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Macroeconomic behavior, European integration
and cointegration analysis
Soren Johansen and Katarina Juselius
University of Copenhagen
1. Introduction
The last few decades have experienced large changes both in the Danish economy and in other European
economies. Trade liberalization within the European Common Market started as early as 1957, but
intra-European movements of goods and labor were, nevertheless, largely restricted by government
regulations and trade barriers. The break-down of the Bretton Woods in the beginning of the seventies,
replaced first by the "snake in the tunnel" and later by the EMS, seemed to trigger off the endeavors to speed
up the European economic integration process. However, the abolishment of restrictions on trade with goods
and capital (and to some extent restrictions on labor movements) has quite fundamentally changed the
functioning of the European economies, and hence changed the scope for macroeconomic policy. The
foundation of the European Monetary Union is likely to have still more fundamental effects on the Danish as
well as other Nordic and European economies independently of whether they axe insiders or outsiders.
Whether the macroeconomic effects of these changes have been sufficiently well understood is another
question. The idea of an integrated Europe was politically "sold" to the public by promising more prosperity,
in particular more employment. Instead, the Europeans seemed to get less prosperity and more
unemployment.
Therefore, both politically and economically there is a strong need to improve our empirical understanding
of how macroeconomic behavior has changed as a result of the increased European integration and the
increased globalization of today's world.
2. Modelling economic variables
To illustrate the ideas we use an analogy from physics and think of the economy as a system of balls
connected by springs. When left alone the system will be in equilibrium, but pushing a ball will bring the
system away from equilibrium. Because all balls are connected, the 'shock' will influence the whole system,
but after a while the effect will die out and the system is back in equilibrium. In the economy, the balls would
correspond to the economic variables and the springs to the transmission mechanisms that describe how
economic shocks are transmitted through the system. As we know, the economy is not a static entity. Instead
of saying that the economy is in equilibrium it is more appropriate to use the word 'steady-state'. Hence, we
need to replace the above picture with a system where the balls are moving with some 'controlled' speed and
by pushing a ball the speed will change and influence all the other balls. Left alone the system will return to
the 'controlled' state, i.e. the steady state.
How can cointegration analysis be used for the purpose of describing quantitatively such complicated
'moving' system as the macroeconomy no doubt is? We will demonstrate below the ideas based on the
cointegrated VAR (VectorAutoregRessive) model. This is a system of equations describing the time path of
each variable (ball). This time path is dependent both on its interrelations with the other variables (the
springs) and on the shocks that have bombarded the system. Without any shocks the time path would
converge to its 'state-state' path. With the frequent bombardment of shocks typical of our macro-economy the
steadystate is essentially never observed but is, nevertheless, present in the system as a force that does not
allow the 'balls' to move too far away the steady-state. As an example of such a system we have chosen a
small monetary system consisting of the following balls: nominal money stock (M) prices (P) real income
(Yr), the bond rate (Rb), and the deposit rate (Rm). In Figure 1 we have graphed the time path of these
variables in logarithmic form, denoted by lower case (e.g. m = log M). Since the development of real money
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is more interesting than nominal money, we have chosen to show (m - p) and the change in prices (pt - pt-1),
i.e. inflation. It seems obvious that these variables do not describe an economy in equilibrium, i.e. the
variables do not seem to evolve around constant means. In figure 2 we report the graphs of the velocity of
money (m - p - y) and the interest rate spread (Rm – Rb) to see if the time paths of the transformed variables
evolve around a constant mean. This does not seem to be the case and we, therefore, ask if these exists a linear
combination between the two that becomes more stable. This is the relation shown in panel 3 which is defined
as:
(m – p - y) - 14.1(Rm - Rb)
where the coefficient 14.1 has been estimated by cointegration techniques.
Figure 2.1: A graphical display of five economic variables in a small monetary system: real money stock and
real income (panel 1), the long-term bond rate and the deposit rate (panel 2), and the inflation rate (panel 3)
From Figure 2 we notice that this relation seems to evolve around a constant mean over time. Even if the
individual variables are pushed away over time there are forces in the economy securing that the above
relationship remains stable. We call the 'less stable' variables in panel 1 and 2 for nonstationary and the 'more
stable' variable in panel 3 for stationary. The basic idea of the cointegration analysis is to find linear
combinations between nonstationary variables that are stationary. This is illustrated by the linear combination
(m - p - y) - 14.1(Rm - Rb) where the nonstationary component in (m - p - y) and (Rm - Rb) cancels. We say
that they have a common stochastic trend.
How can be use this to describe the complicated economy? We now use the estimated cointegration
relation and define:
m* = p + y + 14.1(Rm - Rb)
and define it as a steady-state relation for how much money the Danes have been willing to hold in the bank
over time. Is says that Danes need more money to do their transactions the higher the level of income and
prices. It also says that when the deposit rate (interest on money in the bank) is high relative to alternative
placements (for instance in bonds) then Danes are willing to keep more money in the bank.
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Figure 2.2: The time graph of the velocity of money (panel 1), the interest rate spread (panel 2), and the
deviation from steady-state for money holdings (panel 3).
Standard macroeconomic theories predict that such a relation should exist, but say very little on the
magnitude of the coefficient describing the alternative cost of holding money, or whether this relation is stable
over time, or what happens when the macroeconomic system is exposed to a major shock, such as lifting the
restrictions on capital movements. If such shocks shift the steady-state position and pushes money holdings
away from steady-state, economic theory cannot say much about the magnitude of the speed of adjustment
back to the new steadystate. For example, the graph in panel 3 shows a major steady-state error at around
1983 when Denmark abolished previous restrictions on capital movements. It also shows that the subsequent
adjustment back towards the new steady-state that was reached approximately in 1987.
Based on stringent statistical analysis it is possible to use cointegration analysis (i) to test whether a
hypothetical steady state relation is empirically stationary (mean-reverting), (ii) to estimate the coefficients
describing the relation, (iii) to estimate the speed of adjustment towards this relation, (iv) to estimate how
other variables in the system react on the equilibrium error, and (v) investigate the origins of the shocks that
pushed the money holdings away from the previous steady-state position.
In periods of transition, such as the transition from the previous fairly closed economy during the Bretton
Woods exchange rate period towards the increasingly open economy of today, it is very likely that the big
shocks to the macro-economy have moved the economy towards new steady-state positions. The adjustment
towards these need not be at all fast as illustrated in Figure 2, panel 3. On the contrary! Because structural
reforms are often painful and therefore not politically popular, the adjustment is likely to be very slow. The
recent experience of the long lasting recession in Denmark (and Europe), with modest real growth rates, high
rates of unemployment, low inflation rates and high real interest rates, suggests definitely that the Danish
economy has been out of steady-state in many important sectors.
In brief, the concept cointegration analysis covers a wide variety of statistical procedures for the
formulation and testing of economic models
 that can distinguish between short-term and long-term dynamic responses of economic behavior,
 that can describe interactions and feed-back effects within a system
 that can describe the underlying driving forces.
3. A proposed methodology
In Figure 3 we have indicated how cointegration analysis can be used to address important
macroeconomic problems such as the determination of unemployment, inflation, and interest rates. The
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diagram illustrates how cointegration analysis can be used to restructure and simplify the empirical problem.
The invariance of the cointegration property to increases in the information set can justify the decomposition
of the full set of variables into smaller blocks which can be analyzed partially. By building on the results from
the partial analyses the full analyses can be performed much more efficiently.
The illustration below is for a decomposition of the full variable set into four blocks describing the labor
sector, the money sector, the government sector, and the foreign sector. The idea is that the balance (or
imbalance) of each sector can be measured by the deviation from its steady-state position at each point of
time. It is assumed that the variables of interest, i.e., unemployment, inflation, and interest rates, are primarily
affected by the magnitude of the disequilibrium in each sector. Hence, if a sector is in steady-state, there
should be no pressure arising from that sector. On the other hand, the larger the imbalance the greater the
pressure.
 domestic labor market theories describing domestic wage setting and the relation between price
and wage inflation,
 monetarist theories describing the effect of excess money on inflation, and
 external theories describing the foreign transmission effects on the domestic inflation.
Macroeconomic theory can be used to derive qualitative statements of the consequences of being out
of steady-states, but it is not very informative about how to quantitatively measure such imbalances, nor
how to measure the impact. Economic theory can suggest a number of likely transmission effects, but is
not very precise about the size of the impact, and cannot usually tell whether the effects are fast or slow.
This methodology is illustrated below.
Figure 3. An econometric framework for the analysis of price inflation,
interest rates, and unemployment
For each sector we define an information set Ii, (i = l, 2, 3, 4) that contains the most important
variables for that sector. For example: I1 contains real wages, productivity, the wedge between consumer
and producer prices, unemployment rate, price inflation, and the bond rate; I2 contains real money stock,
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real aggregate income, the deposit rate, the bond rate, and price inflation; I3 contains the public debt,
government deficit, and real GDP: I4 contains the real exchange rate, domestic and foreign inflation
rates, and domestic and foreign bond rates.
Using cointegration analysis we can obtain a measure of the imbalances in each sector. For instance,
w - w*, is a cointegration relation measuring the deviation of real wages from its steady-state value,
w* = f (I1); m - m* is measuring the amount of money holdings in excess of the steady-state demand for
money m* = f (I2); p - p* is measuring how domestic prices compare with international prices, etc. The
final model analysis can then be used to answer questions like how much a wage imbalance, a monetary
imbalance, and an imbalance of the international competitiveness is likely to influence unemployment, price
inflation, and the longterm interest rate.
The increased globalization, and hence, the increased domestic macroeconomic dependency on the outside
world, makes small open economies very vulnerable to changes in the international situation. The pressure on
policy makers to react quickly and adequately to defend public interest in situations of crises created by
changing market conditions is likely to increase. Therefore, it seems important to improve our empirical
understanding of the underlying macroeconomic mechanisms and how they have changed with the increased
globalization. The econometric task is empirically to distinguish between macroeconomic behavior in the
short, medium and the long run as well as the speed with which the economies adjust to these steady-states.
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