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Politicas macroeconomicas, handout and exercises, Miguel Lebre de Freitas ([email protected])

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06/03/2020 https://mlebredefreitas.wordpress.com/teaching-materials/

15. Money, prices and exchange rates in the long run

Index:

15. Money, prices and exchange rates in the long run ................................................... 1

15.1 Introduction ........................................................................................ 2 15.2 The basic model ................................................................................. 2

15.2.1 Consumers.................................................................................................. 2 15.2.2 The general government ............................................................................ 4 15.2.3 Balance of payments .................................................................................. 6 15.2.4 Optimal consumption and money demand ................................................ 7 15.2.5 Arbitrage conditions................................................................................... 8 15.2.6 Steady state ................................................................................................ 9 Box 1. Money growth, inflation, and exchange rate depreciation in Angola ...... 11

15.3 Nominal anchors .............................................................................. 11 15.3.1 Tying down the price level ...................................................................... 11 Box 2: The N-1 rule ............................................................................................. 12 15.3.2 Nominal Anchors and exchange rate regimes ......................................... 13 15.3.3 The long run dilemma .............................................................................. 15 15.3.4 Two-country considerations..................................................................... 15

15.4 Money, prices and the exchange rate under flexible exchange rates17 15.4.1 What happens when M unexpectedly increases once-and-for-all? .......... 17 15.4.2 What happens when the money demand unexpectedly decreases? ......... 20 15.4.3 What happens when the money supply is expected to increase? ............. 21 15.4.4 Anchoring under float .............................................................................. 23

15.5 Money, prices and the exchange rate under fixed exchange rates ... 25 15.5.1 Sterilized credit expansion ....................................................................... 27 15.5.2 Fall in money demand .............................................................................. 28 15.5.3 Devaluation .............................................................................................. 29 15.5.4 Pegged exchanges rates: pros and cons ................................................... 31

15.6 Inflation and inflation stabilization .................................................. 32 15.6.1 Equilibrium with inflation........................................................................ 32 Box 3: Money demand during the Bolivian hyperinflation ................................. 33 15.6.2 Unexpected increase in the rate of money growth ................................... 34 15.6.3 Money based stabilization........................................................................ 35 15.6.4 Exchange rate-based stabilization ............................................................ 37 Box 4. The end of Bolivian hyperinflation .......................................................... 39

15.7 Currency crisis ................................................................................. 39 15.7.1 Unsustainable credit expansion – naïve case ........................................... 40 15.7.2 The speculative attack .............................................................................. 41 15.7.3 The timing of the currency collapse......................................................... 42

15.8 Main ideas ........................................................................................ 43 Further reading ............................................................................................. 44 Appendix 1 – Optimal consumption and money demand ............................ 45 Review questions and exercises ................................................................... 46

Review questions ................................................................................................. 46 Exercises .............................................................................................................. 47


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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 the

corresponding market clearing levels. In the long run, the economy operates at full

employment, and the classical dichotomy holds: real variables, such as the real interest rate,

consumption and the current account are determined on the real side of the economy, while

nominal magnitudes, such as the price level, the nominal interest rate, and the nominal

exchange rate, are determined by the quantity of money.

Because under flexible prices money brings no novelty to the real side of the

economy, in this handout we abstract from the question of how real output is determined, to

focus on the determination of nominal magnitudes. This handout is organized as follows. In

Section 2, we describe the main model. In Section 3 we discuss the long-run constraints

underlying the choice of an exchange rate regime. In section 4, we analyse how the economy

responds to money demand and money supply shocks under a floating exchange rate. In

Section 5, we describe the operation of a fixed exchange rate regime. In Section 6, we

describe an equilibrium with inflation, and we discuss alternative avenues to achieve nominal

stability. In Section 7 we address the problems raised by a fiscal policy that is inconsistent

with a fixed exchange rate regime. Section 8 summarizes the main ideas.

15.2 The basic model

Consider a small open economy inhabited by a large number of infinitely lived

households. Households have perfect foresight and are endowed with an exogenous stream of

a consumption good (Q), which price is determined in the global economy. The household

may hold three assets: an international bond, a bond issued by the domestic government, and

domestic money. The government collects taxes from households and issues bonds to finance

its overall deficit. Government bonds and foreign bonds are perfect substitutes. The central

bank prints money backed by government debt or by foreign assets.

15.2.1 Consumers


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The typical consumer holds three types of nominal assets: government bonds ( GPD ),

foreign bonds ( *PB ), and domestic money (M). Denoting the nominal exchange rate by e , the

nominal value of the household’ net worth is:

*GP P PB D eB M (1)

Taking differences in (1), we obtain the change in the consumer’ net worth:

* *GP P P PB D e B M eB (2)

The term in brackets must match the consumer’ savings, while the second term

corresponds to valuation changes. The consumer’ disposable income consists in Q units of

output minus a lump sum tax (T) plus interest income. The disposable income is used for

consumption (C), and savings ( PS ):

* * *G GP P P P PS P Q T iD i eB PC D e B M (3)

In equation (3), the term in brackets corresponds to the household’ disposable income.

Solving together (2) and (3), we obtain the household’ flow budget constraint:

* * *GP P P P

eB P Q T C iD i eB eB

e

(4)

In what follows, it will be convenient to express the main variables in real terms.

Defining m M P , G GP Pd D P , and * *

P Pb eB P , the real value of the consumer’ net wort

is:

*GPP P P

Bb m d b

P (5)

Dividing (4) by the price level and using 2

P P PP P

P B B P Bb b

P P

, where

P

P , one obtains the change in the household’ net worth in real terms:


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* *GP P P P

eb Q T C id i b b

e

(6)

Since domestic and foreign bonds are perfect substitutes and there is perfect capital

mobility, absence of arbitrage opportunities implies that the individual must be indifferent

between holding domestic bonds and foreign bonds. Hence1:

* ei i

e

(7)

Equation (7) is the uncovered interest rate parity (UIP) condition. Using (5) and (7),

equation (6) can be re-written as:

P Pb Q T C rb im (6a)

Where we defined the real interest rate as:

r i (8)

Equation (6a) reveals that holding money comes at a loss in terms of foregone

interest. The nominal interest rate on domestic bonds is the opportunity cost of holding

money. The presence of money therefore opens a channel through which a nominal variable

may affect the real value of private sector wealth.

15.2.2 The general government

The central bank issues money, backed by purchases of foreign assets, *CeB and

government bonds, GCD . The central bank balancesheet identity is as follows:

*GC C CD eB M NW (9)

1 Formally, you can obtain (7) by choosing *Pb and G

Pd so as to maximize (6) subject to (5).


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Where CNW refers to the central bank’ net worth. When the central bank creates

money buying foreign assets ( *CM e B ), we say that there is a foreign exchange market

intervention. When the central bank creates money by purchasing government bonds

( GCM D ) we say there is debt monetization. When the central bank offsets the monetary

impact of its intervention in one market conducting a symmetric operation in the other

market, there is a sterilized intervention: * 0GC CM D e B .

Changes in the central bank’ net worth are related to interest income and valuation

changes, that is:

* * *GC C C CNW iD ei B B e (10)

From the balancesheet identity, the condition * *GC C C CNW M D e B B e

must hold. Substituting this in (10), we obtain the flow budget constraint of the central bank:

* * *G GC C C CD e B M iD i e B (11)

The central government finances its budget deficit issuing bonds. The corresponding

budget constraint is:

( )G G G GC P C PD D iD iD P G T (12)

The consolidated budget constraint of the general government is obtained from (11)

and (12):

* * *( )G GP C C CM D e B P G T iD ei B (13)

Since the government owns the central bank, the interest paid by the government to

the central bank cancels out in the consolidated account. Equation (13) shows that the general

government deficit can be financed in three ways: printing money, selling bonds to the

private sector, and selling reserve assets.

Dividing both terms in (13) by the price level, defining * *C Cb eB P , using

* * * ** *

2C C C C

C C

Pe B PB e eB P e B eb b

P P e

and the UIP condition (7), one

obtains the real counterpart of (13):

* *( )G GP C P Cd b G T r d b m m (14)


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The last term in equation (14) corresponds to the government seigniorage revenues.

Seigniorage revenues correspond to the amount of goods the government can buy with

money creation. As you can easily check:

Rev

MS m m

P

(15)

Equation (15) shows that seigniorage revenues can be split into two components: the

increase in the public’ demand for real money balances (the first term in the right-hand-side),

and the erosion in the real value of money because of inflation (the second term). The later is

coined inflation tax, because it implies a transfer of purchasing power from money holders to

the central bank that is proportional to the inflation rate. In a steady state with 0m ,

seigniorage revenues are equal to the inflation tax.

15.2.3 Balance of payments

Consolidating the general government with the private sector, one obtains the

country’ aggregate accounts vis-à-vis the rest of the world. The flow budget constraint of the

economy is obtained from (14) and (6a):

* * * * *P C P Cb b b Q C G r b b (16)

Equation (16) is the balance of payments identity: it states that the change in the

country’ NIIP (the current account) must equal to the sum of the trade balance with the Net

financial income from abroad (NFIA). Note that the redistributive effects of money holdings

and of taxation cancel out across domestic agents, and do not show up in the balance of

payments identity2.

2 This is true because we are assuming that domestic agents do not hold foreign monetary assets. Otherwise, there would be an international redistribution of income, amounting to the seigniorage revenues accruing to the foreign central bank.


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An alternative way of presenting the balance of payments identify is to split the

financial account into changes in central bank’ reserves (official settlements balance) and the

non-reserve component of the financial account:

* * * *C P P Cb b Q G C r b b (16a)

This presentation emphasizes the impact of private international transactions on

central bank reserves, and thereby on the money supply.

Figure 1 displays the balance sheets of the four sectors in this economy.

Figure 1 – Balance sheets

M

*PeB

GPD

HouseholdsCentral bank

MGCD

*CeB

Government

GCDGPD

Foreign

*PeB*CeB

P PNW BCNW

GGNW D * *NW B

15.2.4 Optimal consumption and money demand

If monetary assets were useless, the consumer would naturally avoid the cost of

holding money, allocating its total wealth to domestic and foreign bonds, only. However,

money provides liquidity services, in the sense that it reduces the costs of transacting in the

goods market. This explains why money is held, despite being dominated by interest bearing

assets. A simple way of modelling the benefits of holding money is to include money as an

argument in the household’ utility function. In what follows, we adopt a very simple

functional form:

, ln lnu c m c k m (17)

The household maximizes (17) each period subject to the budget constraint (6a).

Continuous optimization requires the equality between the marginal rate of substitution

between money and consumption and the corresponding relative price, which is the nominal


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interest rate. Given (17), the marginal rate of substitution between money and bonds is

, 0c m

dc kcMRS

dudm m

. Setting this equal to the nominal interest rate delivers the

optimal demand for money (for technical details, see Appendix 1):

,d cm c i k

i (18)

Equation (18) states that the demand for money depends positively of real

consumption and negatively on the opportunity cost of holding money3. The term k/i can be

interpreted as the velocity of money: when the nominal interest rate increases, people

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 increases4.

The fact that the real money demand depends on a nominal magnitude (the nominal

interest rate) does not constitute a violation of the classical dichotomy, that states that when

prices are flexible, the real side of the economy is independent of money. The demand for

real money belongs to the monetary side of the economy, and the fact that is influenced by

the nominal interest rate only produces nominal consequences, as we will see next.

15.2.5 Arbitrage conditions

Since in this model there is only one good and trade is frictionless, the purchasing

power parity holds:

*P eP (19)

Log-differentiating both sides, we obtain the relative PPP condition:

3 Note that a micro-founded money demand in general depends on private consumption rather than on income.

4 More generally, money velocity shall be influenced by third factors, like technological progress and macroeconomic uncertainty, which are reflected on k. 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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*e

e (20)

Substituting the later in the UIP condition (7), one obtains:

* * *i i r (21)

Or, in alternative:

*r r (21a)

This equation states that the domestic real interest rate must equal the international

real interest rate. It is labelled the real interest rate parity condition.

15.2.6 Steady state

In the characterization of the steady state, we assume that the rate of time preference

is equal to the international real interest rate. Under this assumption, consumption is constant

over time and equal to the household “permanent income”. We abstract from short term

deviations from permanent income, assuming that output and government expenditures are

constant over time ( Q Q and G G ). Since in that case there is no income variability to

smooth out, the current account is zero each year, and the economy’ net international

financial position remain equal to the initial level, *0b (see appendix 1 for details).

Setting * 0b in (16), and using Q Q , and G G , private consumption each year

becomes equal to the (exogenous) permanent income, Y :

*0C Q G rb Y (22)

In (22) , we see that private consumption is independent of money. Substituting (22)

in the demand for money, we obtain:

,d Ym Y i k

i (18a)

The money market equilibrium corresponds to the equality of money demand and

supply:

,dMm Y i

P (23)


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Taking into account the parity conditions, the money market equilibrium cans also be

described as:

**

,dMm Y r

eP (23a)

When the money demand takes the specific functional form (18a), the equivalent to

(23a) is:

* *

M Yk

eP r

(23b)

To find out the equilibrium inflation rate, one must assume some behaviour for the

supply of money. A steady state is thought to characterize an equilibrium where all

exogenous variables remain invariant. This applies to monetary policy. Hence, a steady state

will be described by a constant rate of money growth, :

M

M

(24)

In what follows, we focus on a “well behaved equilibrium” where the inflation rate -

and henceforth the real money demand - is constant over time5. Log-differentiating both sides

of (23) under 0 , one obtains 0M M P P , or:

(25)

Thus, in the steady state, the inflation rate is equal to the rate of money creation6.

Using this in (21), the nominal interest rate becomes determined:

5 Note that this is not the only solution of the model. A constant rate of money growth (24) is also consistent with an ever-accelerating inflation rate, coupled with an ever-decreasing money demand (hyperinflation). This case is discussed in a different handout.

6 Since consumption is constant over time, the demand for money is constant in the steady state. But the model could easily be extended to the case of a growing economy. To see this, just assume for a moment that the rate of time preference was lower than the real interest rate, implying that consumption was increasing over time at the rate r . In that case, the growth rate of money demand in a well-behaved steady state

would be m m . Log-differentiating both sides of (23) would deliver . Intuitively, the


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*i r (26)

Box 1. Money growth, inflation, and exchange rate depreciation in Angola

Figure 2: Inflation, money growth and exchange rate depreciation in Angola, 1991-2004.

0%

500%

1000%

1500%

2000%

2500%

3000%

3500%

4000%

4500%

5000%

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

Exchange rate depreciation

Money growth

Inflation

Source: IMF, International Financial Statistics.

15.3 Nominal anchors

15.3.1 Tying down the price level

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, and unit of account).

Sometimes, government engage in excessive money printing. This may happen

because central banks are requested to finance government deficits or to rescue failed banks.

equilibrium inflation rate would be equal to the growth rate of money supply in excess of the growth rate of the transactions demand for money.


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Inflation, however, is bad news. When inflation is high and variable, economic planning

becomes more difficult for private agents, 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 comes along with undesirable transfers of income from the

public in general to the central bank and (when unexpected) between debtors and creditors.

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. A nominal anchor is some rule

that the central bank adopts for the behaviour of a variable measured in units of domestic

currency, with the aim to tie down the relationship between money and the price level. This

variable might be the exchange rate, the money supply or a price index. Once the path of this

nominal magnitude is determined, all other prices are determined accordingly.

Box 2: The N-1 rule

A key question that arises is what determines the purchasing power of fiat money.

Why should a note of 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 is a matter of convention.

To illustrate how prices are determined in units of a currency, let’s consider first a

world without money. 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), and that 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 is automatically

determined.


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Now, let’s add a fiat currency (say pesos) to this set of goods. In contrast to pizzas,

pencils and bicycles, pesos are pieces of paper without intrinsic value. The price of a peso bill

cannot be assessed by real-side considerations. Hence, some coordination must be achieved

on the demand side. Coordinating the agent’s expectations regarding the purchasing power of

a currency is the key role of central banks. If the central bank manages to convince the public

that one peso shall be traded for one pizza, then the bicycle will cost 100 pesos and the pencil

will cost 20 cents. If the central bank establishes that one peso is the price on one pencil, then

the pizza will cost 5 pesos and the bicycle 500.

Whether the central bank decides to adopt the pencil or the pizza as nominal anchor, it

is only a matter of convention: in either cases, once the value of an anchor in determined in

currency units, all the other prices will be determined accordingly. On the real side of

economy, relative prices are determined independently of the currency units in which is

output is measured. What the central bank shall not do is to adopt two anchors at the same

time: if the central bank decided that one peso was the right price for a pencil and that one

peso was the right price for a pizza, that would be violating the N-1 rule, opening the window

for arbitrage opportunities.

15.3.2 Nominal Anchors and exchange rate regimes

In the past, a widely adopted nominal anchor among central banks was the price of

gold. By adopting a gold standard – say, declaring that one ounce of gold is equal to 35 pesos

– a central bank provides a benchmark, allowing all other prices in terms of the domestic

currency to be determined. Of course, for this anchor to be credible, the central bank must

subordinate the monetary policy to that goal, standing ready to buy or sell any amount of gold

for domestic currency at the announced price. As a corollary, the central bank will be unable

to choose the quantity of money in circulation.

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.

When a central bank decides to peg its currency to the price of gold, it must be ready 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 deflation caused by

gold discoveries or by gold scarcities where common during the Classic Gold Standard

(1821-1914).


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In today’s world, the most common nominal anchors are money targeting (committing

with a given path for the money supply), exchange rate targeting (committing with a certain

path for the exchange rate), and inflation targeting (committing with a certain 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.

When the central bank elects the exchange rate as nominal anchor, is said to follow a

predetermined exchange rate regime. In a pre-determined exchange rate regime, the central

bank stands ready to buy or sell any amount of foreign currency at the announced exchange

rate. Exchange rate targeting includes the stricter case in which the exchange rate is set to

remain constant over time against a single currency or against a basket of currencies (fixed

exchange rate regime), and other modalities, where the exchange rate is not exactly constant

over time, but it follows some predetermined rule. This includes, for instance, allowing the

nominal exchange rate to devalue at a constant rate (crawling peg), or to vary inside a narrow

band (target zone). 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.

When the central bank adopts a nominal anchor other than the exchange rate, it is said

to follow a flexible exchange regime. In a flexible exchange rate regime, the central bank

refrains from intervening in the forex market, to keep the ability to influence other variables,

such as the money supply or the domestic interest rate. 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 currencies7, or simply to build up foreign reserves. When the Central

Bank declares a float but keeps an eye on the exchange rate and intervenes in the foreign

7 In the short run, prices are sticky, and hence the nominal exchange rate can deviate quite significantly from the parity condition (19). 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.


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exchange market from time to time, it is said to follow a managed float (or dirty float)

regime. This is more common in emerging economies8.

15.3.3 The long run dilemma

Adherence to a nominal anchor helps promote price stability. But it also implies the

subordination of the central bank’ actions to that goal. When the central bank adopts one

nominal anchor, it must abdicate from the temptation of influencing the path of other nominal

variables.

To illustrate this, consider again the money market equilibrium condition (23a).

Rearranging, and using (25), we get:

* *,dMP m Y r

e (27)

Since the variables on the right-hand-side of (27) are all determined, this means that

the left-hand side is equal to some given value. The equation therefore implies that M and e

cannot be chosen independently: 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 mentioned above.

Equation (27) summarises the long run dilemma that underlies the choice of a monetary

regime in the long run.

15.3.4 Two-country considerations

8 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). In September 2000, following a summit of the G7 in Prague, there was also a coordinated intervention by the major central banks to contain a depreciation of the euro that was considered excessive.


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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 might 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:

**

*dM

mP

(23c)

Solving for *P , using (23) and substituting in (19), one obtains:

*

*

d

d

M me

M m (28)

This equation reveals that the exchange rate between the two currencies must be

unique9. Hence, it will be unfeasible for the two monetary authorities to pursue independent

targets for the exchange rate. Considering (28), 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,

when Argentina pegs its currency to the US dollar, it is up to the Argentinean

central bank to adjust its policy in order to maintain the parity10.

2. Both central banks choose the respective money supplies at their own discretion,

and the bilateral exchange rate is free to vary (floating exchange rates).

3. Both countries are committed to adjust the respective money supplies to achieve a

common exchange rate target (cooperative peg)11.

9 More generally, in a World with N currencies, there are only N-1 exchange rates.

10 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 however committed to convert dollars into gold at $35 per ounce. 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”.

11 An example of cooperative peg was the Exchange Rate Mechanism of the European Monetary System that preceded the Euro. When for instance the Portuguese Escudo was devaluing relative to the Deutsche


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15.4 Money, prices and the exchange rate under flexible exchange rates

In a flexible exchange rate regime, the central bank preserves the ability to influence

the quantity of money in circulation. In the context of our model, a monetary expansion

without foreign exchange intervention can be achieved buying government bonds from the

private sector12:

G GC PM D D (29)

Once the quantity of money is set, the nominal exchange rate adjusts endogenously to

clear the money market:

* d

Me

P m (27a)

In what follows, we examine what happens to the nominal variables in the model

under a floating exchange rate. To keep the discussion simple, exogenous changes in money

supply and in the money demand thought to be unexpected and once-and-for-all: agents

didn’t forecast the change before it occurred, and do not expect a new change in the future.

15.4.1 What happens when M unexpectedly increases once-and-for-all?

Consider an initial steady state where the money supply is constant, say at 0M . Since

in this case 0 , we know that the inflation rate is zero, 0 (eq. 25), and the nominal

interest rate is be to the foreign real interest rate, *i r (eq. 26). The initial equilibrium is

represented by point 0 in the left-hand panel of figure 3. Without loss of generality, let’s

assume that * 1P , implying P e (eq. 19).

Mark, the central banks of both countries were required to intervene, buying the weak currency and selling the strong currency to enforce the targeted parity.

12 Alternatively, one may assume that the government sells new debt directly to the central bank to finance a tax cut (“helicopter money”). Since the Ricardian equivalence holds, the effect will be qualitatively the same.


18


Figure 3: Adjustment to a (once-and-for-all) monetary expansion under float

t1

t

M

m

i

t

t

t

0M

1M

*i r

0m

i

M/P

i = r*

( , )m Y i

0=1

M1/P1 =M0/P0

t1

P=e

1P

0P

Gd

Gd

GPd

t

GCd

Now suppose that at t=t1 the central bank unexpectedly decided to expand the money

supply, once-and-for all, to 1M . Since prices are flexible, the real side of the economy,

including consumption, is unaffected. In terms of figure 3, this means that the curve

describing the money demand does not shift. On the other hand, since the change in the

money supply is once-and-for-all, the rate of money growth after t=t1 will be zero ( 0 ).

Hence, the interest rate will remain constant, at *i r , implying that he right-hand-side of

equations (23) does not change.

If the right-hand side of equation (23) remains unchanged, the value in the left-hand

side must remain unchanged too. Thus, any change in the numerator (money supply) must be


19


accommodated by a proportional increase in the denominator (price level). In terms of figure

2, the new equilibrium (point 1) is equal to the old equilibrium (point 0), with the difference

that the nominal money supply is now higher, and the price level is also higher13. The only

effect of the monetary expansion was a proportional increase in the price level14.

Note that for the price level to increase, the exchange rate must have increased. To get

the intuition of this, let’s go back to equation (29), which states that the monetary expansion

is achieved through a purchase of government bonds from the private sector. Households will

find themselves with too much money and will try to get rid of it, buying bonds. Since the

supply of domestic bonds is given, there will be an excess demand for foreign bonds, giving

rise to an excess demand for foreign currency in the foreign exchange market. Since the

central bank does not intervene in the forex market, there is an immediate exchange rate

depreciation15.

As far as wealth effects are concerned, the increase in the price level comes along

with a capital loss for holders of money and domestic bonds. The real value of foreign bonds,

in contrast, does not change, because prices and the exchange rate evolve proportionally. In

figure 3, the private sector loss is captured by the decline in the real value of government

bond held by the public: first, because there was an initial sale of domestic bonds to the

central bank, by the exact amount of money needed to restore the real value of monetary

assets; second, because a higher price level erodes the real value of domestic bonds. This loss

by the private sector corresponds to a gain by the general government. As long as government

13 Note that all the required adjustment in the price level takes place at the exact moment of the shock, with no further change. That is, inflation will be extremely high during one second, and will return to zero immediately after the shock.

14 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: in that case, from (23), any increase in M can only be accommodated by a decline in the nominal interest rate or by an increase in private consumption. Accordingly, in the Keynesian model, prices and money are exogenous, while output and the nominal interest rate are endogenous. In the model above, prices are flexible, output and consumption are exogenous in respect to money, and the price level is endogenous: the real money supply is determined by the money demand.

15 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 must decrease when money supply expands ahead of real money demand.


20


expenditures remain constant, however, the government gain will be transferred to

households in the form of lower taxation in the future. All-in-all, only the composition of

government finance between money and taxes has changed. Like in the Ricardian

equivalence case, the consumer life-time wealth is not be affected, and private consumption

remains unchanged.

This example illustrates the classical neutrality of money: 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 output.

15.4.2 What happens when the money demand unexpectedly decreases?

Now, let’s consider an unexpected fall in the money demand, assuming that the

money supply remains constant ( 0 ). This can occur, for instance, when the household’

permanent income decreases16, or when parameter k declines (this parameter can be thought

as capturing the state of the payments technology). In either case, the demand for money will

shift leftwards, as illustrated in figure 4.

To find out the path of the nominal variables in the model, first note that, since the

growth rate of money is zero, and the money demand shock is once-and-for-all, inflation

must remain equal to zero immediately after the shock. Hence, *i r . Referring to figure 4,

the equilibrium must occur in point 1, with an unchanged nominal interest rate, but with a

lower demand for money. Since the nominal money supply does not change, the equilibrium

in the money market requires the price level to increase. In terms of figure 4, there is a jump

in the price level, so that the real money supply schedule shifts to the left, meeting the money

demand at point 1. Remember that in this model, the real money demand determines the real

money supply.

Figure 4: Adjustment to a once-and-for-all fall in money demand under money targeting.

16 In case the fall in money demand is caused by a decline in Q, there is an immediate fall in consumption, because the shock is permanent. The CA remains unchanged.


21


t1

t

M

i

t

t

t

0M

*i r

0m

i

M/P

i = r*

M0 /P1

t1

P=e

1P

0P

Gd

Gd

GPd

( ', )m Y i

( , )m Y i

1m

m

M0/P0

t

GCd

10

As before, underlying the increase in the price level there is a nominal exchange rate

depreciation. The intuition is as follows: the original decrease in the demand for money

caused an excess supply of money, so that agents tried to buy foreign assets, generating an

excess supply for foreign currency. Since the central bank does not intervene in the foreign

exchange market, the currency depreciated.

As for wealth effects, the increase in the price level eroded the value of government

bonds held by the private sector. If however government expenditures remain unchanged, this

will translate into lower taxes in the future, without affecting the private sector’ permanent

income.

15.4.3 What happens when the money supply is expected to increase?

In the previous exercises, we analysed the impact of unanticipated changes in money

demand and in money supply. In these cases, there is a jump in the price level at the time of

the announcement. Since a jump in the price level comes at a loss for money and bond

holders, it can only occur if agents are caught by surprise: if agents knew that the exchange

rate was to increase, they would try to protect their claims in advance, getting rid of domestic


22


assets and buying foreign bonds. This, in turn, would cause a decline in the money demand

and an exchange rate depreciation ahead of the policy change.

To illustrate this, we refer to figure 5. In the figure, it is assumed that the money

supply will jump from 0M to 2M at time t2, but people become aware of the policy change

before it happens, at time t1<t2. Because the surprise occurs at time t1, it is at time t1 that the

price level jumps. As shown in the figure, at time t1 there is capital loss related to the fall in

the value of real money balances and of real bonds. The increase in the price level at t1

occurs because agents, surprised by the announcement, try to get rid of money, increasing

their demand for foreign assets, and thereby causing the exchange rate to depreciate.

The adjustment in money demand at t1 does not bring however the price level to its

final value, 2P . Intuitively, for the money demand to keep declining, the interest rate must be

increasing, and this is only be possible with an increasing inflation rate before point 2 is

reached. In the figure, we see that the money demand jumps initially from 0m to 1m , causing

the price level to jump from 0P to 1P , and then it decreases slowly over time until reaching

2m (we denote for t2- the time immediately before t2). The decrease in the money demand

from t1 to t2- is necessary for the price level to keep increasing. Moreover, the fall in the

money demand must be such that the price level is in fact accelerating, delivering an

increasing nominal interest rate, as this is what is required for the money demand to keep

decreasing until t2-.

The pattern described in Figure 5 is determined by the need to avoid a price jump at

time t=2, which would be inconsistent with absence of arbitrage opportunities. Since the

increase in money supply is anticipated, agents are adjusting their asset holdings to avoid a

capital loss. At time t2-, the money demand must be exactly at the level that is needed to be

driven to the new steady state by the increase in nominal money, from 0M to 2M . After t2,

the money supply is constant and the money demand is also constant, at the level implied by

the foreign real interest rate.


23


Figure 5: Adjustment to an expected increase in money supply

t1

t

M

i

t

t

t

0M

*i r

0m

i

M/P

M0 /P2

t1

P=e

1P

0P

Gd

Gd

GPd

( , )m Y i

1m

m

M0/P0

=M2/P2

t

GCd

1

0=2

2M

t2t2

*i r

1i

2i

M0 /P1

2-

2P

0m1m

2m

2m

1i

2i

This example shows that when agents forecast a monetary expansion, they will react

at the time of the announcement getting rid of money and causing inflation to increase ahead

of money. The implication in a context of uncertainty is that inflation can arise just because

of wrong expectations: even if it is not the intention of the central bank to expand the

monetary policy, if agents believe in that possibility, they will try to get rid of money in

advance, causing inflation to materialize. The central banks would be punished by a crime

that he did not commit. Credibility is a key ingredient for nominal stability.

15.4.4 Anchoring under float

Under floating exchange rate regime, the central bank preserves the ability to

influence the money supply. At the first sight this looks like a good thing. However, it raises

an important question: how can economic agents be so sure that the central bank will not

expand the money supply in the future without announcement, to achieve a transfer of

resources from the private sector to the general government? To protect citizens from such

risk, an anchor must be adopted.


24


Because the story of high inflation is also a story of excessive money printing, a

natural avenue is to elect the money supply M as nominal anchor. Under money supply

targeting, the central bank sets a path for the quantity of money, and adjusts its policy tools

(for instance, purchases of government bonds) to meet the target. As we just saw, however,

setting the quantity of money to remain constant over time only delivers price stability in case

the demand for real money, m, remains stable. If the money demand is unstable (that is, if it

shifts up and down unpredictably) setting a fixed target for M will not deliver price stability.

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 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 the fixed exchange rate regime, in 1971. But since then, financial

innovation and globalization have challenged the stability of money demands all around the

world, leading most central banks to progressively abandon money targeting and seek for

alternative nominal anchors under float17.

A nominal anchor that is very popular in our days is the so-called inflation targeting,

pioneered by New Zealand in 1990. Under inflation targeting, the central bank announces a

“target” for the inflation rate over the medium run, and then it attempts to reach the

announced target adjusting all its monetary policy tools as necessary. This includes

expanding the money supply in face of an increase in the money demand and contracting the

17 The Federal Reserve abandoned quantitative money targets after realizing that the velocity of money became instable in the 1970s, in 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 has been allowed to expand differently from the target, and in 2003 the ECB stopped announcing targets for the money supply, to focus instead on a “medium run objective”: an inflation rate of 2%, on average. Even though, in the current ECB framework, money still plays a very important role, as the “second pillar” of its monetary policy strategy.


25


money supply in response to a fall in money demand18. Inflation targeting 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, to meet the rule

(“instrumental independence”). A problem with inflation target, is that data on inflation takes

longer to collect and its subject to interpretations. Because the link between monetary policy

and the inflation rate is not immediate, inflation goals are defined over a medium run horizon,

and are intended to be reached on average. The other side of the coin of setting targets over

the medium term, is that it is necessary to judge each moment in time whether existing

deviations from the “medium term target” will vanish over time or constitute a policy

concern. Moreover, inflation may be tilted by factors that are out of the control of the

monetary authorities, such as changes in commodity prices, making it difficult for citizens to

judge accurately the central bank commitment. The credibility of inflation targeting 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

15.5 Money, prices and the exchange rate under fixed exchange rates

In a pre-determined 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

announced exchange rate. Of course, this will only be possible if the central bank has

reserves enough to intervene in the foreign exchange market: whenever this is not the case,

18 In our model, with flexible prices, the key policy instrument is the quantity of money. In the real world, however, most central banks elect instead the money market nominal interest rate as the main tool of monetary policy. Following an interest rate rule automatically implies that the quantity of money will adjust in face of velocity shocks. 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 to fall) when the inflation rate is below target. Such strategy can only be discussed, however, in a context of sticky prices, being therefore beyond the scope of this handout.


26


convertibility cannot be enforced, and the central bank must give up the exchange rate

regime19.

A key measure to evaluate the central bank “firepower” is the “backing ratio”:

*ceB M (30)

The “backing ratio” gives the proportion of money that the central bank could

potentially buy back with its reserve holdings, at the current exchange rate. When the backing

ratio is equal to zero, the central bank has no foreign reserves 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 reserves at the current exchange rate. Some

countries engaged in fixed exchange rate regimes commit themselves with a backing ratio not

less than one, to signal full convertibility of their currencies20. These hard peg regimes are

called “currency board”21.

In what follows, let’s assume that the targeted exchange rate is constant over time,

that is, ee . In this case, the domestic price level is determined as follows:

*P eP (31)

When the central bank targets the exchange rate, it must abdicate from influencing the

money supply. Once the exchange rate is set, the money supply becomes endogenously

determined according to (23):

19 Of course, a central bank without foreign reserves may set an “official exchange rate” administratively. 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 validate it with market intervention, the currency is “non-convertible”. In these cases, there will be an excess demand for foreign currency in the official market, creating the conditions for the emergence of a black-market premium.

20 Note that the backing ratio can be above one if the central bank borrows in domestic currency to buy foreign assets.

21 A currency board is a monetary regime where the commitment with the fixed exchange rate is subject to a specific law. Under this regime, domestic currency can only be issued if backed by reserve assets. Examples of currency boards include the Argentina’s convertibility plan (1991-2001) and Hong-Kong (1983-ownwards).


27


* dM eP m (32)

Equation (32) shows that the money supply shall be allowed to vary, in order to

accommodate price developments abroad or changes in the real money demand: 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 requires the central bank to let the

money supply adjust passively whenever a key exogenous variable changes.

The main mechanism through which the money supply adjusts to exogenous shocks is

the central bank’ intervention in the foreign exchange market. To see how the central bank

reserve assets must adjust, assume that the central bank decides first the amount of credit to

be extended to the government, and then accepts the amount of reserve assets to be

determined endogenously. Substituting (32) in (9), one obtains:

* * d GC C CeB eP m NW D (33)

This equation reveals that the central bank’ reserves are determined as a residual,

given the nominal demand for money implied by (32) and the amount of credit extended to

the government.

15.5.1 Sterilized credit expansion

To analyse the operation of a fixed exchange rate regime, we first examine what

happens when the central bank buys government bonds from the private sector, creating

money: G GC PM D D . As we already know, in the absence of any other policy action,

households will respond to this policy trying to get rid of the excess money, buying foreign

bonds. In a float, that causes a depreciation of the exchange rate. Since the central bank is

committed to a fixed exchange rate, it must step in the foreign exchange market, selling

foreign bonds. Thus, an offsetting move will take place, with the central bank buying back all

the money created before: *Ce B M . Equivalently, the central bank could have

“sterilized” the initial credit expansion from the very beginning, achieving immediately

* GC Ce B D . In one way or the other, the commitment with the fixed exchange rate

determines that only the composition of the central bank asset has changed, while the total

money supply remained tied to the level determined by the money demand and the exchange

rate (eq. 31).


28


All in all, the only effect of the sterilized credit expansion was decline in the central

bank’ baking ratio, matched by a symmetric move in the private sector’ balancesheet22.

Needless to say, a problem may arise in that extending too much credit to the government

may deplete the central bank from valuable reserves to defend the peg.

15.5.2 Fall in money demand

Consider an initial equilibrium under fixed exchange rates. For simplicity, assume

that * 1P , so that initially, 0 and the nominal interest rate is equal to the foreign real

interest rate ( *i r ). The initial equilibrium is represented by point 0 in the left-hand panel of

figure 6. Then, suppose that the demand for domestic money decreases (say, because the

household’ permanent income is revised downwards).

The fall in money demand causes an excess supply of money. Households will try to

get rid of the undesired liquidity buying foreign bonds, and this create a pressure for the

exchange rate to depreciate. To avoid the currency depreciation, the central banks must step

in, selling foreign bonds. When the central bank sells foreign bonds, the money supply

contracts in the exact amount to match the lower demand for money. The change in central

bank reserves matches the purchase of foreign assets by the private sector ( * * dCe B eP m ).

Comparing to the case under float (figure 4), we see that the change in money demand

did not translate into a higher price level. This means that, in a context where the money

demand is unpredictable, a fixed exchange rate regime is more likely to deliver price stability

than a rigid money target. For this to be true, however, the central bank must have firepower

enough to defend the peg.

Foreign reserves provide central banks with an important buffer to face eventual head

winds. This is especially true in the context of emerging economies and developing countries,

22 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”.


29


where the demand for domestic money can be destabilized by many factors. With no surprise,

along the last decades, many central banks in emerging markets tried to increase significantly

their holdings of foreign assets.

Figure 6: Adjustment to a fall in money demand under fix

t1

t

M

i

t

t

t

0M

*i r

0m

i

M/P

i = r*1

M1 /P0

t1

P=e*b

*Pb

( ', )m Y i

( , )m Y i

1m

m

0

M0/P01M

*0b

0e

t

*Cb

15.5.3 Devaluation

Consider again an initial equilibrium under a fixed exchange rate, where * 1P and

*0i r . This equilibrium is represented by point 0 in the left-hand panel of figure 7. Then

assume that, at time t=t1 the government decides to devalue the currency, changing the peg

from 0e e to 1e e . Since the devaluation is once-and-for-all, the expected depreciation

after t1 is zero. Thus, the interest rate remains unchanged at *i r and the demand for real

money balances does not change with the devaluation.

The devaluation causes an immediate increase in the price level that reduces the real

value of government bonds and of money balances. Facing an excess demand for money, the


30


consumer will try to rise liquidity, selling foreign bonds. This move creates a pressure for the

exchange rate to appreciate, but the central bank will deny it, buying the foreign bonds that

households are selling. In consequence, the nominal money supply expands. In the end, the

real money supply will be the same, but foreign bonds have changed hands. With no surprise,

devaluation is a recurrent avenue followed by centrals banks seeking to rebuild their

firepower.

Figure 7: Adjustment to an unexpected devaluation

t1

t

M

m

i

t

t

t

0M

1M

*i r

0m

i

M/P

i = r*

( , )m Y i

0=1

M1/P1 =M0/P0

t1

P=e*b

*0b

*Pb

1e

0e

t

*Cb


31


Regarding the private sector, the fact that the price level has increased translated into

an erosion of the purchasing power of money and in the real value of domestic bonds. The

devaluation acts as a transfer from the private sector to the government sector23.

15.5.4 Pegged exchanges rates: pros and cons

One of the main advantages of a fixed exchange rate regime is its simplicity.

Information on exchange rates is readily available to citizens, and the currency convertibility

can be tested by citizens at any time. This contrasts with money targeting and inflation

targeting, which are less easy to monitor by the public and to make credible by the central

bank.

When the central bank fixes the exchange rate, it becomes a passive importer of

foreign inflation (eq. 19). With no surprise, central banks in the real world choose carefully

the foreign currency to which they peg. The USD has been the most common anchor

currency, because the United States have a long record of price stability, but other currencies

such as the Euro and the British Pound have also been used as anchor currencies.

A caveat of pegged exchange rates is that the central bank becomes constrained on its

role as lender of last resort. If the central bank is requested to extend credit to the government

or to rescue a failed bank, all else equal, that will require the selling of reserves (sterilization).

If reserve assets reach a critical low level, the public confidence in the fixed exchange rate

system may erode, forcing the central bank to devalue the currency or even to abandon the

peg24.

23 In terms of our model, since government expenditures remain constant, this transfer today will give rise to lower taxation in the future, without producing life-time wealth effects.

24 Also note that a fixed exchange rate regime will only deliver a stable inflation rate in case the equilibrium real exchange rate remains invariant over time. Wherever the real exchange rate is destabilized, say because of Balassa-Samuelsson effects or due to terms of trade shocks, a fixed exchange rate regime will hardly deliver price stability.


32


15.6 Inflation and inflation stabilization

By now, we have analysed the implications of once-and-for-all changes in the

quantity of money supplied or in the money demand. In these cases, there is a once-and-for-

all change in the price level, implying that the inflation rate is equal to zero before and after

the shock. In this section we extend the analysis to the case in which the money supply is

growing over time, implying a positive inflation rate.

15.6.1 Equilibrium with inflation

Figure 8 describes a money market equilibrium with a positive inflation rate. In the

equilibrium described by point 1, the money supply is expanding continuously at the rate

1 0 , implying an inflation rate equal to 1 eq.25), and a nominal interest rate is

* *1 1i r r . In this equilibrium, the demand for real money balances is constant

because the nominal interest rate is constant, and the real money supply is constant, because

prices and money are evolving proportionally over time.

Figure 8: Money market equilibrium with a positive inflation rate.

i

M/P

*1 1i r

M/P

( , )m Y i

1

1m


33


The fact that the price level is increasing over time implies a continuous erosion in the

value of real money balances, corresponding to the inflation tax25:

*Re 1 1 1,v

MS m Y r

P

(15a)

Note that this equilibrium can either describe a case under float and steady increase in

the money supply, 1M M , or a case with a pre-determined exchange rate, where the

central bank determines the rate of devaluation to be constant over time 1e e (crawling

peg). Observationally, these two regimes will be equivalent.

Box 3: Money demand during the Bolivian hyperinflation

Figure 1 displays the quarterly inflation rate and money velocity in Bolivia along

1980-1994. During this period, Bolivia was hit by a hyperinflation, with quarterly inflation

reaching 500 percent in the second quarter of 1985.

As shown in the figure, during the hyperinflation episode, money velocity increased

sharply relative to the previous levels. This reflects the fact that, in a context of high inflation,

the cost of holding money increased dramatically, causing a fall in the demand for real money

balances.

Figure 1: Money velocity and Inflation in Bolivia, 1980-1994

25 Since in the steady state the real money demand is constant over time, seigniorage revenues are equal to the inflation tax.


34


0

100

200

300

400

500

0.4

0.8

1.2

1.6

2.0

2.4

1980 1982 1984 1986 1988 1990 1992 1994

Money Velocity Inflation

Quarterly Inflation (%) Money Velocity

Source: International Financial Statistics, IMF

15.6.2 Unexpected increase in the rate of money growth

Consider an economy under flexible exchange rates, that starts out with a constant

rate of money growth and zero inflation, as described by point 0 in figure 9. Then, at time

t=t1, the rate of money growth jumps to 1 0 . As we already know, the inflation rate

will jump permanently to the new level 1 (eq. 25), implying a similar jump in the

nominal interest rate to *1 1i r (eq. 26).

In light of (23), the increase in the rate of money growth 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 in a new, higher, level. In Figure 9, we

see that, the interest rate jump at the time of the regime change causes a decline in the

demand for money from 0m to 1m .

The fall in the demand for money must be accommodated by a fall in real money

supply. At the time of the policy shift, however, the nominal money supply is still at its initial

level, 0M (money will start increasing precisely at that moment). Hence, for the real money

supply to match the money demand, the price level must jump: in figure 9, this is illustrated

by a jump in the price level from 0P to 1P at the time of the shock. The jump in the price

level causes the real money supply to shift leftwards, meeting the demand for money at the

new equilibrium, in point 1. After that jump, the price level and the nominal money supply


35


grow proportionally ( 1 ),and the real money supply remains unchanged in its new

position.

Figure 9: Adjustment to an increase in the rate of money growth (float)

t1

t

M

i

t

t

t

0M

0m

t1

P=e

1P

0P

1m

m

t

i

M/P

M 0 /P 0

1

0

m0m1

( , )m Y i

*1 1i r

*0i r

*1 1i r

*b*0b

*Pb

*Cb

*0i r

M 0 /P 1

15.6.3 Money based stabilization

Using the tools above, one can now discuss the challenges faced by a central bank

aiming to end up with an episode of high inflation. The first strategy under scrutiny will

consist in the central bank suddenly setting the rate of money growth to zero, freezing the

quantity of money in circulation. This strategy is known as “money-based” stabilization.

Referring to figure 10, suppose that the initial money market equilibrium is in point 1.

In this equilibrium, money is expanding continuously at rate 1 , inflation is equal to 1

and the domestic interest rate is *1 1i r . Then, at moment t2, the central bank

unexpectedly freezes the quantity of money, to stop inflation. In Figure 10, this is illustrated

by a money supply that becomes constant at 2M M after t2.


36


If the plan is credible, the fall in expected inflation to 0 comes along with a fall in

the nominal interest rate to *i r and with an increase in money demand to 0m . This, in turn,

requires a fall in the price level at the time of the announcement, from 2P in the moment

immediately before, to '2P . The fall in the price level is essential to drive the real money

supply to the level that is consistent with the new money market equilibrium.

The fall in the price level, in turn, is driven by an exchange rate appreciation: when

the inflation rate declines, the demand for money increases, causing individuals to sell bonds

to rise liquidity. Since the amount of domestic bonds is given, this translates into an excess

supply of foreign bonds, that comes along with an excess supply of foreign currency and an

appreciation of the exchange rate. After t2, money is constant and inflation is zero, so the

economy will remain in point 2.

Figure 10 – Money-based stabilization under flexible prices

t2

t

M

i

t

t

t

2M

0m

t2

P=e

'2P

2P

1m

m

t

i

M/P

M 2 /P’2

1

2=0

m0m1

( , )m Y i

*1 1i r

*0i r

M 2 /P2

*1 1i r

*b*0b

*Pb

*Cb

*0i r

Although at the theoretical level the adjustment just described is intuitive, one may

wonder how realistic is to presume that the price level will fall at the end of a high inflation

episode: economic agents accustomed to raise wages and prices on a daily basis may well be


37


reluctant in engaging in a coordinated downward price adjustment at the time of the

announcement. And the question arises: in case prices failed to decline, how would the

money market equilibrium look like?

Answering to this question in the context of our model is not possible, because we are

assuming that prices are flexible. One may however build some intuition, appealing to a

closed economy variant of the model, where the price level was determined directly by the

money market equilibrium condition, (23): if the disinflation plan was credible so that the

nominal interest rate declined to i , and if the money supply remained unchanged at

2M M , then the only way to balance the money market under sticky prices would be

through a fall in private consumption, causing a recession26.

A central bank committed with stabilization could try an alternative avenue in the

scope of a money-based stabilization programme: instead of setting the money supply to be

continuous at point 2t , it could expand it once-and-for-all, just in the quantity needed to

accommodate the higher demand for real money. The problem, however, is that a jump in

money supply could rise suspicious among the public regarding the central bank true

commitment with low inflation…

As we will see next, an avenue to increase the money supply once-and-for-all at the

time of the adjustment without necessarily challenging the credibility of the central bank is

exchange rate stabilization.

15.6.4 Exchange rate-based stabilization

An alternative strategy to end up with high inflation is to fix the exchange rate. Such

strategy may prove particularly effective in the context of hyperinflation, where virtually all

26 Note that equation (23) delivers a classical “aggregate demand” of the form dQ G i k M P .

When the interest rate declines from *1 1i r to *i r , the aggregate demand shifts down in the (Q,P) space.

If price level remains unchanged at 2P (that would be an horizontal aggregate supply), income will fall.


38


prices become indexed to the exchange rate. In that case, a freeze in the exchange rate implies

an immediate stabilization of the price level. The main advantage of exchange rate

stabilization as compared to money-based stabilization is that its does not require the price

level to fall.

The mechanics of exchange rate stabilization is described in Figure 11. Suppose that

at moment t1 the central bank fixes the exchange rate at the level 2e e . As long as the

program is credible and expected inflation falls down to zero, there will be an increase in the

demand for money, just like in the money-based stabilization. The difference relative to

money-based stabilization is that the central bank is not committed to a constant money

supply. Since at 2P there is an excess demand for money, agents will try to rise liquidity

selling foreign assets, and this will pressure the currency to appreciate. Since the central bank

is committed with a fixed exchange rate, it must intervene, buying the foreign bonds the

private sector is selling. This, in turn, will cause a jump in the money supply to '2M M .

Figure 11. Exchange-rate based disinflation

t1

t

M

i

t

t

t

2M

*i r

0m

t1

P=e

2 2P e

1m

m

t

i

M/P

1

2=0

m0m1

( , )m Y i

*1 1i r

*1i r

*1 1i r

M2 /P2 M’2 /P2

'2M

*0b

*Cb

*Pb

*b


39


At the first sight, the fact that money supply is expanding looks inconsistent with

disinflation: after all, how can the central bank credibly convince people that inflation is to

finish if more money is being printed?

Credibility under this strategy arises from the fact that the increase in the money

supply is backed by foreign reserves. This means that the central bank has firepower to

intervene in the foreign exchange market and buy back the extra money just created, in case

people need to check the central bank’ commitment. Exchange rate stabilization program

entails the mechanism that is needed for the increase in money supply to be credible.

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, either money-based or exchange rate

based, typically require the institution of central bank independence relative to the Minister of

Finance. Central bank autonomy, fiscal reforms aiming to increase government revenues,

fiscal rules such as those that impose a limit on government spending are key elements of

successful stabilization. Nominal stability and fiscal sustainability are two sides of the same

coin.

Box 4. 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 and 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, that prove successful.

15.7 Currency crisis

In the section above, 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


40


exchange rate depreciation, they will seek to minimize capital losses, optimally deciding to

get rid of domestic currency before the currency starts to devalue.

In the discussion that follows, we assume that the central bank is initially committed

with a fixed exchange rate. The perception of unsustainability arises because the government

monetizes its fiscal deficits. For a period of time, the expansion of domestic credit 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 assets. However,

agents will anticipate the scenario in which the central bank reserves are exhausted and the

currency will enter in a float. With such scenario in mind, agents will optimally decide to

swap domestic currency by foreign currency at the moment exactly before the exchange rate

depreciation takes place. This case is referred to as the “first generation crisis model”27.

15.7.1 Unsustainable credit expansion – naïve case

To see how the speculative attack unfolds, let’s refer again to Figure 12. Assume that

the economy is initially under a fixed exchange rate, with zero inflation and *0i r . At time

t=t1, the central bank starts buying government bonds, expanding the domestic credit at a

constant rate 1G GC CD D .

All else equal. the money supply and prices would start increasing, as described in

Figure 9: foreseeing a higher inflation rate, agents would demand less money. The excess

supply of money would generate an increased demand for foreign bonds, and an excess

demand for foreign currency, pressing the depreciation. If the peg was immediately

abandoned, there would be a price jump at moment t1, and domestic agents would face a

capital loss.

In alternative, assume that the central bank wanted to stick with the fixed exchange

rate, by sterilizing the expansion of domestic credit with an offsetting sale of foreign bonds

27 Krugman, Paul. 1979. “A Model of Balance of Payments Crises”. Journal of Money, Credit, and Banking 11, pp. 311-25.


41


( * 0GC CM D e B ). In that case, the money supply would have remained constant for a

while, at 0M . This case is illustrated in figure 12: as the domestic credit expands after t1, the

composition of the central bank assets changes over time, with a growing proportion of the

money supply backed by government debt and with declining reserves.

The question that arises is how long could that pattern persist?

Of course, if nothing else happened, a time would come when the central bank

reserves were exhausted (t3 in the figure). In that case, the money supply would remain

constant at 0M and the price level would remain constant at 0P exactly until moment t3.

Since after this point the central bank could no longer sell reserves to keep the money supply

unchanged, the money supply would start increasing, implying an increase in the inflation

rate, and a price jump from S to T, as we already saw. The problem is that the jump in the

price level would imply a capital loss for the private sector. If agents anticipate this, they will

react before.

15.7.2 The speculative attack

Sterilized interventions give private agents the opportunity to avoid a capital loss

related to a jump in the exchange rate: by observing the central bank actions and the

continuous fall in foreign reserves, agents become aware that the collapse of the exchange

rate regime is imminent. Therefore, they run en mass to the central bank to swap their

undesired domestic currency by foreign currency at the official exchange rate, immediately

before the depreciation takes place. In doing so, they will be precipitating the currency

collapse. As we will see next, the exact timing of the speculative attack is well determined.

In the figure, the run on currency occurs at time t2. At that moment, the demand for

domestic money falls abruptly (to the level consistent with the new inflation rate, 1m ),

implying a sudden increase in the demand for foreign assets. By forcing the central bank to

sell out all its reserves, the public ensures a downwards adjustment in the money supply to

the level that is needed to match the new demand for domestic money. The move from point

0 to point 1 happens without an increase in the price level.

Figure 12: the dynamics of a speculative attack


42


i

M/P

M 0 /P 0

1

0

m0m1

( , )m Y i

M 0 /P 1

*1 1i r

*0i r

t

P=e

Domestic credit

Reserves

Money stock

t2

t2

Money, credit, reserves

0P

Speculative attack

Nominal stability

Inflation

R S

T

GCD

*CeB

0M

t3t1

t1 t3

2M

After t2, the growth rate of money is equal to the growth rate of domestic credit, and

prices will increase proportionally. 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 (which in turn is caused by a run on the central bank reserves), rather

than by a jump in the price level.

15.7.3 The timing of the currency collapse

The key insight of this theory is that the timing of the speculative attack is well

determined by a non-arbitrage condition. To understand this, let’s refer to Figure 12 again.

The new money demand is known, as implied by the new inflation rate ( 1 ). Thus, the

real money supply must move from point 0 to point 1 at the time of the regime shift:

- If the shock is not anticipated, this will be achieved by a price jump at t3 (naïve

case).

- If the regime shift is anticipated, the fall in money supply will be achieved by a

run on the central bank’ reserves, at the time of the speculative attack (t2). The


43


selling of foreign currency will bring down the money supply to the level needed

to match the new money demand.

Absence of arbitrage opportunities imply that at the time of the attack (t2) the

following condition must hold:

*2 0 1,

GCM D P m r Y (34)

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, which 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 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 time28.

15.8 Main ideas

In this note, we used a model with flexible prices, to show how nominal magnitudes

are determined in the long run. In this model, money acts like a “veil”, in the sense that there

is no interaction between the monetary side of the economy and the real side of the economy.

28 A currency crisis may occur even if not unavoidable. For instance, the 1994 Mexican crisis and the 1997 Asian Crisis were not doomed to occur, given the domestic policies. These episodes were instead triggered by confidence crises that altered the agents’ perception regarding the willingness of the authorities to keep defending the peg. As we already know, a lower demand for money causes central bank reserves to decline, even if the central bank does not intend to devalue. If the central bank perceives the cost of maintaining the peg under low credibility to became too high, it may well decide to devalue, self-fulfilling the original expectations, and being punished for a crime that it didn’t commit. The case where countries with arguable sustainable policies are forced to unstable paths because of mere confidence crisis is addressed by the so-called “second generation crisis model” [Obstfeld, M., 1986. Rational and self-fulfilling balance-of-payments crises. American Economic Review. 76 (1): 72–81].


44


In this context, we formulated the fundamental dilemma underlying the choice of an

exchange rate regime in the long run: either the central bank can determine the path of

nominal money supply or the path of the nominal exchange rate, but not both at the same

time.

Although under flexible prices the choice of a nominal anchor does impact on the real

economy, when the central bank decides to target the nominal money supply or instead the

nominal exchange rate, this will in general deliver different time paths for the price level,

depending on how exposed the economy is to different types of shocks. Because different

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

controversial topics in monetary economics and one that has to be evaluated on a case-by-

case basis. “No one size fits all”.

In the long run model inflation arises as monetary phenomenon: a continuous increase

in the price level can only be sustained 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 may 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. The corollary is that fiscal sustainability is

a necessary condition for price stability.

Further reading

Vegh, C., 2013. Open Economy Macroeconomics in Developing Countries. MIT

press.

Feenstra, R, Taylor, A., 2014. International Macroeconomics (3rd ed.). Worth

Macmillan.


45


Appendix 1 – Optimal consumption and money demand

The representative consumer maximizes his life-time utility function

0

exp( ) ,t t

t

U t u m c dt

subject to the flow budget constraint (6a). The current value

Hamiltonian is , Pu c m Q T C rb im . The first order conditions cu

and mu i implicitly define the money demand. In the particular case in which the utility

function takes the form (17), the money demand is equal to (18).

Apart from the first order conditions and the budget constraint (6a), the optimal

programme implies the verification of the transversally condition, ,lim exp 0P t ttt b

,

and the following condition describing the co-state dynamics: r . From the later

and the first order condition 1cu c , we obtain 21ccu c c c , implying

2

1cr

c c

and by then the Euler equation cr

c

. If r , consumption

will be constant over time.

Although the consumer observes the flow budget constraint as given by (6a), the fact

that the government meets its budget constraint (14) implies that the economy resources’

constraint (16) must be met. Integrating the later over time and ruling out bubbles, we obtain

the economy’ inter-temporal resources constraint:

*0

0 0

exp( ) exp( )t t t

t t

b rt Q dt rt C G dt

Assuming that the real interest rate is equal to the rate of time preference,

consumption will be constant over time. Solving for consumption, we get:

*0

0

exp( ) t t

t

C r b rt Q G dt

(a1)

This equation reveals that the household “permanent income” (the term on the right-

hand-side) depends on government expenditures, which reduce his life-time wealth. Whether


46


government expenditures are financed with debt, lump sum taxes or money creation does not

affect the consumer’ wealth and hence real consumption.

Replacing (a1) in (16), one obtains the current account each period:

* * *0

0

exp( ) t t

t

b rb Q G r b rt Q G dt

This expression shows that the consumer will borrow from abroad whenever current

income (first term in brackets) falls short the “permanent income”, and will lend in the

opposite case. To abstract from consumption smoothing considerations, we further assume

that real output Q and government expenditures are constant over time, implying that there is

nothing to smooth out, and the current account becomes equal to zero each moment. In that

case, the optimal consumption (a1) simplifies to (22).

Review questions and exercises

Review questions

15.1. 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.

15.2. 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 policy might have contributed to stabilization.

15.3. 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”.

15.4. Explain how a persistent government deficit may lead to the collapse of a fixed exchange rate regime.

15.5. (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?


47


b) Suppose that the government surprised everyone with a disinflation programme that reduced inflation to 5%. What were the implications for the borrower and for the lender?

c) Which complementary measures should the Argentinean government take to address this problem?

Exercises

15.6. [Money demand instability] Consider an oil exporter, 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 * 1P ; the money demand is given

by iYmD 4 ; the real interest rate is 5%; the central bank balance sheet is initially as

follows: 6020* CC BeBM pesos. Initially, real income stands at 160Y .

a) Describe the money market equilibrium in this economy. What will be the price level and the nominal exchange rate?

b) Analyse the implications of a 100% devaluation.

c) Returning to a), assume that oil prices increased, driving income in this economy to a record high of 200Y . Surfing on prosperity, the government decided to borrow 20 pesos from the central bank to finance a development plan. Would this operation threat the fixed exchange rate and price stability? Explain why.

d) Departing from (c), examine the policy options for the central bank if oil prices suddenly declined, driving income to 130Y . Would the fixed exchange rate regime be at stake? Would a devaluation help? What do you conclude from this exercise?

15.7. [Jump in price level] 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 assumed that the international real interest rate is

* 0.04r and that the demand for real money balances is given by 20Dm Y i , where 100Y refers to income (constant) and i is the nominal interest rate. The foreign price

level is equal to 2.

a) Assume that initially the money supply is constant at 250M . 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.

15.8. [Money based stabilization] Consider an economy with flexible prices where the purchasing power parity and the Fisher principle hold instantaneously. Assume that

1* P , the real interest rate is 5% and the money demand is given by 4Dm Y i , and


48


real income is Y=250. Initially, the money supply is expanding at 20% and the exchange rate is floating.

a) Describe in a graph the money market equilibrium, and quantify: the inflation rate, the nominal interest rate and the real money demand. Draw the time paths of the exchange rate, the price level and the interest rate.

b) Now assume that at the time the domestic money supply reached the level M=12500, the central bank unexpectedly decided to anchor the money supply at that level. b1) Find the new interest rate and money demand. b2) Describe the adjustment and the new money market equilibrium in a graph. b3) Assuming that prices were fully flexible, what would happen to the price level and the exchange rate? Quantify and draw the corresponding time paths.

c) Following b) assume that prices were sticky downwards, and that the money supply stayed fixed at M=12500: c1) how would the economy adjust? Explain and quantify, referring to the money demand market. c2) In face of the complication above, which alternative policy could have been adopted to stop the ongoing inflation? Discuss the pros and cons.

15.9. [Inflation stabilization] 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 1* P ; the international real interest rate is

5%; the money demand is given by iYmD 4 , and income is 200Y .

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 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 out 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 to the nominal exchange rate.

c) 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?

15.10. [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 ( 1* P ), PPP holds, prices are fully flexible and income is 432Y . The real interest rate is the same at home and abroad and equals 5%. In this economy the money demand is

given by iYmD 20 .

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?


49


c) Instead of assuming that agents are caught by surprise, consider a case where agents have rational expectations and perfect foresight. At moment zero, the central bank balance sheet is as follows: 50382* CC BeBM . 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.

15.11. [Role of reserves] The initial assets of a central bank in an economy with flexible prices are given by: 1072* CeB and 128CB pesos. Further assume that the money

multiplier is equal to one and that the real money demand is given by iYmD 10 , where Y=120 is real income and i is the nominal interest rate. The real interest rate is 5%. In this economy, PPP holds and the foreign price level is 1* P .

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 income to Y=110. If the central bank didn’t intervene in the foreign exchange market, what would be the implications for prices and for the exchange rate?

c) Considering the shock described in question b), compare 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.

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