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F A C U L T Y O F S O C I A L S C I E N C E S
D e p a r t m e n t o f E c o n o m i c s
U n i v e r s i t y o f C o p e n h a g e n
BA-thesis
Morten Buur Madsen
The cost and consequences of a monetary union with differentiated economies
Supervisor: Jesper Pedersen
Curriculum + ECTS points:15 ECTS
Date of submission: 22/11/12
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Abstract
This paper will study the dynamics of a monetary union, where the participating countries
differ in their economic structure. We will use a New Keynesian model to analyze how the
economies are affected, when they are governed by a common nominal interest set by the
union central bank. We will see, that due to the structural difference between the economies,
in this model captured by a difference in the natural rate of interest, there will be a difference
in the equilibrium inflation rate. We will argue, that this difference in inflation will cause a
decline in the competiveness for those countries that have a higher than average inflation rate
and that they will end up with an increasing trade deficit. The growing trade deficit is likely to
be financed through public debt, which if it is not dealt with will put the country on an
unsustainable debt tract and into a debt crisis. The predictions made by the model are
compared with the development in Europe from the introduction of the Euro until today and
we find that there are indications that the intuition of the model is correct. With our model as
foundation we conclude the one solution to the potential debt crisis is to form a fiscal union
on top of the monetary union.
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1 Introduction
In January 1999 the third stage of the Economic and Monetary Union (EMU) was
implemented. Twelve countries now had the Euro as an official currency although the actual
coins and notes were first put in circulation in 2002. This was supposed to mark the beginning
of a more unified Europe with higher market integration and more geographical mobility. For
some years the development was going as expected and the union had a strong growth, but in
2008 the international crisis hit and that changed things. The crisis revealed how several of
the European countries had managed to accumulate a large public debt up over the years, and
when the interest rates rose in the new unstable world economy this debt became
unsustainable causing a debt crisis. Many have been blamed for the debt problems, and both
irresponsible politicians and banks are accused of being the cause for the crisis, but this paper
will suggest another reason. We will here investigate how the structure of a monetary union,
such as the Euro, can lead to a development that will allow part of the union to gain
competiveness at the expense of other member countries. Such a development will over time,
if it is not countered probably, create fundamental economic problems for the countries
loosing competiveness and may lead to a debt crisis.
In this paper we will investigate what consequences it may have for a country when it joins a
monetary union. In order to understand why monetary unions are formed, we will discuss
some of the advantages and disadvantages there might be in participating in a monetary
union. The paper will then use and modify a model of inflation in a monetary union with
differentiated economies, and apply it in an analysis of how the economies will be affected by
the common union monetary policy. We will use the model to show how a shared nominal
interest rate is across the union will cause a constant difference in the inflation rates between
the member countries. We will show how a difference in inflation will lead to a fall in export
and an increase in import, and that this over time will give the countries with a high inflation
rate a high incentive to take up an increasing amount of public debt. The paper, its model, and
analysis are inspired by the Euro as a monetary union, and we will use statistics from
European countries to argue for the relevance of the model.
The paper is structured as follows. Section 2 argues how inflation difference between nations
in the same monetary union may cause a buildup of public debt for some countries. In section
3 we look at the development for several European countries from the introduction of the
Page 3 of 27
Euro until today. Section 4 describes some of the costs and benefits associated with joining a
monetary union. In section 5 we construct the model that will form the central part of this
papers analysis. We analyze the dynamics of the model in section 6 and investigate how
policymakers are able to affect the equilibrium. Section 7 presents this papers conclusion.
2 The consequences of difference in inflation1
A relatively high inflation rate can be costly for a nation, but if the inflation level is held
stable and the central bank is creditable then it would not necessarily be major a problem, as
inflation expectations would adapt and changes in the nominal exchanges rate will help keep
competitiveness. This however changes if the country is part of a monetary union or has a
fixed exchanges rate regime, which theoretically speaking is essentially the same thing when
it comes to monetary policy.
Within a monetary union the exchanges rate between participating countries are completely
fixed, as all transactions takes place in the same currency. There are a number of advantages
with this and we will go through some of those later in this paper, but it also has the
implication that the nominal exchange rate no longer compensates for a country’s increasing
price level. Instead a country, with an inflation rate higher than the average of the monetary
union, will see the domestic prices increase at a pace faster than union average. The goods
produced by the country will therefore become relatively more expensive compared to
countries with a lower inflation rate, and the result will be a decrease in export. Over time a
country with high inflation will see its exports crumble and imports grow as competitiveness
decline. At the same time the incentive to import foreign goods will rise since these will
become relatively cheaper and this will push the trade balance in a negative direction towards
a trade deficit. Mueller (2010) describes how the negative net export will have to be met by a
positive inflow of foreign capital in order to keep the balance of payments. The inflow of
capital can be both foreign investments in the domestic economy, or it can be obtained by
selling domestic assets, like government bonds, to foreign investors. The general negative
trade net export will make it increasingly hard to produce goods domestically as the demand
for those goods fall. On top of this, high inflation will also increase the marginal cost of
producing goods domestically, since wages and raw materials will grow with inflation, and
this will make domestic production less attractive for investors. It is therefore unlikely that the
1 This section uses the framework set by Whitta-Jacobsen and Sørensen in ”Introducing advanced
macroeconomics” chapter 22 and 23 to analyze the case where exchange rates are fixed but inflation differ.
Page 4 of 27
capital inflow needed to counter the trade deficit will come from foreign investments into the
real economy, since such investments may not be very profitable. The implication is that the
trade deficit will be financed by selling government bonds and that will increase the public
debt. If something is not done to change the domestic inflation it will in the long run lead to
an ever growing public debt as exports decrease and imports increase. This could be
countered if the reduction in domestic and foreign demand were strong enough to create a
negative output gap, which would reduce inflation and thus bring the economy towards a
sustainable equilibrium. We will later show why this does not necessarily happen when a
country is part of a monetary union. The reason is, that the low real interest rate created from
the high inflation and the union nominal interest rate fuels domestic demand and the housing
markets by letting consumers and firms lend money cheaply. The growth from the low real
interest rate offsets the effect from the decreasing exports and this allows the inflation level to
be high in equilibrium.
Uctum and Wickens (1993) argue that it is necessary for a country to hold its national
intertemporal budget constraint and how the financial markets may ensure this. As the public
debt of a country grows so such the interest rate on government bonds, which will increase
the government’s cost of obtaining debt, but also have a positive wealth effect for the holders
of government bonds. This positive wealth effect should help decrease trade deficit due to an
increased consumption by foreign investors. In an optimal setting that will happen before the
debt grows too large for the country to handle, but if investors regard the monetary union
more as a whole rather than a group of individual countries, it might not be so. If the market
believes that the union has a joint debt liability, then it might keep buying bonds from a
specific country beyond the point where it is sustainable, because the other countries in the
monetary union have more reasonable debt levels. A country, that finances a trade deficit
through the financial markets, is then able to borrow money at too low a price, since investors
demand the same interest rate on their money across the union. The potential consequence is
that a country borrows more than it is able to pay back, and when investors eventually realize
this they will stop the capital inflow. The country is now in a situation where it is no longer
able to finance its trade deficit and it will therefore have to reduce imports. The result will be
a sudden drop in the welfare of the citizens, as fewer goods are now available due to the
decrease in imports and because domestic production is at a very low level. On top of this,
consumption of domestic goods has to be reduced as well since an increase in export is
necessary to reduce the public debt. If the debt have become so large that the interests alone is
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too much to pay off and the population is not willing to accept the reduction in welfare, then
the debt crisis will be a reality.
3 The development from the introduction of the Euro
We have argued how a difference in inflation between countries will lead to a growing trade
deficit, and that due to the way interest rates on government bonds behave in a monetary
union, governments will have an incentive to finance the trade deficit with public debt. As
will be shown later, our model predicts that high government expenditure will tend to drive up
inflation. In this section we want to investigate whether there are signs of the predicted
correlations between expenditure, inflation, trade balance, and debt or not. We compare a
selection of European countries where some participate in the Euro and some do not. The
Euro countries chosen are Austria, France, Germany, Greece, Italy, Portugal, and Spain. The
non-euro countries are Denmark, Sweden, and Unite Kingdom. Denmark has a fixed
exchange rate regime towards the Euro and should therefore behave more or less as a Euro
country, whereas Sweden and the United Kingdom have flexible exchange rates and will
serve as benchmarks.
Figure 1: Government consolidated gross debt in 2011 as percent of GDP composed of
debt in 2000 and the change in debt from 2000 to 2011
Source: Eurostat
Figure 1 shows that Greece, Portugal, and United Kingdom are the countries that have had the
biggest increase in their debt level from 2000 to 2011. We also see that Greece and Italy had
the largest debt level in 2011.
66 52 57 60103 109
51 59 54 41
6
-6
29 20
6712
5710
-16
4472
47
86 81
171
121108
6938
85
-50
0
50
100
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200
-50
0
50
100
150
200
Au
stri
a
Den
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k
Fran
ce
Ger
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y
Gre
ece
Ital
y
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Spai
n
Swed
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Un
ited
Kin
gdo
m
Percent of GDPPercent of GDP
Changes in debt from 2000 - 2011 Debt in 2000
Page 6 of 27
We will argue, that the inflation difference between countries is what causes structural
problems in a monetary union, and we therefor look at the inflation rates.
Figure 2: HICP index from 1996 to 2011 (1996 = 100)
Source: Eurostat
Figure 2 shows the indexed increase in prices from 1996 to 2011. It is clear that the countries,
which today have accumulated a large debt, also are the countries with a high price increase
over the period, namely Greece, Portugal, and Italy. The slope of the curves is the year to year
inflation rate, and we see that these are relatively stable over time.
Figure 3: HICP index 2010 (1996 = 100) and 2010 indexed government expenditure as
percent of GDP (1996 = 100)
Source: Eurostat
The model presented in this paper predicts a positive correlation between the growth in
government expenditure and inflation. Figure 3 plots the 2010 value of the HICP index
against the 2010 value of the indexed government expenditure as percent of GDP both with
1996 as the base year. We see from the figure 2 that there is a positive correlation between the
100
110
120
130
140
150
160
170
180
100
110
120
130
140
150
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180
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
IndexIndex
Austria Denmark France GermanyGreece Italy Portugal SpainSweden United Kingdom
DenmarkGermany
Greece
Spain
France
Italy
Austria
Portugal
SwedenUnited Kingdom
y = 0,7776x + 48,241R² = 0,4417
110
120
130
140
150
160
170
90 95 100 105 110 115 120 125 130
Agg
rega
te in
flat
ion
fro
m 1
99
6 t
o 2
01
0
Indexed government expenditure in 2010 (1996 = 100)
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price increase and the change in government expenditure. A high increase in expenditure is
associated with a high inflation.
One of the main claims of this paper is that high inflation will over time lead to an external
trade deficit. Figure 4 plots the 2011 indexed price level with 1996 as the base year together
with average trade balance over the period.
Figure 4: 2011 indexed HICP (1996 = 100) and average trade balance from 1996 to 2011
Source: Eurostat
The figure shows a correlation between the average trade deficit and the increase in the price
level. We see from the figure that Greece, Portugal, and Spain all have high inflation and a
negative trade balance. This is in line with the prediction that the countries with a high
inflation would suffer from a negative trade balance and that this could lead to severe debt
problems.
The increasing trade deficit will have to be financed through the capital markets, and we
argued that because the members of a monetary union potentially can be viewed as one by the
financial markets, the interest rate may be the same for all countries. This will lead to some
countries to borrow more than what is efficient, because the interest rate of government bond
is set to low and without a true evaluation of the risk.
Denmark
Germany
Greece
Spain
France
Italy
Austria
Portugal
Sweden
United Kingdom
y = -4,8297x + 129,46R² = 0,6077
120
125
130
135
140
145
150
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160
165
170
-15 -10 -5 0 5 10
Agg
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o 2
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1
Average trade balance from 1996 to 2011 in percent of GDP
Page 8 of 27
Figure 5: Annual interest rate on 10 year government bonds
Source: OECD Economic Outlook
Figure 5 shows that there has been a conversion of the interest rates from 1995 to the start of
the Euro for all Euro countries. From 2000 to 2009 the countries all have almost the same
interest rate on their 10 year government bonds, but when the crisis strikes in 2009 the rate for
Greece, Portugal, Spain, and Italy rises. The rise happened as talks of debt problems started,
and it appears as if financial investors realize that some countries had some fundamental
problems with their debt. This is an indication that the interest rate has been too low through
the 00’s for those countries that are now in a debt rises.
The development since the introduction of Euro indicates that the predictions made by our
model are to some extent correct. There is a connection between the high government
expenditure, high inflation and a negative trade balance.
4 Costs and benefits when joining a monetary union
We have described how a difference in inflation between countries in the same monetary
union can lead to a public debt buildup for countries with a high inflation rate. This may serve
as an argument for not participating in a monetary union, but there are other costs and benefits
that will have to be taken into account. The cost and benefits are of both economic and
political nature, but in this paper we focus on the economic side, which are described by De
Grauwe (2009).
0
5
10
15
20
25
0
5
10
15
20
251
99
5
19
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19
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01
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02
20
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20
11
20
12
PercentPercent
Austria Denmark France GermanyGreece Italy Portugal SpainSweden United Kingdom
Page 9 of 27
4.1 A change of policy options
The cost of joining a monetary union depends to a large extent on what exchange rate regime
the country had before entering the union. Countries with a fixed exchange rates system are
very limited in their ability to perform independent monetary policy, because they will need
to set the nominal interest rate at the same level as the country which they fix their exchange
rate towards2. For these countries the main cost is giving up the national currency and
knowing that it will be much harder to go from a currency union back to a national currency,
whereas countries with a fixed exchange rate system can chose to switch to a system with
flexible exchange rates. For countries that does not have fixed exchange rates, the one of the
main costs is losing the ability to perform an independent monetary policy, which is
especially painful during a crisis, as the country cannot independently decide to use expansive
monetary policy to stabilize output. In the case of a negative shock to the economy the central
bank can, when it is not part of a larger union, lower the nominal interest rate which will for a
given inflation level lower the real interest rate and thereby stimulate demand, increase
output, and reduce unemployment. The cost of giving up this instrument depends on how it
was used before entering the union and how effective it was. Very conservative central banks
that are mainly focused on holding the inflation at a target level are already limited in their
use of the interest rate as a tool to stabilize output, as there is a tradeoff between stabilizing
output and inflations when the economy is hit by a supply shock. These central banks will not
give up as much in terms of output stabilization, but they will on the other hand not be able to
stabilize inflation which can also be cost full. The effectiveness of the interest rate as an
instrument depends on the credibility of the central bank. A low credibility will reduced the
central bank’s ability to hold inflation at a target level, as the public will not believe that the
central bank is committed to the inflation target and they will therefore expect a high inflation
level. These central banks will have less to loss from joining a monetary union, as their ability
to stabilize output and inflation were already very limited.
In addition to losing the interest rate as instrument to stabilize the economy, all countries in
the union now share the same currency. For a country with a flexible exchange rate a negative
demand shock will typical induce the central bank to lower the interest rate which will lead to
an outflow of capital as investor sell domestic currency in order to by capital in a country with
a higher interest rate. This will lower the price on domestic currency in terms of foreign
2 Whitta-Jacobsen and Birch Sørensen: ”Introducing advanced macroeconomics” chapter 23
Page 10 of 27
currency, meaning that the nominal exchange rate will decrease. A lower nominal exchange
rate will increase the competiveness of domestic goods as these become relatively cheaper.
The effect will be an increase in exports which will lower the effect from the negative demand
shock. Since this is not possible when the country is part of a monetary union it is left with
only fiscal policy if it wants to stabilize output.
4.2 Trade effects from a common currency
The most noticeable change for the private agents of an economy when it enters a monetary
union is that it now shares a common currency with the rest of the union. This removes the
exchange rate risk, which will improves trade conditions between members of the currency
union. When companies trade across borders with a flexible exchange rate system they run
the risk that a change in the nominal exchange rate can alter the value or cost of a contract.
The risk may therefore induce firms to discard trades that would have been profitable, but
when nations trading with each other have a common currency the risk is removed. A
common currency insure that the nominal exchange rate remains the same between the
participants of the union and companies trading across boarders do therefore not have to make
contracts or insurances against such changes. This makes it easier for them to do business
with other member states and that will increase international trade. In general the effects on
trade when a country joins a monetary union are one of the most important gains. Because of
the lowered trade barriers between countries in a monetary union, they will often find that
international trade grows and make up a larger part of the total economy. Trade improves
consumer welfare as more products become available and it allows for an increased
specialization, which should benefit efficiency and thereby reduce marginal cost and make
goods cheaper.
Baldwin and Di Nino (2006) argues how the decrease in marginal cost makes international
trade more profitable and how profit maximizing firms will therefore expand their foreign
trade both exporting and importing more. Companies will increase current international trade,
but also starting trading in sectors and with goods that was previously to costly which will
cause overall trade to grow. It is however hard to estimate the direct effect of a monetary
union on trade, as the introduction of a union often coincides with many other political and
legal changes that may enhance trade between the members of the union. In the case of the
Euro and the European Union, the monetary union was implemented alongside a general
increase in market integration, lower tariffs on import, and more unified legislation which all
Page 11 of 27
have a positive effect on trading conditions. The market integration in the European Union is
constantly evolving and this makes it relatively complicated to estimate the effects on trade
from a single currency. Despite of this, there have been several attempts to isolate how much
international trade have grown in the Euro Area due to the Euro, and although they differ on
how big the effect from a common currency is, most of them find that there is a positive and
significant effect. Baldwin and Di Nino (2006) sum up some of these attempts and states that
most recent research papers have found a trade effect between 5 and 20 %.
We have mainly focused on how joining a monetary union affects trade and monetary policy
since these are the important elements in this papers model and in our analysis. There are
costs and benefits that have not been mention here, as a monetary union affects the economy
and national central banks in numerous ways. And although all cost and benefits should be
weighted together when a country decides to participate in a monetary union or not, we will
show that if the countries forming the union are different from each other in their economic
structure, the union is likely to fail due to a debt crisis. We will suggest that a fiscal union
might be a way of dealing with the fundamental problem, that the difference between the
economies give rise to a difference in inflation rates. The possibility of having to join a fiscal
union should however then be taken into account when a country decides to participate in a
monetary union.
5 Creating the model
In section 2 we argued how a difference in inflation rate can cause a trade deficit which over
time will result in a buildup of public debt, and we how then showed the development for
several European countries was to some degree in line with our predictions. We now we want
to create a model that can give an explanation for the constant difference in inflation rates
between members of the same monetary union.
5.1 The basic foundation
Countries in a monetary union will be governed by the same monetary policy and will have
the same nominal interest rate which is set by a common central bank. The central bank will
typical aim at stabilizing inflation and output, but the weight given to deviations for the two
variables depends on the mandate of the central bank. In the case of the European Central
Page 12 of 27
Bank its mandate states that the main focus is the inflation target3. The overall inflation target
is defined as the weighted average of the inflation rate in the countries of the union. The
central bank will set a nominal interest rate with regards to the union inflation rate, the
inflation target and perhaps the output gap. The nominal interest rate determines the real
interest rate for a given inflation rate as describe by the Fisher equation
The real interest rate influences the economic output though two different channels4. It affects
the consumption of households as the real interest rate determines the price of consumption
relative to saving. A high real interest rate increases the return from savings making it more
profitable to substitute away from consumption over to savings, but at the same time it
increases the value of the current savings, which in turn might increase consumption today.
Generally a change in the real interest rate has both a substitution and an income effect and
we cannot say which one dominates. The real interest rate does however also affect firms, as
it determines the discount rate for investments. A lower real interest rate makes more
investments profitable and this will increase the demand from firms. We assume that the
aggregated affect from a lowered real interest rate is an increase in overall consumption. The
changes in consumption then affect the inflation through the supply curve which will be
described later. This way the central bank can use the nominal interest rate to affect output
and inflation in the economy.
The central bank sets the nominal interest rate for the whole union, but unless every country
has the same inflation rate, most countries will experience a real interest rate different from
the union average. In the case where a country’s inflation rate is above the union average the
country will have a lower than average real interest. If a country on the other hand has an
inflation rate below average then the real interest rate will be above average. There are two
main effects that move the economy when the real interest rate differs across countries5. First
the countries with a high inflation rate will have a relatively low real interest rate, and this
will act as a stimulus to the economy increasing both output and inflation. In the same way
countries with a low inflation rate will experience relatively low output and inflation, and the
inflation rates of the economies will thereby be pushed further from each other. There is
however another effect that counteracts this. Countries with a high inflation rate will
3 According to the Maastricht treaty article 105 the primary objective of the central bank is price stability. 4 The arguments for the effect of the real interest rate builds on the framework of short run macro economy
described by Whitta-Jacobsen and Birch Sørensen: ”Introducing advanced macroeconomics” chapter 14 to 18 5 Wickens (2007)
Page 13 of 27
experience an increase in their relative prices compared to low inflation rate countries. Under
a common currency the goods of high inflation countries will become more expensive than
the goods of low inflation countries and they will therefore loss competiveness over time. The
increasing prices will tend to lower export which dampens the economic activity and thereby
inflation. The opposite is true for the low inflation countries. They will gain competiveness
which will lead to increasing exports and this will drive up the inflation. These two effects
affects the inflation development differently, and depending on their strength, they may either
increase inflation difference between the countries over time, lower inflation difference over
time or keep it more or less unchanged.
The model constructed here is based on the assumption that the two above mentioned effects
in fact will offset each other and leave the inflation level of the individual economies
unchanged. This also means that the inflation difference between countries will be stable and
cause the difference in the price level of the countries to expand. This corresponds to some
extent with what we saw in figure 2. The model built in this paper is based on a model made
by Wickens (2010), but is expanded with a government that can affect the economy of the
individual countries. The model is a New Keynesian model which have a micro foundation
where the actions households optimizing utility and firms maximizing profits are aggregated
together to form the short run supply curve, the aggregated demand curve, and the natural
output level as described by Gali (2007). The New Keynesian models are based on an
assumption of nominal rigidities and imperfect competition. The model presented here uses
the New Keynesian supply and demand curves, but is not micro founded, as the model is
expanded with a government. One can form a micro foundation for this model by describing
the government’s effect on households and firms decisions, but this is not within the scope of
this paper6.
5.2 The model equations
From the actions of the firms and the households in the economic the natural or long run level
of output is found7. The natural rate of output is determined by a production function where
the production of the individual firm is given by a technology level and a labour input. The
labour is supplied by households who work in order to earn money to use for consumption.
6 To do so one would have to account for the government’s role in the economy by describing the effects from
government expenditure and taxation on household and firm behavior. 7 Gali (2007): “Monetary Policy, Inflation and the Business Cycle” Chapter 3
Page 14 of 27
The optimal labour supply balances the marginal utility gained from consumption with the
marginal disutility from working. The firms determine their demand for labour by
maximizing profits in a setting with differentiated goods. The firms demand labour to the
point where the marginal product of labour is equal to the profit maximizing markup over
marginal cost. The markup is determined by the firm’s ability to differentiate its goods. The
markup will move towards one as the market move towards perfect competition. The natural
rate of output is the point where labour supply meets labour demand and where prices are as if
they were fully flexible. In this model we have incorporated government spending which have
a negative impact on the long run output level in the economy. This is because public
spending is financed with taxes on both income and capital and it therefore increases
distortions in the economy. The natural rate of output is given by
(1)
Where is a constant determined by the utility and production functions. ait is the log of the
technology level in the economic for country I, and is its effect on long run output. is
the public spending. In this model the natural level of output is different from the efficient
level, as the firms set prices higher than they would under perfect competition and because the
taxes increases costs. The higher prices reduce the production and hence the labour demand.
The short run aggregated demand, AD, curve is given by the households’ demand for
consumption and is derived under the condition that consumption must equal production at all
times.
( ) ( ( ) ) (2)
yit is the production for country i at time t, It is the nominal interest rate set by the common
central bank and is not country specific, is the expected inflation, and ρi is the discount
factor, which is assumed to be constant over time. The output gap of country i is created using
the equation 1 and 28
( ) ( ( )
) (3)
( )
(4)
is the natural rate of return. In the long run equilibrium the natural rate of return will be
equal to the discount rate and the expected growth in the natural rate of output. In this model
an increase in the natural rate of return can come from an expected increase in the technology
level of the economy or from an expected decrease in public spending. This means that the 8 See appendix A.1 for derivation
Page 15 of 27
government can actually influence the return rate of the economy with active fiscal policy and
thereby affect the output gap. In this model the natural rate of return is determined by defined
model variables, but it can also be generalized so that it captures all effects on the output gap
not directly included in the model.
The inflation rate is derived from the price setting behavior of firms and comes from the fact
that there is a degree of price stickiness in economy and that firms have some market power.
This gives the short run aggregated supply, SRAS, curve.
(5)
Equation 3 gives us the aggregated demand curve and equation 5 gives the aggregated supply
for the individual countries in the monetary union. The central bank of the union will however
have to take the whole union into account when it conducts its policy and we therefore
construct a common AD and SRAS curve. This is done by taking the weighted average of the
countries individual AD and SRAS, done here with only 2 countries.
, is the weight of the country and can e.g. be determined by the
relative population size.
Doing so for both the AD and the SRAS curve gives the union curves.
(6)
(7)
We assume that the central bank has a cost function in the following form.
(8)
The central banks cost function is given by deviations both from the inflation target and from
the output gap. If the central bank is only adverse towards inflation deviation it would
correspond to the special case where η2 = 0.
5.3 Finding equilibrium
The central bank will set an interest rate which minimizes the loss function under the
constraint given by the SRAS and AD curves. The central bank finds the optimal solution
taking shocks and expected future inflation as given, as it cannot affect these. This gives the
result
(9)
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Equation 9 is the optimal balance between the output gap and deviation from the target
inflation rate. Equation 9 is substituted into (7) to find the optimal inflation rate and is solved
using iteration9.
(10)
The optimal output gap is then given by
(11)
The central bank controls the inflation with the nominal interest rate through the AD curve.
The real interest rate affects aggregated demand which in turn affects the inflation rate. The
optimal real interest rate is found by substituting (11) and (10) into (6)10
.
(12)
The central bank sets the nominal interest rate with a markup over the inflation target such
that the overall cost function of the central bank is minimized both with respect to inflation
and output gap. From equation 10 and 11 one can see that the more weight the central bank
puts on the output gap in the cost function, the more will it let inflation deviate from the target
value. This also goes the other way around that there more weight is put on inflation deviation
the larger the output gap. In the case where the central bank does not put any weight on the
output gap then the inflation rate will be set equal to the target inflation which also insures
that the real interest rate is equal to the natural rate of return of the monetary union. This will
be the assumption throughout the rest of the model.
By using the rule for the optimal nominal interest rate found in 12 we can find both realized
inflation and the realized output gap. To do so we first combine the AD and the SRAS curves
to get inflation as a function of the nominal interest rate.
(13)
The expected value of future inflation and future output gap is found by taking the expected
value of equation 10 and 11 under the assumption that η2 = 0.
(
)
(
)
9 See appendix A2 for derivation
10 See appendix A2 for derivation
Page 17 of 27
Substitution this into the combined AD and SRAS curve then gives
(14)
The realized inflation rate will be the target inflation rate plus the effect from the unforeseen
shocks. This result is not surprising. The central bank only values keeping the inflation rate on
target and does therefore not have any incentive to create surprise inflation and consequently
have a creditable inflation target.
With the rule for the nominal interest rate we are now able to determine the inflation rate of
the individual countries in steady state. In steady state all expected variables must equal the
realized variables and using that we find the actual country specific inflation rate.
( ) ( ( ) )
In steady state all shock are defined as zero and we therefore get
The optimal nominal interest rate set by the central bank was calculated to be
Inserting that in the AD curve for country i and rewriting
(15)
With the rule for the nominal interest rate and the expression for the country specific AD and
SRAS we can use the method of undetermined coefficients to find the solution for the
inflation11
.
(16)
The inflation is given by the steady state inflation and the innovation that comes from the
demand and supply shocks in period t.
In steady state the inflation rate of the individual countries differ from the union average due
to a difference in the natural rate of return of the countries from the average. A country that
has a higher than average natural rate of return, will have a lower than average inflation rate
as the natural rate of return of the country must always equal the real interest rate in
equilibrium. With a high natural rate of return comes a high natural rate of output which
means that the economy can have a higher economic activity before inflation increase.
11 See appendix A3 for derivation
Page 18 of 27
Countries with a lower natural rate of return than the average will have a higher inflation rate
in order to ensure equilibrium. The conclusion from equation 15 is that even though the
central bank is able to set a nominal interest rate that ensures an average inflation rate equal to
the inflation target, it is unable to affect the inflation rates difference between countries, as the
central bank cannot affect the natural rate of return. This constant inflation difference between
countries in the same monetary union can have long term negative consequences for some of
the countries as described in section 2.
6 The dynamics of the model
In this section we want to examine the dynamics of the model to see how changes in model
parameters or shocks to the economy affect equilibrium. This is important as it gives an
insight in what drives the model and what consequences a given monetary policy will have
for the economy as a whole and for the individual countries. In equilibrium we have that there
is no output gap and that the inflation rate for each country is given by the central bank’s
inflation target and the difference between the country’s natural rate of return and the union
average natural rate of return. We therefore have that only changes in the country individual
natural rate of return or changes to the inflation target will affect the long run equilibrium. In
the short run the output gap and inflation is also affected by shocks to the economy, which
can hit both the individual countries and the union as a whole. In our simple model the central
bank cannot foresee the shocks and we have not incorporated any autocorrelation in the
shocks. This means that the monetary policy will not change when a shock hits the economy,
because the central bank will already have set the interest rate and does not receive any
information on future shocks. So in each period the central bank will conduct monetary policy
based on the assumption that the economy is in its long run equilibrium, since this is the best
guess of the economic situation at time t. This is a direct result of the way the model is
formulated, and the short run dynamics of the model would change, if we changed the way
the shocks was generated and added autocorrelation.
We know from equation 15 that the long run inflation rate of a country depends on its natural
rate of return. If the natural rate of return of a country suddenly rises due to a change in the
economic environment of that nation, then the equilibrium will be broken and the natural rate
of return will be higher than the real interest rate. The average rate of return for the whole
monetary union will also increase, but not to the same extent. The central bank will react to
Page 19 of 27
the increase in the union natural rate of return by raising the nominal interest rate such that the
real interest rate is again equal to the natural rate of return. The rise in the nominal interest
rate will be equal for all countries, but it will not be enough to ensure equilibrium in the
country where the natural rate of return increased. To do so the inflation rate of the country
must fall, as it is the only way the real interest rate can be changed once the nominal interest
rate has been set. The decrease in the inflation rate of country A happens because the increase
in the natural rate of return increases the total possible production of the country and thereby
its long run level of output. If the long run level of output is suddenly shifted upwards then
output gap will become negative and this will imply that the economy is now
underperforming. When the output gap is negative there will a downwards pressure on prices
and that decreases inflation. The decrease in inflation lowers the real interest rate, which have
a positive effect on economic activity allowing the production to increase and close the output
gap.
An increase or decrease in the natural rate of interest can in this model by caused by two
factors, a change in the growth rate of the technology level, or a change in the growth rate of
public expenditure. An increase in the growth rate of the technology level will increase the
production of the firms in the economy and the long run output level causing the inflation to
fall as described above. The last case, when the government decreases its expenditure, should
also be accompanied with a decrease in taxes on income, capital, production, and other
distorting taxes. A general decrease in distorting taxes will lower the marginal cost of the
firms in the economy, as they are taxed less and because a decrease in income taxes lowers
the cost on labour. The lowered marginal cost will lead to an increase in production and the
long run output level which in turn decreases long run inflation.
7 Affecting the equilibrium
We have shown how deviation between countries’ inflation rates is caused by a difference in
the countries’ natural rates of return. In section 2 we argued how the differences in the
inflation level between the countries of a monetary union can cause long term problems for
the economy and lead to a debt crisis. It is therefore in the interest of the government of
countries that have a high inflation rate to try to bring it down. Since the government and the
national central banks do not have direct control over the nominal interest rate, they can only
affect the inflation level by trying to change the domestic natural rate of interest. A country
that has a high inflation rate will need to increase its natural rate of interest in order to lower
Page 20 of 27
the inflation rate. The natural rate of interest is given by the discount rate, the expected
growth in the technology level and the expected growth in the government expenditure. The
discount rate is formed by household preferences and is beyond government control. The
growth in the technology level in the economy is very hard for the government to affect in a
systematic way, and although different policies can try to enhance the growth there is no
guaranteed result. The only variable that the government has direct control over is the change
in the government expenditure which the government can choose to decrease or increase. By
decreasing the expenditure level it will leave room for more private investment and it will be
able to decrease taxes together with the expenditures, thus lowering the marginal cost for
firms in the economy and in the end decrease inflation. If the government on the other hand
increases its expenditure it will have the opposite effect and lead to an increase in inflation.
This means that the government needs to be careful with its way of conducting fiscal policy as
it will affect the long term equilibrium of the country’s economy.
The fact that government spending affects equilibrium has the implication, that if there is a
difference in the natural rate of interest between the countries in the monetary union, there
will be a need for the governments across the union to perform active fiscal policy to equalize
the natural rate of return and thereby inflation. If this those not happen the monetary union
will have a hard time surviving in the long run as the difference in inflation rates will cause
major structural problems for some economies. Active fiscal policy should be coordinated
throughout the monetary union in order to be most efficient, since countries with a low natural
rate of return can raise it by reducing government spending, while countries with a high
natural rate of return can reduce it by increasing their spending. Although it is in the interest
of all participating economies to ensure the survival of the monetary union, there is a potential
free rider problem as it is in the individual interest of countries with a high natural rate of
return to keep it high. These countries have a high export and will not be interested in
bringing it down as it is better for them to let the other countries do the decrease in their
natural rate of return needed to secure a stable long run union equilibrium. This is true for
every country with low inflation as they all have the same incentive to free ride and it will
therefore be difficult to commit these countries to increase their inflation. They have no
interest in increasing government spending, which leaves it up to the high inflation countries
to do all the conversion. In order to avoid the possibility of some countries with low inflation
free riding while other increase inflation, there will be a need to ensure a commitment of
inflation adjustment from all countries. A fiscal union along with the monetary union is a way
Page 21 of 27
of dealing with this problem, as some part of government spending then will be coordinated at
a higher level and with the interest of the union as whole in mind. A fiscal union will
effectively remove the free rider problem, as the countries are forced to conduct fiscal policy
in a way the benefits the union and not the individual countries. There are reasons why a
fiscal union can improve the conditions for a monetary union, but these mainly focus on the
possibility to form active fiscal policy to counter shock. We have here argued that the fiscal
union will be a way of dealing with a fundamental problem in the structure of the union.
8 Conclusion
The purpose of this paper was to investigate how it would affect an economy if it joined a
monetary union, where the participating countries differed in their economic structure, in this
paper modeled by a difference in the countries’ natural rate of return. We have seen that in
such case the inflation rate will also differ and this have the potential to erode the
competiveness of a country and thereby create an ever growing trade deficit. If this trade
deficit was not handled it could lead to a development where the government took up an
increasing foreign debt in order to secure the balance of payments. Because the financial
markets have a tendency to think that countries in the same monetary union share debt, the
interest rate on government bonds will often be the same for countries in a monetary union.
The interest rate on bonds for a country that finances a negative trade balance will therefore
by relatively low, and this will allow the country to acquire a much larger debt than it would
otherwise have been able to, had the country not been part of a monetary union. If the
politicians do not restrain themselves there is a chance that a country will accumulate more
debt than is sustainable and that can lead to a debt crisis once the financial market realizes
this. We saw that there was a possibility to counteract this development by conducting a fiscal
policy that reduced the difference in the natural rate of return between the countries. This
would ensure a common inflation level and avoid that some countries had their competiveness
destroyed by increasing prices. The main obstacle in doing so was the fact that the countries
that have a low inflation rate benefits from this as their net export will be growing. They will
therefore have an incentive to avoid an equalization in the inflation rates since they are better
off without it. It may therefore be necessary to form a fiscal union to force the participants of
the union to coordinating their fiscal policy in a way that aims at reducing the inflation
difference. Through the fiscal union the governments should be able to reduce the inflation
differences and thereby deal with the structural problem presented in this paper.
Page 22 of 27
Appendix
A.1
The natural rate of output is given by
The AD curve is given by
( ) ( ( ) )
The output gap is defined as
( ) ( ( ) )
( ) ( ) (
) ( ( ) )
( ) ( ( ) ) ( )
( ) ( ( ) ) ( )
( ) ( ( ) ) ( ) ( )
( ) ( ( )
( )
)
( ) ( ( ) )
A.2
The cost function of the central bank is given by
(17)
The object of the central bank is to minimize the cost subject to the constraint given by the
SRAS curve rewritten such the it gives the deviation from the inflation target.
The central bank cannot either affect the expectations to future inflation nor the shock to the
economy and therefore takes those as given whene minimizing the cost function.
To find the optimum we first setup the Lagrangian
Then find the first order conditions
Page 23 of 27
This gives the optimality condition
(18)
Substitution the expression for the optimal output gap into the SRAS curve gives us
(
) (
)
The expression is forwarded one period by taking the expected value of it.
By inserting the expression for the expected inflation into the expression for the inflation rate
we get
(
)
(
)
Continuing this proses and we get
(
)
∑ ((
)
)
We then use the assumption that
(
)
We the k ∞ and get
(19)
From this we find
(20)
Then central bank sets the nominal interest rate from its expectations to the output gap and
inflation rate to time t. When it sets the nominal interest rate the shocks in time t is not known
Page 24 of 27
by the central bank since we have assumed that the shocks are first realized after the central
bank sets the nominal interest rate. Using the expression for the optimal output gap together
with the expression for the optimal inflation and inserting them in the AD curve we get
(21)
We get the expected inflation and the expected output gap from (19) and (20)
Inserting this in equation 5 gives us
We then investigate the system when the central bank does not put any weight on the output
gap.
(
)
(
)
(
)
A.3
The AD curve for the individual countries is given by
( ) ( ( ) )
The SRAS curve is given by
Together with the AD curve we have
( ( ) )
We can rewrite the SRAS curve and get
Page 25 of 27
Taking expectations to this
( )
This is substituted into the SRAS curve
( ( )
)
( ) ( )
( ) ( ) (22)
We now have an expression for the inflation as a function of future expected inflation, the
nominal interest rate, the natural rate of return, and the shocks to the economy.
To solve this equation and find the inflation we use the method of undetermined coefficients,
which means that we will first have to come up with a qualified guess of what the solution
should be. Because the model is linear and depends on the nominal interest rate and the
shocks we guess that the solution is on the form.
The goal is now to determine A.
First we recognize that
( ) ( )
We insert this and get
With an expression for A we can find the expression for actual inflation
(
)
We know that
Inserting this in the inflation rate
(
) (23)
Page 26 of 27
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