
raise liquidity, domestic agents will sell foreign bonds (or hire external liabilities). The
implied capital inflow will cause an excess demand for domestic money, and pressures for
the domestic currency to appreciate. To avoid this, the central bank must buy foreign
currency. Recalling the central bank balance sheet (4), we see that purchases of foreign assets
cause the domestic money supply to expand. In the end, the domestic money supply increases
exactly the enough to meet the higher demand for domestic money.
In a fixed exchange rate regime, the central bank announces that it stands ready to buy
and sell any amount of foreign exchange that agents may wish to trade at the official
exchange rate. Of course, this will be possible only if the central bank has reserves enough to
intervene in the foreign exchange market: whenever this is not the case, convertibility cannot
be assured and the central bank has to give up the exchange rate regime.
A caveat of fixed exchange rate regimes is that the central bank is required to expand
the money supply when foreign prices increase. This, in turn, will result in a proportional
increase in the domestic price level: by targeting the exchange rate, the central bank becomes
a passive importer of foreign inflation. With no surprise, central banks in the real world
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choose carefully the foreign currency to which they peg. The USD is the most common
anchor currency, because the United States have a long record of price stability. But also the
Euro, the SDR and the British Pound have been used as anchor currencies.
A second source of nominal instability may arise in case the country fixing the
exchange rate experiments a productivity growth that is higher than in the anchor economy.
~
In that case, we know that the equilibrium real exchange rate has to appreciate (that is,  has
to decline). Given the denominator of (3a), the only way of achieving this in a fixed exchange
rate regime is accepting an inflation rate that is higher than abroad. Note however that as long
as this is an equilibrium phenomenon, such increase in the inflation rate should not be a
problem for competitiveness or for the sustainability of the peg.
15.3.8 Money targeting
Under flexible exchange rates, a central bank preserves the ability to set
independently its money supply. At the first sight this looks like a good thing. However, in
practice it raises an important question: how can economic agents be so sure that the central
bank will not expand indefinitely the money supply, creating high inflation? In order to
protect citizens from such risk, an alternative anchor needs to be adopted.
Because the story of high inflation is also a story of excessive money printing, there
was a time when most central banks under flexible exchange rates elected money supply M
as the nominal anchor for their monetary regimes. Under money supply targeting, the central
bank sets an objective for the quantity of money, or – more precisely - for its growth rate,
and adjusts its instruments (for instance, interest rates or reserve requirements) so as to meet
the target.
Using the money market equilibrium condition, we have, each moment in time:
PM m
(8b)
Once the quantity of money is chosen, the nominal exchange rate shall be free to
adjust. In the long run, the following behaviour is expected:
~
M
e *
Pm
(9b)
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From (8b), we see that setting the quantity of money as nominal anchor will deliver
price stability only in case the demand for real money, m, is stable. If the money demand is
unstable (that is, if velocity varies in an unpredictable way) setting a fixed target for M will
not deliver price stability.
In practice, a main problem with money targeting is to find out an appropriate
monetary aggregate to target, that is, one that maintains a stable long term relationship with
the price level.
Instability of money demand is particularly pervasive in the context of emerging
economies. In these countries, terms of trade shocks, political instability, financial contagion,
and changes in economic sentiment regarding growth opportunities give rise to large swings
in output and on interest rates and, by then, on money demand. Because of this, money
targeting was never very popular in emerging economies.
In the context of industrial countries, money targeting became very popular after the
collapse of fixed exchange rates, in 1971. But since then, financial innovation and
globalization favoured the arrival of close substitutes to money, weakening the relationship
between monetary aggregates and the price level. After the late 1980s, records of instability
of money demand led most central banks to progressively abandon money targeting and seek
for an alternative nominal anchor.10
15.3.9 Inflation targeting
The understanding that financial liberalization and globalization came along with
more volatile money demands, turning money targeting less effective in promoting price
10
The Federal Reserve abandoned quantitative money targets after realizing that the velocity of money
became instable in the 1970s, as a consequence of financial innovation. Notably, one of the last advocates of
money targeting, the German Bundesbank, was able to pass its genes to the European Central Bank, which
initially announced the commitment to expand the money supply at 4.5%, per year, on average. However, in
practice, the money supply was allowed to expand differently from the target, and the ECB slowly abandoned
money targeting, to focus on its “medium run objective”: an inflation rate of 2%, on average. Still, in the ECB
framework, money still plays a very important role, as the “second pillar” of its monetary policy strategy.
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stability lead many central banks around the world to experiment an alternative anchor under
flexible exchange rates, which became known as “inflation targeting”. The move to inflation
targeting has been a pragmatic response to the failure of policies that targeted the money
supply or the exchange rate11.
Under inflation targeting, the central bank announces a “target” inflation rate and then
attempts to reach the announced target, adjusting all its policy tools as necessary. This
strategy combines a rule (announced inflation rate) with discretionary power: the central bank
is free to adjust its policy instruments in any desired direction in reaction to shocks, so as to
meet the rule (“instrumental independence”).
In terms of our model, setting a target for the price level implies the subordination of
money and of the exchange rate:
M  Pm
(8c)
~
e
P
P*
(3c)
For instance, if the money demand declines, then the money supply has to decline, to
keep the price level on target. By the same token, if foreign prices increase, then the nominal
11
The first country to adopt inflation targeting was New Zealand, in 1990.
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exchange rate has to appreciate, in order to avoid the implied inflationary pressures. Because
of (9), these two moves have to be consistent in the long run12.
Under inflation targeting, the central bank has full discretion to adjust its monetary
policy tools whenever it anticipates the risk of missing the inflation target. Of course, this
presumes that the central bank trusts the link between its monetary policy instruments
(interest rates, exchange rates, money supply) and inflation – the transmission mechanism.
Since this link is not immediate or automatic, inflation targeting typically focus on the
medium run: that is, the central bank is not committed to reach the target each moment in
time, but instead “on average, over a medium run horizon.
On the negative side, the commitment with a certain path for the price level over the
medium term is more difficult to monitor by the general public than the commitment with a
fixed the exchange rate. First, because a fixed exchange rate regime can be tested by citizens
at any time, by exerting the right of convertibility. Second, information on exchange rates is
simple and readily available for the general public, while data on inflation takes longer to
collect and can be manipulated by the statistical office. Third, because it is necessary to judge
whether occasional gaps between the actual inflation rate and the “medium term target” will
naturally vanish or require additional actions. Finally, prices are affected by factors out of
control of policymakers, such as changes in oil and other commodity prices, making difficult
for citizens to judge accurately the central bank commitment with low inflation.
12
Note that in this simple model, the available tools are M and e, and we define a target on the price
level. In the real World, however, central banks set instead a target for the inflation rate and typically elect the
nominal interest rate as the main tool of monetary policy. Most central banks follow the so-called “Taylor
Principle”, setting the central bank funds’ rate to increase faster than inflation (rising the real interest rate)
whenever inflation increases above target, and to decrease (causing the real interest rate on to fall) when the
inflation rate is below target. To this, central banks may add a concern with output fluctuations. This behaviour
is captured by a rule-of-thumb of the form: i  r            Qˆ  Qˆ n , which is known as Taylor Rule.
1
2


With 1  0 , this implies increasing the money market real interest rate by 1  1 percentage points whenever
inflation increases one percentage point above the target, and vice-versa. By allowing a positive term on output
(  2  0 ), a central bank is using the short term flexibility provided by the medium term commitment with price
stability, to deal with output fluctuations in the short run. The Taylor rule was first proposed by John Taylor, in:
Taylor, J., 1993. "Discretion versus Policy Rules in Practice". Carnegie-Rochester Conference Series on Public
Policy. 39: 195–214.
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With no question, the credibility of this regime is much more dependent on the quality
of domestic policymakers (and of institutions that govern the behaviour of the central bank)
than in the case with fixed exchange rates.
15.3.10
Two-country considerations
The discussion above applies to the case of an economy that unilaterally sets its
nominal anchor. A question that arises is whether the choice of a nominal anchor will be
constrained by the actions of the foreign central bank.
To see this, let’s first consider the money market equilibrium in the foreign country:
M*
 m*
*
P
(10)
As we already know, this equation determines the foreign price level, given the
exogenous money supply and demand. Solving for P * and substituting in (9), one obtains:
eM *  m*  ~
  
M
m
(11)
This equation reveals that the exchange rate between the two currencies has to be
13
unique . Hence, it will be unfeasible for the two monetary authorities to pursue independent
targets for the exchange rate. In light of (11), there are only three possibilities:
1. The foreign country (centre) sets independently its monetary policy ( M * ) and the
home country sets a target for the exchange rate (unilateral peg). For instance,
13
More generally, in a World with N currencies, there are only N-1 exchange rates.
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when Argentina pgs its currency to the US dollar, it is up to the Argentinean
central bank to adjust its policy in order to maintain the parity14.
2. The two central banks choose the respective money supplies at their own
discretion, and the mutual exchange rate is free to vary (floating exchange rates).
3. Both countries are committed to adjust the respective money supplies to achieve a
desired (common) target for the mutual exchange rate (cooperative peg). An
example of cooperative peg was the Exchange Rate Mechanism of the European
Monetary System that preceded the Euro. In light of this arrangement, when for
instance the Portuguese Escudo was devaluing relative to the Deutsche Mark, the
central banks of the two countries were required to intervene, buying the weak
currency and selling the strong currency, so as to ensure the desired parity.
15.3.11
Foreign reserves as an insurance for price stability
Both under fixed exchange rates and under inflation targeting, a central bank
committed with nominal stability needs to stand ready to adjust the money supply upwards or
downwards whenever the public demand for domestic currency shifts up or down.
The problem with large adjustments in money supply is that they may require
dramatic shifts in domestic credit. To see this, just use the money market equilibrium
condition (8a) together with the central bank balance sheet identity, (4):
M  eBC*  BC  Pm (12)
In changes:
14
During the Bretton Woods System (1944- 1971), all countries except the United States operated on a
unilateral peg to the dollar. Individual countries had the responsibility to sustain the exchange rate, while the
US could vary the money supply without regard to the exchange rate. The United States was required however
to stand ready to convert dollars into gold at $35 per once. That is: the US dollar was anchored to gold and all
other currencies were anchored to the US dollar. This is why the Bretton Woods System was categorized as “a
Gold-Exchange Standard”.
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eBC*  BC  Pm
(13)
This equation shows that, at given prices and exchange rates (ie, under nominal
stability), the central bank has two alternative avenues to meet any exogenous level of money
demand: (a) buying and selling foreign assets; (b) expanding or contracting the domestic
credit.
Thus, for instance, when the real demand for domestic money falls (say, because of an
output contraction, or because of a financial crisis in a related country), a central bank
concerned with price stability needs to contract the money supply. This can be achieved
through changes in the domestic credit (drawing liquidity from banks via open market
operations) or by selling foreign currency in the foreign exchange market.
The problem with the first avenue is that it impacts directly on the domestic economy:
entrepreneurs need stable economic environments to make their business decisions. If,
following a recession that drives down the money demand, the central bank tightens the
credit conditions, the economic situation will go worse (this is not captured in the model, but
it is intuitive) .
The second avenue – selling foreign reserves - has the advantage of protecting
domestic agents from the instability of money demand. Exploring this avenue, however,
requires the central bank to hold a buffer of foreign reserves. If the central bank had no
reserves at all, a fall in demand for money could only be met by a corresponding contraction
of domestic credit (unless the central bank gave up price stability).
Foreign reserves provide central banks with an important buffer to face eventual head
winds. This is especially true in environments where the demand for domestic money is
highly volatile, as it is the case of most emerging and developing countries. With no surprise,
along the last decades, many central banks in emerging markets tried to increase significantly
their holdings of foreign assets.
15.3.12
No one size fits all
In sum, the alternative nominal anchors deliver different degrees of flexibility for
central banks to deal with all types of shocks that destabilize the economy. Because
economies are differently exposed to different types of shocks, no single monetary anchor
serves all economies at all times: the choice of a nominal anchors is one of the most
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controversial topics in monetary economics and one that has to be evaluated on a case-bycase basis. “No one size fits all”.
15.4 Inflation
By now, we have analysed the implications of once-and-for-all changes in money
supply or in money demand, leading to once-and-for-all adjustments in the price level. In that
case, the inflation rate before and after the shock are the same (actually zero, in our
examples). In the real life, however, an economy can be tilted away from a regime with low
inflation and low money velocity to another with high inflation and high money velocity, and
vice-versa. In this section, we extend the previous analysis to account for that possibility.
15.4.1 Baseline case: equilibrium with inflation
As for a baseline case, let’s see how the equilibrium in our model looks like in the
presence of a positive inflation rate. Assume that money supply expands continuously at the
rate :

M
M
In order to account for inflation, we need to consider again the money market
equilibrium condition (8a), but now in growth rates:
  
m
m
(14)
According to (14), the inflation rate (increase in the price level) is determined by the
difference between the growth rate of money supply and the growth rate of money demand.
Finding out the solution of (14) formally is a tedious exercise. However, one can
easily prove that    is an equilibrium: indeed, in case    , then the nominal interest
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rate will be constant over time (equal to i  r   e  r   ) (eq. 7); then, with a constant
nominal interest rate, and given Q n , the money demand ought to be constant (eq. 8a); finally,
if the money demand is constant, then (8b) implies that    15 16.
This equilibrium is illustrated in Figure 6. In the figure, we see that prices are
increasing continuously, in the same proportion as the money supply. The fact than money
and prices are increasing in the same proportion implies that the real money supply is
constant. This is what we need to balance the money market, because the real money demand
is also constant, as implied by a constant nominal interest rate.
In Figure 7, the curve describing the real money supply does not move along time,
because money supply and prices are evolving exactly in the same proportion. However, the
nominal interest rate is now higher (through the Fisher effect) and the money demand is
lower than in the zero-inflation case.
Figure 6: Prices, money demand and interest rate when the money supply expands at a
constant rate.
15
Other possibilities are excluded ruling out Ponzi schemes. We skip this discussion for simplicity.
16
In the example above, the economy is not growing, and hence there is no increase in money demand
in the steady state. But the model can easily be extended for the case of a growing economy. To see this, assume
for a moment that full employment output was expanding at the constant rate g  Q n Q n . In that case, from
(6a), the growth rate of money demand would be m m  g , and the inflation rate would be     g . That is,
the equilibrium inflation rate would be equal to the growth rate of money supply in excess of the growth rate of
money demand.
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M
i
Time
m
Time
i=r+
P
Time
Time
Figure 7: Money market equilibrium with a positive inflation rate.
.
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15.4.2 Unexpected increase in the rate of money growth
Assume that, until time t=1, the rate of monetary expansion is zero. Then, at time t=1,
the money supply starts expanding at the rate  . In that case, we already know that the
inflation rate will increase to    , implying an equal increase in the nominal interest rate.
In light of (8a), the increase in the interest rate comes along with a fall in money demand.
This fall in money demand (increase in money velocity) is permanent, because from now on
the nominal interest rate will be higher.
The regime shift is described in Figures 8 and 9. In Figure 8, we see that, at the time
of the announcement, the nominal interest rate jumps, so as to incorporate the new expected
inflation ( i  r   e  r   ). This, in turn, causes the money demand to fall, from m0 to m1 .
At the time of the policy change, however, the nominal money supply is still at its initial
level, M 0 (money will start increasing precisely at that moment). Hence, for the real money
supply to match the money demand, the price level has to jump: in the figure, this is
illustrated by a jump in the price level from P0 to P1 at the time of the shock.
Figure 8: Prices, money demand and interest rate when the rate of money increases.
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In figure 9, the adjustment in the money market is described by a shift from point 0
(low interest rate and high demand for money) to point 1 (high interest rate and low demand
for money). The money demand falls because the interest rate jumped, and the price level
jumps to equal the real money supply and demand.
After that jump, the real money supply becomes constant: in the new steady state, the
price level and the nominal money supply grow proportionally, and the real money supply
remains unchanged at its new position, which – remember – is determined by money demand.
Figure 9: Money market equilibrium when the inflation rate increases
15.4.3 Wealth effects
A jump in the price level implies a sudden fall in the purchasing power of money.
Hence, holders of domestic money will lose.
A jump in the price level would not be possible if it was anticipated by economic
agents: if agents knew in advance that the price and the exchange rate were to jump, they
would try to protect their wealth by swapping money balances for goods or for foreign
currency before any price jump. This – in turn – would imply a downward shift in the
demand for money before the money supply started increasing. In consequence, the increase
in prices would have started earlier (equation 14). A price jump at t1 can only take place
when the regime shift is not anticipated.
Also note that, in the new regime, agents will face a continuous capital loss related to
the erosion in the value of their money holdings, due the inflation. The extra cost of holding
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money – that underlies the lower money demand – is labelled as inflation tax. It is a tax, in
the sense that it implies a transfer of purchasing power from money holders to the central
bank. However, there is nothing private agents can do about it. There will be continuous
erosion in agent’s wealth, but agents are willing to accept it, because they need money for
transaction purposes.
15.4.4 Money based stabilization
Using the tools above, one can now discuss the challenges facing a central bank
aiming to end up with a situation of very high inflation. This case is illustrated in Figure 10.
Suppose that initially the economy is at point 0. In this equilibrium, money is
expanding continuously, prices are increasing proportionally to money (inflation), and the
demand for money is low. Then, the central bank decides to stop with inflation, by
immediately freezing the quantity of money in the economy. In Figure 10, this is illustrated
by a money supply that becomes constant after time t0 .
If the plan is credible, the fall in expected inflation to zero will come along with a fall
in the nominal interest rate, and with an increase in money demand. In terms of Figure 10, the
demand for real money balances increases to point 1. As before, the adjustment in the money
market requires the real money supply to adjust so as to meet the new money demand at point
1. As long as prices are flexible, this will not be a problem: as depicted in Figure 10, the fall
in prices at the time of the announcement will drive the real money supply up to the level that
is consistent with the new money market equilibrium.
One may question, however, how realistic is to presume that prices will adjust
downwards at the end of a hyperinflation episode: economic agents accustomed to raise
wages and prices on a daily basis may well fail to engage in nominal reductions at the time of
the announcement. In case prices fail to decline, how will the money market equilibrium be
met?
To answer that question, suppose that prices do not move at all, so that at the time of
the announcement the real money supply remained unchanged at M P 0 . In this case the
real money demand could not change. Thus, if the new inflation target was credible and
money velocity declined accordingly, the only way of balancing the money market would be
to a fall in Q: a recession in the economy, by reducing the transactions demand for money,
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would exactly offset the decrease in money velocity caused by the fall in interest rate,
keeping the demand for real money balances at the initial level.
Figure 10 – Money-based disinflation
15.4.5 Exchange rate based stabilization
In the money based stabilization programme outlined above, if the price level fails to
adjust downwards, there will be a recession in the economy. To avoid such scenario, the
central bank may decide another strategy: instead of setting the money supply to be constant
after t0 , it may decide to stabilize the exchange rate at the level observed in t0 . In this case,
the anchor for the disinflation program will be the exchange rate.
This avenue is analysed in Figure 12. Since prices and the exchange rate are
proportional, prices will remain constant after t0 . As long as the program is credible and
inflation expectations fall down to zero, then the real money demand will increase, just as
before. Since in this case prices do not jump (they are determined by the exchange rate), the
increase in the real money supply must be achieved through an increase in the nominal
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money supply: at t0 , the nominal money supply jumps once-and-for-all to a new higher level,
to accommodate the larger demand for money that comes along with nominal stability.
Figure 12. Exchange-rate based disinflation
At the first sight, the fact that money supply expands at the time the central bank
wants to stop with high inflation looks inconsistent. However, this may not be the case:
remember that if the disinflation programme is credible, the interest rate will fall down and
people will desire extra money. Since the money demand is increasing, setting the money
supply to increase along with money demand is not inflationary at all.
Of course, credibility is a critical issue in such a strategy: if people suspected that the
increase in money supply was more of the same (e.g, financing government deficits), they
would anticipate an even larger inflation, and the programme would fail.
An interesting feature of an exchange rate stabilization program is that its entails the
mechanism that is needed for the increase in money supply to be credible. To see this, first
note that at the time inflation expectations decline ( t0 ), the demand for real money increases.
If the central bank does nothing but to stick with the exchange rate target, agents will try to
raise liquidity in domestic currency selling foreign bonds (or hiring foreign liabilities). This
will create an excess supply of foreign currency and a pressure for the domestic currency to
appreciate in the foreign exchange market. Because the central bank is committed with the
fixed exchange rate, it will intervene in the foreign exchange market, buying foreign currency
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and by then expanding the money supply. In the end, the money supply will increase the
enough to accommodate the increase in the money demand (as depicted in Figure 12). The
fact that the increase in the money supply is backed by foreign reserves is a source of
credibility, because it means the central bank has munitions to intervene in the foreign
exchange market and buy back the extra money just created, in case people become
suspicious about the central bank’ intentions.
Of course, the credibility of a disinflation program cannot rely on central bank actions
alone: it is necessary to convince the general public that policymakers will not turn again to
the printing press. Successful disinflation programs typically involve the affirmation of the
central bank independence relative to the Minister of Finance. Fiscal reforms aiming to
increase government revenues, and the building up of fiscal institutions, such as those that
impose a limit on government spending are key elements of successful stabilization. Nominal
stability and fiscal sustainability are just two sides of the same coin.
Box. The end of Bolivian hyperinflation
Along 1985, the Bolivian government launched a stabilization program intended to
end up an ongoing hyperinflation. Although initially the exchange rate was allowed to float,
the authorities soon embraced the view that the exchange rate was the key instrument for
stabilization, resisting the temptation to depreciate the currency to improve competitiveness.
At the same time, the authorities promoted the unification of the black market and the official
exchange rates, by adopting full convertibility on the current and capital accounts. In the
months that followed, much of the gradual increase in the money supply in the economy was
backed by capital inflows, in a context of excess demand for domestic money. This was a key
source of credibility to the programme.
15.5 Currency crisis
In the last section, we examined a case in which the move towards high inflation was
not anticipated by economic agents. In this section, we discuss the case in which economic
agents perceive nominal stability to be unsustainable. Since agents anticipate the exchange
rate depreciation, they will optimally decide to get rid of domestic currency before the
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currency starts to devalue. In doing so, they avoid the capital losses that would result from a
sudden exchange rate depreciation.
In the model that follows, the central bank is initially committed with a fixed
exchange rate. The perception of unsustainability arises because the government monetizes
its fiscal deficits. During some time, domestic credit expansion does not cause the money
supply to increase (and the peg to collapse), because the central bank is able to sterilize the
purchases of government bonds with the sale of foreign reserves. However, agents will
anticipate the scenario in which central bank reserves are exhausted and the exchange rate
will start devaluing. With such scenario in mind, agents will optimally decide to swap its
domestic currency by foreign currency before the exchange rate depreciation takes place.
15.5.1 Sterilized credit expansion
Consider a country under fixed exchange rates. At time t0, the central bank starts
expanding the domestic credit at a constant rate   BC BC (say, lending to the
government).
If nothing else happened, the money supply and prices would start increasing, just like
as described in Figure 8: anticipating a higher inflation, agents would demand less money,
finding themselves with more money than they would like to hold at the given (higher)
interest rates. If the peg was immediately abandoned, there would be a price jump, and
domestic agents would face a capital loss.
In alternative, assume that the central bank tried to stick with the fixed exchange rate
regime (or with nominal stability), by sterilizing the domestic credit expansion with an
17
Krugman, Paul. 1979. “A Model of Balance of Payments Crises”. Journal of Money, Credit, and
Banking 11, pp. 311-25.
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offsetting sale of foreign currency in the foreign exchange market. With sterilized
interventions, the nominal money supply would not increase for a while. That is18:
M  eBc*  Bc  0
(15)
The question that arises is how long could that strategy persist?
Of course, if nothing changed, a moment would come when the central bank reserves
were exhausted. At that time, the currency would move to float, prices and the exchange rate
would jump, and the private sector would face a capital loss.
Sterilized interventions give however agents the opportunity to avoid the capital loss.
By observing the intervention in the foreign exchange market and the continuous fall in
foreign reserves, agents become aware that the collapse of the exchange rate regime is
imminent. Hence, they will choose the right moment to get rid of domestic currency, trading
it for foreign currency at the official exchange rate, and precipitating the currency collapse on
time to avoid the price jump.
15.5.2 The speculative attack
To see how the speculative attack operates, we refer to Figure 13. In the figure,
money supply is initially constant at M 0 . Then, as the domestic credit expands, the
composition of money supply changes over time: as time goes by, a greater proportion of the
money supply becomes backed by loans to the government, rather than by holdings of foreign
reserves (the backing ratio, (5), is declining).
If agents did nothing to protect their claims, the price level would remain constant (at
P0 ) until the central bank’ reserves were exhausted (at time t3). As explained above, since
after this point the central bank could no longer sell reserves to keep the money supply
18
The fact that lending to the government under fixed exchange rates forces the central bank to sell
foreign reserves inspires a well known proposition: “in a fixed exchange rate regime, even if the government
tries to borrow from the central bank, in effect it will be borrowing from abroad”.
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unchanged, the money supply would start increasing, implying an increase in the inflation
rate, and a price jump from S to T.
If however economic agents anticipate the collapse of the currency, they will try to
swap the domestic currency by foreign currency before any price jump. The speculative
attack occurs because people understand that, as prices are about to increase and the
exchange rate is about to depreciate, there will be a capital loss for holders of domestic
currency. Therefore, they run en mass to the central bank in order to swap their undesired
monetary assets for foreign bonds, before a discontinuous jump materializes.
In the figure, this is captured by a run on the currency at time t2. At that moment, the
demand for domestic money falls abruptly (to the level consistent with the new inflation rate,
m1 ), implying a sudden increase in the demand for foreign assets. By selling out all its
reserves, the central bank adjusts downwards the nominal money supply to exactly equal the
new money demand, without the need for prices (or the exchange rate) to jump.
Figure 13: the dynamics of a speculative attack
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Money,
credit, reserves
Money stock
M0
Domestic credit
BC
eBC*
Reserves
t2
t1
t3
Pt
Time
T
R
P0
t1
t2
S
t3
Time
Speculative attack
Nominal
stability
High inflation
After t2, the growth rate of money is equal to the growth rate of domestic credit, and
prices will increase in the same proportion. The real money supply will be at the level
determined by the new money demand. The big difference relative to the case depicted in
Figure 8 is that the adjustment of real money supply towards the new money demand is
achieved by a fall in the stock of nominal money, induced by a run on the central bank
reserves, rather then by a jump in the price level.
15.5.3 The timing of the currency collapse
The important property of this adjustment is that the timing of the speculative attack is
well determined, by a non-arbitrage condition. To understand this, let’s refer to Figure 9
again. The new money demand is well known, as implied by the new inflation rate (    ).
Thus, the real money supply has to move from point 0 to point 1 at the time of the regime
shift:
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-
If the shock is not anticipated, this will be achieved by a price jump at the time of
the surprise (Figure 8).
-
If the shock is anticipated, the fall in money supply will be achieved by a fall in
foreign reserves, induced by a massive sell of domestic currency at the time of the
speculative attack. This selling of foreign currency will bring down the money
supply to the level needed to match the new money demand.
The arbitrage condition is as follows:

M  BC  P0 m r   , Q n

(16)
This condition determines the timing of the currency collapse. At time t2, there is a
speculative attack that completely drains out the foreign exchange reserves of the central
bank, turning the nominal money supply equal to domestic credit. The arbitrage (non-price
jump) condition is such that this level of money supply equals the new money demand.
If the run on central bank reserves occurred before time t2, then the money supply
would fall to a level that was lower than the new money demand: hence, the price level would
need to jump downwards: this would be inconsistent with the absence of arbitrage
opportunities. If, in alternative, the attack occurred after t2, then the money supply after the
attack would be already too high, requiring a jump in the price level and a capital loss. Hence
the only moment when it is rational for agents to run on the central bank’ reserves is at time
t2.
This example describes a case in which the currency crisis is unavoidable: since the
fiscal policy is inconsistent with nominal stability, the abandonment of the peg is just a
question of time. This case is referred to as the “first generation crisis model”19.
19
Not all currency crises can be, however, described by this model. For instance, the currency crisis in
Mexico, in 1994, and the Asian Crisis, in 1997, were not doomed to occur, but were triggered by market
expectations. The “second generation model” accounts for the possibility of self-fulfilling crisis: that is,
countries with arguable sustainable policies may be forced to unlikely but possible unstable paths, due to
confidence crises that alter the agents’ perception regarding the willingness of the authorities to keep defending
the peg.
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15.5.4 Fiscal sustainability and monetary stability
Inflation is a monetary phenomenon: a continuous increase in the price level can only
happen if the central bank engages in continuous money printing. This proposition stands
however for the proximate cause of inflation, only. Going deeper in the ultimate causes of
high inflation, one shall question why central banks sometimes engage in excessive money
printing, giving away the goal of price stability. The discussion above suggests that the deep
cause of high inflation lies on the fiscal side: when the central bank is required to extend
loans to the government on a continuous basis, sooner or later this will come at the cost of
high inflation.
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15.6 Review questions and exercises
Review questions
15.1. Explain why policies to end hyperinflations often include measures to reset
administratively the interest rates in past financial contracts.
15.2. Suppose that a small open economy begins to use credit cards for the first time, so
that money velocity increases. Discuss the impact of this event, assuming that the central
bank follows alternative monetary anchors: (i) money targeting; (ii) fixed exchange rates;
(iii) inflation targeting.
15.3. The strategy followed by Bolivia to stop its hyperinflation was to validate a large
capital inflow. Working with the equation that relates the change in the monetary base
with the change in domestic credit and international reserves, explain how this may have
contributed to stabilization.
15.4. Comment: “Under a fixed exchange rate regime, even if the government tries to
borrow from the central bank, in effect it will be borrowing from abroad”.
15.5. Explain how a persistent government deficit may lead to the collapse of a fixed
exchange rate regime.
Exercises
15.6. (Fisher effect) Consider a borrower that signed a one month 1000 pesos loan at a
55% monthly nominal interest rate during the Argentinean hyperinflation process in 1985.
At that time the expected inflation was about 50% per month.
a) What was the approximate real interest rate?
b) The government surprised everyone with a disinflation programme that reduced
inflation to 5%. What were the implications for the borrower and the lender?
c) Which complementary measures should be taken by the Argentinean government to
solve this problem?
15.7. Consider a world with two economies, Pesoland and Poundland, where the respective
currencies are Peso and Pound. In Poundland, there are N=1000 workers and the
production level is Y=1000 units. In Pesoland, there are N=100 workers and Y=50 units.
The Central Bank of Poundoland issues M=1000. To simplify, assume along the whole
exercise that PPP holds and that Money velocity is unitary.
a) How much should one unit of output cost in Poundoland (in Pounds)?
b) How much should be the average wage rate of one worker in Poundland (in pounds)?
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c) If in Pesoland M was equal to 50000 pesos, how much would be prices and wages (in
pesos)?
d) Assuming that both countries produce exactly the same good and that this good can be
both exported and imported, how much should be the price of a peso in terms of
pounds?
e) Keeping the previous assumptions, where is purchasing power higher? Why?
f) Now imagine that the central bank of Pesoland decided to duplicate the quantity of
money in its economy. What would happen to prices, wages and the exchange rate?
g) Explain what would happen to prices, nominal wages and the exchange rate if labour
productivity in Pesoland declined by one half. If the objective of the central bank was to
keep inflation at zero, what should it do?
15.8. Consider a small open economy producing a tradable good (T) and a non-tradable (N)
good. The corresponding production functions are YT  aLT and YN  bL N , where
LT  60 and LN  60 are immobile across sectors. In this economy, the demand
functions are CT  M 2 PT , C N  M 2 PN , where M=120 denotes for nominal money
balances, and the weight of each good in the consumer price index is 50%. Finally,
assume that the TB is always zero, and foreign prices are PT*  PN*  1 .
a) Assume first that a  b  1 . Find out the nominal exchange rate, the domestic price
level, and the real exchange rate.
b) (Money-target): Now consider the case of a productivity increase in the tradable good
sector, from a  1 to a  2 . Assuming that the money supply was kept constant, what
would be the equilibrium levels of: (a1) the nominal exchange rate; (a2) the price level;
(a3) the real exchange rate. [0.5; ¾; 2/3]
c) (inflation-target) Considering the same productivity shock, analyze what should happen
if the central bank wanted to keep the inflation rate at zero. In particular, compute the
implied levels of: (b1) the exchange rate; (b2) money supply; (b3) real exchange rate
[2/3; 160; 2/3].
d) (exchange rate target) Finally, consider the case in which the central bank wanted the
exchange rate to remain fixed after the productivity shock. In particular, compute the
implied levels of: (c1) the exchange rate; (c2) money supply; (c3) real exchange rate [1;
240; 2/3].
e) Based on this exercise, explain why the EMU entry criteria, of a stable exchange rate
with the euro and low inflation could not suit the enlargement countries in the East.
15.9.
Consider the following initial balance sheet of given central bank: eBC*  20 and
BC  80 pesos. Further assume that the money multiplier is equal to one and that the real
money demand is given by mD  Y 10i , where Y is output (assumed 50) and i is the
nominal interest rate. The real interest rate is 5%. In this economy, PPP holds and the
*
foreign price level is P  1 .
a) Describe in a graph the money market equilibrium. Find out the equilibrium levels of
prices and of the exchange rate.
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b) Suppose that the central bank decided to expand the domestic credit by 20 pesos. What
would be the implications for the price level and for the nominal exchange rate? Could
the central bank keep prices and the exchange rate constant despite the expansion of
domestic credit? How?
c) Suppose that there was a fall in output to Y=40. What would be the implications for
prices and the exchange rate? Could the central bank keep prices and the exchange rate
constant and at the same time avoid the contraction of domestic credit? What if output
fell to Y=35?
d) On the basis of your results, explain why is a good idea for central banks to accumulate
foreign reserves in good times.
15.10. Consider an oil exporter economy, where the domestic currency (peso) is initially
pegged to the dollar. Assume that: the PPP and the Fisher effect hold instantaneously; the
*
foreign price level is constant at P  1 ; the money demand is given by mD  Y 4i ; the
real interest rate is 5%; the central bank balance sheet is initially as follows:
M  eBC*  BC  20  60 pesos. Initially, oil prices are peaking up in international
markets, and full employment output stands at Y  160 .
e) Describe the money market equilibrium in this economy, assuming that the money
supply remains constant. What will be the price level and the nominal exchange rate?
f) Assume that oil prices increased further, driving output in this economy to a record high
of Y  200 . Surfing on prosperity, the government in this economy decided to
borrowed 20 pesos from the central bank to finance a development plan. Would this
operation threat the fixed exchange rate and price stability? Explain why.
g) Departing from (i), examine the policy options for the central bank if oils prices
suddenly declined, driving GDP to Y  130 . Would the fixed exchange rate regime be
at stake? What can you conclude from this exercise?
15.11. Consider an economy where both prices and the exchange rate are fully flexible, and
where the Fisher principle and the purchasing power parity hold instantaneously.
Moreover, it is known that the domestic real interest rate is constant and equal to r  0.04
and that the demand for real money balances is given by m D  Y 20 i  , where Y  100
refers to output (constant) and i is the nominal interest rate. The foreign price level is
constant and equal to 2.
a) Assume that initially the money supply is constant and equal to M  250 . Describe the
initial equilibrium, quantifying: the inflation rate; the nominal interest rate; the real
money demand; the price level; money velocity; the nominal exchange rate.
b) Unexpectedly, the central bank decided to expand the money supply by 16% per year.
What should happen to the inflation rate, the interest rate, real money demand and
money velocity? Describe graphically the new money market equilibrium in the (M/P,
i) space.
c) Explain, quantifying, what should happen to the price level at the time of the policy
change.
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15.12. Consider an economy with flexible prices, where money supply is initially expanding
at 20% per year. Assume that: the PPP and the Fisher effect hold instantaneously; the
foreign price level is constant at P *  1 ; the real interest rate is 5%; the money demand is
given by m D  Y 4i , full employment output is Y f  200 .
d) Describe in a graph the money market equilibrium of this economy, as well as the time
paths of the price level, the exchange rate and the nominal interest rate.
e) Assume now that, at the time the domestic money supply reached the level M=10000,
the central bank unexpectedly decided to anchor the money supply at that level, so as to
stop the ongoing inflation. Find the new interest rate and money demand. Describe the
new money market equilibrium in a graph. Assuming that prices were fully flexible,
find out what would happen to the price level and the nominal exchange rate.
f) In alternative, suppose that, when domestic money reached the level M=10000, the
central bank decided to fix the exchange rate at e=50. In that case, what would happen
to the money supply? Why?
15.13. [1st Generation Crisis model] Consider an economy where the currency (peso) is
initially pegged to the dollar at e=1. Assume that the foreign price level is constant
( P *  1 ), PPP holds, prices are fully flexible and full employment is always met
( Y f  432 ). The real interest rate is the same at home and abroad and equals 5%. In this
economy the money demand is given by mD  Y 20i .
a) Assume first that agents expect the money supply to remain constant at M=432.
Describe the money market equilibrium, assuming that the peg is credible. How does
the interest parity condition look like in that case?
b) Consider now the case where, unexpectedly, the central bank abandons the fixed
exchange rate regime and the nominal money supply starts increasing at 20% per year.
What would happen to the interest rate, real money demand and the price level at the
time of the surprise?
c) Instead of assuming that agents are taken by surprise, consider a case where agents have
rational expectations and perfect foresight. At moment zero, the central bank balance
sheet is as follows: M  eBC*  BC  382  50 . In the years that follow, the domestic
credit component expands 20% each year. Assuming that the domestic credit expansion
is fully sterilized by a foreign market intervention:
c1) Describe the central bank balance sheet at t=2, and compute the backing ratio.
Would it make sense for economic agents to launch a speculative attack at that date?
Explain.
c2) Assuming that there was no attack at t=2, describe the central bank balance sheet at
t=3, and compute the backing ratio. Would it make sense for economic agents to launch a
speculative attack at that date? Explain.
c3) Assuming that there was no attack at t=3, describe the central bank balance sheet at
t=4. Would it make sense for economic agents to launch a speculative attack at that date?
Explain.
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15.14. The initial assets of a central bank in an economy with flexible prices are given by:
eBC*  1072 and BC  128 pesos. Further assume that the money multiplier is equal to one
and that the real money demand is given by mD  Y 10i , where Y=120 is output and i is
the nominal interest rate. The real interest rate is 5%. In this economy, PPP holds and the
foreign price level is P*  1 .
a) Describe in a graph the money market equilibrium. Find out the equilibrium level of
prices and of the exchange rate.
b) Suppose that there was a fall in output to Y=110. If the central bank didn’t intervene in
the foreign exchange market, what would be the implications for prices and the
exchange rate?
c) Considering the shock in question b), describe the two possible intervention avenues the
central bank could follow to avoid the inflationary impact. On the basis of your answer,
explain why many central banks in the world have been building up large stocks of
foreign reserves.
d) Returning to the case with Y=120, suppose now that the central was forced to expand
domestic credit by 25% each year, maintaining at the same time a fixed exchange rate
regime. Find out the timing of the (unavoidable) speculative attack.
15.15. Consider an economy with flexible prices, where PPP and the Fisher effect hold
instantaneously. Further assume that the real interest rate is 5%, the money demand is
given by mD  60 i , and the foreign price level is constant at P *  1 . In this economy, the
central banks holds a stock of foreign reserves equal to eBC*  2000 , and is engaged in a
continuous, non-sterilized, expansion of domestic credit, BC , so that money supply in
increasing 25% each year.
a) Describe in a graph the money market equilibrium of this economy, as well as the time paths of the price level, the exchange rate and the nominal interest rate. b) Assume now that, at the time the domestic money supply reached M=12000, the central bank unexpectedly decided to anchor the money supply at that level. Find the new interest rate and money demand. Describe the new money market equilibrium in a graph. Find out what would happen to the price level and to the nominal exchange rate. c) Departing from k, assume instead that, at the time the exchange rate reached the level e=60, the central bank irrevocably fixed it at that level, and refrained from expanding further the domestic credit. In that case, how would the equilibrium in the money market be achieved? Describe the adjustment, and quantify the impact on the central bank balance sheet. 44
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