De Nederlandsche Bank Research Department Eurozone ... - Dnb
Research Department Eurozone Money Demand: time series and dynamic panel results E.M. Bosker Research Memorandum WO no 750 November 2003
De Nederlandsche Bank
EUROZONE MONEY DEMAND: Time series and dynamic panel results E.M. Bosker*
* I am especially grateful to Jean-Pierre Urbain, Franz Palm and Peter Vlaar for their comments. Moreover I would like to thank Peter van Els and the other interns for their suggestions and Peter Keus for statistical assistance. Views expressed are those of the individual author and do not necessarily reflect official positions of De Nederlandsche Bank. Maarten Bosker had an internship at De Nederlandsche Bank from June until November 2003, under the supervision of prof.dr. F.C. Palm, dr. J.R.Y.J. Urbain (Universiteit Maastricht) and dr. P.J.G. Vlaar (Research Department, DNB). This research memorandum is an abbreviated version of his master’s thesis.
Research Memorandum WO no 750/0339 November 2003
De Nederlandsche Bank NV Research Department P.O. Box 98 1000 AB AMSTERDAM The Netherlands
ABSTRACT Eurozone money demand: time series and dynamic panel results E.M. Bosker The effectiveness of the important role for money in the monetary policy of the European Central Bank (ECB) is usually assessed by looking at time series estimates of the eurozone money demand equation. This implicitly calls for a choice of aggregation method to construct data series long enough to obtain meaningful econometric results. This study discusses different aggregation methods and finds that variable weight growth rate aggregation has the nicest properties. The results based on the hereby constructed series confirm the effectiveness of the ECB´s monetary policy. Next this study tries to avoid the issue of aggregation by adopting a (nonstationary) dynamic panel method that uses the data series for each of the eurozone countries by itself. This shows that differences in the money demand equation across the eurozone countries are likely to exist. Not being able to quantify these differences makes it difficult to give specific implications for the ECB´s monetary policy. The found differences could however influence the time series estimates and through these have implications for the ECB´s monetary policy. Key words: money demand, eurozone, aggregation, time series, dynamic panel estimation JEL codes: C12, C32, C33, E41, E52
SAMENVATTING Geldvraag in de eurozone: tijdreeks en dynamische panel resultaten E.M. Bosker De effectiviteit van de belangrijke rol voor de geldhoeveelheid in het monetair beleid van de Europese Centrale Bank (ECB) wordt normaal gesproken bekeken door te kijken naar tijdreeksschattingen van de geldvraagfunctie in de eurozone. Dit brengt echter de keuze voor een aggregatiemethode, waarmee voldoende lange datareeksen gevormd worden om goede econometrische resultaten te verkrijgen, met zich mee. Deze studie belicht verschillende aggregatiemethoden en laat zien dat variabele groeiratio aggregatie de beste eigenschappen heeft. De resultaten van de op die manier geconstrueerde reeksen bevestigen de effectiviteit van het monetair beleid van de ECB. Hiernaast probeert deze studie de aggregatieproblematiek te vermijden door een (niet-stationaire) dynamische panel methode te gebruiken die de landspecifieke datareeksen gebruikt. De resultaten laten zien dat verschillen in de geldvraagfunctie voor de eurozone landen waarschijnlijk zijn. Het niet kunnen kwantificeren van deze verschillen maakt het moeilijk specifieke implicaties te geven voor het monetair beleid van de ECB. Echter de gevonden verschillen zouden de tijdreeksschattingen kunnen beïnvloeden en hierdoor implicaties hebben voor het monetair beleid van de ECB. Trefwoorden: geldvraag, eurozone, aggregatie, tijdreeksanalyse, dynamische panel schattingen JEL codes: C12, C32, C33, E41, E52
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INTRODUCTION
´The primary objective of the European System of Central Banks (ESCB) shall be to maintain price stability in the medium term´ (Article 105(1) of the Treaty establishing the European Community). In accordance with this primary objective, the main elements of the stability-oriented monetary policy strategy of the Governing Council of the European Central Bank (ECB), as announced in October and December 1998, are aimed at maintaining price stability. Price stability is defined as a year-on-year increase in the Harmonised Index of Consumer Pric es for the eurozone below 2%. As of May 8th 2003, the Governing Council has extended this definition to below, but close to, 2%, to underline the ECB´s commitment to guard against deflation. One of the ‘two pillars’ announced to achieve the strategy’s obje ctive is a prominent role for money as money constitutes a natural, firm and reliable ‘nominal anchor’ for monetary policy aiming at the maintenance of price stability (ECB Monthly Bulletin, January 1999). The development of the price level is believed to be a monetary phenomenon in the long run and useful information about future price movements may thus be revealed by the development of the amount of money held. It can offer important signals when setting the monetary policy. This and the fact that the monetary policy strategy of the ECB is aimed at the medium term, requires the definition of a monetary aggregate which is a stable and reliable indicator of the price level over the medium term. The Governing Council of the ECB has decided to give M3, the broad money aggregate, a prominent role in the monetary policy strategy. It has chosen M3, because it is believed to have better properties than more narrow money aggregates in terms of stability and information content with respect to price developments in the long term (ECB Monthly Bulletin, February 1999). The Governing Council even announced a quantitative reference value for the growth of M3 of 4.5% per year (ECB Monthly Bulletin, January 1999). This reference value is not a monetary target but deviatio ns from the reference value are closely analysed in the context of other economic data in order to obtain useful information regarding possible risks to price stability. Recently (ECB Press Release, May 8th 2003), the Governing Council announced that this reference value will not be reviewed every year, keeping it fixed at 4.5% per year. To be able to say that setting a reference value for the growth of M3 is consistent with the main objective of price stability in the medium term, there must exist a stable relationship between M3 and the price level at this time horizon. The aim of this paper is to conduct empirical research in order to test for the existence of such a stable relationship at the eurozone level. If evidence of such a stable relationship can not be found, this would shed serious doubts on the role for money in the monetary policy of the ECB. It would imply that the ECB bases its monetary policy on the incorrect assumption of the existence of a stable
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relationship between M3 and the price level, causing damage to its credibility and subsequently the effectiveness of its monetary policy. First the existence of a long run money demand equation is verified using the usual framework, in which first the national series of all eurozone countries are aggregated into series for the eurozone and then cointegration techniques are used to test for and identify the long run relationship(s). Besides discussing the exact method used and the resulting outcomes, a thorough discussion of the type of aggregation method used to construct the series for the eurozone is given.
In the second part of this paper, a nonstationary panel data framework is used to answer the question whether or not a long run money demand equation exists. Using nonstationary panel data techniques makes the issue of which type of aggregation method to use irrelevant, each country´s individual series are used in the analysis. Another nice feature is that the framework allows for testing the equality of the long run relations across the countries in the panel. If a long run money demand equation is found for each country in the panel, these tests can be used to test for and, if found, identify differences in that relation between the countries (or groups of countries), that have handed over their monetary policy to the ECB in joining the European Monetary Union. As the ECB is only in charge of monetary policy as of 1999, it would not be very surprising to find such differences. If differences are found, identifying them is important as that allows the policy makers at the ECB to take account of these differences when deciding on a meaningful monetary policy. The paper is organised as follows. Section 2 introduces the economic model and gives a short review of past research stating also the econometric methods that have been used in the past in the analysis of money demand. Section 3 discusses the methods of aggregation used in constructing eurozone data series. Section 4 provides estimation results obtained using a time series framework. In Section 5 the nonstationary panel framework is introduced, giving an overview of recent developments in that field of econometrics and explaining the choice of test that is used in this paper. Estimation results using this econometric framework are presented. Finally Section 6 concludes.
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MODEL AND ECONOMETRIC METHODS
The existence of a long run money demand equation is typically assessed in the context of standard economic theories of money demand. As indicated in Ericsson (1998), in standard theories of money demand, money may be demanded for at least two reasons. First, out of transaction motives, it can be used as an inventory to smooth differences between income and expenditure streams and second as an asset among other assets in a portfolio. Both reasons for money to be demanded, lead to the following long run specification, M d / P = g(I,R)
(1)
where M d is nominal money demanded, P is the price level, I a scale variable and R a vector of returns on various assets. The theory suggests that g(.,.) is increasing in I, decreasing in those asset returns included in R that are excluded from M, and increasing in those asset returns in R that are included in M. In the literature one commonly finds (1) in the following log-linear form: md – p = α + β y + γ1 Rout + γ2 Rown + δ ∆p,
(2)
where lowercase letters indicate variables in logs, α, β, γ1 , γ2 , and δ are coefficients and ∆ is the difference operator. Rout are the rates of return on financial assets alternative to money and Rown the return on the components included in the definition of money itself. As argued in Fair (1987) both the outside and own rate are not transformed into logs. y is the real gross domestic product (GDP), a choice of scale variable that is very common in the existing literature, although one can also find studies in which it is chosen to be financial wealth, e.g. Fase and Winder (1998). Finally ∆p is the inflation rate (growth rate of the GDP deflator, i.e. nominal GDP divided by real GDP), included as a proxy for the return on goods alternative to money. Some indication of the signs and the magnitudes of the coefficients are β = 1 (quantity theory) or β = 0.5 (Baumol-Tobin), γ1 ≤ 0, γ2 ≥ 0 and δ ≤ 0, as holding money is an alternative to buying goods. The own an outside rates may have coefficients of equal magnitude but opposite signs. If this is the case, one can use γ1 (Rout - Rown ), instead of γ1 Rout + γ2 Rown in (2). The difference (Rout - Rown ) is often called the term spread and can be seen as the opportunity cost of money. It captures the effect of the return on alternative financial assets on the demand for real M3.
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Past research on money demand (see Golinelli and Pastorello (2001) for a good overview up to 1999) in the eurozone has focused on the loglinear long run money demand specification as in (2). Analysing money demand in the setup of equation (2) poses a number of questions. What variables are chosen to appear in the equation? How to choose the countries included in the sample, the sample period and periodicity of the data? What econometric framework to use in estimating the parameters of (2)? Since the ECB made clear that it would take M3 as the relevant indicator for money, most studies choose M3 to be the dependent variable of equation (2). Before this, other measures of money, like M1 and M2 are found in some studies. Some researchers advocated the inclusion of cross border holdings in the definition of money, but, as shown in Fagan and Henry (1998), this inclusion does not improve the estimation results. As mentioned before, GDP is most often chosen to represent the scale variable in (2). The use of GDP is supported by the demand for money based on transaction motives, consequently it can be argued to be suitable for more narrow definitions of money. The portfolio theory of asset demand suggests the use of financial wealth as a choice of scale variable more suitable for analysing broader money definitions. However, the lack of reliable financial wealth data is often used to justify the use of GDP for the scale variable. As for the choice of own and outside rates, most papers use the 3-month interest rate as a measure of the own rate, as this is included in the definition of M3, and the 10-year government bond yield (or a proxy) as a measure of the outside rate. One also finds studies in which only one of the two rates or only the term spread is included in the money demand equation. Finally inflation is measured by the growth rate of the GDP-deflator, i.e. nominal GDP divided by real GDP. With very few exceptions most studies take the end of the seventies as the beginning of their sample period. The European Monetary System (EMS) began in that period and the Exchange Rate Mechanism (ERM) was established (March 1979). The periodicity of the time series data is usually quarterly. The choice of countries to include in the analysis differs over past research done on European money demand. The last few years, research has mainly focused on the eurozone, where some studies exclude Luxembourg from the analysis. Usually the reason for omitting Luxembourg is unavailability of data (Beyer et al., 2001) and justified by its small quantitative importance (Clausen, 1998). Also, due to the monetary union between Belgium and Luxembourg, Luxembourg´s M3 is probably already included in Belgian M3 (Beyer et al. 2001).
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The usual econometric framework in which (2) is estimated is that of a time series setup. As most research finds that all the variables in (2) are non-stationary, the money demand equation is usually estimated in a cointegration framework. The estimation of the cointegrating relationship differs per author. Most recently the Johansen (1995) framework (Vlaar and Schuberth, 1999; Coenen and Vega, 1999; Brand and Cassola, 2000; Fagan and Henry, 1998) is used, while in the past the Engle and Granger (1987) two-step-approach was popular. Most recent studies focus on eurozone money demand only. First eurozone-wide aggregates are constructed using a certain method of aggregation (as prior to the introduction of the euro only national accounts are available), and then the cointegration techniques are ´unleashed´ on these constructed area-wide aggregates (Coenen and Vega, 1999; Brand and Cassola, 2000; Vlaar, 2004). In this analysis the first step, obtaining aggregate time series for the eurozone long enough to be able to make reliable estimates that do not suffer from small sample distortion, is crucial. The choice of aggregation method is thus important and needs to be considered carefully. Besides a thorough discussion of the method of aggregation to be used, another contribution of this paper is to adopt a dynamic panel approach in estimating the money demand equation. In doing so a number of problems using aggregated data are avoided. First of all the need to choose for a certain aggregation method does no longer exist, as all series for each individual country are expressed in local currency. Secondly the power of the usual cointegration tests is shown to depend on the time span of the data series used. Increasing the amount of information available by analysing time series across similar cross-sections, i.e. adapting a panel approach, leads to tests with better power properties (Levin and Lin, 1992). Another nice feature of the panel setup is that it explicitly takes account of the national differences in financial structures and markets and the country specific structural breaks by using the national series. Both effects are less evident when using eurozone aggregates as their impact is ´canceled out´ in the aggregation process. However, as noted by Dedola, Gaiotti and Silipo (2001), these country specific effects may result in differences in national money demand functions. If the monetary policy of the ECB has different consequences for different countries of the eurozone, it can be very helpful to identify and take account of these differences. The panel setup allows for testing homogeneity restrictions on the resulting money demand equations if similar relations are found for the countries in the panel. It allows for explicit tests that check whether or not the same long run relations hold for all eurozone countries or subgroups of eurozone countries. If substantial cross-country differences are found, looking also at national data can be of importance for polic ymakers.
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3
EUROZONE-WIDE AGGREGATES
3.1
Overview of aggregation methods
As already mentioned in the introduction, many previous studies on eurozone-wide money demand have focused on the estimation of the money demand equation (2) using area-wide aggregates. As data for the eurozone are only available as of January 1999, the problem is how to get a dataset for the eurozone large enough to be able to conduct meaningful econometric analyses. To overcome this problem, area-wide aggregates are constructed; i.e. the national time series are aggregated into overall area-wide aggregates. These aggregates are then used in the estimation of the money demand equation. The aggregation method chosen to construct the area-wide time series from the respective national time series needs to be considered carefully. Using the best possible method is essential, as the ECB could make non-optimal policy choices based on inappropriate figures used in analysing economic relationships (e.g. the money demand equation). Past research has acknowledged the importance of the choice of aggregation method and several suggestions have been made. A good review of four possible aggregation methods that have been used in the literature and focus on aggregating the level series is given in Winder (1997). The four methods discussed in that paper are: i) using fixed base period exchange rates, ii) using current exchange rates, iii) using fixed base period PPP rates, and iv) using current PPP rates. As shown in (3) below the use of current exchange or PPP rates to transform the national data in levels into euro, introduces an extra and unwanted component in the growth rate series.
∆ ln( xt et) = ∆ ln(xt ) − ∆ ln(et )
(3)
where xt is the series to be converted from local currency into the common currency and et is the corresponding exchange rate, i.e. units of local currency per unit of common currency. The growth rate will also depend on changes in the exchange or PPP rates. In an extreme case a country might have a positive growth rate in the serie s expressed in local currency but, because the local currency has experienced a large depreciation with respect to the common currency chosen, a negative growth rate in the series expressed in the common currency. When using fixed base period rates the problem is avoided as in that case: ∆ ln(et ) = ∆ ln( eT ) = 0 in (3), where T denotes the fixed base period. Another problem when using current rates is that the constructed series will depend, as can be easily seen in (3), on the choice of common currency. However it has to be noted that this problem may seem less
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important because all data will be expressed in euro. A useful property of the constructed aggregated level series obtained when using fixed base period rates,
xtEU = ∑ i xti eTi
(4)
is that the corresponding growth rate series will be a weighted average of each countries´ own growth rate, with weights being the respective current shares of the countries in the aggregate series, i.e.
∆ ln( xtEU ) = ∑ i
xti eTi ∆ ln( xti ) EU xt
(5)
Many of the researchers constructing area wide data use, based on the results by Winder, fixed base period rates to construct their aggregate series. For example, Fagan and Henry (1998) use fixed base period PPP rates for 1993, Coenen and Vega(1999) use fixed base period PPP rates for 1995 and Golinelli and Pastorello (2001) use fixed base exchange rates for 1999. Fagan and Henry (1998) argue in favour of the use of PPP-rates when choosing between fixed base period exchange rates or PPPrates. However as pointed out in Beyer et al. (2000) it is very difficult to construct PPP rates that are accurate and they are therefore an unattractive option compared to exchange rates. In two papers on constructing aggregate eurozone data Beyer et al. (2000, 2001) argue in favour of another aggregation method. They suggest constructing aggregate growth rates using variable weights, i.e.
∆ ln( xtEU ) = ∑ i
xti−1 eti−1 ∆ ln( xti ) EU xt−1
(6)
That is the eurozone growth rates are calculated by aggregating each country´s own growth rate using as weights the corresponding shares of the countries in the total aggregate in the previous period. The exchange rate used to calculate each country´s share is not fixed at a base period but varies with each period. Using the constructed aggregate growth rates, they then construct the level series by cumulating backwards starting from a given value at the end of the sample period. They have good reasons for using this method of aggregation. They aggregate growth rates instead of levels as they argue that aggregating levels using either fixed base period or variable weights leads to distorted aggregate series. Using variable weights when aggregating levels leads the to inclusion of an
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unwanted exchange rate effect in the constructed aggregates as shown in (3). Using fixed base period level aggregation, as argued in Winder (1997) and very commonly used in previous research, is not appropriate because the choice of base year is crucial in this case. Given the substantial relative pricechanges due to currency de- and reva luations, using for instance 1979 as base year would lead to an aggregate series which is different from the aggregate series constructed using 1999 as base year. They also use this dependence on the choice of base year to argue against using fixed base period weights when aggregating growth rates, leaving only aggregating growth rates using variable weights as the appropriate aggregation method.
The construction of aggregate growth rates using variable weights also has some nice properties. Namely that sub-aggregates (both regional and temporal) also aggregate correctly and that the result of aggregating the growth rate of the implicit price deflator for each country coincides with the growth rate of the implicit price deflator of the aggregate nominal and real data (price-aggregation matching holds). A useful property, since the growth rate of the price deflator is used as the inflation rate series. In the case of aggregating the level series using fixed base period weights, this property holds for the level series but not for the series of interest the growth rate series, i.e. inflation. 3.2
Constructing aggregate series using two different methods and comparing the results
In this paper aggregate series are constructed using both methods (fixed weight level aggregation and variable weight growth rate aggregation). After constructing the series, they are compared. The fixed weight method of Winder (1997) is used, but a small refinement is made. That is, the representation of the growth rate series resulting from the aggregation of the series in levels using fixed weights is improved in the following way:
∆ ln( xtEU ) ≅
i i i i i i ∆xtEU ∑ i xt / eT − ∑ i xt−1 / eT ∑ i ∆xt / eT xti−1 / eTi = = ≅ ∆ ln( xti ) ∑ EU EU EU EU i xt−1 xt −1 xt −1 xt−1
(7)
where the approximation ∆ ln xt ≅ ∆xt xt−1 is used. When (7) is compared with the expression that Winder (1997), using the approximation d ln xt ≅ dxt xt , finds (5), one can see that in (7) the weights are based on the previous period whereas in (5) weights based on the current period are used. The impact of this change has only an impact on the construction of the short and long term interest rates, as these two are the only two series aggregated using GDP-shares under the fixed weight aggregation method.
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To be able to compare the method of Beyer et al. (2000) a little better to the method proposed by Winder (1997), an extension is made to the representation of the aggregation method as in (6):
∆ ln( xtEU ) = ∑ i
xti−1 / eti−1 xti−1 / e t−i 1 ∆xti ∆xti / eti−1 i ∆ ln( x ) ≅ = t ∑ i x EU x i ∑ i x EU = xtEU −1 t −1 t −1 t −1
∑ x /e −∑ x ∑ x /e i
i t
i t −1 i
i
i t −1
i t −1
/ eti−1
i t −1
(8)
where again the approximation ∆ ln xt ≅ ∆xt xt−1 is used. Writing the aggregation method as in (8) shows that the aggregate growth rate at period t is calculated by first fixing the exchange rates at period t-1, then calculating the aggregate in levels at period t and t-1 using those exchange rates and finally calculating the growth rate using these to aggregate level series. When this is compared to (7) one can immediately see that whereas in (7) a fixed base year is chosen for the whole sample period, in (8) this fixed base year is each year set at the previous year. 3.2.1
Constructing the aggregate series using fixed base period weights to aggregate national level
series The aggregate series are constructed using the fixed weight level aggregation method as argued in Winder (1997). The 1999 fixed conversion rates (for Greece 2001) are used to convert the series in local currency into euro. Note that in this way 2001 is implicitly chosen as the fixed base year. The nominal GDP, real GDP and nominal M3 aggregates are constructed as in (4). The aggregate price series is constructed by dividing the aggregate nominal GDP series by the aggregate real GDP series. As shown in Winder (1997) this is equivalent to constructing the aggregate price series by aggregating national price series using each countries´ current real GDP share of total eurozone GDP as weights. Aggregate real M3 is constructed by dividing aggregate nominal M3 by the aggregate price series. Both the aggregate long term interest rate and the aggregate short term interest rate series are constructed by aggregating them according to (7). Growth rates of all series are constructed by taking first differences of the series in logs. 3.2.2
Constructing the aggregate series using variable weights to aggregate national growth rate
series The aggregate series are constructed using the variable weight growth rate aggregation method of Beyer et al. (2000). That is, using (8) the growth rates of the following national series are aggregated into an aggregate eurozone growth rate series. Aggregate real and nominal GDP growth rates are calculated using real GDP shares. The same weights for nominal and real GDP are chosen to ensure
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that price-aggregation matching holds. Instead of choosing real weights also nominal weights could be chosen for each of the series, but by choosing real weights only the nominal GDP measure is affected, which may be considered the least interesting for the money demand study. Aggregate short and long term interest rate growth rates are also calculated using real GDP shares. Finally the aggregate nominal M3 growth rate is calculated using nominal M3 shares. The aggregate inflation rate is constructed by subtracting the aggregate real GDP growth rate from the aggregate nominal GDP growth rate, which, because of the just explained price-aggregation matching, is the same as aggregating the national inflation rate series using real GDP shares as weights. Level series are constructed by cumulating the series backwards using as starting values the figures on eurozone nominal and real GDP and nominal M3 for 2002.4 as published by the ECB and the 2002.4 long and short term interest rates for the eurozone. 3.2.3
Comparing the results of the two methods
Figure 1 Aggregates for all variables 14.5
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Note: going from upper left to lower right the graphs represent the variable (red) and fixed (blue) aggregates for nominal GDP, real GDP, inflation, long term bond yield, nominal M3, real M3, GDP deflator and short term interest rate.
As can be seen in Figure 1, both aggregates are close to each other at the end of the sample period, while differences occur at the beginning of the period. Comparing the two nominal GDP series, the aggregate obtained using variable weight growth rate aggregation starts at a lower value and moves towards the fixed weight level aggregate. A similar pattern is seen for the price aggregates and, although to a lesser extent the nominal M3 aggregates. Real M3 aggregates show the reverse pattern,
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i.e. the variable weight growth rate aggregate starts at a higher level and moves to the other aggregate. Real GDP series move very close together in a similar, be it much less evident, pattern as the real M3 aggregates. The long and short term interest rate series also show more differing patterns during the beginning of the sample period but the differences last longer than for the other series just described. Finally the inflation rate series shows the same pattern as the real M3 series. Table 1 Descriptive statistics all aggregate variables constructed using fixed base period level aggregation. The statistics for GDP and M3 are based on growth rates Nominal Real Nominal Real M3 Inflation Long term Short term GDP GDP M3 (annualised) interest rate interest rate _______ _______ ________ _______ __________ _________ _________ Mean 1.52 0.52 1.79 0.80 3.97 8.89 8.35 Median 1.35 0.53 1.86 0.82 3.69 9.08 8.20 Maximum 3.61 1.64 3.12 1.85 9.58 14.78 15.56 Minimum -0.10 -0.74 0.40 -1.20 0.51 4.00 2.68 Std. Dev. 0.72 0.52 0.60 0.49 2.27 2.83 3.52
Table 2 Descriptive statistics all aggregate variables constructed using fixed base period growth rate aggregation. The statistics for GDP and M3 are based on growth rates Nominal Real Nominal Real M3 Inflation Long term Short term GDP GDP M3 (annualised) interest rate interest rate _______ _______ ________ _______ __________ _________ _________ Mean 1.76 0.51 1.88 0.63 4.99 8.58 7.89 Median 1.55 0.53 1.93 0.68 3.91 8.79 7.77 Maximum 4.50 1.55 3.38 1.81 13.45 13.88 14.35 Minimum 0.14 -0.75 0.39 -1.74 0.51 4.00 2.65 Std. Dev. 0.97 0.54 0.68 0.59 3.54 2.57 3.20
The findings are confirmed by the results in Tables 1 and 2 where it can be seen that indeed the average growth rate of nominal GDP and nominal M3 are lower for the variable growth rate aggregates. The reverse is true for the real GDP and real M3 series. The descriptive statistics of the inflation and the two interest rate series also confirm the findings when looking at the graphs. The difference between the aggregates obtained using the two different methods of aggregation, can be explained by the impact of the de- and/or revaluations of the local currencies with respect to the common currency, the euro. The fixed base period level aggregation method does not take these changes in exchange rates into account. The variable weight growth rate aggregation method does take them into account (see (8)) by shifting the base period one year forward every year. The larger
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difference between the series at the beginning of the sample period can be explained by the implicit use of 2001 as the base year in the fixed weight aggregation approach. As most exchange rates show a gradual convergence to the fixed conversion rates as set by the ECB, the difference between the two approaches gets smaller over the sample period. To take a closer look at the differences, and since the growth rates of the two approaches are more easily compared based on (7) and (8), Figure 2 shows the difference between the growth rate aggregates for GDP and M3 (nominal and real) and the difference between the level aggregates for inflation and the two interest rates. As can be clearly seen, the difference between the two aggregation methods goes to zero over the sample period. This is exactly as expected when looking at the formulas in (7) and (8), the two series should move very close together when the difference between the exchange rates, used in the two methods to convert the series into euro, is small. Obviously when looking at Figure A1.6 the exchange rates move towards the fixed exchange rates used in the fixed base period aggregation method and this makes the difference in the aggregate growth rates between the two methods smaller over time. The actual size of the differences in growth rates is also quite substantial, ranging from several percentages for the inflation series, to several tenths of a percentage for nominal M3. Figure 2 The difference between the two approaches (variable minus fixed) .005
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1980
1985
D I F F D LN _ M 3 R _ V A R _F I X
.006
.06
.004
.05
.000
.04
-.002
.03
-.004
.02
-.006
.01
-.008
.002
1990
1995
2000
D I F F D L N _ Y N _ V A R _F I X
.002
.000 -.002 -.004
.00
-.006
-.010
-.01 1980
1985
1990
1995
2000
D I F F D LN _ Y R _ V A R _ F I X
-.012 1980
1985
1990
1995
D I F F I N F L _ V A R _F I X
2000
1980
1985
1990
1995
2000
D I F F _ V A R _F I X _L R
.005 .000 -.005 -.010 -.015 -.020 -.025 1980
1985
1990
1995
2000
D I F F _V A R _ F I X_ S R
Note: going from upper left to lower right the graphs represent differences between the two aggregation methods for nominal M3, real M3, nominal GDP, real GDP, inflation, long term bond yield and short term interest rate.
- 13 -
To see what the impact of a change in base year in the fixed base period method is, two more aggregate series are constructed. One takes 1979 (the beginning of the sample period) and the other 1990 (the middle of the sample period) as its base year. The constructed level series differ for a different base year. To be able to take a closer look at the differences, Figure 3 shows the growth rates of the three constructed fixed base period aggregates compared to the growth rate of the aggregate obtained using the variable weight growth rate aggregation method (only the results for real GDP are shown, the other series show a similar pattern). As expected from formulas (7) and (8) when, comparing the results for the aggregates using different base years, it can be clearly seen in Figure 3 that the aggregate using 1979 as base year starts with small deviations from the variable weight aggregate and the deviations increase over the sample period. The aggregate using 1990 as base year exhibits large deviations in the beginning of the sample period, the deviations diminish around the base year 1990 and increase again towards the end of the sample period. These differing patterns can be ascribed (and are again in compliance with formulas (7) and (8)) to the difference between the fixed base year exchange rate and the current exchange rate. The more (less) the current exchange rate differs from the fixed base year exchange rate, the greater (smaller) the difference. Figure 3 Comparing the growth rates of different fixed base period aggregates to the variable weight growth rate aggregate for real GDP 0.006
0.004
0.002
0.000
-0.002
-0.004
-0.006 1980
Note:
1985
1990
1995
difference between variable aggregate and fixed aggregate using as base year 1. 1979 () 2. 1990 (- - - -) 3. 2001 ()
2000
- 14 -
Thus changing the base year in the fixed base period aggregation method does have a substantial impact on the constructed aggregated time series. The inability of the approach to take currency deand revaluations into account accounts for this difference. This has the effect that, given the substantial currency depreciations for seven of the Euro-12 countries and the substantial appreciation for three of them, fixing the exchange rate at 2001 results in the seven countries, that have had a depreciating currency, being ´underrepresented´ in the aggregate series of the eurozone and the three countries, that have had an appreciating currency, being ´overrepresented´ in the eurozone aggregates when using the fixed base period method. Another effect of this aggregation method is that the countries with a (ap-)depreciated currency have too (high) low GDP shares at the beginning of the sample period. Because of the convergence of the exchange rates the above-described effects are more evident at the beginning of the sample period. The variable weight growth rate aggregation does take exchange rate effects into account without introducing an unwanted component in the aggregate series as variable weight level aggregation does, see (3). Therefore it is suggested that this method provides the best possible aggregates to be used in the econometric analysis of eurozone money demand1. For simplicity in the rest of the paper, the aggregates formed by the variable weight growth rate aggregation method are referred to as ´variable aggregates´ and ´fixed aggregates´ refers to the aggregates based on the fixed base period aggregation method.
1 An argument that might save the fixed base period aggregation method is that the (over-)underrepresentation of countries that have had a (ap-)depreciating currency does not matter that much as the countries that have had an appreciating currency are more representative of the economic situation in the eurozone today. However choosing a different base period leads to different weights and choosing the base period that provides weights that represent the economic situation in the eurozone today may not be that easy.
- 15 -
4
MONEY DEMAND ESTIMATES BASED ON AGGREGATES
As tests for a double unit root do not find evidence for this in any of the aggregated series and tests for a unit root clearly show that all series have a unit root irrespective of the aggregation method used, the existence of a long run eurozone money demand equation is assessed in a cointegration framework. More specifically the Johansen methodology is used to test for the number of cointegrating relations, and (if found) to test restrictions on these relations. The Johansen framework is chosen as it allows to test for the cointegration rank whereas other types of methods (Engle and Granger (1987) two-step procedure or Phillips and Hansen (1990) Fully Modified OLS estimates) implicitly assume the number of cointegration relations. Also, and maybe even more important, the results of these other tests may rely on the specific ordering of the variables and the normalisation chosen for the cointegrating vector(s). The Johansen framework does not suffer from these drawbacks. Starting point is an unrestricted vector autoregressive model of order k, VAR(k),
xt = α + δ t + Π 1xt−1 + ... + Π k xt − k + ε t
t = 1,…,T
(9)
where x=(m-p, y, il , is ,∆p), α a 5x1 vector of constants, δ a 5x1 vector of trend coefficients, Π i , i = 1,…,k 5x5 matrices of coefficients and ε t ~ N (0, Ω ε ) , a 5-dimensional vector of innovations that is normally distributed with a nonsingular covariance matrix Ω ε.
First the appropriate lag length, k, to use in (9), including only a constant as deterministic component, is chosen based on information criteria. Table 3 shows that for the variable aggregates all three criteria select a lag length of two. Table 3 Lag length selection in the VAR model
k
Variable
Fixed
_______________________ AIC SBC HQ
__________________________ AIC SBC HQ
0
-24.01
-23.95
-24.04
-25.21
-25.07
-25.16
1
-38.47
-37.62
-38.12
-38.31
-37.46*
-37.97
2
-39.19*
-37.63*
-38.56*
-38.87*
-37.31
-38.24*
3
-39.07
-36.80
-38.16
-38.68
-36.41
-37.77
4
-38.93
-35.96
-37.74
-38.54
-35.57
-37.34
Note: * denotes selected by corresponding IC.
- 16 -
For the fixed aggregates also a lag length of two is chosen since, although the SBC indicates a lag length of one, both the AIC and HQ criterion indicate this as the appropriate. lag length to choose. After setting k equal to two, tests on the residuals are done to check if the model is correctly specified. Table 4 shows the results of tests for autocorrelation in and normality of the residuals of (9). Note that the tests as shown in the table are tests on the vector of residuals, ε t . Table 4 Residual tests, test statistics and corresponding p-values Variable LM(1) Chi2(25)
Fixed
_____________ ___________ 31.45 [0.18] 24.59 [0.49]
LM(4) Chi2(25)
26.39 [0.39]
28.27 [0.30]
Normality Chi2(10)
10.84 [0.37]
25.07* [0.01]
Portmanteau 9 lags
199.08 [0.10]
185.95 [0.27]
Note: p-values in brackets, * denotes significance at the 5% level.
For the variable aggregates the tests indicate normality of the residuals and no evidence of residual autocorrelation is found. This suggests the VAR with two lags to be correctly specified for the variable aggregates. For the fixed aggregates no autocorrelation in the residuals is found, but some nonnormality of the residuals is revealed. Fatter tails in the distribution of the residuals for the equation for real money holdings and thinner tails in the distribution of the residuals for the equation for inflation appear to be the main reasons for this, based on tests on the residuals of the individual equations in the VAR2. Although not totally correctly specified, the VAR with two lags seems to be a reasonable specification for the fixed aggregates. The next step is to test for the number of cointegrating relations. Let L denote the lag operator and define Π ( L ) = I n −
∑
k i =1
Πi Li . Decomposing the matrix lag polynomial Π ( L ) = Π (1) L + Φ ( L) ∆ ,
where ∆ = (1-L) is the difference operator, the VAR(k) as in (9) can be rewritten as a vector errorcorrection model (VECM),
∆xt = α + δ t + Π (1) xt −1 + Φ1 ∆xt −1 + ... + Φ k −1∆xt− k +1 + ε t
2 Results not shown here, they are available upon request
t = 1,…,T
(10)
- 17 -
where Φ i = −
∑
k j =i +1
Π j , i = 1,…,k-1. Each Φ i , i = 1,…,k-1 is a matrix containing parameters for the
short run dynamics. Note that only Φ 1 enters (10) in our case as k is equal to two. Now under the following assumption
Assumption 1: 1. rank(Π(1)) = r, 0 < r < 5; 2. the characteristic equation Π ( z ) = 0 has 5-r roots equal to 1 and all other roots outside the unit circle. xt has r cointegrating relations (see Hamilton, 1994), and Π(1) can be written as
Π (1) = −BA´
(11)
where A is a 5×r matrix of full column rank, the columns of which are the cointegrating relations such that zt ≡ A´ xt is a stationary 5×1 vector. B is another 5×r matrix of full column rank containing loading factors representing the speed of the short-run response to disequilibrium in the cointegrating relations. To formally test for the number of cointegrating relations, r, the trace test of Johansen (1988) is used. Before testing it is important to choose the type of deterministic components included in the model. Testing for the type(s) of deterministic components gives evidence of the need for the inclusion of a linear trend in both the cointegrating relationships and the data. However from an economic point of view (see (2)) a trend in the cointegrating relationships is not expected and therefore it is decided not to allow for a deterministic trend (δ = 0 in (10)) in the cointegrating relationships, a common choice in the existing literature on money demand (Coenen and Vega, 1999; Brand and Cassola, 2000). To test for the number of cointegrating relations, the trace test is used. As it is shown in Cheung and Lai (1993), this test is more robust to non-normality encountered in the data (found for the fixed aggregates) than the other test proposed by Johansen, the λmax test. The trace test has as its null hypothesis that there are exactly r cointegrating relations and as alternative that there are n cointegrating relations, where n is the number of variables in xt . The test statistics used in the test can be written as follows (see Hamilton (1994) for a detailed derivation):
- 18 -
λtrace = −T ∑ i= r+1 log(1 − λˆi ) n
(12)
where λi denotes the ith squared population canonical correlation between ∆xt and xt-1 . The results of these tests, shown in Table 5 below, show a difference in outcome between the two aggregation methods regarding the number of cointegrating relations found. For the variable aggregates, the tests indicate a cointegrating rank of three (four) at a 1% (5%) level, whereas for the fixed aggregates a cointegrating rank of two (three) at a 1% (5%) level is found. Table 5 Trace statistics for both aggregates and corresponding 1% and 5% critical values
H0 : r =
Variable
Fixed
_______ λtrace
_____ λtrace
1% critical value
5% critical value
0
91.24(**)
94.00(**)
76.07
68.52
1
58.04(**)
61.03(**)
54.46
47.21
2
35.81(**)
33.89(*)
35.65
29.68
3
18.12(*)
14.73
20.04
15.41
4
0.68
0.10
6.65
3.76
Note: (**) resp. (*) denotes significance at a 1% resp. 5% level.
As the choice of cointegrating rank is not exactly clear, economic arguments are used to decide on the number of cointegrating relationships. It is clear that one of the cointegrating relations should represent a long run money demand equation. As we did not allow for a linear trend in the cointegrating relations, another cointegrating relation including real GDP is not expected. Possible candidates are therefore, a stationary term structure or a stationary real interest rate representing the Fisher equation. Besides these economic arguments used to choose the cointegrating rank, importance is also given to stationarity tests of the individual variables used in the analysis and in particular to stationarity tests for the real interest rate and the term spread. These tests are done within the Johansen framework assuming a cointegrating rank of two, three and four. Table 6 shows the results of these individual stationarity tests done within the Johansen framework.
- 19 -
Table 6 Tests for stationarity Rank (dgf)
∆p
is
il
y
m-p
il -∆p
il - is
_________ _____ _____ _____ _____ _____ ______ ______ Variable 2 (3)
9.99
18.27
17.43
15.44
16.71
3.22*
9.97
3 (2)
7.21
13.78
12.92
14.89
15.74
1.41*
5.85*
4 (1)
7.19
13.77
12.76
14.64
15.49
1.34*
5.69
2 (3)
17.61
23.02
23.51
26.31
25.87
18.60
13.29
3 (2)
14.29
15.32
15.97
18.93
19.01
13.05
5.37*
4 (1)
10.59
11.32
11.42
14.48
14.50
9.69
5.04
Fixed
Note: (*) denotes significance at a 5% level.
As expected the results regarding the individual variables indicate that all variables are rejected to be individually stationary. More interesting are the results when testing for stationarity of the real interest rates and the term spread. For the variable aggregates, when r = 3, both the term spread and the real long term interest rate are found to be stationary. Stationarity of the long term interest rate represents a long run Fisher equation and stationarity of the term spread is in favour of the expectations theory of the term structure. For the fixed aggregates also evidence in favour of the expectations theory of the term structure is found but the stationarity of the real long term interest rate is rejected in this case. Given the lack of a plausible interpretation of a fourth cointegrating relation based on economic theory and the statistical results of the previous paragraph(s) a rank of three is imposed. For both aggregates the same cointegrating rank is imposed. Next the cointegrating vectors need to be identified. Usually the cointegrating vectors are identified by imposing restrictions on each cointegrating vector (the columns of the A matrix) in the system. However, all variables in the system are a priori expected to appear in the long run money demand equation. Therefore, to put all information that is of importance for real money in the first cointegrating vector, the coefficients for real money in the B-matrix in the second and third cointegrating vector are restricted to be zero (see Vlaar and Schuberth (1999) who impose a similar restriction on the B-matrix). In this way, the first cointegrating vector represents the long run money demand equation. The second cointegrating vector is restricted to represent a Fisher equation (either homogeneous or heterogeneous) and the third to represent the expectations theory of the term structure.
- 20 -
Table 7 Estimates of the A- and B-matrix in the identified model Variable
A (s.e.)
_______
___________________________________ _____________________________________ Money Demand Fisher Yield equation spread 0 -1 0 0.10 (2.29) 0.17 (2.67) 0.02 (0.28)
∆p
B (t-value)
is
0
0
-1
-0.01 (-0.23)
-0.09 (-2.26)
0.08 (1.71)
il
0.84 (0.31)
1
1
-0.01 (-0.59)
-0.08 (-2.89)
-0.02 (-0.67)
y
-1.27 (0.05)
0
0
-0.01 (-0.29)
-0.03 (-0.69)
0.13 (2.72)
1
0
0
-0.10 (-5.88)
0
0
m-p LR χ 2 (6)
11.53 [0.07]
Fixed
A (s.e.)
_____
___________________________________ _____________________________________ Money Demand Fisher Yield equation spread 0 1 0 -0.03 (-0.51) 0.24 (4.90) -0.09 (-1.02)
∆p
B (t-value)
is
0
0
-1
-0.08 (-2.16)
-0.07 (-2.11)
0.19 (3.02)
il
-0.30 (0.21)
-0.51 (0.06)
1
0.03 (1.21)
-0.05 (-2.14)
-0.01 (-0.31)
Y
-1.52 (0.04)
0
0
0.08 (2.61)
-0.02 (-0.68)
0.12 (2.25)
1
0
0
-0.09 (-3.27)
0
0
m-p LR χ (5) 2
5,73 [0.33]
Note: p-value in brackets.
For both aggregates the results show that the standard deviations of the coefficients for inflation and the short term interest rate in the money demand equation are large with respect to the coefficients themselves, for most cases even larger than the coefficients. As formal tests accept the validity of restricting these coefficients to be zero; they are fixed at zero. Furthermore a homogeneous Fisher equation is accepted for the variable aggregates and is therefore imposed on the second cointegrating vector in this case. For the fixed aggregates a homogeneous Fisher equation is rejected but a heterogeneous Fisher equation is accepted and subsequently imposed. Table 7 above the resulting model for each of the aggregates. To check for possible model misspecification, Table 8 shows tests for normality of and autocorrelation in the residuals. The tests show similar results as the residual tests on the residuals of the unrestricted VAR model (see Table 4). No evidence of autocorrelation is found for both aggregates and non-
- 21 -
normality is again only found for the fixed aggregate residuals. The results indicate that the specification used is acceptable. Table 8 Residual analysis for reduced form residual vectors Variable LM(1) Chi2(25)
Fixed
___________ ___________ 32.76 [0.14] 29.39 [0.28]
LM(4) Chi2(25)
31.66 [0.17]
31.05 [0.19]
Normality Chi2(10)
12.92 [0.23]
25.49 [0.01]
Portmanteau 9 lags
197.39 [0.54]
187,12 [0.73]
Note: p-value in brackets.
To be complete, also tests for weak exogeneity of each individual variable with respect to all long run relations are done within the Johansen framework. If all entries in a row of the B-matrix, containing information on the speed of adjustment to disequilibrium, are equal to zero, i.e. α ij = 0, i ∈ {1,…,5}, j = 1,…,r, it is said that the variable corresponding to this row is weakly exogenous with respect to all long run relations. For example if all elements in the first row of the B-matrix (see Table 7) were equal to zero, this would indicate weak exogeneity of the inflation rate with respect to all long run relations. A variable that is found to be weakly exogenous can actually enter on the right side of the VECM without leading to a loss of information, when estimating the parameters of the model. Table 9 shows the results of formal tests for weak exogeneity in the reduced form model as represented in Table 7. Table 9 Tests for weak exogeneity Series
Variable
Fixed
_____ ∆p
______________ ______________ 20.46 [0.005]*** 21.22 [0.002]***
is
16.32 [0.022]**
19.21 [0.004]***
il
18.49 [0.010]***
10.39 [0.109]
y
16.24 [0.023]**
17.59 [0.007]***
m-p Test distribution
23.52 [0.001]*** χ (7) 2
12.59 [0.050]** χ (6) 2
Note: p-values in brackets; (***), (**), (*) indicates significance at a 1%, 5%, 10% level.
- 22 -
As can be seen in Table 9, weak exogeneity is rejected for all variable aggregates at a 1% or 5% level. For the fixed aggregates weak exogeneity is rejected at a 1% or 5% level for all variables except for the long term interest rate, for which weak exogeneity would be rejected at a 11% level. Except for the long term interest rate in the case of the fixed aggregates, all variables seem to contain information about the long run relationships. As can be seen from Table 7, quite a number of coefficients of the B-matrix have t-values that are below the 5% critical value. This indicates that the coefficients are not significantly different from zero. Variables whose coefficients in column i, i ∈ {1,…,r}, of the B-matrix are not significantly different from zero do not enter the vector representing the short run response to disequilibrium in the long run relationship corresponding to the ith column of the A-matrix. It is jointly tested whether or not setting all coefficients, whose t-value is below the 5% critical value, are equal to zero. For the variable aggregates the resulting test statistic, with χ 2 (12)-distribution, is 12.86 with corresponding p-value of 0.38. The test statistic for the fixed aggregates, distributed χ 2 (10), is 8.60 with corresponding p-value of 0.57. For both aggregates the test statistics support the acceptance of the null hypothesis. 4.1
Interpreting the results
The results for the variable aggregate show that real output has a positive effect on money that is larger than one. This result is as expected and the high value can probably be ascribed to wealth effects (see Fase and Winder, 1998; and Vlaar and Schuberth, 1999). The negative effect of the long term interest rate is also as expected, as an increase of the long term interest rate, representing the rate of return on assets not included in the money definition, makes alternatives to money more attractive and thus decreases real money holdings. Furthermore the Fisher equation is accepted to be homogeneous and stationarity of the term spread is also not rejected. Stationarity of the term spread is in accordance with the expectations theory of the term structure, stating that the long term interest rate reflects a weighted average of future short term interest rates. The loading factors in the B-matrix also show some interesting features. A significant impact of deviations from the long run money demand equation on real money holdings and inflation is found. The significant pos itive impact of money holdings in excess of the long run equilibrium on inflation is important, as it makes money growth a useful indicator for future inflation and justifies a monetary targeting strategy as conducted by the ECB. The effect on real money holdings is as expected. Deviations from the Fisher equation have a significant impact on inflation and both interest rates. Both effects are as expected. Finally the slope of the term spread has a significant impact on real output, which is in line with the findings of Estrella and Mishkin (1997) regarding the leading indicator properties of the slope of the yield curve for future output growth.
- 23 -
Results on the fixed aggregates are somewhat different and perhaps more questionable. First the coefficient of the long term interest rate in the money demand equation is positive, be it insignificant. This is very strange because, as explained in the previous paragraph, a rise in the long term interest rate makes assets outside of the money definition more attracting and thus is expected to decrease real money holdings. A reverse effect as found here seems highly unlikely. Secondly homogeneity of the Fisher equation is rejected. Brand and Cassola (2000) also find this result (be it with the long term interest rate coefficient closer to –1 than the –0.51 found here). A possible explanation of this heterogeneity of the Fisher equation might be the existence of an ´EMS risk premium´. A country that experiences high inflation but at the same time is bound to a fixed exchange rate system (or monetary union), cannot depreciate its currency to the extent it may want to and thus the interest rate has to compensate3. When looking at the loading factors in the B-matrix, the insignificant impact of money holdings in excess of the long run equilibrium on inflation may be regarded as ´unwanted´. This implies that money only has a weak role as indicator for future inflation. Hereby questioning the usefulness of the ECB´s monetary targeting strategy. The other results for the loading factors do not differ much from the results found for the variable aggregates. Figure 4 Recursive estimates of the identified cointegrating space (variable aggregates) STABILITY OF Sp(beta) SIGNIFICANCE LEVEL= 95%
1.6
R_MODEL Z_MODEL NORMCVAL
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0 1994
1995
1996
1997
1998
1999
2000
2001
2002
3 This however would be expected to also have an impact on the variable aggregates given the fact that the countries with a depreciating currency get a bigger weight in those aggregates than in the fixed aggregates.
- 24 -
To check for the parameter constancy over time of the money demand equation, recursive estimates are performed for the variable aggregates. Figure 4 above, shows the parameter constancy of the identified cointegrating space, where the analysis is based on the approach by Hansen and Johansen (1999). According to the so-called R-model, in which the short term dynamics, the Φ -matrices, are kept constant and only the A- and B-matrix, are recursively estimated, stability is accepted at a 95% level. The Z-model, in which all parameters, also the Φ-matrices, are recursively estimated, indicates some instability until the second half of 1995. However, recursive estimates in the Z-model can be unreliable at the beginning due to the relatively few observations available at the beginning of the sample (e.g. in 1994 only 57 observations are used in the estimation) and the many parameters to be estimated. Recursive estimates of the two freely estimated parameters in the money demand equation are shown in Figure 5. As can be seen in Figure 5, both parameters are found to be stable over time. The long term interest rate elasticity seems to fluctuate a little more over time compared to the real output coefficient. Based on the results of the recursive estimation, no evidence of an impact of the euro on the empirical relationships is found. The results for the fixed aggregates (not shown here) show some more instability. Figure 5 Recursive estimates of the parameters of real GDP and the long term interest rate in the money demand equation (variable aggregates) R E C U R S I V E
E S T I M A T E S :
y
- 1 . 1 5
- 1 . 2 0
- 1 . 2 5
- 1 . 3 0
- 1 . 3 5
- 1 . 4 0
- 1 . 4 5 1 9 9 4
1 9 9 5
R
-
1
.
5
0
1
.
2
5
1
.
0
0
0
.
7
5
0
.
5
0
0
.
2
5
0
.
0
0
0
.
2
5 1
9
9
4
E
C
1
9
1 9 9 6
U
9
R
5
S
I
V
1
1 9 9 7
E
9
9
E
6
S
T
I
1
M
9
9
1 9 9 8
A
7
T
E
S
1
1 9 9 9
:
9
i
9
8
2 0 0 0
2 0 0 1
2 0 0 2
l
1
9
9
9
2
0
0
0
2
0
0
1
2
0
0
2
- 25 -
The previous chapter on aggregation concludes in favour of the variable weight growth rate aggregation method. In this chapter it is shown that the estimation results, obtained using aggregates constructed by the two different aggregation methods, clearly differ. As the variable aggregates are preferred from the aggregation point of view and the fixed aggregates also show evidence of some model misspecification (a result also found in other recent research (Coenen and Vega, 1999; Brand and Cassola, 2000), at this point attention is focused on the results based on the variable aggregates. Results in the next chapter on panel estimation of the long run money demand equation will thus only be compared with the findings in this chapter that are obtained using the variable aggregates.
- 26 -
5
MONEY DEMAND ESTIMATES BASED ON PANEL METHODS
Econometric inference within nonstationary panels is a field that has emerged only recently. The interest in this field has increased over the last few years, starting with papers by Quah (1994) and Levin and Lin (1994), who test for unit roots within a panel setup. The main reason for this, is the fact that tests for stationarity or cointegration within a time series setup tend to suffer from low power if the time span of the data used is not large enough, a phenomenon that is not very rare for macroeconomic data. Using a panel setup adds additional observations by drawing data from among similar cross-sections to increase the power of the tests. Furthermore a panel setup allows for the exploitation of similarities across the individuals in the panel. By pooling the information of several individuals, the panel setup may provide better evidence on the (non)existence of economic relationships. The panel cointegration literature mainly focuses on residual based tests (Kao, 1999; Banerjee, 1999; Pedroni, 2002), that are based on pooling the individual residual based test statistics. These residual based tests however only focus on the question whether or not cointegration is present in the panel. The same drawbacks as in the case of residual based tests for cointegration in a time series setup apply for these tests. The estimated cointegrating relation may differ with the ordering of the variables and the choice of normalisation of the cointegrating relation. The tests also do not allow to test for the number of cointegrating relations. There are however some papers that do derive tests for the number of cointegrating relations within a panel setup (Larsson, Lyhagen and Löthgren, 2001; Groen and Kleibergen, 2002). These tests do not suffer from the drawbacks described above, however are only useful (i.e. the test has the correct size for, or requires, fixed N) for panels with a small cross-section dimension compared to the time dimension 4. Another important issue that has received a lot of attention in the nonstationary panel literature is the assumption of cross-sectional independence between the units in the panel. Most existing residual based tests use this assumption to be able to get a nice asymptotic distribution for the test statistic as the cross-section dimension goes to infinity. The cross-sectional independence allows for the use of standard asymptotic tools, like the (standard) Central Limit Theorem. As shown in Monte Carlo experiments, see O´Connell (1998) inappropriately assuming cross-sectional independence can severely distort the size of panel tests in a nonstationary world. Recently some tests have been
4 As (at the moment) the eurozone includes twelve countries, this does not seem to constitute a big problem. One might even be more doubtful regarding panel cointegration tests that rely on large N asymptotics
- 27 -
proposed that do allow for the units in the panel to have some form of dependency (Bai and Ng, 2003; Moon and Phillips, 2003; Chang, 2002; Groen and Kleibergen, 2002; Larsson and Lyhagen, 2000). Studies that use a nonstationary panel framework to test for the existence of a long run money demand equation are relatively few. Mark and Sul (2002) use a residual based cointegration test, Pedroni´s (1999) panel t-test, where they use a panel of nineteen countries. Golinelli and Pastorello (2001) and Dedola, Gaiotti and Silipo (2001) also use a residual based cointegration test on countries in the eurozone (excluding Greece or Luxembourg and Greece from the analysis). Focarelli (2000) applies a bootstrap biased-correction procedure, correcting the Mean Group estimator of Pesaran and Smith (1995). All papers apply a panel cointegration test that does not allow for cross-dependence of the units in the panel and that does not explicitly test for the cointegrating rank. As mentioned before inappropriately assuming cross-sectional independence can lead to a severe distortion of the size of the test when this assumption is not valid. In this paper the test of Groen and Kleibergen (2002) is used. This test does allow for cross-sectional transitory dependence among the units in the panel. A nice feature, as the data for the countries in our panel are evidently not independent of each other. Looking only at the correlation between the individual time series gives evidence of this (see Table 10 for the correlation between the individual GDP growth rate series, similar correlations are found for the other variables). Table 10 Correlation matrix of the individual GDP growth rate series
AU BE ES FI FR GE GR IER IT LU NE PT
AU BE ES FI FR GE GR IER IT LU NE PT ___ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ 1 0.34 0.28 0.05 0.40 0.41 0.13 0.14 0.24 0.21 0.28 0.23 1 0.44 0.18 0.46 0.25 0.27 0.30 0.31 0.28 0.27 0.18 1 0.08 0.33 0.12 0.35 0.21 0.07 0.33 0.29 0.27 1 0.35 0.09 0.20 0.24 0.30 0.06 0.07 0.32 1 0.41 0.16 0.37 0.45 0.30 0.24 0.21 1 0.25 0.22 0.29 0.23 0.22 0.13 1 0.11 0.13 0.11 0.08 0.24 1 0.26 0.08 0.22 0.11 1 0.16 0.18 0.04 1 0.33 0.09 1 0.16 1
The test does however not allow for cointegration across members of the panel. The cross-sectional dependency is purely transitory and not persistent. The next section will come back to this issue. Another nice feature of the test is that it does not suffer from the drawbacks that apply to residual
- 28 -
based tests and it allows testing for the cointegrating rank. Finally the fact that the test should be used only for panels with a relatively small cross-sectional dimension compared to the time-dimension, does not seem to be a big problem as the cross-section dimension in the panel used is fixed at ten5 (excluding Luxembourg and Greece due to data problems) and the time span of the data is from 1979:2 – 2002:4. 5.1
The Groen and Kleibergen (2002) Panel VECM test
The test developed by Groen en Kleibergen (2002) (hereafter GK-2002) is based on the vector error correction model (VECM) framework of Johansen (1991) for each of the individuals in the panel. A VECM for each individual is stacked into one system, a Panel VECM,
Φ1 0 L 0 0 Φ2 O M ∆Yt = Y + ε = Φ AYt−1 + ε t M O O 0 t−1 t 0 L 0 ΦN
(13)
where Φ A is a Nm×Nm matrix contain ing the individual Φ i , i = 1,…,N, m×m matrices (m is the number of variables), relating for each individual ∆yit to yi,t -1 . Yt −1 = ( y1,′ t −1... y N′ , t −1 )′ , ∆Yt = Yt − Yt −1 and
εt = (ε1′t ...ε ′Nt )′ are Nm×1 vectors. The vector ε t contains the Nm×1 disturbance vectors for each individual VECM and it is distributed ε t : N (0, Ω) with the Nm×Nm nondiagonal covariance matrix,
Ω11 L Ω1N Ω= M O M Ω N 1 L Ω NN
(14)
where Ω ij = Cov(εit ,εjt ) is not restricted to be zero for any i,j = 1,…,N. Note that notation is changed with respect to the previous section. Where in the y previously denoted GDP, here yit denotes a vector of all variables contained in the VECM, i.e. here yit =(m-p, y, il , is ,∆p)it .
5To be sure that the test has nice power and size properties at N = 10, simulations would have been nice. However due to computational power restrictions these could not be performed.
- 29 -
As can be seen, the model as specified in (13) does allow for cross-sectional dependency through the disturbance terms (14), i.e. transitory cross-sectional dependence. However as the off-diagonal elements of the Φ A matrix are set equal to zero, the model is a restricted version of the model in which the off-diagonal elements are left to be estimated. These restrictions on the Φ A matrix impose that there is no linear dependence between the variables of individual i and lags of the variables of individual j, for j ≠ i, i.e. no persistent cross-sectional dependence. By imposing the restrictions, crossdependence in the panel is only allowed through the non-diagonal covariance structure of the error term (14). Larsson and Lyhagen (1999) do allow for non-zero off-diagonal elements which also implicitly allows for the possibility of cointegration between series of different individuals in the panel. The reason why these restrictions are imposed here is that if these restrictions are not imposed, all the off-diagonal elements of the Φ A matrix would also have to be estimated. This is very likely not to be efficient due to the large number of parameters that have to be estimated in the estimation procedure6. The GK-2002 test for cointegration is developed to test for a common cointegrating rank for each individual i within the panel, i.e. rank ( Φ i ) = r for each i = 1,…,N. Now cointegration within the panel imposes a rank reduction on the different Φ i ´s in (13) identical to all individuals in the panel,
0 L 0 B1 A1′ 0 B2 A2′ O M ∆Yt = Y + ε = Φ BYt−1 + ε t M O O 0 t −1 t L 0 BN A′N 0
(15)
where the m × r matrices Ai contain the cointegrating vectors and the m × r matrices Bi the loading factors, the adjustment factors to the long run equilibrium, for each of the i = 1,…,N individuals. Now the test for a common cointegrating rank r developed by GK-2002 tests the following:
H 0 : ΦB
vs.
H1 : Φ A
(16)
6 Although persistent cross-sectional dependence between series of different members might be expected a priori, e.g. the inflation series of Germany and the Netherlands.
- 30 -
where Φ B is as in (15) and Φ A is as in (13). GK-2002 develops maximum likelihood estimators of the cointegrating vectors, the loading factors and the covariance matrix of the disturbance term using Generalised Method of Moments estimators. Using these estimators they construct the following likelihood ratio statistics to test for a common cointegrating rank among the individuals in the panel.
(
( )) − l (Φˆ
ˆ Φ ˆ A, Ω ˆA LR( Φ B | Φ A ) = 2 l Φ
(
B
( ))
ˆ Φ ˆB ,Ω
(17)
( ) ) , Θ ∈ {A,B}, is the value of the maximised log-likelihood function. Now
ˆ Φ ˆ Θ,Ω ˆΘ where l Φ Θ
keeping N fixed and letting T go to infinity the limiting distribution of the test statistic in (17) equals, −1 N LR ( Φ B | ΦA ) ⇒ ∑ i=1 tr ∫ dBm −r ,i B′m−r , i ∫Bm −r ,i B′m−r , i ∫ Bm−r , idB′m−r ,i T →∞
(18)
where Bm-r,i is a (m-r)-dimensional Brownian motion for individual i with an identity covariance matrix. As can be seen in (18) the limiting distribution as T → ∞ of the likelihood ratio statistic (17) is the sum of N individual limiting distributions for the Johansen (1991) trace statistic. GK-2002 extend the result for the more general case of model (13) that allows for deterministic components and higher order dynamics,
∆Yt = α +δ t + Φ $ Yt−1 + ΓWt + ε t
(19)
where α = (α1...α N )′ is a vector containing constants, δ t = ( δ1...δ N )′ t represents the individual
(
linear trends, Wt = ∆y1,′t −1... ∆y1,′ t − k1 ... ∆y ′N ,t −1... ∆y ′N , t− kN
)
contains the k i lagged first differences of
individual i, and
Γ1 0 Γ = M 0
0 Γ2 O 0
L 0 O M O 0 L ΓN
contains the parameters for each of the individual lagged differences.
(20)
- 31 -
The higher order dynamics and deterministic components can be concentrated out in the usual way (Johansen, 1991), through OLS regressions of ∆yi,t -1 and yi,t -1 on the included higher order dynamics and deterministic components for each of the individuals i. In doing so, one implicitly assumes heterogeneity across individuals with respect to the deterministic components and short run dynamics. Now the test statistic can be computed using the maximum likelihood estimators were ∆yi,t -1 and yi,t -1 in (13) are replaced by the residuals of the corresponding OLS regressions for each individual. The limiting distributions are only affected by the inclusion of deterministic components. Including higher order dynamics does not affect them as they only affect the short-run properties of the model. The change in limiting distribution depends on the type of deterministic components included. As in the time series case, five different cases (see Johansen, 1995) can be distinguished. One can allow for: 1.
zero mean in the cointegrating relations and non-zero mean in the data
2.
non-zero mean in both the cointegrating relations and the data
3.
non-zero mean in the cointegrating relations and a linear trend in the data
4.
linear trend in both the cointegrating relations and the data
5.
linear trend in the cointegrating relations and a quadratic trend in the data
Here attention is focused on the third case only to allow for the same type of deterministic components as in the time series analysis of the aggregated variables. Hence case 3 is chosen for sake of comparability and for the same reason k i is set equal to one for all individuals in the panel. Subsequently the limiting distribution of the likelihood ratio statistic is changed in the following way, −1 N ′ LR ( Φ B | ΦA ) ⇒ ∑ i=1 tr ∫ dBm −r ,i Si′ ∫ Si Si′ ∫ SdB i m−r ,i T →∞
(21)
where in Si ≡ Bm −r ,i − ∫ Bm−r ,i . As can be seen the likelihood ratio statistic (21) remains the sum of the N individual limiting distributions of the Johansen trace statistic adjusted for the presence of deterministic components as in case 3. In their paper GK-2002 focus on case 2 and case 4 and calculate critical values for these two cases. As the point of interest here is case 3, critical values had to be obtained through simulation. To do this discrete-time approximations to (21) were used. First the N individual limiting distributions are approximated by their discrete-time counterparts, i.e.
- 32 -
T tr ∑ t=1 ∆xi ,t Fit′
(∑
T
F F′ t=1 it it
)
−1
∑
T t=1
Fit ( ∆xi, t )′
(22)
where the Brownian motions are replaced by Gaussian random walks and T is the number of discretetime approximations. More explicitly , let xt denote an (m-r)-vector whose elements follow a random walk with N(0,I) innovations with x0 = 0. Then ∆xi ,t = x i, t − x i ,t −1 and Fit = xi, t −
1 T ∑ xi ,t . After all T t =1
N individual approximations are made, the discrete-time approximation of (21) is calculated as the sum of the individual approximations. To obtain the critical values, the above is repeated 50,000 times for T = 1000. Thus 50,000 discrete-time approximations of (21) are obtained and the critical values are calculated as being the qth (q = 99%, 95% or 90%) quantile of these 50,000 replications. Table 11 shows the critical values thus obtained for a cointegrating rank up to four. Table 11 Critical values for the GK-2002 test with N = 10 r 1% 5% 10% __ ______ ______ ______ 1 415.92 398.79 389.32 2 255.46 241.34 234.13 3 135.17 124.00 118.17 4 52.58 45.02 41.43
Next the tests are performed for a panel consisting of all eurozone countries except Luxembourg and Greece. First the cointegrating rank has to be determined. In order to do this the likelihood ratio statistic as in (17) is calculated for the cases where r = 1, 2, 3, 4. As can be seen in Table 12 below, the tests indicate a common cointegrating rank of three. Table 12 GK-2002 likelihood ratio statistics r Test-stat __ ________ 1 723.14** 2 341.75** 3 100.69 4 7.87 Note: (**), (*) denotes significance at a 1%, 5% level.
This finding is similar to the cointegrating rank found in the case of the European aggregate. However by using the European aggregates, it is implicitly assumed that the relationships found, hold for all member countries of the eurozone. In the panel case, the relationships found can differ per individual
- 33 -
member of the panel, as each individual i has its own Ai matrix containing the individual specific cointegrating vectors. 5.1.1
Testing for homogeneity of the cointegration space
However one can test for the equality of the cointegrating vectors for all individuals. In order to do so, one has to estimate the following regression (after again first concentrating out the deterministic components and higher order dynamics):
0 L 0 B1 A′ 0 B2 A′ O M ∆Yt = Y + ε = Φ CYt−1 + ε t M O O 0 t−1 t L 0 BN A′ 0
(23)
where the matrix containing the cointegrating vectors is the same for all individuals, i.e. Ai = A for all i ∈ {1,…,N}. Groen and Kleibergen (2002) develop a test that is based on the likelihood ratio test to test for the validity of a homogeneous cointegrating space for all individuals in the panel. As in the time series case, the cointegrating rank is fixed before testing and the resulting test statistic is distributed as a χ2 ((N-1)r(m-r)) variable, i.e.
ˆ B ,Ω ˆ (Φ ˆ B )) − l (Φ ˆ C,Ω ˆ (Φ ˆ C )) ~ χ 2 (( N − 1)r (m − r )) LR( Φ C | Φ B ) = 2 l( Φ
(24)
As the test for the common cointegrating rank indicated a rank of three, the test for a homogeneous cointegrating space across individuals is done keeping the cointegrating rank fixed at three. The resulting test statistic is 318.13, which is larger than the corresponding χ 2 (54) 1% critical value, i.e. 86.0. The hypothesis of a homogeneous cointegrating space across individuals is clearly rejected, indicatin g differences in the long run relationships across the different members of the eurozone. As the ten countries included in our analysis of the eurozone do not share the same economic history, the rejection of a homogeneous cointegrating space may not be that surprising 7. Some countries joined the European Union later than others. This might have caused some countries to already integrate more economically (and non-economically) than others. Also countries have shown historical
7 Based on individual country analyses, Fase and Winder (1993) already found considerable differences in the nature of the demand for money.
- 34 -
differences in economic polic y and economic development. The economic policy of some countries (for instance Germany, the Netherlands) was much more stable than others (Spain, Portugal). These historical economic differences between countries in the eurozone might explain the rejection of a homogeneous cointegrating space. However it also gives rise to another question, i.e. ´Can we identify groups of countries within the eurozone that share the same long run developments?´. In order to answer this question, a test is needed that tests for the homogeneity of the cointegrating space for predefined groups of countries. To do this the test developed by Groen and Kleibergen (2002) to test for a homogeneous cointegrating space across all individuals is adapted in the way the likelihood under the null is calculated. Under the null of s, 1< s < N, groups with the same cointegrating space each group containing n1 , n2 ,…, ns-1 , ns individuals respectively and
∑
s i =1 i
n = N such that all individuals are assigned to one group, the
following model is estimated (again after first concentrating out the deterministic components and higher order dynamics):
B A′ 11 0 0 ∆Yt =
∅ 0 Bn1 A1′ ′ Bn1+1A2 0 0 0 O 0 Yt−1 +εt = ΦGYt−1 +εt (25) 0 0 Bn1+n2 A2′ O ′ Bn1+...+ns−1+1 As 0 0 ∅ 0 O 0 0 0 Bn1 +...+ns As′
0 O
0 0
To test for the validity of a homogeneous cointegrating space within each of the s groups, a likelihood ratio test is used. As in the case of testing for a homogeneous cointegrating space across all individuals in the panel, the common cointegrating rank is fixed, and the resulting distribution of the test statistic is again χ 2 but with degrees of freedom equal to (N-s)r(m-r), i.e.
ˆ B, Ω ˆ (Φ ˆ B )) − l (Φ ˆ G ,Ω ˆ (Φ ˆ G )) ~ χ 2 (( N − s ) r ( m − r )) LR( Φ G | Φ B ) = 2 l (Φ
(26)
- 35 -
To calculate the maximised value of the likelihood function under specification (25), the procedure used by Groen and Kleibergen (2002) is adapted. The log-likelihood function for any of the panel VECM specification, Φ Θ, Θ ∈ {A, B, C, G}, is:
l(Φ Θ , Ω ) = −
NkT T 1 ln(2π ) − ln Ω − tr ( Ω −1 (∆Y −Y−1Φ′Θ )′( ∆Y − Y−1Φ′Θ )) 2 2 2
(27)
∆Y1′ Y0′ where ∆Y = M and Y−1 = M are (T × Nm) matrices. In their paper, Groen and Kleibergen ∆Y ′ Y ′ N T −1 (2002) show that the log-likelihood function in (27) can be rewritten as
l(Φ Θ , Ω ) = −
NkT T 1 1 ln(2π ) − ln Ω − tr (Ω −1∆Y ′M Y−1 ∆Y ) − G (Φ Θ , Ω ), 2 2 2 2
(28)
−1
where M Y−1 = I − Y−1 (Y−′1Y−1 ) Y−′1 and
G ( Φ Θ , Ω) = vec(Y−′1ε )′(Ω ⊗ Y−′1Y−1 ) −1 vec(Y−′1ε )
(29)
which can be interpreted as a GMM objective function with all variables in Y-1 acting as instruments. Now in (28) Ω can be estimated conditional on Φ Θ using the conditional maximum likelihood estimator of Ω given Φ Θ, i.e.
ˆ (Φ ) = 1 (∆Y − Y Φ′ ) ′( ∆Y − Y Φ ′ ) Ω Θ −1 Θ −1 Θ T
(30)
and Φ Θ can be estimated given Ω using GMM objective function (29). By sequentially applying this estimation procedure of Ω and Φ Θ until convergence, the log-likelihood function (27) is maximised. As the cases for which Θ = A, B or C are explained in detail in Groen and Kleibergen (2002), p.10-15, here only the case Θ = G is explained in more detail. The group specification (25) implies that the GMM objective function (29) can be written as:
G ( Φ G , Ω) = vec(Y−′1 (∆Y −Y−1Φ G′ ) )′( Ω ⊗ Y−′1Y−1 ) −1vec (Y−′1 ( ∆Y − Y−1 Φ G′ ))
(31)
- 36 -
Rewrite part of this objective function (31) as,
vec (Y−′1( ∆Y − Y−1Φ ′G )) = vec(Y−′1∆ Y) − vec( Y−′1 Y−1 A1 B1′,K Y−′1Y−1 A1Bn′1 , Y−′1Y−1A 2 Bn′1+ 1, KY−′1Y−1 A2 Bn′1 + n12 , K, Y−′1Y−1 As Bn′1 +K+ ns )
vec( Α1 ) vec ( Α2 ) ′ = vec(Y−1∆ Y) − R M vec ( Αs )
(32)
where
R = ( I Nm ⊗ Y−′1Y−1) Rsure
(33)
and
Rsure
B1 ⊗ (e1 ⊗ I m ) M 0 0 Bn1 ⊗ (en1 ⊗ I m ) Bn1 +1 ⊗ (en1 +1 ⊗ I m ) 0 M 0 = Bn1 + n2 ⊗ (en1 + n2 ⊗ I m ) O Bn1 +... +ns−1 +1 ⊗ (en1 +...+ ns−1 +1 ⊗ I m ) 0 0 M Bn1 +... + ns ⊗ (en1 +...+ ns ⊗ I m )
(34)
where e i is the ith N-dimensional unity vector and Im a (m × m) identity matrix. In Groen and Kleibergen (2002) it is shown that under the null the common cointegrating rank is fixed at r and the estimate of the covariance matrix in (30) yields a consistent estimate of Ω. Furthermore under normalisation of the cointegrating spaces A1 ,…,As , a consistent estimator of Bi is:
Bˆ i ≡ the first r columnsof Φ i from (15) fori = 1,..., N
(35)
- 37 -
ˆ =Ω ˆ (Φ ˆ A ) , can then be substituted in the GMM objective These estimates, Bˆ i , i = 1,..., N and Ω function (31). Minimising this objective function with respect to A1 ,…, As gives the following GMMestimates,
vec( Aˆ1) ˆ ⊗ Y−′1Y−1 ) −1 Rˆ ) −1 Rˆ´(Ω ˆ ⊗ Y−′1Y−1 ) −1 vec(Y−′1 ∆Y ) M = ( Rˆ ′(Ω ˆ vec ( As )
ˆ −1 ⊗ Y−′1Y−1) −1 Rˆ sure ) −1 Rˆ ′sure ( Ω ˆ −1 ⊗ I T )vec (Y−′1∆Y ) ′ (Ω = ( Rˆ sure
(36)
ˆ ,..., A ˆ to construct the estimate of Φ ˆG The next step is to use the estimates Bˆ i , i = 1,..., N and A 1 s ˆ =Ω ˆ (Φ ˆ G) . and use that in estimating the conditional maximum likelihood estimator (30) to obtain Ω Now the estimates of the individual specific loading factors can be made by minimising the GMM
ˆ ,..., A ˆ and objective function (31) with respect to Bi , i = 1,..., N conditional on the estimates A 1 s ˆ =Ω ˆ (Φ ˆ G ) . This results in the following estimates: Ω vec ( Bˆ1′) ˆ ˆ −1 −1 ˆ ⊗ Y−′1Y−1 ) −1 vec(Y−′1 ∆Y ) M = ( Γ′R ( Ω ⊗ Y−′1Y−1 ) Γˆ R ) Γˆ ′R (Ω vec ( Bˆ ′ ) N ˆ −1 ⊗ Y ′ Y ) −1 Γˆ ˆ −1 ⊗ I )vec (Y ′ ∆Y ) = ( Γˆ ′Rsure (Ω ) −1 Γˆ ′R , sure ( Ω , −1 −1 Rsure , T −1
(37)
where
Γ Rsure = ((e1 ⊗ I m ) ⊗ ( e1 ⊗ Aˆ1 )K ( en1 ⊗ I m ) ⊗ ( en1 ⊗ Aˆ1 ) (en1 +1 ⊗ Im ) ⊗ (en1 +1 ⊗ Aˆ 2 ) K , ( en1 +n2 ⊗ I m ) ⊗ (en1 + n2 +1 ⊗ Aˆ 2 ) K ( en1 +K +ns−1 +1 ⊗ I m ) ⊗ ( en1 +K+ ns ⊗ Aˆ s ))
(38)
and
Γ R = ( I Nm ⊗ Y−′1Y−1) Γ R ,s u r e .
(39)
Now through iteratively applying the estimators (36), (30) and (37), one obtains the maximum likelihood estimates of Bi , i = 1,..., N , A1 ,…, As and Ω and, based on these estimates, the value of the
- 38 -
likelihood function (27). Each iteration step results in an improvement of the likelihood and after convergence of the likelihood function to its maximum, the maximum likelihood estimates are obtained. Finally, using the maximum value of the likelihood function, the test statistic can be calculated using (26). The above outlined test procedure is done for several group specifications. Table 13 shows the results of the tests. Table 13 Tests for group-wise homogeneous cointegration spaces χ 2 (dgf) 1% critical value
Group specification(s)
Test statistic
__________________ (AU,GE), (BE,NL), (ES,PT), (FI,IER), (FR,IT)
__________ ____________________ 152.01 χ 2 (30) 50.89
(AU,GE), (BE,NL), (ES,PT,FR,IT), FI, IER
138.48
χ 2 (30) 50.89
(BE,GE,NL,FR,IT), (ES,PT), (AU,FI), IER
213.19
χ 2 (36) 58.62
(AU,BE,GE,NL), FR, IT, ES, FI, IER, PT
139.70
χ 2 (18) 34.81
(AU,GE), (BE,NL), (ES,PT), FI, IER, FR, IT
116.66
χ 2 (18) 34.81
(AU,GE), (ES,PT), FI, IER, FR, IT, BE, NL
78.58
χ 2 (12) 26.22
As can be seen in Table 13, none of the tests shows evidence of a homogeneous cointegrating space across certain groups of eurozone countries. However as the main focus of this paper is the verification of the existence of a stable long run money demand equation across eurozone countries, the above tests can be viewed as too restrictive. Under the null of homogeneity of the cointegrating space for groups of or all eurozone countries, all three cointegrating vectors are equal. Now only one of these cointegrating vectors, say the first, represents the money demand equation. Thus when the only thing to be verified is the homogeneity of the money demand equation, testing for the homogeneity of all three cointegrating vectors can be argued too restrictive. Before testing the homogeneity of the money demand equation, the cointegrating space has to be identified such that one of the cointegrating vectors can be said to represent a long-term money demand equation. The issue of identification however is more complicated than in the case of a time series setup, as several ´problems´ arise in identifying the cointegrating space(s). In a ´worst case scenario´ the cointegrating space for each individual country in the panel is identified in a different way, leaving a very large number of possible combinations of identifying restrictions. Can a common identification be accepted? If not, how to find the right identification for each of the cointegrating
- 39 -
spaces? As one can imagine, the issue of identification is not that straightforward as it might seem at first hand. 5.1.2
Identifying the individual cointegrating spaces within a Panel VECM
To identify the cointegrating space, (m-r)-restrictions have to be placed on each cointegrating vector. Econometrically any type of (m-r)-restrictions can be chosen, however as in the time series case, economic theory may help to suggest some likely specifications. The Fisher equation, relating the interest rate to inflation and the expectations theory of the term structure, relating long and short term interest to each other, are examples of good candidates. In imposing the Fisher equation and/or the term structure more restrictions are imposed than actually needed to identify the cointegrating space. These restrictions are called overidentifying restrictions and their validity can be tested. In order to identify the cointegrating space and/or test for the validity of overidentifying restrictions, a similar maximum likelihood procedure as explained in section 6.1.1 is used to obtain the estimates. To (over)identify the cointegrating spaces, restrictions are imposed on each single vector of the Ai -
~
matrices as in (15) resulting in the identified Ai -matrices:
~ Ai = (V1i a~1i
V2i a~2i
K Vri a~ri )
i = 1,…,N
(40)
where Vqi , i = 1,…,N, q = 1,…,r, are the matrices that ´contain´ the restriction(s) on the qth cointegrating vector of the A-matrix of the ith individual and a~qi , i = 1,…N, q = 1,…,r are vectors containing the coefficients of the restricted qth cointegrating vector of the A-matrix of individual i. For example, in our case with k = 5 and r = 3, the following specification of Vqi and a~qi would impose the restriction that the last two elements of the qth cointegrating vector of the A-matrix of the ith individual are equal to zero:
1 0 Viq = 0 0 0
0 1 0 0 0
0 0 1 0 0
and
a qi,1 ~ a qi = a qi, 2 a qi, 3
(41)
where a qi,1 , a qi, 2 and a qi, 3 denote the first, second and third respective element of the cointegrating vector. Now under imposing all restrictions on all individual cointegrating spaces in the panel VECM,
- 40 -
each individual Ai -matrix, the model would look like (15) with the Ai -matrices replaced by the definition in (40). The maximum likelihood procedure as described in the previous section can now be used to calculate the maximised value of the likelihood function under the restrictions imposed and to provide estimates of the coefficients. However some small changes have to be made in the calculation procedure as in section 6.1.1 to take account of the imposed restrictions. The matrices R (33) and Rsure (34) matrices have to be replaced by Erestricted and Esure,restricted respectively, where
Esurerestricted = (( e1 ⊗ B1) ⊗ (e1 ⊗ I m ) K (eN ⊗ BN ) ⊗ (eN ⊗ I m )) V ,
(42)
V11 ∅ O ∅ Vr1 V = O V1N ∅ ∅
(43)
where
∅ ∅ O VrN
and
Erestricted = ( I Nm ⊗ Y−′1Y−1 ) Esure, restricted
(44)
Using these two matrices, the elements of the restricted cointegrating vectors can be estimated by the following formula, replacing (36) in section 6.1.1:
a~ˆ 11 M ~ˆ a r 1 −1 ˆ M = ( Eˆ ′ ˆ −1 ⊗ Y ′ Y ) Eˆ ˆ −1 ⊗ I ) vec(Y ′ ∆ Y ) ′ sure, restricted ( Ω −1 −1 sure , restricted ) E sure, restricted (Ω Nm −1 ~ˆ a1 N M ~ˆ arN
(45)
- 41 -
~
Having obtained the above estimates, the Ai -matrices can be constructed and subsequently used in the rest of the procedure, which remains the same as in section 6.1.1. After convergence of the likelihood function, estimates of the coefficients and the maximised likelihood value are obtained. In the case of testing for overidentifying restriction this maximised likelihood value can be used to calculate the following likelihood ratio test statistic in order to test for the validity of the overidentifying restrictions:
ˆ B,Ω ˆ (Φ ˆ B )) − l ( Φ ˆ BI , Ω ˆ (Φ ˆ BI )] ~ χ 2 ( ∑ N z i ) LR( Φ BI ] | Φ B ) = 2[l ( Φ i =1
(46)
~
where Φ BI is as Φ B (15) but with the Ai -matrices instead of the Ai -matrices and zi is the number of overidentifying restrictions imposed on the A-matrix of individual i. To delimit the number of possible combinations of identifying restrictions, it is chosen to confine attention to combinations of (over-)identifying that adhere to the following conditions:
Condition 1 1.1 The first cointegrating vector represents a long run money demand equation. 1.2 The second cointegrating vector represents a Fisher equation. 1.3 The third cointegrating vector represents the expectations theory of the term structure. These conditions are assumed based on economic theory and they also allow for comparison with the time series results in section 5. The second and third condition each impose one overidentifying restriction. Ideally the same specification of the cointegrating space for all countries can be accepted. Table 14 below shows the results of tests for such a common specification. Table 14 Test for a common specification of the cointegrating space across countries Specification
Test statistic
______________________ ___________ (m-p, y, il ), (il , is ), (il ,∆p) 83.25 (m-p, y, is ), (il , is ), (is ,∆p)
91.53
(m-p, y, ∆p), (il , is ), (is ,∆p)
68,96
Note: all test statistics are χ2 (20)-distributed, corresponding 1% critical value is 37,6.
- 42 -
As Table 14 clearly indicates, no common specification can be accepted that adheres to Condition 1. This complicates matters as the number of possible specifications, that allow every country or groups of countries to have their own specification, is quite large even under Condition 1. Dropping Condition 1 would complicate finding the right identification(s) even more as the number of possible combinations of (over)identifying restrictions would get very large. To get an indication of possible differences in specification, a look at each country´s individual cointegrating space is taken. Assuming a cointegrating rank of three8, a specification of the cointegrating space of an individual country is looked for. For most countries individually a specification cannot be rejected at a 1% level that adheres to Condition 1. However in the case of Spain and Finland this does not hold. Concerning the money demand equation, for all countries except Ireland the money demand equation relates real M3, real GDP and the long (or short) term interest rate to each other. For Ireland instead of one of the interest rates, inflation enters the money demand equation. 9 Taking these results, found for the individual countries, as an indication, several different combinations of overidentifying restrictions are tested, still assuming Condition 1. Several different combinations of restrictions are tested. Table 15 shows the results. Table 15 Tests for possible combinations of overidentifying restrictions. Specification
Identified Countries
___________________ _________________________________ (m-p,y,il ), (il ,is ), (il ,∆p) AU,BE,GE,FR,IT,NL
Test statistic, χ 2 (dgf) __________________ 29.23 [0.004], χ 2 (12)
(m-p,y,il ), (il ,is ), (il ,∆p)
AU,BE,GE,FR,IT,NL,IER
35.07 [0.002], χ 2 (14)
(m-p,y,il ), (il ,is ), (il ,∆p)
AU,BE,GE,FR,IT,NL,PT
41.59 [0.002], χ 2 (14)
(m-p,y,il ), (il ,is ), (il ,∆p)
AU,BE,GE,FR,IT,NL,IER(m-p,y,∆p)
35.01 [0.001], χ 2 (14)
(m-p,y,il ), (il ,is ), (il ,∆p)
AU,BE,GE,FR,IT,NL,ES,
48.03 [0.000],χ 2 (14)
(m-p,y,il ), (il ,is ), (il ,∆p)
AU,BE,GE,FR,IT,NL,PT,IER(m-p,y,∆p)
48.27 [0.000], χ 2 (16)
(m-p,y,il ), (il ,is ), (il ,∆p)
AU,BE,GE,FR,IT,NL,PT,IER
48.25 [0.000], χ 2 (16)
Note: p-values in brackets. Replacing the long term by the short term interest in the first and third cointegrating vector leads to similar results.
8 Although formal tests for cointegrating rank indicate cross-country differences in cointegrating rank. 9 The results stated in this paragraph are available upon request. They merely serve as an indication that could be helpful in identifying the cointegrating spaces in the Panel VECM.
- 43 -
As can be seen in Table 15, even at a 1% level each of the specifications is clearly rejected. Finding a suitable specification of the cointegrating spaces (even when it is left unidentified for some countries), that allows for the identification of a long run money demand equation is not that easy within the Panel VECM framework. However imposing equality of the long run money demand equation might still be accepted if tested for. Imposing the corresponding restrictions on the identified cointegrating spaces increases the number of degrees of freedom. This increase in the number of degrees of freedom might result in the acceptance of the null hypothesis if the imposing of the restrictions does not decrease the maximised value of the likelihood function too much. After having identified the first cointegrating vector as representing a possible long run money demand equation, the equivalence of this first cointegrating vector across individuals can be tested using a similar procedure as described in 6.1.1 to calculate the maximised value of the likelihood function under the null hypothesis. 5.1.3
Testing for homogeneity of the first cointegrating vector only10
Assuming a cointegrating rank of r, the model, under the null of homogeneity of the first cointegrating equation across the individuals in each of the s, 1 ≤ s < N, subgroups (s = 1 denotes the case of homogeneity of the first cointegrating equation across all individuals in the panel) assigned to one group, is similar to (25).
B A)′ 11 0 0 ∆Yt =
0 O
0 0 ) 0 Bn1 A1′
∅
∅ ) Bn1 +1A2′ 0 0 0 O 0 ) Yt−1 +εt =ΦG1Yt−1 +εt 0 0 Bn1 +n2 A2′ O )′ Bn1 +...+ns−1 +1 As 0 0 0 O 0 )′ 0 0 Bns As
(47)
- 44 -
Again the deterministic components and higher order dynamics are concentrated out before estimating (47). As in (40) a certain identification is needed to be able to say that a test for the equivalence of the first cointegrating vector is indeed a test for the equivalence of a meaningful long term relation.
)
Therefore in (47) the Ai -matrices are defined as,
) ) Ai = (V1i a1i
) V2 j a 2 j
) K Vrj a rj )
for all individuals j in group i, i ∈ {1,…,s}
(48)
)
The definition of the Ai -matrices as in (48) allows for an individual specific 2nd , 3rd, … , rth cointegrating vector but restricts the first cointegrating vector to be equal for all individuals in a group. Note that in order to have the same first cointegrating vector for a groups of individuals, the imposed (over)identification on this vector in a specific group has to be the same for every individual in that group. Testing for the validity of the homogeneity of the first cointegrating vector across groups can be done using a similar procedure as described for the case of testing for the homogeneity of the whole cointegrating space across groups. That is, after having calculated the maximum likelihood under the null hypothesis, specification (47), the following test statistic can be constructed
ˆ B ,Ω ˆ (Φ ˆ B )) − l ( Φ ˆ G1 , Ω ˆ (Φ ˆ G1 )) ~ χ 2 ( ∑ s ( n j −1) f j + ∑ N z i ) (49) LR( Φ G1 | Φ B ) = 2 l ( Φ j =1 i =1
where
∑
N
z are the number of restrictions imposed in order to overidentify the cointegrating spaces
i =1 i
(equal to zero in case of no overidentifying restrictions) and for j = 1,…,s, nj denotes the number of individuals in group j and fj the number of elements of the first cointegrating vector restricted to be equal across the individuals in group j. The way to calculate the maximum likelihood under the null hypothesis is similar to the procedure described previously in case of the null of homogeneity of the cointegrating space across groups. The only difference being that the matrices R (33) and Rsure (34) are replaced by K and K sure respectively, where K and K sure are defined as follows:
10 For simplicity attention is focused merely on testing for equivalence of the first cointegrating vector. The procedure as described here can easily be modified to allow for tests on other cointegrating vectors or groups of cointegrating vectors.
- 45 -
K = ( I Nm ⊗ Y−′1Y−1 ) K sure
(50)
and
K sure
B%1,1:m M B% n1 ,1: m = 0 0
0
B% n1 +1,1:m
L
0
O
M
M
0
O
B% n1 +...+ ns−1 +1,1:m
B% n1 + n2 ,1:m O
L
e1 ⊗ B%1, m+1:rm
M
0
B% n1 + ...+ ns ,1: m
% L e N ⊗ BN , m+1:rm V (51)
where V is a matrix similar to (43), imposing the (over)identifying restrictions on each cointegrating vector, B% i = Bi ⊗ ( ei ⊗ Im ) for i = 1,…,N and the subscript h:j refers to column h up to column j, column j inclusive, of the matrix of which it is a subscript. Using (50) and (51) estimates of the
)
coefficients of the Ai -matrices can be obtained as follows:
) aˆ11 M )ˆ a s1 = ( Kˆ ′ ( Ω ˆ − 1 ⊗ Y−′1Y−1 ) Kˆ sure ) −1 Kˆ sure ˆ −1 ⊗ I Nm ) vec(Y−′1 ∆Y ) ′ (Ω sure vec( (a)ˆ L a)ˆ ) ) 12 1r M vec ( ( a)ˆ L a)ˆ ) ) N2 Nr
(52)
) where aˆi1 , i = 1,…,s, are the estimates of the coefficients of the group specific first cointegrating ) ) vector and aˆ j 2 L aˆ jr , j = 1,…,N the individual specific estimates of the coefficients of the other (r-1)
)
cointegrating vectors. After having estimated (52), the individual Ai -matrices can be constructed and used in (37). After convergence of the maximum likelihood under the null the test statistic can be constructed as in (49) and compared to the corresponding critical value.
- 46 -
Table 16a shows the test results obtained when testing for the equivalence of the first cointegrating vector, when the cointegrating spaces are identified as in the two cases with the highest p-value in Table 15. Table 16a Testing for the equivalence of the long run money demand relation Specification
Identified Countries (same money demand)
Test statistic, χ 2 (dgf)
___________________ ___________________________________ _________________ (m-p,y,il ), (il ,is ), (il ,∆p) (AU,BE,GE,FR,IT,NL) 130.34 [0.000], χ 2 (22) (m-p,y,il ), (il ,is ), (il ,∆p)
(AU,BE,GE,FR,IT,NL),IER(m-p,y,∆p)
131.31 [0.000], χ 2 (24)
Note: p-values in brackets
Table 16b Testing for the equivalence of the term structure Specification
Identified Countries (same term structure)
Test statistic, χ 2 (dgf)
___________________ ___________________________________ _________________ (m-p,y,il ), (il ,is ), (il ,∆p) (AU,BE,GE,FR,IT,NL) 34.88 [0.006], χ 2 (17) (m-p,y,il ), (il ,is ), (il ,∆p)
(AU,BE,GE,FR,IT,NL),IER(m-p,y,∆p)
38.46 [0.005], χ 2 (19)
Note: p-values in brackets
The equivalence of the first cointegrating vector, representing a long run money demand equation, is clearly rejected in both cases. The two cases in Table 16b, where the equality of the cointegrating vector representing the term structure is tested across six countries, are shown to illustrate that the increase in degrees of freedom (by imposing more restrictions) can lead to an increase in the significance level at which the null hypothesis can be accepted (p-values). However, note that also in this case the null hypothesis cannot be accepted at a 1% level. 5.2
Interpreting the results
Adopting a Panel VECM framework in order to verify the existence of a long run money demand equation leads to results that are a bit twofold. Using the GK-2002 test for common cointegrating rank clearly indicates a common cointegrating rank of three. As in the time series case, the variables included in the analysis of the money demand equation (real M3, real GDP, the long and short term interest rates and inflation), share three long run relations. This finding reinforces the choice for a dynamic panel method that allows for a cointegrating rank larger than one. Applying a dynamic panel method that restricts the number of possible long run relations, e.g. a residual based testing procedure,
- 47 -
seems inappropriate. Tests for the equivalence of the cointegrating spaces of the countries included in the Panel VECM clearly show that (group-wise) homogeneity of these cointegrating spaces is rejected. This indicates differences in the long run relationships between the countries (or groups of countries) in the eurozone. However, this finding per se does not give an indication as to whether a long run money demand equation exists for each country and more specifically if these money demand relations are similar for some (groups of) countries in the eurozone. To be able to draw meaningful conclusions about long run money demand, the cointegrating spaces of each of the countries have to be identified in such a way that one of the three cointegrating vectors specifies a long run money demand equation. This identification poses several problems. The number of possible combinations of (over)identifying restrictions is quite large and testing only one combination already requires a substantial amount of computational time. To restrict the number of possibilities, attention is confined to specifications that are reasonable from an economic perspective (see Condition 1). This, however, does not result in the acceptance of a common specification across the countries of the eurozone. Also when leaving some countries´ cointegrating space unidentified and allowing for differing identifications per country, an identification of a long term money demand equation for each of the ´identified´ countries can not be found. Not surprisingly a homogeneous money demand equation, which could have been accepted due to the increase in degrees of freedom obtained by imposing this extra restriction, is clearly rejected. The effect of national differences in financial structures and markets and country specific structural breaks seems to have an influence on the specific long run relations that are shared by the five variables included in the analysis for each eurozone member country respectively. However, as no specification for the cointegrating spaces is found that can be accepted when tested for, the Panel VECM framework does not yet provide quantitative results by which the effectiveness of the ECB´s monetary policy can be assessed11. Based on the test results it is tempting to say that differences across the countries in the eurozone do exist with respect to long run money demand, confirming earlier panel results by Golinelli and
11 This problem might be the result of modelling the higher order dynamics by only including the first lagged differences for all countries in the panel (ki = 1, see p.33), possibly resulting in autocorrelation in the residuals. The AIC indeed suggests differing short term dynamics when looking at the individual countries, the HQ criterion on the other hand indicates that including only one lag for each country may not be so bad. Allowing for country specific short term dynamics may be able to filter out the country specific effects more effectively, leaving only the ´core´ relations. This, and also allowing for country specific deterministic components (this might change the distribution of the test statistics!), may lead to better quantitative results, but is left to future research.
- 48 -
Pastorelli (2000). Not being able to quantify these differences12 is a major drawback of the Panel VECM framework, as it does not allow for specific comments and/or suggestions in order to take account of these differences13. Direct implications for the ECB´s monetary policy are difficult to indicate. However the difference in the long term relations between the countries that comprise the eurozone, as shown by the differences in their cointegrating spaces, may have an effect on the results that are obtained from the time series analysis using the aggregate series. Some care has therefore to be taken when basing policy decisions on the results obtained from the aggregate analysis. Dedola et al. (2000) and Golinelli and Pastorello (2001) both claim, based on not very rigorous results obtained using residual based testing procedures, that the results obtained from the area-wide aggregates are still useful. In case of Johansen type estimation procedures the impact of using aggregates, constructed from individual series that share different long run relations on the disaggregated level, is not yet clear. Identifying the impact of these differences is therefore an important issue to be looked at in future studies on eurozone money demand.
12 This may also be due to poor size/power of the test given the (relatively) large N-dimension and the number of variables included. However the problem of finding quantitative results remains valid also when using ´smaller´ panels, only a panel consisting of ´D-mark´-countries (see footnote 12) provides quantitative results. This may be viewed as an indication that cross-country differences are a more important reason for the lack of quantitative results, however to be sure simulations need to be performed. 13 Evidence from tests using ´smaller´ panels consisting of subgroups of eurozone countries also shows difficulties finding an identification for each of the cointegrating spaces. Only when focusing on ´the D-mark´ area, consisting of Germany, Austria and the Netherlands, a (common) identification is found. Subsequent tests on the cointegrating vector representing the long run money demand equation reject a common relation for the three countries. This results indicates differences w.r.t. the long run money demand equation even for these three countries that can be said to have a similar history regarding monetary policy.
- 49 -
6
CONCLUSIONS
One of the ´pillars´ of the ECB´s monetary policy aimed at the maintenance of price stability in the medium term, is a prominent role for the amount of money held as inflation is believed to be a monetary phenomenon in the long run. This prominent role for money is based on the assumption that a stable relation exists between money and inflation. This paper tries to verify the existence of such a stable relation using two different econometric methods. First a time series framework is used, a choice very common in recent research on money demand. To allow for the use of a time series approach, eurozone wide aggregates have to be constructed in order to have data series that are long enough to be able to obtain meaningful estimation results. The choice of aggregation method is important as it is shown in section 4 that the estimation results depend on it. The thorough discussion of different aggregation methods in section 3, shows that variable weight growth rate aggregation is the best method to obtain eurozone wide aggregates. This method takes historical exchange rate movements into account without introducing an unwanted exchange rate effect in the aggregated series. The estimation results obtained using the aggregates constructed by this method, see section 4, give clear evidence that a long run money demand equation exists for the eurozone, and that this relation has been quite stable over the past few years. Besides a long run money demand equation, also evidence in favour of the expectations theory of the term structure and the Fisher equation is found. The actual coefficients of the long run money demand equation confirm economic theory, i.e. a positive effect of an increase in real GDP and a negative effect of an increase in the long term interest rate on the amount of money held. More importantly, the effectiveness of the ECB´s monetary targeting strategy is confirmed as a (de-)increase in money holdings (below) above the actual ´equilibrium´ amount, as indicated by the long run money demand equation, leads to a (de-) increase in inflation. The second econometric framework used is that of the (relatively new) dynamic panel data setup. This setup does not call for a specific aggregation method. All national series are used by itself, which allows for the exploitation of commonalities across the countries in the eurozone and also takes country specific effects into account. A thorough discussion of available dynamic (nonstationary) panel methods, leads to the choice for the Panel VECM setup. The Groen and Kleibergen (2002) test is used to verify the number of long run relations that are shared by the countries in the eurozone. As in the time series case, three long run relations are found. A finding that strengthens the argument against using a test procedure that restrict the number of long run relatio ns. A subsequent test for the homogeneity of these three long run relations across all (or within groups of) countries is rejected, indicating differences in each of the countries´ long run relations.
- 50 -
However only one of these long run relations represents a long run money demand equation. To be able to identify and perform tests on the long run money demand equation only, the Groen and Kleibergen (2002) procedure is adapted. Results show difficulties in finding an appropriate identification for each of the country specific long run relations that can be said to correspond to a priori beliefs based on economic theory. The Panel VECM setup seems to be affected too much by potential misspecifications imposed by the panel setup for some specific countries and country specific shocks (evident when looking at the graphs in Appendix B, e.g. Finland´s GDP, Italy´s M3). These country specific effects are of much less influence in the time series analysis as they are ´aggregated´ away when constructing the eurozone wide aggregates. Finding clear quantitative results on which the effectiveness of the monetary targeting strategy of the ECB can be assessed, is difficult. The evidence, obtained from the Panel VECM results, gives the overall impression that differences in the long term money demand equation are likely to exist across the countries of the eurozone. The problem is that the approach is unable to quantify these differences which makes it difficult to draw conclusions about the (differences in) effectiveness of the ECB´s monetary targeting strategy across the individual member countries of the eurozone. As quantifying these differences can be of importance with respect to the effect of the ECB´s monetary policy, looking for other (newer) dynamic nonstationary panel methods or different specification(s) of the Panel VECM (see footnote 10), that are able to give clearer (quantitative) evidence constitutes a possible direction for future research. The results from the time series analysis give very clear quantitative results about the effectiveness of the ECB´s monetary targeting strategy, confirming its effectiveness with respect to maintaining price stability in the eurozone and thereby strengthening the credibility of the ECB´s monetary policy. These results however are based on aggregates that, by construction (statistical averaging effect), dampen the impact of country specific shocks. Moreover these results might be influenced by the differences in long run relations found for the individual national variables. Finding the exact influence of aggregation on the estimation results from a Johansen-type estimation procedure is of importance to the ECB, as it bases its monetary policy on these aggregate results and constitutes another possible direction for future research.
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APPENDIX A THE DATA Table A1 Country Codes Code ____ AU BE ES FI FR GE GR IER IT NE PT LU
Country ___________ Austria Belgium Spain Finland France Germany Greece Ireland Italy Netherlands Portugal Luxembourg
Data Sources Nominal and real GDP Table A2 Nominal and real GDP, data sources Country
Period
Source
______ AU
_____________ 1979.1 – 2002.4
_________________ OECD, QNA 2003.1
BE
1980.1 – 2002.4 1979.1 – 1979.4 1979.1 – 2002.4 1979.1 – 2002.4 1979.1 – 2002.4 1979.1 – 2002.4 1979.1 – 2002.4 1997.1 – 2002.4 1979.1 – 1996.4 1979.1 – 2002.4 1979.1 – 2002.4 1986.1 – 2002.4 1979.1 – 1985.4 1985 – 2002 1979 – 1984
OECD, QNA 2003.1 ECB OECD, QNA 2003.1 OECD, QNA 2003.1 OECD, QNA 2003.1 ECB ECB OECD, QNA 2003.1 Economic Outlook 69 OECD, QNA 2003.1 OECD, QNA 2003.1 OECD, QNA 2003.1 Economic Outlook 69 ECB Economic Outlook 72
ES FI FR GE GR IER IT NE PT LU
Seasonally Adjusted (SA) / Non-Seasonally Adjusted (NSA) ___________________________ NSA, adjusted using Multiplicative X12-ARIMA SA SA SA SA SA, adjusted for unification SA NSA, adjusted using Multiplicative X12-ARIMA SA SA SA SA
Quarterly nominal and real GDP series in levels for each of the twelve Euro-countries. All series are in millions of euro using the irrevocable conversion rates as set by the ECB on December 31st 1998. Whenever two sources are given, the older series is multiplicatively added to the newer series, using the quarterly growth rates in the older series to ´update´ the newer series, e.g. x1985.4,new = x1986.4,new ×
- 55 -
x1985.4,old /x1985.4,old. As most available series were seasonally adjusted (SA), the series for Ireland and Austria, which were only available non seasonally adjusted (NSA), are seasonally adjusted using the multiplicative X12-ARIMA method (see Findley et al. 1998). The multiplicative X12-ARIMA method is chosen as the ECB also uses this method for its published data. 1995 is taken as the base year for the GDP series. For Luxembourg only yearly data are available so these data are made into quarterly data using the Lisman-method. The data obtained from Economic Outlook are semi-annual and are also transformed into quarterly data. Short term interest rates Quarterly short term interest rates expressed in yearly return for each of the twelve Euro-countries for the period 1979.1 – 2002.4. For 1979.1 – 2000.4 3-month interest rates for all countries are obtained from the BIS (Bank of International Settlements) database. For the period 2001.1 – 2002.4, the 3month euro-deposit rate is used for all countries. Long term bond yields Quarterly long term bond yields expressed in yearly return for each of the twelve Euro-countries for the period 1979.1 – 2002.4. 10-year interest rates on government bonds (or a proxy) for 1979.1 – 2000.4 are obtained from the BIS database and for 2001.1 – 2002.4 these are taken from Datastream. M3 M3 data for each of the twelve Euro-countries for the period 1979.1 – 2002.4. A monthly series for each country is obtained from the European Central Bank (ECB) database. The series are in millions of euro using the irrevocable conversion rates of December 31st 1998. The monthly series are converted into quarterly series taking the average of the three corresponding months for each quarter. Then the quarterly series are seasonally adjusted using the multiplicative X12-ARIMA method (see Findley et al. 1998). The German series is corrected for the effect of the unification by first regressing the growth rates on a dummy for 1990.3 (see Fagan and Henry, 1998; Beyer et al., 2001; Wesche, 1997). The effect was found to be 8.1% with a standard error of 0.98. Using this estimated effect the growth rate of 1990.3 is corrected by subtracting the unification effect. These corrected growth rates are then used to calculate back the series in lo glevels (and levels). Exchange rates Exchange rates of each of the twelve Euro-countries against the ECU/EURO for the period 1979.1 – 2002.4. A monthly series is obtained from the Dutch Central Bank – FM database for each country. These series are converted into quarterly series taking the average of the three corresponding months
- 56 -
for each respective quarter. For the period 1999.1 – 2002.4 the irrevocable conversion rates as set by the ECB are used (for Greece from 2001.1 on). Data Analysis In this section a thorough inspection of the data used in our estimation of the money demand equation (2) is presented. For each of the twelve Euro-countries graphs are given in Appendix B for the series as represented in (2) and descriptive statistics for these series are given in first differences to be able to give a meaningful comparison between the countries; the results for inflation and interest rates are only shown in levels. As we do not yet have the series for the GDP-deflator and real M3, we construct the GDP-deflator series for each country respectively by dividing the nominal GDP series by the real GDP series and the real M3 series for each country respectively as the M3 series divided by the GDPdeflator series. We also transform all variables, except long and short term interest rates, in logs as specified in (2) and take first differences of the GDP-deflator series to construct the inflation series ∆p. The inflation series is thereafter multiplied by four to make it compatible to the two interest rate series. For the same reason of compatibility, the long run bond yield and the short term interest series are divided by one hundred. Real M3 (md -p) Table A3.1 Descriptive statistics for quarterly real M3 (md -p) growth rates AU BE ES FI FR GE _________ _________ _________ __________ __________ __________ Mean 0.69 0.73 0.92 0.96 0.70 0.87 Median 0.81 0.74 0.89 1.24 0.85 0.88 Maximum 3.87 4.34 4.54 5.10 2.36 4.04 Minimum -5.59 -3.31 -1.64 -6.45 -2.17 -1.72 Std. Dev. 1.18 1.40 0.94 2.11 0.98 1.02 GR IER IT LU NE PT _________ _________ _________ __________ __________ __________ Mean 1.02 1.22 0.27 0.72 1.16 0.92 Median 0.94 0.93 0.20 0.96 1.16 0.96 Maximum 6.11 7.98 3.41 17.04 3.67 8.44 Minimum -3.26 -5.28 -4.04 -16.85 -1.14 -4.33 Std. Dev. 1.88 2.77 1.26 3.19 1.07 1.86
As can be seen from Figure B1.1. in Appendix B and Table A3.1, all real M3 show an upward trending behaviour. The average quarterly growth rate (multiplied by four to express them in yearly rates) ranges from 1.08% for Italy to 4.88% for Ireland. The growth rate in Spain deviates the least
- 57 -
from its average over the period. The graph for Luxembourg shows an extraordinary decline during the end of the nineties followed by a recline of almost the same magnitude. Real GDP (y) Table A3.2 Descriptive statistics for quarterly real GDP (y) growth rates AU BE ES FI FR GE _________ _________ _________ __________ __________ __________ Mean 0.55 0.50 0.65 0.65 0.51 0.48 Median 0.69 0.49 0.61 0.65 0.53 0.37 Maximum 2.04 4.12 2.84 4.09 1.55 3.28 Minimum -1.31 -1.37 -1.03 -2.29 -0.65 -2.71 Std. Dev. 0.74 0.82 0.70 1.32 0.51 0.97 GR IER IT LU NE PT _________ _________ _________ __________ __________ __________ Mean 0.39 1.29 0.49 1.12 0.59 0.63 Median 0.47 1.07 0.53 0.93 0.70 0.75 Maximum 9.92 6.88 2.33 3.17 2.67 3.87 Minimum -7.09 -1.95 -1.03 -0.30 -2.37 -3.64 Std. Dev. 2.77 1.55 0.59 0.94 0.82 1.41
As Figure B1.2 clearly shows, most series show a smooth increase in real GDP over the sample period. Only Portugal and Greece show a less smooth increase over the years although being seasonally adjusted. The average quarterly growth rates range (multiplied by four to express them in yearly rates) from 1.56% for Greece to 5.16% for Ireland. As expected from Figure B1.2 the standard deviation of the growth rate is the highest for Greece. Inflation ∆p (growth rate GDP-deflato r) Table A3.3 Descriptive statistics for quarterly inflation, ∆p, in yearly returns AU BE ES FI FR GE _________ _________ _________ __________ __________ __________ Mean 2.72 3.01 6.66 4.40 3.96 2.43 Median 2.48 2.64 6.20 3.62 2.36 2.33 Maximum 10.54 15.92 16.76 25.08 13.27 8.48 Minimum -0.84 -10.40 -0.41 -6.99 -0.02 -1.75 Std. Dev. 2.09 2.99 3.75 5.08 3.54 2.07 GR IER IT LU NE PT _________ _________ _________ __________ __________ __________ Mean 12.74 5.73 7.24 3.55 2.46 11.08 Median 12.40 4.36 5.78 2.95 2.27 8.52 Maximum 38.07 19.39 22.15 11.61 10.11 31.33 Minimum -1.17 -8.55 0.21 -0.88 -5.76 -0.57 Std. Dev. 7.50 5.00 5.50 2.74 2.60 7.94
- 58 -
As expected the inflation rate for Germany is on average the lowest (2.43%) followed by the Netherlands and Austria. Greece has experienced the highest (12.74%) inflation on average. From the graphs it can be seen that all series show a convergence to low levels of inflation. Note that the graph of Luxembourg, in Figure B1.3, is very smooth due to the formation of the quarterly data out of yearly series. Short term interest rate Table A3.4 Descriptive statistics for quarterly short term interest rates in yearly returns AU BE ES FI FR GE _________ _________ _________ __________ __________ __________ Mean 6.02 7.89 11.19 9.13 8.66 5.86 Median 5.36 7.90 12.60 9.93 8.27 5.13 Maximum 12.20 16.64 22.69 16.52 23.44 12.59 Minimum 2.60 2.60 2.60 2.60 2.60 2.60 Std. Dev. 2.41 3.84 5.08 4.48 4.61 2.45 GR IER IT LU NE PT _________ _________ _________ __________ __________ __________ Mean 15.96 9.17 11.24 7.89 6.20 13.05 Median 17.81 9.42 11.37 7.90 5.68 14.39 Maximum 25.91 18.38 20.47 16.64 13.02 27.01 Minimum 3.04 2.60 2.60 2.60 2.60 2.60 Std. Dev. 5.94 4.20 5.08 3.84 2.59 6.54
As can be expected from the inflation series, Germany has on average the lowest short term interest rate (5.86%) and Greece the highest (15.96%). Looking at the individual series the main observation in Figure B1.4 is the convergence of all series to the same low value of short term interest rate (they are actually the same since the introduction of the euro). Furthermore many countries show a period of higher short term interest rates during the beginning of the nineties. Long term bond yield Table A3.5 Descriptive statistics for quarterly long term bond yield in yearly returns AU BE ES FI FR GE _________ _________ _________ __________ __________ __________ Mean 7.21 8.53 11.20 9.76 8.90 6.84 Median 7.16 8.27 11.74 11.10 8.72 6.70 Maximum 11.17 13.81 17.80 14.75 16.86 10.61 Minimum 4.00 4.07 4.10 4.06 3.94 3.85 Std. Dev. 1.61 2.72 4.09 3.15 3.37 1.53
- 59 -
GR IER IT LU NE PT _________ _________ _________ __________ __________ __________ Mean 15.93 9.92 11.25 8.17 7.18 16.13 Median 17.11 9.10 11.28 7.78 6.88 19.17 Maximum 25.91 19.03 21.21 13.13 11.72 32.24 Minimum 4.71 4.00 4.09 4.00 3.97 4.04 Std. Dev. 6.08 3.97 4.45 2.53 1.82 8.11
Looking at Figure B1.5 and B1.4, the movement of the long term interest rate shows great similarity with the short term interest rate, but the series are a bit smoother. This is intuitive as the long term interest rates are more determined by the long run fundamentals in the economy, which do not change that rapidly over time. Again Germany has the lowest long term interest rate on average (6.84%) and the highest long term interest rate (16.13%) can be found for Portugal. Exchange rates Table A3.6 Descriptive statistics for quarterly exchange rate growth rates until fixed euro conversion rates are used. (all series until 1999.1 except Greece 2000.1) AU BE ES FI FR GE _________ _________ _________ __________ __________ __________ Mean -0.36 0.02 0.71 0.13 0.16 -0.31 Median -0.24 -0.08 0.42 -0.07 -0.02 -0.22 Maximum 1.29 4.87 9.46 10.92 4.80 1.25 Minimum -3.26 -3.36 -5.49 -6.12 -3.08 -3.23 Std. Dev. 0.94 1.13 2.31 2.63 1.08 0.91 GR IER IT LU NE PT _________ _________ _________ __________ __________ __________ Mean 2.19 0.20 0.67 0.02 -0.26 1.43 Median 1.58 0.07 0.38 -0.08 -0.19 0.95 Maximum 20.04 4.98 9.30 4.87 1.40 12.77 Minimum -2.69 -3.90 -4.93 -3.36 -3.72 -2.29 Std. Dev. 3.12 1.47 2.08 1.13 0.94 2.38
Looking at the graphs in Figure B1.6 and the descriptive statistics in Table A3.6 it is cle ar that for most countries their currencies have depreciated a lot with respect to the euro. Only the Dutch Guilder, the German Mark and the Austrian Shilling have appreciated on average over the sample period. Also the Belgian Franc has a period in which it appreciates with respect to the euro, but at the beginning of the sample period it depreciated a lot in a few years time. The Austrian Shilling appreciated the most on average and the Greek Drachma depreciated the most on average.
- 60 -
APPENDIX B FIGURES Figure B1.1 Quarterly real M3 (md -p) series in loglevels 11.9
12.5
11.8
12.4
13.2
12.3
11.7
11.4 11.2
13.0
12.2
11.6
11.0 12.8
12.1 11.5
10.8
12.0
11.4
12.6
11.9
11.3
11.8
11.2
11.7
11.1
10.6 12.4
11.6 80 82 84 86 88 90 92 94 96 98 00 02
10.4
12.2 8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 9 8 00 0 2
LN_AU
10.2 8 0 8 2 8 4 8 6 88 9 0 9 2 9 4 9 6 9 8 0 0 0 2
LN_BE
13.9
14.2
13.8
14.1
13.7
14.0
L N_FI
11.6
11.4 11.2
11.4
11.0
13.9
13.6
8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 98 0 0 0 2
L N_ ES
11.2
10.8
13.8 13.5
11.0
13.7
13.4
13.6
13.3
13.4
13.1
13.3 80 82 84 86 88 90 92 94 96 98 00 02
10.4 10.2
13.5
13.2
10.6
10.8 10.6
10.0
10.4 8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 9 8 00 0 2
LN_FR
9.8 8 0 8 2 8 4 8 6 88 9 0 9 2 9 4 9 6 9 8 0 0 0 2
LN_GE _ADJ
13.5
12.2
11.6
12.6
12.0 11.9
13.3
LN_I ER
12.8
12.1 13.4
11.4
12.4 11.2
11.8
12.2
11.7
13.2
11.0
11.6
12.0
11.5
13.1
11.3 80 82 84 86 88 90 92 94 96 98 00 02
11.6 8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 9 8 00 0 2
L N_IT
Note:
10.8
11.8
11.4 13.0
8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 98 0 0 0 2
LN_G R
10.6 8 0 8 2 8 4 8 6 88 9 0 9 2 9 4 9 6 9 8 0 0 0 2
L N_ LU
8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 98 0 0 0 2
L N_ NE
LN_PT
going from upper left to lower right the graphs represent the series for country AU, BE, ES, FI, FR, GE, GR, IER; IT, LU, NE, PT
Figure B1.2 Quarterly real GDP (y) in loglevels 10.9
11.0
11.9
10.5
10.8
10.9
11.8
10.4
11.7
10.3
11.6
10.2
11.5
10.1
11.4
10.0
10.7
10.8
10.6 10.7 10.5 10.6
10.4
10.5
10.3 10.2
11.3
10.4 80
82
84
86
88 90
92
94
96
98
00
02
9.9
11.2 80
82
84
86
88
LN_AU
90
92
94
96
98
00
02
9.8 80
82
84
86
88
LN_ BE
12.8
13.2
12.7
13.1
12.6
13.0
12.5
12.9
12.4
12.8
90
92
94
96
98
00
02
10.2
84
86
88 90
92
94
96
98
00
02
92
94
96
98
00
02
94
96
98
00
02
94
96
98
00
02
9.6 9.4 9.2 9.0
9.7 80
82
84
86
88
90
92
94
96
98
00
02
8.8 80
82
84
86
88
LN_G E
12.4
90
10.2
9.8
LN_FR
12.5
88
9.8
12.6 82
86
10.0
12.7
80
84
10.1
9.9
12.2
82
LN_FI
10.0
12.3
80
L N_ES
90
92
94
96
98
00
02
80
82
84
86
88
LN_G R
11.5
10.2
8.4
11.4
10.1
11.3
10.0
11.2
9.9
11.1
9.8
11.0
9.7
12.3
92
LN_I ER
8.6
8.2
90
8.0 12.2 7.8 12.1
7.6
12.0
7.4 80
82
84
86
88 90
92
L N_IT
Note:
10.9
94
96
98
00
02
9.6
10.8 80
82
84
86
88
90
92
L N_LU
94
96
98
00
02
9.5 80
82
84
86
88
90
92
94
96
98
00
02
L N_NE
going from upper left to lower right the graphs represent the series for country AU, BE, ES, FI, FR, GE, GR, IER; IT, LU, NE, PT
80
82
84
86
88
90
92
LN_PT
- 61 -
Figure B1.3 Quarterly inflation ∆p in yearly returns (growth rate GDP deflator) .12
.20
.20
.10
.15
.16
.08
.10
.06
.05
.28 .24 .20
.12
.16 .12
.08 .04
.08
.00 .04
.02
-.05
.00
-.10
.00
-.02
-.15
-.04
80
82
84
86
88
90
92
94
96
98
00
02
.04 .00 -.04
80
82
84
86
88
DLN_AU_YR
90
92
94
96
98
00
02
-.08 80
82
84
86
88
DLN_BE_YR
.14
.10
.12
90
92
94
96
98
00
02
82
84
86
88
92
94
96
98
00
02
96
98
00
02
96
98
00
02
94
96
98
00
02
94
96
98
00
02
94
96
98
00
02
.20 .15
.3
.10
90
DLN_FI_YR
.4
.08 .06
.08
80
DLN_ES_YR
.10 .2
.06
.04
.05 .1
.04
.02
.00
.02
.0
.00
.00 -.02
-.02 80
82
84
86
88
90
92
94
96
98
00
02
-.05
-.1 80
82
84
86
88
DLN_FR_YR
90
92
94
96
98
00
02
-.10 80
82
84
86
88
DL N_ GE_ YR
.24
.12
.20
.10
90
92
94
96
98
00
02
.12
-.02 80
82
84
86
88
90
92
94
96
98
00
02
92
94
.16 .12
.00
.08 -.04
.04
-.08
-.04
.00
80
82
84
86
88
DL N_ IT_YR
Note:
90
.20
.02
.00
88
.24
.04
.04
.00
86
.28
.12
.04
84
.32
.08
.06
.08
82
DLN_ IER_YR
.08
.16
80
DL N_GR_ YR
90
92
94
96
98
00
02
80
82
84
86
88
DLN_L U_YR
90
92
94
96
98
00
02
80
82
84
86
88
DLN_NE_YR
90
92
94
DLN_PT_YR
going from upper left to lower right the graphs represent the series for country AU, BE, ES, FI, FR, GE, GR, IER; IT, LU, NE, PT
Figure B1.4 Quarterly short term interest rate in yearly returns .14
.18
.24
.16
.12
.18 .16
.20
.14 .10
.14 .16
.12
.08
.10
.06
.12
.12
.08
.10 .08
.08
.06 .04
.06 .04
.04
.02
.02 80
82
84
86
88
90
92
94
96
98
00
02
.04
.00 80
82
84
86
88
SR_AU
90
92
94
96
98
00
02
.02 80
82
84
86
88
SR_ BE
90
92
94
96
98
00
02
80
82 84
86
88
SR_ES
.24
.14
.30
.20
.12
.25
.16
.10
.20
.12
.08
.15
.08
.06
.10
.04
.04
.05
.00
.02
.00
90
92
SR_FI
.20
.16
.12
.08
80
82
84
86
88
90
92
94
96
98
00
02
80
82
84
86
88
SR_FR
90
92
94
96
98
00
02
.04
.00 80
82
84
86
88
SR_G E
.24
92
94
96
98
00
02
80
82 84
86
88
SR_G R
.18 .16
.20
90
90
92
SR_ IER
.14
.30
.12
.25
.10
.20
.08
.15
.06
.10
.04
.05
.14 .16
.12
.12
.10 .08
.08
.06 .04
.04
.00
.02 80
82
84
86
88
90
92
SR_I T
Note:
94
96
98
00
02
.02 80
82
84
86
88
90
92
SR_LU
94
96
98
00
02
.00 80
82
84
86
88
90
92
94
96
98
00
02
SR_NE
going from upper left to lower right the graphs represent the series for country AU, BE, ES, FI, FR, GE, GR, IER; IT, LU, NE, PT
80
82 84
86
88
90
92
SR_PT
- 62 -
Figure B1.5 Quarterly long term bond yield in yearly returns .12
.14
.11 .12 .10 .09
.10
.18
.16
.16
.14
.14
.12
.12 .10
.08 .08
.10
.07
.08
.06
.08
.06
.06
.06
.05 .04
.04
.04
.04 .03
.02 80
82
84
86
88
90
92
94
96
98
00
02
.02 80
82
84
86
88
LR_AU
.11
.16
.10
.14
.09
.12
.08
.10
.07
.08
.06
.06
.05
.04
.04
.02
.03 82
84
86
88
90
92
92
94
96
98
00
02
.02 80
82
84
86
88
90
LR_BE
.18
80
90
94
96
98
00
02
.12
98
00
02
80
82 84
86
88
90
92
94
96
98
00
02
94
96
98
00
02
94
96
98
00
02
L R_ FI
.28
.20
.24
.16
.12
.08 .12 .04
.08 .04 82
84
86
88
90
92
94
96
98
00
02
.00 80
82
84
86
88
90
L R_GE
.14
96
.16
80
.20
94
.20
LR_FR
.24
92
LR_ES
92
94
96
98
00
02
80
82 84
86
88
LR_ GR
90
92
LR_I ER
.12
.35
.11
.30
.10 .16
.10
.12
.08
.08
.06
.04
.04
.25
.09 .08
.20
.07
.15
.06 .10 .05 .05
.04 .00
.02 80
82
84
86
88
90
92
94
96
98
00
02
.03 80
LR_I T
Note:
82
84
86
88
90
92
94
96
98
00
02
.00 80
82
84
86
88
90
LR_ LU
92
94
96
98
00
02
80
LR_NE
82 84
86
88
90
92
LR_PT
going from upper left to lower right the graphs represent the series for country AU, BE, ES, FI, FR, GE, GR, IER; IT, LU, NE, PT
Figure B1.6 Quarterly exchange rates in local currency per euro 19
47
2.6
46
2.5
45
2.4
18 17
44
7.0
6.5
2.3
6.0
43 16
2.2
42
15
41
2.0
40
14
38 80
82 84 86 88 90
92 94
96 98 00 02
1.8 80
82 84 86 88 90
AU
92 94 96 98 00 02
170
360
7.0
160
320
6.6
.80
240
130
6.4
.76
200
120 6.2
100
120
5.8
90
80
80 80
82 84 86 88 90
92 94
96 98 00 02
.68
40 80
82 84 86 88 90
FR
92 94 96 98 00 02
.64 80 82 84 86 88 90 92 94 96 98 00 02
ES
2400
.72
160
110
6.0
5.6
FI
.84
280
140
80 82 84 86 88 90 92 94 96 98 00 02
GE
7.2
150
4.5 80 82 84 86 88 90 92 94 96 98 00 02
BE
6.8
5.0
1.9
39 13
5.5
2.1
80 82 84 86 88 90 92 94 96 98 00 02
GR
I ER
47
2.9
220
46
2.8
200
45
2.7
44
2.6
1800
43
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41
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2200 2000
180 160 140
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38 80
82 84 86 88 90
92 94 IT
Note:
96 98 00 02
120 100 80
2.0 80
82 84 86 88 90
92 94 96 98 00 02 LU
60 80 82 84 86 88 90 92 94 96 98 00 02 NE
going from upper left to lower right the graphs represent the series for country AU, BE, GE, FI, FR, ES, GR, IER; IT, LU, NE, PT
80 82 84 86 88 90 92 94 96 98 00 02 PT
De Nederlandsche Bank
EUROZONE MONEY DEMAND: Time series and dynamic panel results E.M. Bosker*
* I am especially grateful to Jean-Pierre Urbain, Franz Palm and Peter Vlaar for their comments. Moreover I would like to thank Peter van Els and the other interns for their suggestions and Peter Keus for statistical assistance. Views expressed are those of the individual author and do not necessarily reflect official positions of De Nederlandsche Bank. Maarten Bosker had an internship at De Nederlandsche Bank from June until November 2003, under the supervision of prof.dr. F.C. Palm, dr. J.R.Y.J. Urbain (Universiteit Maastricht) and dr. P.J.G. Vlaar (Research Department, DNB). This research memorandum is an abbreviated version of his master’s thesis.
Research Memorandum WO no 750/0339 November 2003
De Nederlandsche Bank NV Research Department P.O. Box 98 1000 AB AMSTERDAM The Netherlands
ABSTRACT Eurozone money demand: time series and dynamic panel results E.M. Bosker The effectiveness of the important role for money in the monetary policy of the European Central Bank (ECB) is usually assessed by looking at time series estimates of the eurozone money demand equation. This implicitly calls for a choice of aggregation method to construct data series long enough to obtain meaningful econometric results. This study discusses different aggregation methods and finds that variable weight growth rate aggregation has the nicest properties. The results based on the hereby constructed series confirm the effectiveness of the ECB´s monetary policy. Next this study tries to avoid the issue of aggregation by adopting a (nonstationary) dynamic panel method that uses the data series for each of the eurozone countries by itself. This shows that differences in the money demand equation across the eurozone countries are likely to exist. Not being able to quantify these differences makes it difficult to give specific implications for the ECB´s monetary policy. The found differences could however influence the time series estimates and through these have implications for the ECB´s monetary policy. Key words: money demand, eurozone, aggregation, time series, dynamic panel estimation JEL codes: C12, C32, C33, E41, E52
SAMENVATTING Geldvraag in de eurozone: tijdreeks en dynamische panel resultaten E.M. Bosker De effectiviteit van de belangrijke rol voor de geldhoeveelheid in het monetair beleid van de Europese Centrale Bank (ECB) wordt normaal gesproken bekeken door te kijken naar tijdreeksschattingen van de geldvraagfunctie in de eurozone. Dit brengt echter de keuze voor een aggregatiemethode, waarmee voldoende lange datareeksen gevormd worden om goede econometrische resultaten te verkrijgen, met zich mee. Deze studie belicht verschillende aggregatiemethoden en laat zien dat variabele groeiratio aggregatie de beste eigenschappen heeft. De resultaten van de op die manier geconstrueerde reeksen bevestigen de effectiviteit van het monetair beleid van de ECB. Hiernaast probeert deze studie de aggregatieproblematiek te vermijden door een (niet-stationaire) dynamische panel methode te gebruiken die de landspecifieke datareeksen gebruikt. De resultaten laten zien dat verschillen in de geldvraagfunctie voor de eurozone landen waarschijnlijk zijn. Het niet kunnen kwantificeren van deze verschillen maakt het moeilijk specifieke implicaties te geven voor het monetair beleid van de ECB. Echter de gevonden verschillen zouden de tijdreeksschattingen kunnen beïnvloeden en hierdoor implicaties hebben voor het monetair beleid van de ECB. Trefwoorden: geldvraag, eurozone, aggregatie, tijdreeksanalyse, dynamische panel schattingen JEL codes: C12, C32, C33, E41, E52
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1
INTRODUCTION
´The primary objective of the European System of Central Banks (ESCB) shall be to maintain price stability in the medium term´ (Article 105(1) of the Treaty establishing the European Community). In accordance with this primary objective, the main elements of the stability-oriented monetary policy strategy of the Governing Council of the European Central Bank (ECB), as announced in October and December 1998, are aimed at maintaining price stability. Price stability is defined as a year-on-year increase in the Harmonised Index of Consumer Pric es for the eurozone below 2%. As of May 8th 2003, the Governing Council has extended this definition to below, but close to, 2%, to underline the ECB´s commitment to guard against deflation. One of the ‘two pillars’ announced to achieve the strategy’s obje ctive is a prominent role for money as money constitutes a natural, firm and reliable ‘nominal anchor’ for monetary policy aiming at the maintenance of price stability (ECB Monthly Bulletin, January 1999). The development of the price level is believed to be a monetary phenomenon in the long run and useful information about future price movements may thus be revealed by the development of the amount of money held. It can offer important signals when setting the monetary policy. This and the fact that the monetary policy strategy of the ECB is aimed at the medium term, requires the definition of a monetary aggregate which is a stable and reliable indicator of the price level over the medium term. The Governing Council of the ECB has decided to give M3, the broad money aggregate, a prominent role in the monetary policy strategy. It has chosen M3, because it is believed to have better properties than more narrow money aggregates in terms of stability and information content with respect to price developments in the long term (ECB Monthly Bulletin, February 1999). The Governing Council even announced a quantitative reference value for the growth of M3 of 4.5% per year (ECB Monthly Bulletin, January 1999). This reference value is not a monetary target but deviatio ns from the reference value are closely analysed in the context of other economic data in order to obtain useful information regarding possible risks to price stability. Recently (ECB Press Release, May 8th 2003), the Governing Council announced that this reference value will not be reviewed every year, keeping it fixed at 4.5% per year. To be able to say that setting a reference value for the growth of M3 is consistent with the main objective of price stability in the medium term, there must exist a stable relationship between M3 and the price level at this time horizon. The aim of this paper is to conduct empirical research in order to test for the existence of such a stable relationship at the eurozone level. If evidence of such a stable relationship can not be found, this would shed serious doubts on the role for money in the monetary policy of the ECB. It would imply that the ECB bases its monetary policy on the incorrect assumption of the existence of a stable
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relationship between M3 and the price level, causing damage to its credibility and subsequently the effectiveness of its monetary policy. First the existence of a long run money demand equation is verified using the usual framework, in which first the national series of all eurozone countries are aggregated into series for the eurozone and then cointegration techniques are used to test for and identify the long run relationship(s). Besides discussing the exact method used and the resulting outcomes, a thorough discussion of the type of aggregation method used to construct the series for the eurozone is given.
In the second part of this paper, a nonstationary panel data framework is used to answer the question whether or not a long run money demand equation exists. Using nonstationary panel data techniques makes the issue of which type of aggregation method to use irrelevant, each country´s individual series are used in the analysis. Another nice feature is that the framework allows for testing the equality of the long run relations across the countries in the panel. If a long run money demand equation is found for each country in the panel, these tests can be used to test for and, if found, identify differences in that relation between the countries (or groups of countries), that have handed over their monetary policy to the ECB in joining the European Monetary Union. As the ECB is only in charge of monetary policy as of 1999, it would not be very surprising to find such differences. If differences are found, identifying them is important as that allows the policy makers at the ECB to take account of these differences when deciding on a meaningful monetary policy. The paper is organised as follows. Section 2 introduces the economic model and gives a short review of past research stating also the econometric methods that have been used in the past in the analysis of money demand. Section 3 discusses the methods of aggregation used in constructing eurozone data series. Section 4 provides estimation results obtained using a time series framework. In Section 5 the nonstationary panel framework is introduced, giving an overview of recent developments in that field of econometrics and explaining the choice of test that is used in this paper. Estimation results using this econometric framework are presented. Finally Section 6 concludes.
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2
MODEL AND ECONOMETRIC METHODS
The existence of a long run money demand equation is typically assessed in the context of standard economic theories of money demand. As indicated in Ericsson (1998), in standard theories of money demand, money may be demanded for at least two reasons. First, out of transaction motives, it can be used as an inventory to smooth differences between income and expenditure streams and second as an asset among other assets in a portfolio. Both reasons for money to be demanded, lead to the following long run specification, M d / P = g(I,R)
(1)
where M d is nominal money demanded, P is the price level, I a scale variable and R a vector of returns on various assets. The theory suggests that g(.,.) is increasing in I, decreasing in those asset returns included in R that are excluded from M, and increasing in those asset returns in R that are included in M. In the literature one commonly finds (1) in the following log-linear form: md – p = α + β y + γ1 Rout + γ2 Rown + δ ∆p,
(2)
where lowercase letters indicate variables in logs, α, β, γ1 , γ2 , and δ are coefficients and ∆ is the difference operator. Rout are the rates of return on financial assets alternative to money and Rown the return on the components included in the definition of money itself. As argued in Fair (1987) both the outside and own rate are not transformed into logs. y is the real gross domestic product (GDP), a choice of scale variable that is very common in the existing literature, although one can also find studies in which it is chosen to be financial wealth, e.g. Fase and Winder (1998). Finally ∆p is the inflation rate (growth rate of the GDP deflator, i.e. nominal GDP divided by real GDP), included as a proxy for the return on goods alternative to money. Some indication of the signs and the magnitudes of the coefficients are β = 1 (quantity theory) or β = 0.5 (Baumol-Tobin), γ1 ≤ 0, γ2 ≥ 0 and δ ≤ 0, as holding money is an alternative to buying goods. The own an outside rates may have coefficients of equal magnitude but opposite signs. If this is the case, one can use γ1 (Rout - Rown ), instead of γ1 Rout + γ2 Rown in (2). The difference (Rout - Rown ) is often called the term spread and can be seen as the opportunity cost of money. It captures the effect of the return on alternative financial assets on the demand for real M3.
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Past research on money demand (see Golinelli and Pastorello (2001) for a good overview up to 1999) in the eurozone has focused on the loglinear long run money demand specification as in (2). Analysing money demand in the setup of equation (2) poses a number of questions. What variables are chosen to appear in the equation? How to choose the countries included in the sample, the sample period and periodicity of the data? What econometric framework to use in estimating the parameters of (2)? Since the ECB made clear that it would take M3 as the relevant indicator for money, most studies choose M3 to be the dependent variable of equation (2). Before this, other measures of money, like M1 and M2 are found in some studies. Some researchers advocated the inclusion of cross border holdings in the definition of money, but, as shown in Fagan and Henry (1998), this inclusion does not improve the estimation results. As mentioned before, GDP is most often chosen to represent the scale variable in (2). The use of GDP is supported by the demand for money based on transaction motives, consequently it can be argued to be suitable for more narrow definitions of money. The portfolio theory of asset demand suggests the use of financial wealth as a choice of scale variable more suitable for analysing broader money definitions. However, the lack of reliable financial wealth data is often used to justify the use of GDP for the scale variable. As for the choice of own and outside rates, most papers use the 3-month interest rate as a measure of the own rate, as this is included in the definition of M3, and the 10-year government bond yield (or a proxy) as a measure of the outside rate. One also finds studies in which only one of the two rates or only the term spread is included in the money demand equation. Finally inflation is measured by the growth rate of the GDP-deflator, i.e. nominal GDP divided by real GDP. With very few exceptions most studies take the end of the seventies as the beginning of their sample period. The European Monetary System (EMS) began in that period and the Exchange Rate Mechanism (ERM) was established (March 1979). The periodicity of the time series data is usually quarterly. The choice of countries to include in the analysis differs over past research done on European money demand. The last few years, research has mainly focused on the eurozone, where some studies exclude Luxembourg from the analysis. Usually the reason for omitting Luxembourg is unavailability of data (Beyer et al., 2001) and justified by its small quantitative importance (Clausen, 1998). Also, due to the monetary union between Belgium and Luxembourg, Luxembourg´s M3 is probably already included in Belgian M3 (Beyer et al. 2001).
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The usual econometric framework in which (2) is estimated is that of a time series setup. As most research finds that all the variables in (2) are non-stationary, the money demand equation is usually estimated in a cointegration framework. The estimation of the cointegrating relationship differs per author. Most recently the Johansen (1995) framework (Vlaar and Schuberth, 1999; Coenen and Vega, 1999; Brand and Cassola, 2000; Fagan and Henry, 1998) is used, while in the past the Engle and Granger (1987) two-step-approach was popular. Most recent studies focus on eurozone money demand only. First eurozone-wide aggregates are constructed using a certain method of aggregation (as prior to the introduction of the euro only national accounts are available), and then the cointegration techniques are ´unleashed´ on these constructed area-wide aggregates (Coenen and Vega, 1999; Brand and Cassola, 2000; Vlaar, 2004). In this analysis the first step, obtaining aggregate time series for the eurozone long enough to be able to make reliable estimates that do not suffer from small sample distortion, is crucial. The choice of aggregation method is thus important and needs to be considered carefully. Besides a thorough discussion of the method of aggregation to be used, another contribution of this paper is to adopt a dynamic panel approach in estimating the money demand equation. In doing so a number of problems using aggregated data are avoided. First of all the need to choose for a certain aggregation method does no longer exist, as all series for each individual country are expressed in local currency. Secondly the power of the usual cointegration tests is shown to depend on the time span of the data series used. Increasing the amount of information available by analysing time series across similar cross-sections, i.e. adapting a panel approach, leads to tests with better power properties (Levin and Lin, 1992). Another nice feature of the panel setup is that it explicitly takes account of the national differences in financial structures and markets and the country specific structural breaks by using the national series. Both effects are less evident when using eurozone aggregates as their impact is ´canceled out´ in the aggregation process. However, as noted by Dedola, Gaiotti and Silipo (2001), these country specific effects may result in differences in national money demand functions. If the monetary policy of the ECB has different consequences for different countries of the eurozone, it can be very helpful to identify and take account of these differences. The panel setup allows for testing homogeneity restrictions on the resulting money demand equations if similar relations are found for the countries in the panel. It allows for explicit tests that check whether or not the same long run relations hold for all eurozone countries or subgroups of eurozone countries. If substantial cross-country differences are found, looking also at national data can be of importance for polic ymakers.
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3
EUROZONE-WIDE AGGREGATES
3.1
Overview of aggregation methods
As already mentioned in the introduction, many previous studies on eurozone-wide money demand have focused on the estimation of the money demand equation (2) using area-wide aggregates. As data for the eurozone are only available as of January 1999, the problem is how to get a dataset for the eurozone large enough to be able to conduct meaningful econometric analyses. To overcome this problem, area-wide aggregates are constructed; i.e. the national time series are aggregated into overall area-wide aggregates. These aggregates are then used in the estimation of the money demand equation. The aggregation method chosen to construct the area-wide time series from the respective national time series needs to be considered carefully. Using the best possible method is essential, as the ECB could make non-optimal policy choices based on inappropriate figures used in analysing economic relationships (e.g. the money demand equation). Past research has acknowledged the importance of the choice of aggregation method and several suggestions have been made. A good review of four possible aggregation methods that have been used in the literature and focus on aggregating the level series is given in Winder (1997). The four methods discussed in that paper are: i) using fixed base period exchange rates, ii) using current exchange rates, iii) using fixed base period PPP rates, and iv) using current PPP rates. As shown in (3) below the use of current exchange or PPP rates to transform the national data in levels into euro, introduces an extra and unwanted component in the growth rate series.
∆ ln( xt et) = ∆ ln(xt ) − ∆ ln(et )
(3)
where xt is the series to be converted from local currency into the common currency and et is the corresponding exchange rate, i.e. units of local currency per unit of common currency. The growth rate will also depend on changes in the exchange or PPP rates. In an extreme case a country might have a positive growth rate in the serie s expressed in local currency but, because the local currency has experienced a large depreciation with respect to the common currency chosen, a negative growth rate in the series expressed in the common currency. When using fixed base period rates the problem is avoided as in that case: ∆ ln(et ) = ∆ ln( eT ) = 0 in (3), where T denotes the fixed base period. Another problem when using current rates is that the constructed series will depend, as can be easily seen in (3), on the choice of common currency. However it has to be noted that this problem may seem less
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important because all data will be expressed in euro. A useful property of the constructed aggregated level series obtained when using fixed base period rates,
xtEU = ∑ i xti eTi
(4)
is that the corresponding growth rate series will be a weighted average of each countries´ own growth rate, with weights being the respective current shares of the countries in the aggregate series, i.e.
∆ ln( xtEU ) = ∑ i
xti eTi ∆ ln( xti ) EU xt
(5)
Many of the researchers constructing area wide data use, based on the results by Winder, fixed base period rates to construct their aggregate series. For example, Fagan and Henry (1998) use fixed base period PPP rates for 1993, Coenen and Vega(1999) use fixed base period PPP rates for 1995 and Golinelli and Pastorello (2001) use fixed base exchange rates for 1999. Fagan and Henry (1998) argue in favour of the use of PPP-rates when choosing between fixed base period exchange rates or PPPrates. However as pointed out in Beyer et al. (2000) it is very difficult to construct PPP rates that are accurate and they are therefore an unattractive option compared to exchange rates. In two papers on constructing aggregate eurozone data Beyer et al. (2000, 2001) argue in favour of another aggregation method. They suggest constructing aggregate growth rates using variable weights, i.e.
∆ ln( xtEU ) = ∑ i
xti−1 eti−1 ∆ ln( xti ) EU xt−1
(6)
That is the eurozone growth rates are calculated by aggregating each country´s own growth rate using as weights the corresponding shares of the countries in the total aggregate in the previous period. The exchange rate used to calculate each country´s share is not fixed at a base period but varies with each period. Using the constructed aggregate growth rates, they then construct the level series by cumulating backwards starting from a given value at the end of the sample period. They have good reasons for using this method of aggregation. They aggregate growth rates instead of levels as they argue that aggregating levels using either fixed base period or variable weights leads to distorted aggregate series. Using variable weights when aggregating levels leads the to inclusion of an
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unwanted exchange rate effect in the constructed aggregates as shown in (3). Using fixed base period level aggregation, as argued in Winder (1997) and very commonly used in previous research, is not appropriate because the choice of base year is crucial in this case. Given the substantial relative pricechanges due to currency de- and reva luations, using for instance 1979 as base year would lead to an aggregate series which is different from the aggregate series constructed using 1999 as base year. They also use this dependence on the choice of base year to argue against using fixed base period weights when aggregating growth rates, leaving only aggregating growth rates using variable weights as the appropriate aggregation method.
The construction of aggregate growth rates using variable weights also has some nice properties. Namely that sub-aggregates (both regional and temporal) also aggregate correctly and that the result of aggregating the growth rate of the implicit price deflator for each country coincides with the growth rate of the implicit price deflator of the aggregate nominal and real data (price-aggregation matching holds). A useful property, since the growth rate of the price deflator is used as the inflation rate series. In the case of aggregating the level series using fixed base period weights, this property holds for the level series but not for the series of interest the growth rate series, i.e. inflation. 3.2
Constructing aggregate series using two different methods and comparing the results
In this paper aggregate series are constructed using both methods (fixed weight level aggregation and variable weight growth rate aggregation). After constructing the series, they are compared. The fixed weight method of Winder (1997) is used, but a small refinement is made. That is, the representation of the growth rate series resulting from the aggregation of the series in levels using fixed weights is improved in the following way:
∆ ln( xtEU ) ≅
i i i i i i ∆xtEU ∑ i xt / eT − ∑ i xt−1 / eT ∑ i ∆xt / eT xti−1 / eTi = = ≅ ∆ ln( xti ) ∑ EU EU EU EU i xt−1 xt −1 xt −1 xt−1
(7)
where the approximation ∆ ln xt ≅ ∆xt xt−1 is used. When (7) is compared with the expression that Winder (1997), using the approximation d ln xt ≅ dxt xt , finds (5), one can see that in (7) the weights are based on the previous period whereas in (5) weights based on the current period are used. The impact of this change has only an impact on the construction of the short and long term interest rates, as these two are the only two series aggregated using GDP-shares under the fixed weight aggregation method.
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To be able to compare the method of Beyer et al. (2000) a little better to the method proposed by Winder (1997), an extension is made to the representation of the aggregation method as in (6):
∆ ln( xtEU ) = ∑ i
xti−1 / eti−1 xti−1 / e t−i 1 ∆xti ∆xti / eti−1 i ∆ ln( x ) ≅ = t ∑ i x EU x i ∑ i x EU = xtEU −1 t −1 t −1 t −1
∑ x /e −∑ x ∑ x /e i
i t
i t −1 i
i
i t −1
i t −1
/ eti−1
i t −1
(8)
where again the approximation ∆ ln xt ≅ ∆xt xt−1 is used. Writing the aggregation method as in (8) shows that the aggregate growth rate at period t is calculated by first fixing the exchange rates at period t-1, then calculating the aggregate in levels at period t and t-1 using those exchange rates and finally calculating the growth rate using these to aggregate level series. When this is compared to (7) one can immediately see that whereas in (7) a fixed base year is chosen for the whole sample period, in (8) this fixed base year is each year set at the previous year. 3.2.1
Constructing the aggregate series using fixed base period weights to aggregate national level
series The aggregate series are constructed using the fixed weight level aggregation method as argued in Winder (1997). The 1999 fixed conversion rates (for Greece 2001) are used to convert the series in local currency into euro. Note that in this way 2001 is implicitly chosen as the fixed base year. The nominal GDP, real GDP and nominal M3 aggregates are constructed as in (4). The aggregate price series is constructed by dividing the aggregate nominal GDP series by the aggregate real GDP series. As shown in Winder (1997) this is equivalent to constructing the aggregate price series by aggregating national price series using each countries´ current real GDP share of total eurozone GDP as weights. Aggregate real M3 is constructed by dividing aggregate nominal M3 by the aggregate price series. Both the aggregate long term interest rate and the aggregate short term interest rate series are constructed by aggregating them according to (7). Growth rates of all series are constructed by taking first differences of the series in logs. 3.2.2
Constructing the aggregate series using variable weights to aggregate national growth rate
series The aggregate series are constructed using the variable weight growth rate aggregation method of Beyer et al. (2000). That is, using (8) the growth rates of the following national series are aggregated into an aggregate eurozone growth rate series. Aggregate real and nominal GDP growth rates are calculated using real GDP shares. The same weights for nominal and real GDP are chosen to ensure
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that price-aggregation matching holds. Instead of choosing real weights also nominal weights could be chosen for each of the series, but by choosing real weights only the nominal GDP measure is affected, which may be considered the least interesting for the money demand study. Aggregate short and long term interest rate growth rates are also calculated using real GDP shares. Finally the aggregate nominal M3 growth rate is calculated using nominal M3 shares. The aggregate inflation rate is constructed by subtracting the aggregate real GDP growth rate from the aggregate nominal GDP growth rate, which, because of the just explained price-aggregation matching, is the same as aggregating the national inflation rate series using real GDP shares as weights. Level series are constructed by cumulating the series backwards using as starting values the figures on eurozone nominal and real GDP and nominal M3 for 2002.4 as published by the ECB and the 2002.4 long and short term interest rates for the eurozone. 3.2.3
Comparing the results of the two methods
Figure 1 Aggregates for all variables 14.5
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Note: going from upper left to lower right the graphs represent the variable (red) and fixed (blue) aggregates for nominal GDP, real GDP, inflation, long term bond yield, nominal M3, real M3, GDP deflator and short term interest rate.
As can be seen in Figure 1, both aggregates are close to each other at the end of the sample period, while differences occur at the beginning of the period. Comparing the two nominal GDP series, the aggregate obtained using variable weight growth rate aggregation starts at a lower value and moves towards the fixed weight level aggregate. A similar pattern is seen for the price aggregates and, although to a lesser extent the nominal M3 aggregates. Real M3 aggregates show the reverse pattern,
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i.e. the variable weight growth rate aggregate starts at a higher level and moves to the other aggregate. Real GDP series move very close together in a similar, be it much less evident, pattern as the real M3 aggregates. The long and short term interest rate series also show more differing patterns during the beginning of the sample period but the differences last longer than for the other series just described. Finally the inflation rate series shows the same pattern as the real M3 series. Table 1 Descriptive statistics all aggregate variables constructed using fixed base period level aggregation. The statistics for GDP and M3 are based on growth rates Nominal Real Nominal Real M3 Inflation Long term Short term GDP GDP M3 (annualised) interest rate interest rate _______ _______ ________ _______ __________ _________ _________ Mean 1.52 0.52 1.79 0.80 3.97 8.89 8.35 Median 1.35 0.53 1.86 0.82 3.69 9.08 8.20 Maximum 3.61 1.64 3.12 1.85 9.58 14.78 15.56 Minimum -0.10 -0.74 0.40 -1.20 0.51 4.00 2.68 Std. Dev. 0.72 0.52 0.60 0.49 2.27 2.83 3.52
Table 2 Descriptive statistics all aggregate variables constructed using fixed base period growth rate aggregation. The statistics for GDP and M3 are based on growth rates Nominal Real Nominal Real M3 Inflation Long term Short term GDP GDP M3 (annualised) interest rate interest rate _______ _______ ________ _______ __________ _________ _________ Mean 1.76 0.51 1.88 0.63 4.99 8.58 7.89 Median 1.55 0.53 1.93 0.68 3.91 8.79 7.77 Maximum 4.50 1.55 3.38 1.81 13.45 13.88 14.35 Minimum 0.14 -0.75 0.39 -1.74 0.51 4.00 2.65 Std. Dev. 0.97 0.54 0.68 0.59 3.54 2.57 3.20
The findings are confirmed by the results in Tables 1 and 2 where it can be seen that indeed the average growth rate of nominal GDP and nominal M3 are lower for the variable growth rate aggregates. The reverse is true for the real GDP and real M3 series. The descriptive statistics of the inflation and the two interest rate series also confirm the findings when looking at the graphs. The difference between the aggregates obtained using the two different methods of aggregation, can be explained by the impact of the de- and/or revaluations of the local currencies with respect to the common currency, the euro. The fixed base period level aggregation method does not take these changes in exchange rates into account. The variable weight growth rate aggregation method does take them into account (see (8)) by shifting the base period one year forward every year. The larger
- 12 -
difference between the series at the beginning of the sample period can be explained by the implicit use of 2001 as the base year in the fixed weight aggregation approach. As most exchange rates show a gradual convergence to the fixed conversion rates as set by the ECB, the difference between the two approaches gets smaller over the sample period. To take a closer look at the differences, and since the growth rates of the two approaches are more easily compared based on (7) and (8), Figure 2 shows the difference between the growth rate aggregates for GDP and M3 (nominal and real) and the difference between the level aggregates for inflation and the two interest rates. As can be clearly seen, the difference between the two aggregation methods goes to zero over the sample period. This is exactly as expected when looking at the formulas in (7) and (8), the two series should move very close together when the difference between the exchange rates, used in the two methods to convert the series into euro, is small. Obviously when looking at Figure A1.6 the exchange rates move towards the fixed exchange rates used in the fixed base period aggregation method and this makes the difference in the aggregate growth rates between the two methods smaller over time. The actual size of the differences in growth rates is also quite substantial, ranging from several percentages for the inflation series, to several tenths of a percentage for nominal M3. Figure 2 The difference between the two approaches (variable minus fixed) .005
.002
.020
.004
.000
.016
-.002
.003
.012
-.004 .002
.008 -.006
.001
.004
-.008
.000
.000
-.010
-.001
-.012 1980
1985
1990
1995
2000
-.004 1980
D I F F D L N _M 3 N _ V A R _F I X
1985
1990
1995
2000
1980
1985
D I F F D LN _ M 3 R _ V A R _F I X
.006
.06
.004
.05
.000
.04
-.002
.03
-.004
.02
-.006
.01
-.008
.002
1990
1995
2000
D I F F D L N _ Y N _ V A R _F I X
.002
.000 -.002 -.004
.00
-.006
-.010
-.01 1980
1985
1990
1995
2000
D I F F D LN _ Y R _ V A R _ F I X
-.012 1980
1985
1990
1995
D I F F I N F L _ V A R _F I X
2000
1980
1985
1990
1995
2000
D I F F _ V A R _F I X _L R
.005 .000 -.005 -.010 -.015 -.020 -.025 1980
1985
1990
1995
2000
D I F F _V A R _ F I X_ S R
Note: going from upper left to lower right the graphs represent differences between the two aggregation methods for nominal M3, real M3, nominal GDP, real GDP, inflation, long term bond yield and short term interest rate.
- 13 -
To see what the impact of a change in base year in the fixed base period method is, two more aggregate series are constructed. One takes 1979 (the beginning of the sample period) and the other 1990 (the middle of the sample period) as its base year. The constructed level series differ for a different base year. To be able to take a closer look at the differences, Figure 3 shows the growth rates of the three constructed fixed base period aggregates compared to the growth rate of the aggregate obtained using the variable weight growth rate aggregation method (only the results for real GDP are shown, the other series show a similar pattern). As expected from formulas (7) and (8) when, comparing the results for the aggregates using different base years, it can be clearly seen in Figure 3 that the aggregate using 1979 as base year starts with small deviations from the variable weight aggregate and the deviations increase over the sample period. The aggregate using 1990 as base year exhibits large deviations in the beginning of the sample period, the deviations diminish around the base year 1990 and increase again towards the end of the sample period. These differing patterns can be ascribed (and are again in compliance with formulas (7) and (8)) to the difference between the fixed base year exchange rate and the current exchange rate. The more (less) the current exchange rate differs from the fixed base year exchange rate, the greater (smaller) the difference. Figure 3 Comparing the growth rates of different fixed base period aggregates to the variable weight growth rate aggregate for real GDP 0.006
0.004
0.002
0.000
-0.002
-0.004
-0.006 1980
Note:
1985
1990
1995
difference between variable aggregate and fixed aggregate using as base year 1. 1979 () 2. 1990 (- - - -) 3. 2001 ()
2000
- 14 -
Thus changing the base year in the fixed base period aggregation method does have a substantial impact on the constructed aggregated time series. The inability of the approach to take currency deand revaluations into account accounts for this difference. This has the effect that, given the substantial currency depreciations for seven of the Euro-12 countries and the substantial appreciation for three of them, fixing the exchange rate at 2001 results in the seven countries, that have had a depreciating currency, being ´underrepresented´ in the aggregate series of the eurozone and the three countries, that have had an appreciating currency, being ´overrepresented´ in the eurozone aggregates when using the fixed base period method. Another effect of this aggregation method is that the countries with a (ap-)depreciated currency have too (high) low GDP shares at the beginning of the sample period. Because of the convergence of the exchange rates the above-described effects are more evident at the beginning of the sample period. The variable weight growth rate aggregation does take exchange rate effects into account without introducing an unwanted component in the aggregate series as variable weight level aggregation does, see (3). Therefore it is suggested that this method provides the best possible aggregates to be used in the econometric analysis of eurozone money demand1. For simplicity in the rest of the paper, the aggregates formed by the variable weight growth rate aggregation method are referred to as ´variable aggregates´ and ´fixed aggregates´ refers to the aggregates based on the fixed base period aggregation method.
1 An argument that might save the fixed base period aggregation method is that the (over-)underrepresentation of countries that have had a (ap-)depreciating currency does not matter that much as the countries that have had an appreciating currency are more representative of the economic situation in the eurozone today. However choosing a different base period leads to different weights and choosing the base period that provides weights that represent the economic situation in the eurozone today may not be that easy.
- 15 -
4
MONEY DEMAND ESTIMATES BASED ON AGGREGATES
As tests for a double unit root do not find evidence for this in any of the aggregated series and tests for a unit root clearly show that all series have a unit root irrespective of the aggregation method used, the existence of a long run eurozone money demand equation is assessed in a cointegration framework. More specifically the Johansen methodology is used to test for the number of cointegrating relations, and (if found) to test restrictions on these relations. The Johansen framework is chosen as it allows to test for the cointegration rank whereas other types of methods (Engle and Granger (1987) two-step procedure or Phillips and Hansen (1990) Fully Modified OLS estimates) implicitly assume the number of cointegration relations. Also, and maybe even more important, the results of these other tests may rely on the specific ordering of the variables and the normalisation chosen for the cointegrating vector(s). The Johansen framework does not suffer from these drawbacks. Starting point is an unrestricted vector autoregressive model of order k, VAR(k),
xt = α + δ t + Π 1xt−1 + ... + Π k xt − k + ε t
t = 1,…,T
(9)
where x=(m-p, y, il , is ,∆p), α a 5x1 vector of constants, δ a 5x1 vector of trend coefficients, Π i , i = 1,…,k 5x5 matrices of coefficients and ε t ~ N (0, Ω ε ) , a 5-dimensional vector of innovations that is normally distributed with a nonsingular covariance matrix Ω ε.
First the appropriate lag length, k, to use in (9), including only a constant as deterministic component, is chosen based on information criteria. Table 3 shows that for the variable aggregates all three criteria select a lag length of two. Table 3 Lag length selection in the VAR model
k
Variable
Fixed
_______________________ AIC SBC HQ
__________________________ AIC SBC HQ
0
-24.01
-23.95
-24.04
-25.21
-25.07
-25.16
1
-38.47
-37.62
-38.12
-38.31
-37.46*
-37.97
2
-39.19*
-37.63*
-38.56*
-38.87*
-37.31
-38.24*
3
-39.07
-36.80
-38.16
-38.68
-36.41
-37.77
4
-38.93
-35.96
-37.74
-38.54
-35.57
-37.34
Note: * denotes selected by corresponding IC.
- 16 -
For the fixed aggregates also a lag length of two is chosen since, although the SBC indicates a lag length of one, both the AIC and HQ criterion indicate this as the appropriate. lag length to choose. After setting k equal to two, tests on the residuals are done to check if the model is correctly specified. Table 4 shows the results of tests for autocorrelation in and normality of the residuals of (9). Note that the tests as shown in the table are tests on the vector of residuals, ε t . Table 4 Residual tests, test statistics and corresponding p-values Variable LM(1) Chi2(25)
Fixed
_____________ ___________ 31.45 [0.18] 24.59 [0.49]
LM(4) Chi2(25)
26.39 [0.39]
28.27 [0.30]
Normality Chi2(10)
10.84 [0.37]
25.07* [0.01]
Portmanteau 9 lags
199.08 [0.10]
185.95 [0.27]
Note: p-values in brackets, * denotes significance at the 5% level.
For the variable aggregates the tests indicate normality of the residuals and no evidence of residual autocorrelation is found. This suggests the VAR with two lags to be correctly specified for the variable aggregates. For the fixed aggregates no autocorrelation in the residuals is found, but some nonnormality of the residuals is revealed. Fatter tails in the distribution of the residuals for the equation for real money holdings and thinner tails in the distribution of the residuals for the equation for inflation appear to be the main reasons for this, based on tests on the residuals of the individual equations in the VAR2. Although not totally correctly specified, the VAR with two lags seems to be a reasonable specification for the fixed aggregates. The next step is to test for the number of cointegrating relations. Let L denote the lag operator and define Π ( L ) = I n −
∑
k i =1
Πi Li . Decomposing the matrix lag polynomial Π ( L ) = Π (1) L + Φ ( L) ∆ ,
where ∆ = (1-L) is the difference operator, the VAR(k) as in (9) can be rewritten as a vector errorcorrection model (VECM),
∆xt = α + δ t + Π (1) xt −1 + Φ1 ∆xt −1 + ... + Φ k −1∆xt− k +1 + ε t
2 Results not shown here, they are available upon request
t = 1,…,T
(10)
- 17 -
where Φ i = −
∑
k j =i +1
Π j , i = 1,…,k-1. Each Φ i , i = 1,…,k-1 is a matrix containing parameters for the
short run dynamics. Note that only Φ 1 enters (10) in our case as k is equal to two. Now under the following assumption
Assumption 1: 1. rank(Π(1)) = r, 0 < r < 5; 2. the characteristic equation Π ( z ) = 0 has 5-r roots equal to 1 and all other roots outside the unit circle. xt has r cointegrating relations (see Hamilton, 1994), and Π(1) can be written as
Π (1) = −BA´
(11)
where A is a 5×r matrix of full column rank, the columns of which are the cointegrating relations such that zt ≡ A´ xt is a stationary 5×1 vector. B is another 5×r matrix of full column rank containing loading factors representing the speed of the short-run response to disequilibrium in the cointegrating relations. To formally test for the number of cointegrating relations, r, the trace test of Johansen (1988) is used. Before testing it is important to choose the type of deterministic components included in the model. Testing for the type(s) of deterministic components gives evidence of the need for the inclusion of a linear trend in both the cointegrating relationships and the data. However from an economic point of view (see (2)) a trend in the cointegrating relationships is not expected and therefore it is decided not to allow for a deterministic trend (δ = 0 in (10)) in the cointegrating relationships, a common choice in the existing literature on money demand (Coenen and Vega, 1999; Brand and Cassola, 2000). To test for the number of cointegrating relations, the trace test is used. As it is shown in Cheung and Lai (1993), this test is more robust to non-normality encountered in the data (found for the fixed aggregates) than the other test proposed by Johansen, the λmax test. The trace test has as its null hypothesis that there are exactly r cointegrating relations and as alternative that there are n cointegrating relations, where n is the number of variables in xt . The test statistics used in the test can be written as follows (see Hamilton (1994) for a detailed derivation):
- 18 -
λtrace = −T ∑ i= r+1 log(1 − λˆi ) n
(12)
where λi denotes the ith squared population canonical correlation between ∆xt and xt-1 . The results of these tests, shown in Table 5 below, show a difference in outcome between the two aggregation methods regarding the number of cointegrating relations found. For the variable aggregates, the tests indicate a cointegrating rank of three (four) at a 1% (5%) level, whereas for the fixed aggregates a cointegrating rank of two (three) at a 1% (5%) level is found. Table 5 Trace statistics for both aggregates and corresponding 1% and 5% critical values
H0 : r =
Variable
Fixed
_______ λtrace
_____ λtrace
1% critical value
5% critical value
0
91.24(**)
94.00(**)
76.07
68.52
1
58.04(**)
61.03(**)
54.46
47.21
2
35.81(**)
33.89(*)
35.65
29.68
3
18.12(*)
14.73
20.04
15.41
4
0.68
0.10
6.65
3.76
Note: (**) resp. (*) denotes significance at a 1% resp. 5% level.
As the choice of cointegrating rank is not exactly clear, economic arguments are used to decide on the number of cointegrating relationships. It is clear that one of the cointegrating relations should represent a long run money demand equation. As we did not allow for a linear trend in the cointegrating relations, another cointegrating relation including real GDP is not expected. Possible candidates are therefore, a stationary term structure or a stationary real interest rate representing the Fisher equation. Besides these economic arguments used to choose the cointegrating rank, importance is also given to stationarity tests of the individual variables used in the analysis and in particular to stationarity tests for the real interest rate and the term spread. These tests are done within the Johansen framework assuming a cointegrating rank of two, three and four. Table 6 shows the results of these individual stationarity tests done within the Johansen framework.
- 19 -
Table 6 Tests for stationarity Rank (dgf)
∆p
is
il
y
m-p
il -∆p
il - is
_________ _____ _____ _____ _____ _____ ______ ______ Variable 2 (3)
9.99
18.27
17.43
15.44
16.71
3.22*
9.97
3 (2)
7.21
13.78
12.92
14.89
15.74
1.41*
5.85*
4 (1)
7.19
13.77
12.76
14.64
15.49
1.34*
5.69
2 (3)
17.61
23.02
23.51
26.31
25.87
18.60
13.29
3 (2)
14.29
15.32
15.97
18.93
19.01
13.05
5.37*
4 (1)
10.59
11.32
11.42
14.48
14.50
9.69
5.04
Fixed
Note: (*) denotes significance at a 5% level.
As expected the results regarding the individual variables indicate that all variables are rejected to be individually stationary. More interesting are the results when testing for stationarity of the real interest rates and the term spread. For the variable aggregates, when r = 3, both the term spread and the real long term interest rate are found to be stationary. Stationarity of the long term interest rate represents a long run Fisher equation and stationarity of the term spread is in favour of the expectations theory of the term structure. For the fixed aggregates also evidence in favour of the expectations theory of the term structure is found but the stationarity of the real long term interest rate is rejected in this case. Given the lack of a plausible interpretation of a fourth cointegrating relation based on economic theory and the statistical results of the previous paragraph(s) a rank of three is imposed. For both aggregates the same cointegrating rank is imposed. Next the cointegrating vectors need to be identified. Usually the cointegrating vectors are identified by imposing restrictions on each cointegrating vector (the columns of the A matrix) in the system. However, all variables in the system are a priori expected to appear in the long run money demand equation. Therefore, to put all information that is of importance for real money in the first cointegrating vector, the coefficients for real money in the B-matrix in the second and third cointegrating vector are restricted to be zero (see Vlaar and Schuberth (1999) who impose a similar restriction on the B-matrix). In this way, the first cointegrating vector represents the long run money demand equation. The second cointegrating vector is restricted to represent a Fisher equation (either homogeneous or heterogeneous) and the third to represent the expectations theory of the term structure.
- 20 -
Table 7 Estimates of the A- and B-matrix in the identified model Variable
A (s.e.)
_______
___________________________________ _____________________________________ Money Demand Fisher Yield equation spread 0 -1 0 0.10 (2.29) 0.17 (2.67) 0.02 (0.28)
∆p
B (t-value)
is
0
0
-1
-0.01 (-0.23)
-0.09 (-2.26)
0.08 (1.71)
il
0.84 (0.31)
1
1
-0.01 (-0.59)
-0.08 (-2.89)
-0.02 (-0.67)
y
-1.27 (0.05)
0
0
-0.01 (-0.29)
-0.03 (-0.69)
0.13 (2.72)
1
0
0
-0.10 (-5.88)
0
0
m-p LR χ 2 (6)
11.53 [0.07]
Fixed
A (s.e.)
_____
___________________________________ _____________________________________ Money Demand Fisher Yield equation spread 0 1 0 -0.03 (-0.51) 0.24 (4.90) -0.09 (-1.02)
∆p
B (t-value)
is
0
0
-1
-0.08 (-2.16)
-0.07 (-2.11)
0.19 (3.02)
il
-0.30 (0.21)
-0.51 (0.06)
1
0.03 (1.21)
-0.05 (-2.14)
-0.01 (-0.31)
Y
-1.52 (0.04)
0
0
0.08 (2.61)
-0.02 (-0.68)
0.12 (2.25)
1
0
0
-0.09 (-3.27)
0
0
m-p LR χ (5) 2
5,73 [0.33]
Note: p-value in brackets.
For both aggregates the results show that the standard deviations of the coefficients for inflation and the short term interest rate in the money demand equation are large with respect to the coefficients themselves, for most cases even larger than the coefficients. As formal tests accept the validity of restricting these coefficients to be zero; they are fixed at zero. Furthermore a homogeneous Fisher equation is accepted for the variable aggregates and is therefore imposed on the second cointegrating vector in this case. For the fixed aggregates a homogeneous Fisher equation is rejected but a heterogeneous Fisher equation is accepted and subsequently imposed. Table 7 above the resulting model for each of the aggregates. To check for possible model misspecification, Table 8 shows tests for normality of and autocorrelation in the residuals. The tests show similar results as the residual tests on the residuals of the unrestricted VAR model (see Table 4). No evidence of autocorrelation is found for both aggregates and non-
- 21 -
normality is again only found for the fixed aggregate residuals. The results indicate that the specification used is acceptable. Table 8 Residual analysis for reduced form residual vectors Variable LM(1) Chi2(25)
Fixed
___________ ___________ 32.76 [0.14] 29.39 [0.28]
LM(4) Chi2(25)
31.66 [0.17]
31.05 [0.19]
Normality Chi2(10)
12.92 [0.23]
25.49 [0.01]
Portmanteau 9 lags
197.39 [0.54]
187,12 [0.73]
Note: p-value in brackets.
To be complete, also tests for weak exogeneity of each individual variable with respect to all long run relations are done within the Johansen framework. If all entries in a row of the B-matrix, containing information on the speed of adjustment to disequilibrium, are equal to zero, i.e. α ij = 0, i ∈ {1,…,5}, j = 1,…,r, it is said that the variable corresponding to this row is weakly exogenous with respect to all long run relations. For example if all elements in the first row of the B-matrix (see Table 7) were equal to zero, this would indicate weak exogeneity of the inflation rate with respect to all long run relations. A variable that is found to be weakly exogenous can actually enter on the right side of the VECM without leading to a loss of information, when estimating the parameters of the model. Table 9 shows the results of formal tests for weak exogeneity in the reduced form model as represented in Table 7. Table 9 Tests for weak exogeneity Series
Variable
Fixed
_____ ∆p
______________ ______________ 20.46 [0.005]*** 21.22 [0.002]***
is
16.32 [0.022]**
19.21 [0.004]***
il
18.49 [0.010]***
10.39 [0.109]
y
16.24 [0.023]**
17.59 [0.007]***
m-p Test distribution
23.52 [0.001]*** χ (7) 2
12.59 [0.050]** χ (6) 2
Note: p-values in brackets; (***), (**), (*) indicates significance at a 1%, 5%, 10% level.
- 22 -
As can be seen in Table 9, weak exogeneity is rejected for all variable aggregates at a 1% or 5% level. For the fixed aggregates weak exogeneity is rejected at a 1% or 5% level for all variables except for the long term interest rate, for which weak exogeneity would be rejected at a 11% level. Except for the long term interest rate in the case of the fixed aggregates, all variables seem to contain information about the long run relationships. As can be seen from Table 7, quite a number of coefficients of the B-matrix have t-values that are below the 5% critical value. This indicates that the coefficients are not significantly different from zero. Variables whose coefficients in column i, i ∈ {1,…,r}, of the B-matrix are not significantly different from zero do not enter the vector representing the short run response to disequilibrium in the long run relationship corresponding to the ith column of the A-matrix. It is jointly tested whether or not setting all coefficients, whose t-value is below the 5% critical value, are equal to zero. For the variable aggregates the resulting test statistic, with χ 2 (12)-distribution, is 12.86 with corresponding p-value of 0.38. The test statistic for the fixed aggregates, distributed χ 2 (10), is 8.60 with corresponding p-value of 0.57. For both aggregates the test statistics support the acceptance of the null hypothesis. 4.1
Interpreting the results
The results for the variable aggregate show that real output has a positive effect on money that is larger than one. This result is as expected and the high value can probably be ascribed to wealth effects (see Fase and Winder, 1998; and Vlaar and Schuberth, 1999). The negative effect of the long term interest rate is also as expected, as an increase of the long term interest rate, representing the rate of return on assets not included in the money definition, makes alternatives to money more attractive and thus decreases real money holdings. Furthermore the Fisher equation is accepted to be homogeneous and stationarity of the term spread is also not rejected. Stationarity of the term spread is in accordance with the expectations theory of the term structure, stating that the long term interest rate reflects a weighted average of future short term interest rates. The loading factors in the B-matrix also show some interesting features. A significant impact of deviations from the long run money demand equation on real money holdings and inflation is found. The significant pos itive impact of money holdings in excess of the long run equilibrium on inflation is important, as it makes money growth a useful indicator for future inflation and justifies a monetary targeting strategy as conducted by the ECB. The effect on real money holdings is as expected. Deviations from the Fisher equation have a significant impact on inflation and both interest rates. Both effects are as expected. Finally the slope of the term spread has a significant impact on real output, which is in line with the findings of Estrella and Mishkin (1997) regarding the leading indicator properties of the slope of the yield curve for future output growth.
- 23 -
Results on the fixed aggregates are somewhat different and perhaps more questionable. First the coefficient of the long term interest rate in the money demand equation is positive, be it insignificant. This is very strange because, as explained in the previous paragraph, a rise in the long term interest rate makes assets outside of the money definition more attracting and thus is expected to decrease real money holdings. A reverse effect as found here seems highly unlikely. Secondly homogeneity of the Fisher equation is rejected. Brand and Cassola (2000) also find this result (be it with the long term interest rate coefficient closer to –1 than the –0.51 found here). A possible explanation of this heterogeneity of the Fisher equation might be the existence of an ´EMS risk premium´. A country that experiences high inflation but at the same time is bound to a fixed exchange rate system (or monetary union), cannot depreciate its currency to the extent it may want to and thus the interest rate has to compensate3. When looking at the loading factors in the B-matrix, the insignificant impact of money holdings in excess of the long run equilibrium on inflation may be regarded as ´unwanted´. This implies that money only has a weak role as indicator for future inflation. Hereby questioning the usefulness of the ECB´s monetary targeting strategy. The other results for the loading factors do not differ much from the results found for the variable aggregates. Figure 4 Recursive estimates of the identified cointegrating space (variable aggregates) STABILITY OF Sp(beta) SIGNIFICANCE LEVEL= 95%
1.6
R_MODEL Z_MODEL NORMCVAL
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0 1994
1995
1996
1997
1998
1999
2000
2001
2002
3 This however would be expected to also have an impact on the variable aggregates given the fact that the countries with a depreciating currency get a bigger weight in those aggregates than in the fixed aggregates.
- 24 -
To check for the parameter constancy over time of the money demand equation, recursive estimates are performed for the variable aggregates. Figure 4 above, shows the parameter constancy of the identified cointegrating space, where the analysis is based on the approach by Hansen and Johansen (1999). According to the so-called R-model, in which the short term dynamics, the Φ -matrices, are kept constant and only the A- and B-matrix, are recursively estimated, stability is accepted at a 95% level. The Z-model, in which all parameters, also the Φ-matrices, are recursively estimated, indicates some instability until the second half of 1995. However, recursive estimates in the Z-model can be unreliable at the beginning due to the relatively few observations available at the beginning of the sample (e.g. in 1994 only 57 observations are used in the estimation) and the many parameters to be estimated. Recursive estimates of the two freely estimated parameters in the money demand equation are shown in Figure 5. As can be seen in Figure 5, both parameters are found to be stable over time. The long term interest rate elasticity seems to fluctuate a little more over time compared to the real output coefficient. Based on the results of the recursive estimation, no evidence of an impact of the euro on the empirical relationships is found. The results for the fixed aggregates (not shown here) show some more instability. Figure 5 Recursive estimates of the parameters of real GDP and the long term interest rate in the money demand equation (variable aggregates) R E C U R S I V E
E S T I M A T E S :
y
- 1 . 1 5
- 1 . 2 0
- 1 . 2 5
- 1 . 3 0
- 1 . 3 5
- 1 . 4 0
- 1 . 4 5 1 9 9 4
1 9 9 5
R
-
1
.
5
0
1
.
2
5
1
.
0
0
0
.
7
5
0
.
5
0
0
.
2
5
0
.
0
0
0
.
2
5 1
9
9
4
E
C
1
9
1 9 9 6
U
9
R
5
S
I
V
1
1 9 9 7
E
9
9
E
6
S
T
I
1
M
9
9
1 9 9 8
A
7
T
E
S
1
1 9 9 9
:
9
i
9
8
2 0 0 0
2 0 0 1
2 0 0 2
l
1
9
9
9
2
0
0
0
2
0
0
1
2
0
0
2
- 25 -
The previous chapter on aggregation concludes in favour of the variable weight growth rate aggregation method. In this chapter it is shown that the estimation results, obtained using aggregates constructed by the two different aggregation methods, clearly differ. As the variable aggregates are preferred from the aggregation point of view and the fixed aggregates also show evidence of some model misspecification (a result also found in other recent research (Coenen and Vega, 1999; Brand and Cassola, 2000), at this point attention is focused on the results based on the variable aggregates. Results in the next chapter on panel estimation of the long run money demand equation will thus only be compared with the findings in this chapter that are obtained using the variable aggregates.
- 26 -
5
MONEY DEMAND ESTIMATES BASED ON PANEL METHODS
Econometric inference within nonstationary panels is a field that has emerged only recently. The interest in this field has increased over the last few years, starting with papers by Quah (1994) and Levin and Lin (1994), who test for unit roots within a panel setup. The main reason for this, is the fact that tests for stationarity or cointegration within a time series setup tend to suffer from low power if the time span of the data used is not large enough, a phenomenon that is not very rare for macroeconomic data. Using a panel setup adds additional observations by drawing data from among similar cross-sections to increase the power of the tests. Furthermore a panel setup allows for the exploitation of similarities across the individuals in the panel. By pooling the information of several individuals, the panel setup may provide better evidence on the (non)existence of economic relationships. The panel cointegration literature mainly focuses on residual based tests (Kao, 1999; Banerjee, 1999; Pedroni, 2002), that are based on pooling the individual residual based test statistics. These residual based tests however only focus on the question whether or not cointegration is present in the panel. The same drawbacks as in the case of residual based tests for cointegration in a time series setup apply for these tests. The estimated cointegrating relation may differ with the ordering of the variables and the choice of normalisation of the cointegrating relation. The tests also do not allow to test for the number of cointegrating relations. There are however some papers that do derive tests for the number of cointegrating relations within a panel setup (Larsson, Lyhagen and Löthgren, 2001; Groen and Kleibergen, 2002). These tests do not suffer from the drawbacks described above, however are only useful (i.e. the test has the correct size for, or requires, fixed N) for panels with a small cross-section dimension compared to the time dimension 4. Another important issue that has received a lot of attention in the nonstationary panel literature is the assumption of cross-sectional independence between the units in the panel. Most existing residual based tests use this assumption to be able to get a nice asymptotic distribution for the test statistic as the cross-section dimension goes to infinity. The cross-sectional independence allows for the use of standard asymptotic tools, like the (standard) Central Limit Theorem. As shown in Monte Carlo experiments, see O´Connell (1998) inappropriately assuming cross-sectional independence can severely distort the size of panel tests in a nonstationary world. Recently some tests have been
4 As (at the moment) the eurozone includes twelve countries, this does not seem to constitute a big problem. One might even be more doubtful regarding panel cointegration tests that rely on large N asymptotics
- 27 -
proposed that do allow for the units in the panel to have some form of dependency (Bai and Ng, 2003; Moon and Phillips, 2003; Chang, 2002; Groen and Kleibergen, 2002; Larsson and Lyhagen, 2000). Studies that use a nonstationary panel framework to test for the existence of a long run money demand equation are relatively few. Mark and Sul (2002) use a residual based cointegration test, Pedroni´s (1999) panel t-test, where they use a panel of nineteen countries. Golinelli and Pastorello (2001) and Dedola, Gaiotti and Silipo (2001) also use a residual based cointegration test on countries in the eurozone (excluding Greece or Luxembourg and Greece from the analysis). Focarelli (2000) applies a bootstrap biased-correction procedure, correcting the Mean Group estimator of Pesaran and Smith (1995). All papers apply a panel cointegration test that does not allow for cross-dependence of the units in the panel and that does not explicitly test for the cointegrating rank. As mentioned before inappropriately assuming cross-sectional independence can lead to a severe distortion of the size of the test when this assumption is not valid. In this paper the test of Groen and Kleibergen (2002) is used. This test does allow for cross-sectional transitory dependence among the units in the panel. A nice feature, as the data for the countries in our panel are evidently not independent of each other. Looking only at the correlation between the individual time series gives evidence of this (see Table 10 for the correlation between the individual GDP growth rate series, similar correlations are found for the other variables). Table 10 Correlation matrix of the individual GDP growth rate series
AU BE ES FI FR GE GR IER IT LU NE PT
AU BE ES FI FR GE GR IER IT LU NE PT ___ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ 1 0.34 0.28 0.05 0.40 0.41 0.13 0.14 0.24 0.21 0.28 0.23 1 0.44 0.18 0.46 0.25 0.27 0.30 0.31 0.28 0.27 0.18 1 0.08 0.33 0.12 0.35 0.21 0.07 0.33 0.29 0.27 1 0.35 0.09 0.20 0.24 0.30 0.06 0.07 0.32 1 0.41 0.16 0.37 0.45 0.30 0.24 0.21 1 0.25 0.22 0.29 0.23 0.22 0.13 1 0.11 0.13 0.11 0.08 0.24 1 0.26 0.08 0.22 0.11 1 0.16 0.18 0.04 1 0.33 0.09 1 0.16 1
The test does however not allow for cointegration across members of the panel. The cross-sectional dependency is purely transitory and not persistent. The next section will come back to this issue. Another nice feature of the test is that it does not suffer from the drawbacks that apply to residual
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based tests and it allows testing for the cointegrating rank. Finally the fact that the test should be used only for panels with a relatively small cross-sectional dimension compared to the time-dimension, does not seem to be a big problem as the cross-section dimension in the panel used is fixed at ten5 (excluding Luxembourg and Greece due to data problems) and the time span of the data is from 1979:2 – 2002:4. 5.1
The Groen and Kleibergen (2002) Panel VECM test
The test developed by Groen en Kleibergen (2002) (hereafter GK-2002) is based on the vector error correction model (VECM) framework of Johansen (1991) for each of the individuals in the panel. A VECM for each individual is stacked into one system, a Panel VECM,
Φ1 0 L 0 0 Φ2 O M ∆Yt = Y + ε = Φ AYt−1 + ε t M O O 0 t−1 t 0 L 0 ΦN
(13)
where Φ A is a Nm×Nm matrix contain ing the individual Φ i , i = 1,…,N, m×m matrices (m is the number of variables), relating for each individual ∆yit to yi,t -1 . Yt −1 = ( y1,′ t −1... y N′ , t −1 )′ , ∆Yt = Yt − Yt −1 and
εt = (ε1′t ...ε ′Nt )′ are Nm×1 vectors. The vector ε t contains the Nm×1 disturbance vectors for each individual VECM and it is distributed ε t : N (0, Ω) with the Nm×Nm nondiagonal covariance matrix,
Ω11 L Ω1N Ω= M O M Ω N 1 L Ω NN
(14)
where Ω ij = Cov(εit ,εjt ) is not restricted to be zero for any i,j = 1,…,N. Note that notation is changed with respect to the previous section. Where in the y previously denoted GDP, here yit denotes a vector of all variables contained in the VECM, i.e. here yit =(m-p, y, il , is ,∆p)it .
5To be sure that the test has nice power and size properties at N = 10, simulations would have been nice. However due to computational power restrictions these could not be performed.
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As can be seen, the model as specified in (13) does allow for cross-sectional dependency through the disturbance terms (14), i.e. transitory cross-sectional dependence. However as the off-diagonal elements of the Φ A matrix are set equal to zero, the model is a restricted version of the model in which the off-diagonal elements are left to be estimated. These restrictions on the Φ A matrix impose that there is no linear dependence between the variables of individual i and lags of the variables of individual j, for j ≠ i, i.e. no persistent cross-sectional dependence. By imposing the restrictions, crossdependence in the panel is only allowed through the non-diagonal covariance structure of the error term (14). Larsson and Lyhagen (1999) do allow for non-zero off-diagonal elements which also implicitly allows for the possibility of cointegration between series of different individuals in the panel. The reason why these restrictions are imposed here is that if these restrictions are not imposed, all the off-diagonal elements of the Φ A matrix would also have to be estimated. This is very likely not to be efficient due to the large number of parameters that have to be estimated in the estimation procedure6. The GK-2002 test for cointegration is developed to test for a common cointegrating rank for each individual i within the panel, i.e. rank ( Φ i ) = r for each i = 1,…,N. Now cointegration within the panel imposes a rank reduction on the different Φ i ´s in (13) identical to all individuals in the panel,
0 L 0 B1 A1′ 0 B2 A2′ O M ∆Yt = Y + ε = Φ BYt−1 + ε t M O O 0 t −1 t L 0 BN A′N 0
(15)
where the m × r matrices Ai contain the cointegrating vectors and the m × r matrices Bi the loading factors, the adjustment factors to the long run equilibrium, for each of the i = 1,…,N individuals. Now the test for a common cointegrating rank r developed by GK-2002 tests the following:
H 0 : ΦB
vs.
H1 : Φ A
(16)
6 Although persistent cross-sectional dependence between series of different members might be expected a priori, e.g. the inflation series of Germany and the Netherlands.
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where Φ B is as in (15) and Φ A is as in (13). GK-2002 develops maximum likelihood estimators of the cointegrating vectors, the loading factors and the covariance matrix of the disturbance term using Generalised Method of Moments estimators. Using these estimators they construct the following likelihood ratio statistics to test for a common cointegrating rank among the individuals in the panel.
(
( )) − l (Φˆ
ˆ Φ ˆ A, Ω ˆA LR( Φ B | Φ A ) = 2 l Φ
(
B
( ))
ˆ Φ ˆB ,Ω
(17)
( ) ) , Θ ∈ {A,B}, is the value of the maximised log-likelihood function. Now
ˆ Φ ˆ Θ,Ω ˆΘ where l Φ Θ
keeping N fixed and letting T go to infinity the limiting distribution of the test statistic in (17) equals, −1 N LR ( Φ B | ΦA ) ⇒ ∑ i=1 tr ∫ dBm −r ,i B′m−r , i ∫Bm −r ,i B′m−r , i ∫ Bm−r , idB′m−r ,i T →∞
(18)
where Bm-r,i is a (m-r)-dimensional Brownian motion for individual i with an identity covariance matrix. As can be seen in (18) the limiting distribution as T → ∞ of the likelihood ratio statistic (17) is the sum of N individual limiting distributions for the Johansen (1991) trace statistic. GK-2002 extend the result for the more general case of model (13) that allows for deterministic components and higher order dynamics,
∆Yt = α +δ t + Φ $ Yt−1 + ΓWt + ε t
(19)
where α = (α1...α N )′ is a vector containing constants, δ t = ( δ1...δ N )′ t represents the individual
(
linear trends, Wt = ∆y1,′t −1... ∆y1,′ t − k1 ... ∆y ′N ,t −1... ∆y ′N , t− kN
)
contains the k i lagged first differences of
individual i, and
Γ1 0 Γ = M 0
0 Γ2 O 0
L 0 O M O 0 L ΓN
contains the parameters for each of the individual lagged differences.
(20)
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The higher order dynamics and deterministic components can be concentrated out in the usual way (Johansen, 1991), through OLS regressions of ∆yi,t -1 and yi,t -1 on the included higher order dynamics and deterministic components for each of the individuals i. In doing so, one implicitly assumes heterogeneity across individuals with respect to the deterministic components and short run dynamics. Now the test statistic can be computed using the maximum likelihood estimators were ∆yi,t -1 and yi,t -1 in (13) are replaced by the residuals of the corresponding OLS regressions for each individual. The limiting distributions are only affected by the inclusion of deterministic components. Including higher order dynamics does not affect them as they only affect the short-run properties of the model. The change in limiting distribution depends on the type of deterministic components included. As in the time series case, five different cases (see Johansen, 1995) can be distinguished. One can allow for: 1.
zero mean in the cointegrating relations and non-zero mean in the data
2.
non-zero mean in both the cointegrating relations and the data
3.
non-zero mean in the cointegrating relations and a linear trend in the data
4.
linear trend in both the cointegrating relations and the data
5.
linear trend in the cointegrating relations and a quadratic trend in the data
Here attention is focused on the third case only to allow for the same type of deterministic components as in the time series analysis of the aggregated variables. Hence case 3 is chosen for sake of comparability and for the same reason k i is set equal to one for all individuals in the panel. Subsequently the limiting distribution of the likelihood ratio statistic is changed in the following way, −1 N ′ LR ( Φ B | ΦA ) ⇒ ∑ i=1 tr ∫ dBm −r ,i Si′ ∫ Si Si′ ∫ SdB i m−r ,i T →∞
(21)
where in Si ≡ Bm −r ,i − ∫ Bm−r ,i . As can be seen the likelihood ratio statistic (21) remains the sum of the N individual limiting distributions of the Johansen trace statistic adjusted for the presence of deterministic components as in case 3. In their paper GK-2002 focus on case 2 and case 4 and calculate critical values for these two cases. As the point of interest here is case 3, critical values had to be obtained through simulation. To do this discrete-time approximations to (21) were used. First the N individual limiting distributions are approximated by their discrete-time counterparts, i.e.
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T tr ∑ t=1 ∆xi ,t Fit′
(∑
T
F F′ t=1 it it
)
−1
∑
T t=1
Fit ( ∆xi, t )′
(22)
where the Brownian motions are replaced by Gaussian random walks and T is the number of discretetime approximations. More explicitly , let xt denote an (m-r)-vector whose elements follow a random walk with N(0,I) innovations with x0 = 0. Then ∆xi ,t = x i, t − x i ,t −1 and Fit = xi, t −
1 T ∑ xi ,t . After all T t =1
N individual approximations are made, the discrete-time approximation of (21) is calculated as the sum of the individual approximations. To obtain the critical values, the above is repeated 50,000 times for T = 1000. Thus 50,000 discrete-time approximations of (21) are obtained and the critical values are calculated as being the qth (q = 99%, 95% or 90%) quantile of these 50,000 replications. Table 11 shows the critical values thus obtained for a cointegrating rank up to four. Table 11 Critical values for the GK-2002 test with N = 10 r 1% 5% 10% __ ______ ______ ______ 1 415.92 398.79 389.32 2 255.46 241.34 234.13 3 135.17 124.00 118.17 4 52.58 45.02 41.43
Next the tests are performed for a panel consisting of all eurozone countries except Luxembourg and Greece. First the cointegrating rank has to be determined. In order to do this the likelihood ratio statistic as in (17) is calculated for the cases where r = 1, 2, 3, 4. As can be seen in Table 12 below, the tests indicate a common cointegrating rank of three. Table 12 GK-2002 likelihood ratio statistics r Test-stat __ ________ 1 723.14** 2 341.75** 3 100.69 4 7.87 Note: (**), (*) denotes significance at a 1%, 5% level.
This finding is similar to the cointegrating rank found in the case of the European aggregate. However by using the European aggregates, it is implicitly assumed that the relationships found, hold for all member countries of the eurozone. In the panel case, the relationships found can differ per individual
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member of the panel, as each individual i has its own Ai matrix containing the individual specific cointegrating vectors. 5.1.1
Testing for homogeneity of the cointegration space
However one can test for the equality of the cointegrating vectors for all individuals. In order to do so, one has to estimate the following regression (after again first concentrating out the deterministic components and higher order dynamics):
0 L 0 B1 A′ 0 B2 A′ O M ∆Yt = Y + ε = Φ CYt−1 + ε t M O O 0 t−1 t L 0 BN A′ 0
(23)
where the matrix containing the cointegrating vectors is the same for all individuals, i.e. Ai = A for all i ∈ {1,…,N}. Groen and Kleibergen (2002) develop a test that is based on the likelihood ratio test to test for the validity of a homogeneous cointegrating space for all individuals in the panel. As in the time series case, the cointegrating rank is fixed before testing and the resulting test statistic is distributed as a χ2 ((N-1)r(m-r)) variable, i.e.
ˆ B ,Ω ˆ (Φ ˆ B )) − l (Φ ˆ C,Ω ˆ (Φ ˆ C )) ~ χ 2 (( N − 1)r (m − r )) LR( Φ C | Φ B ) = 2 l( Φ
(24)
As the test for the common cointegrating rank indicated a rank of three, the test for a homogeneous cointegrating space across individuals is done keeping the cointegrating rank fixed at three. The resulting test statistic is 318.13, which is larger than the corresponding χ 2 (54) 1% critical value, i.e. 86.0. The hypothesis of a homogeneous cointegrating space across individuals is clearly rejected, indicatin g differences in the long run relationships across the different members of the eurozone. As the ten countries included in our analysis of the eurozone do not share the same economic history, the rejection of a homogeneous cointegrating space may not be that surprising 7. Some countries joined the European Union later than others. This might have caused some countries to already integrate more economically (and non-economically) than others. Also countries have shown historical
7 Based on individual country analyses, Fase and Winder (1993) already found considerable differences in the nature of the demand for money.
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differences in economic polic y and economic development. The economic policy of some countries (for instance Germany, the Netherlands) was much more stable than others (Spain, Portugal). These historical economic differences between countries in the eurozone might explain the rejection of a homogeneous cointegrating space. However it also gives rise to another question, i.e. ´Can we identify groups of countries within the eurozone that share the same long run developments?´. In order to answer this question, a test is needed that tests for the homogeneity of the cointegrating space for predefined groups of countries. To do this the test developed by Groen and Kleibergen (2002) to test for a homogeneous cointegrating space across all individuals is adapted in the way the likelihood under the null is calculated. Under the null of s, 1< s < N, groups with the same cointegrating space each group containing n1 , n2 ,…, ns-1 , ns individuals respectively and
∑
s i =1 i
n = N such that all individuals are assigned to one group, the
following model is estimated (again after first concentrating out the deterministic components and higher order dynamics):
B A′ 11 0 0 ∆Yt =
∅ 0 Bn1 A1′ ′ Bn1+1A2 0 0 0 O 0 Yt−1 +εt = ΦGYt−1 +εt (25) 0 0 Bn1+n2 A2′ O ′ Bn1+...+ns−1+1 As 0 0 ∅ 0 O 0 0 0 Bn1 +...+ns As′
0 O
0 0
To test for the validity of a homogeneous cointegrating space within each of the s groups, a likelihood ratio test is used. As in the case of testing for a homogeneous cointegrating space across all individuals in the panel, the common cointegrating rank is fixed, and the resulting distribution of the test statistic is again χ 2 but with degrees of freedom equal to (N-s)r(m-r), i.e.
ˆ B, Ω ˆ (Φ ˆ B )) − l (Φ ˆ G ,Ω ˆ (Φ ˆ G )) ~ χ 2 (( N − s ) r ( m − r )) LR( Φ G | Φ B ) = 2 l (Φ
(26)
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To calculate the maximised value of the likelihood function under specification (25), the procedure used by Groen and Kleibergen (2002) is adapted. The log-likelihood function for any of the panel VECM specification, Φ Θ, Θ ∈ {A, B, C, G}, is:
l(Φ Θ , Ω ) = −
NkT T 1 ln(2π ) − ln Ω − tr ( Ω −1 (∆Y −Y−1Φ′Θ )′( ∆Y − Y−1Φ′Θ )) 2 2 2
(27)
∆Y1′ Y0′ where ∆Y = M and Y−1 = M are (T × Nm) matrices. In their paper, Groen and Kleibergen ∆Y ′ Y ′ N T −1 (2002) show that the log-likelihood function in (27) can be rewritten as
l(Φ Θ , Ω ) = −
NkT T 1 1 ln(2π ) − ln Ω − tr (Ω −1∆Y ′M Y−1 ∆Y ) − G (Φ Θ , Ω ), 2 2 2 2
(28)
−1
where M Y−1 = I − Y−1 (Y−′1Y−1 ) Y−′1 and
G ( Φ Θ , Ω) = vec(Y−′1ε )′(Ω ⊗ Y−′1Y−1 ) −1 vec(Y−′1ε )
(29)
which can be interpreted as a GMM objective function with all variables in Y-1 acting as instruments. Now in (28) Ω can be estimated conditional on Φ Θ using the conditional maximum likelihood estimator of Ω given Φ Θ, i.e.
ˆ (Φ ) = 1 (∆Y − Y Φ′ ) ′( ∆Y − Y Φ ′ ) Ω Θ −1 Θ −1 Θ T
(30)
and Φ Θ can be estimated given Ω using GMM objective function (29). By sequentially applying this estimation procedure of Ω and Φ Θ until convergence, the log-likelihood function (27) is maximised. As the cases for which Θ = A, B or C are explained in detail in Groen and Kleibergen (2002), p.10-15, here only the case Θ = G is explained in more detail. The group specification (25) implies that the GMM objective function (29) can be written as:
G ( Φ G , Ω) = vec(Y−′1 (∆Y −Y−1Φ G′ ) )′( Ω ⊗ Y−′1Y−1 ) −1vec (Y−′1 ( ∆Y − Y−1 Φ G′ ))
(31)
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Rewrite part of this objective function (31) as,
vec (Y−′1( ∆Y − Y−1Φ ′G )) = vec(Y−′1∆ Y) − vec( Y−′1 Y−1 A1 B1′,K Y−′1Y−1 A1Bn′1 , Y−′1Y−1A 2 Bn′1+ 1, KY−′1Y−1 A2 Bn′1 + n12 , K, Y−′1Y−1 As Bn′1 +K+ ns )
vec( Α1 ) vec ( Α2 ) ′ = vec(Y−1∆ Y) − R M vec ( Αs )
(32)
where
R = ( I Nm ⊗ Y−′1Y−1) Rsure
(33)
and
Rsure
B1 ⊗ (e1 ⊗ I m ) M 0 0 Bn1 ⊗ (en1 ⊗ I m ) Bn1 +1 ⊗ (en1 +1 ⊗ I m ) 0 M 0 = Bn1 + n2 ⊗ (en1 + n2 ⊗ I m ) O Bn1 +... +ns−1 +1 ⊗ (en1 +...+ ns−1 +1 ⊗ I m ) 0 0 M Bn1 +... + ns ⊗ (en1 +...+ ns ⊗ I m )
(34)
where e i is the ith N-dimensional unity vector and Im a (m × m) identity matrix. In Groen and Kleibergen (2002) it is shown that under the null the common cointegrating rank is fixed at r and the estimate of the covariance matrix in (30) yields a consistent estimate of Ω. Furthermore under normalisation of the cointegrating spaces A1 ,…,As , a consistent estimator of Bi is:
Bˆ i ≡ the first r columnsof Φ i from (15) fori = 1,..., N
(35)
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ˆ =Ω ˆ (Φ ˆ A ) , can then be substituted in the GMM objective These estimates, Bˆ i , i = 1,..., N and Ω function (31). Minimising this objective function with respect to A1 ,…, As gives the following GMMestimates,
vec( Aˆ1) ˆ ⊗ Y−′1Y−1 ) −1 Rˆ ) −1 Rˆ´(Ω ˆ ⊗ Y−′1Y−1 ) −1 vec(Y−′1 ∆Y ) M = ( Rˆ ′(Ω ˆ vec ( As )
ˆ −1 ⊗ Y−′1Y−1) −1 Rˆ sure ) −1 Rˆ ′sure ( Ω ˆ −1 ⊗ I T )vec (Y−′1∆Y ) ′ (Ω = ( Rˆ sure
(36)
ˆ ,..., A ˆ to construct the estimate of Φ ˆG The next step is to use the estimates Bˆ i , i = 1,..., N and A 1 s ˆ =Ω ˆ (Φ ˆ G) . and use that in estimating the conditional maximum likelihood estimator (30) to obtain Ω Now the estimates of the individual specific loading factors can be made by minimising the GMM
ˆ ,..., A ˆ and objective function (31) with respect to Bi , i = 1,..., N conditional on the estimates A 1 s ˆ =Ω ˆ (Φ ˆ G ) . This results in the following estimates: Ω vec ( Bˆ1′) ˆ ˆ −1 −1 ˆ ⊗ Y−′1Y−1 ) −1 vec(Y−′1 ∆Y ) M = ( Γ′R ( Ω ⊗ Y−′1Y−1 ) Γˆ R ) Γˆ ′R (Ω vec ( Bˆ ′ ) N ˆ −1 ⊗ Y ′ Y ) −1 Γˆ ˆ −1 ⊗ I )vec (Y ′ ∆Y ) = ( Γˆ ′Rsure (Ω ) −1 Γˆ ′R , sure ( Ω , −1 −1 Rsure , T −1
(37)
where
Γ Rsure = ((e1 ⊗ I m ) ⊗ ( e1 ⊗ Aˆ1 )K ( en1 ⊗ I m ) ⊗ ( en1 ⊗ Aˆ1 ) (en1 +1 ⊗ Im ) ⊗ (en1 +1 ⊗ Aˆ 2 ) K , ( en1 +n2 ⊗ I m ) ⊗ (en1 + n2 +1 ⊗ Aˆ 2 ) K ( en1 +K +ns−1 +1 ⊗ I m ) ⊗ ( en1 +K+ ns ⊗ Aˆ s ))
(38)
and
Γ R = ( I Nm ⊗ Y−′1Y−1) Γ R ,s u r e .
(39)
Now through iteratively applying the estimators (36), (30) and (37), one obtains the maximum likelihood estimates of Bi , i = 1,..., N , A1 ,…, As and Ω and, based on these estimates, the value of the
- 38 -
likelihood function (27). Each iteration step results in an improvement of the likelihood and after convergence of the likelihood function to its maximum, the maximum likelihood estimates are obtained. Finally, using the maximum value of the likelihood function, the test statistic can be calculated using (26). The above outlined test procedure is done for several group specifications. Table 13 shows the results of the tests. Table 13 Tests for group-wise homogeneous cointegration spaces χ 2 (dgf) 1% critical value
Group specification(s)
Test statistic
__________________ (AU,GE), (BE,NL), (ES,PT), (FI,IER), (FR,IT)
__________ ____________________ 152.01 χ 2 (30) 50.89
(AU,GE), (BE,NL), (ES,PT,FR,IT), FI, IER
138.48
χ 2 (30) 50.89
(BE,GE,NL,FR,IT), (ES,PT), (AU,FI), IER
213.19
χ 2 (36) 58.62
(AU,BE,GE,NL), FR, IT, ES, FI, IER, PT
139.70
χ 2 (18) 34.81
(AU,GE), (BE,NL), (ES,PT), FI, IER, FR, IT
116.66
χ 2 (18) 34.81
(AU,GE), (ES,PT), FI, IER, FR, IT, BE, NL
78.58
χ 2 (12) 26.22
As can be seen in Table 13, none of the tests shows evidence of a homogeneous cointegrating space across certain groups of eurozone countries. However as the main focus of this paper is the verification of the existence of a stable long run money demand equation across eurozone countries, the above tests can be viewed as too restrictive. Under the null of homogeneity of the cointegrating space for groups of or all eurozone countries, all three cointegrating vectors are equal. Now only one of these cointegrating vectors, say the first, represents the money demand equation. Thus when the only thing to be verified is the homogeneity of the money demand equation, testing for the homogeneity of all three cointegrating vectors can be argued too restrictive. Before testing the homogeneity of the money demand equation, the cointegrating space has to be identified such that one of the cointegrating vectors can be said to represent a long-term money demand equation. The issue of identification however is more complicated than in the case of a time series setup, as several ´problems´ arise in identifying the cointegrating space(s). In a ´worst case scenario´ the cointegrating space for each individual country in the panel is identified in a different way, leaving a very large number of possible combinations of identifying restrictions. Can a common identification be accepted? If not, how to find the right identification for each of the cointegrating
- 39 -
spaces? As one can imagine, the issue of identification is not that straightforward as it might seem at first hand. 5.1.2
Identifying the individual cointegrating spaces within a Panel VECM
To identify the cointegrating space, (m-r)-restrictions have to be placed on each cointegrating vector. Econometrically any type of (m-r)-restrictions can be chosen, however as in the time series case, economic theory may help to suggest some likely specifications. The Fisher equation, relating the interest rate to inflation and the expectations theory of the term structure, relating long and short term interest to each other, are examples of good candidates. In imposing the Fisher equation and/or the term structure more restrictions are imposed than actually needed to identify the cointegrating space. These restrictions are called overidentifying restrictions and their validity can be tested. In order to identify the cointegrating space and/or test for the validity of overidentifying restrictions, a similar maximum likelihood procedure as explained in section 6.1.1 is used to obtain the estimates. To (over)identify the cointegrating spaces, restrictions are imposed on each single vector of the Ai -
~
matrices as in (15) resulting in the identified Ai -matrices:
~ Ai = (V1i a~1i
V2i a~2i
K Vri a~ri )
i = 1,…,N
(40)
where Vqi , i = 1,…,N, q = 1,…,r, are the matrices that ´contain´ the restriction(s) on the qth cointegrating vector of the A-matrix of the ith individual and a~qi , i = 1,…N, q = 1,…,r are vectors containing the coefficients of the restricted qth cointegrating vector of the A-matrix of individual i. For example, in our case with k = 5 and r = 3, the following specification of Vqi and a~qi would impose the restriction that the last two elements of the qth cointegrating vector of the A-matrix of the ith individual are equal to zero:
1 0 Viq = 0 0 0
0 1 0 0 0
0 0 1 0 0
and
a qi,1 ~ a qi = a qi, 2 a qi, 3
(41)
where a qi,1 , a qi, 2 and a qi, 3 denote the first, second and third respective element of the cointegrating vector. Now under imposing all restrictions on all individual cointegrating spaces in the panel VECM,
- 40 -
each individual Ai -matrix, the model would look like (15) with the Ai -matrices replaced by the definition in (40). The maximum likelihood procedure as described in the previous section can now be used to calculate the maximised value of the likelihood function under the restrictions imposed and to provide estimates of the coefficients. However some small changes have to be made in the calculation procedure as in section 6.1.1 to take account of the imposed restrictions. The matrices R (33) and Rsure (34) matrices have to be replaced by Erestricted and Esure,restricted respectively, where
Esurerestricted = (( e1 ⊗ B1) ⊗ (e1 ⊗ I m ) K (eN ⊗ BN ) ⊗ (eN ⊗ I m )) V ,
(42)
V11 ∅ O ∅ Vr1 V = O V1N ∅ ∅
(43)
where
∅ ∅ O VrN
and
Erestricted = ( I Nm ⊗ Y−′1Y−1 ) Esure, restricted
(44)
Using these two matrices, the elements of the restricted cointegrating vectors can be estimated by the following formula, replacing (36) in section 6.1.1:
a~ˆ 11 M ~ˆ a r 1 −1 ˆ M = ( Eˆ ′ ˆ −1 ⊗ Y ′ Y ) Eˆ ˆ −1 ⊗ I ) vec(Y ′ ∆ Y ) ′ sure, restricted ( Ω −1 −1 sure , restricted ) E sure, restricted (Ω Nm −1 ~ˆ a1 N M ~ˆ arN
(45)
- 41 -
~
Having obtained the above estimates, the Ai -matrices can be constructed and subsequently used in the rest of the procedure, which remains the same as in section 6.1.1. After convergence of the likelihood function, estimates of the coefficients and the maximised likelihood value are obtained. In the case of testing for overidentifying restriction this maximised likelihood value can be used to calculate the following likelihood ratio test statistic in order to test for the validity of the overidentifying restrictions:
ˆ B,Ω ˆ (Φ ˆ B )) − l ( Φ ˆ BI , Ω ˆ (Φ ˆ BI )] ~ χ 2 ( ∑ N z i ) LR( Φ BI ] | Φ B ) = 2[l ( Φ i =1
(46)
~
where Φ BI is as Φ B (15) but with the Ai -matrices instead of the Ai -matrices and zi is the number of overidentifying restrictions imposed on the A-matrix of individual i. To delimit the number of possible combinations of identifying restrictions, it is chosen to confine attention to combinations of (over-)identifying that adhere to the following conditions:
Condition 1 1.1 The first cointegrating vector represents a long run money demand equation. 1.2 The second cointegrating vector represents a Fisher equation. 1.3 The third cointegrating vector represents the expectations theory of the term structure. These conditions are assumed based on economic theory and they also allow for comparison with the time series results in section 5. The second and third condition each impose one overidentifying restriction. Ideally the same specification of the cointegrating space for all countries can be accepted. Table 14 below shows the results of tests for such a common specification. Table 14 Test for a common specification of the cointegrating space across countries Specification
Test statistic
______________________ ___________ (m-p, y, il ), (il , is ), (il ,∆p) 83.25 (m-p, y, is ), (il , is ), (is ,∆p)
91.53
(m-p, y, ∆p), (il , is ), (is ,∆p)
68,96
Note: all test statistics are χ2 (20)-distributed, corresponding 1% critical value is 37,6.
- 42 -
As Table 14 clearly indicates, no common specification can be accepted that adheres to Condition 1. This complicates matters as the number of possible specifications, that allow every country or groups of countries to have their own specification, is quite large even under Condition 1. Dropping Condition 1 would complicate finding the right identification(s) even more as the number of possible combinations of (over)identifying restrictions would get very large. To get an indication of possible differences in specification, a look at each country´s individual cointegrating space is taken. Assuming a cointegrating rank of three8, a specification of the cointegrating space of an individual country is looked for. For most countries individually a specification cannot be rejected at a 1% level that adheres to Condition 1. However in the case of Spain and Finland this does not hold. Concerning the money demand equation, for all countries except Ireland the money demand equation relates real M3, real GDP and the long (or short) term interest rate to each other. For Ireland instead of one of the interest rates, inflation enters the money demand equation. 9 Taking these results, found for the individual countries, as an indication, several different combinations of overidentifying restrictions are tested, still assuming Condition 1. Several different combinations of restrictions are tested. Table 15 shows the results. Table 15 Tests for possible combinations of overidentifying restrictions. Specification
Identified Countries
___________________ _________________________________ (m-p,y,il ), (il ,is ), (il ,∆p) AU,BE,GE,FR,IT,NL
Test statistic, χ 2 (dgf) __________________ 29.23 [0.004], χ 2 (12)
(m-p,y,il ), (il ,is ), (il ,∆p)
AU,BE,GE,FR,IT,NL,IER
35.07 [0.002], χ 2 (14)
(m-p,y,il ), (il ,is ), (il ,∆p)
AU,BE,GE,FR,IT,NL,PT
41.59 [0.002], χ 2 (14)
(m-p,y,il ), (il ,is ), (il ,∆p)
AU,BE,GE,FR,IT,NL,IER(m-p,y,∆p)
35.01 [0.001], χ 2 (14)
(m-p,y,il ), (il ,is ), (il ,∆p)
AU,BE,GE,FR,IT,NL,ES,
48.03 [0.000],χ 2 (14)
(m-p,y,il ), (il ,is ), (il ,∆p)
AU,BE,GE,FR,IT,NL,PT,IER(m-p,y,∆p)
48.27 [0.000], χ 2 (16)
(m-p,y,il ), (il ,is ), (il ,∆p)
AU,BE,GE,FR,IT,NL,PT,IER
48.25 [0.000], χ 2 (16)
Note: p-values in brackets. Replacing the long term by the short term interest in the first and third cointegrating vector leads to similar results.
8 Although formal tests for cointegrating rank indicate cross-country differences in cointegrating rank. 9 The results stated in this paragraph are available upon request. They merely serve as an indication that could be helpful in identifying the cointegrating spaces in the Panel VECM.
- 43 -
As can be seen in Table 15, even at a 1% level each of the specifications is clearly rejected. Finding a suitable specification of the cointegrating spaces (even when it is left unidentified for some countries), that allows for the identification of a long run money demand equation is not that easy within the Panel VECM framework. However imposing equality of the long run money demand equation might still be accepted if tested for. Imposing the corresponding restrictions on the identified cointegrating spaces increases the number of degrees of freedom. This increase in the number of degrees of freedom might result in the acceptance of the null hypothesis if the imposing of the restrictions does not decrease the maximised value of the likelihood function too much. After having identified the first cointegrating vector as representing a possible long run money demand equation, the equivalence of this first cointegrating vector across individuals can be tested using a similar procedure as described in 6.1.1 to calculate the maximised value of the likelihood function under the null hypothesis. 5.1.3
Testing for homogeneity of the first cointegrating vector only10
Assuming a cointegrating rank of r, the model, under the null of homogeneity of the first cointegrating equation across the individuals in each of the s, 1 ≤ s < N, subgroups (s = 1 denotes the case of homogeneity of the first cointegrating equation across all individuals in the panel) assigned to one group, is similar to (25).
B A)′ 11 0 0 ∆Yt =
0 O
0 0 ) 0 Bn1 A1′
∅
∅ ) Bn1 +1A2′ 0 0 0 O 0 ) Yt−1 +εt =ΦG1Yt−1 +εt 0 0 Bn1 +n2 A2′ O )′ Bn1 +...+ns−1 +1 As 0 0 0 O 0 )′ 0 0 Bns As
(47)
- 44 -
Again the deterministic components and higher order dynamics are concentrated out before estimating (47). As in (40) a certain identification is needed to be able to say that a test for the equivalence of the first cointegrating vector is indeed a test for the equivalence of a meaningful long term relation.
)
Therefore in (47) the Ai -matrices are defined as,
) ) Ai = (V1i a1i
) V2 j a 2 j
) K Vrj a rj )
for all individuals j in group i, i ∈ {1,…,s}
(48)
)
The definition of the Ai -matrices as in (48) allows for an individual specific 2nd , 3rd, … , rth cointegrating vector but restricts the first cointegrating vector to be equal for all individuals in a group. Note that in order to have the same first cointegrating vector for a groups of individuals, the imposed (over)identification on this vector in a specific group has to be the same for every individual in that group. Testing for the validity of the homogeneity of the first cointegrating vector across groups can be done using a similar procedure as described for the case of testing for the homogeneity of the whole cointegrating space across groups. That is, after having calculated the maximum likelihood under the null hypothesis, specification (47), the following test statistic can be constructed
ˆ B ,Ω ˆ (Φ ˆ B )) − l ( Φ ˆ G1 , Ω ˆ (Φ ˆ G1 )) ~ χ 2 ( ∑ s ( n j −1) f j + ∑ N z i ) (49) LR( Φ G1 | Φ B ) = 2 l ( Φ j =1 i =1
where
∑
N
z are the number of restrictions imposed in order to overidentify the cointegrating spaces
i =1 i
(equal to zero in case of no overidentifying restrictions) and for j = 1,…,s, nj denotes the number of individuals in group j and fj the number of elements of the first cointegrating vector restricted to be equal across the individuals in group j. The way to calculate the maximum likelihood under the null hypothesis is similar to the procedure described previously in case of the null of homogeneity of the cointegrating space across groups. The only difference being that the matrices R (33) and Rsure (34) are replaced by K and K sure respectively, where K and K sure are defined as follows:
10 For simplicity attention is focused merely on testing for equivalence of the first cointegrating vector. The procedure as described here can easily be modified to allow for tests on other cointegrating vectors or groups of cointegrating vectors.
- 45 -
K = ( I Nm ⊗ Y−′1Y−1 ) K sure
(50)
and
K sure
B%1,1:m M B% n1 ,1: m = 0 0
0
B% n1 +1,1:m
L
0
O
M
M
0
O
B% n1 +...+ ns−1 +1,1:m
B% n1 + n2 ,1:m O
L
e1 ⊗ B%1, m+1:rm
M
0
B% n1 + ...+ ns ,1: m
% L e N ⊗ BN , m+1:rm V (51)
where V is a matrix similar to (43), imposing the (over)identifying restrictions on each cointegrating vector, B% i = Bi ⊗ ( ei ⊗ Im ) for i = 1,…,N and the subscript h:j refers to column h up to column j, column j inclusive, of the matrix of which it is a subscript. Using (50) and (51) estimates of the
)
coefficients of the Ai -matrices can be obtained as follows:
) aˆ11 M )ˆ a s1 = ( Kˆ ′ ( Ω ˆ − 1 ⊗ Y−′1Y−1 ) Kˆ sure ) −1 Kˆ sure ˆ −1 ⊗ I Nm ) vec(Y−′1 ∆Y ) ′ (Ω sure vec( (a)ˆ L a)ˆ ) ) 12 1r M vec ( ( a)ˆ L a)ˆ ) ) N2 Nr
(52)
) where aˆi1 , i = 1,…,s, are the estimates of the coefficients of the group specific first cointegrating ) ) vector and aˆ j 2 L aˆ jr , j = 1,…,N the individual specific estimates of the coefficients of the other (r-1)
)
cointegrating vectors. After having estimated (52), the individual Ai -matrices can be constructed and used in (37). After convergence of the maximum likelihood under the null the test statistic can be constructed as in (49) and compared to the corresponding critical value.
- 46 -
Table 16a shows the test results obtained when testing for the equivalence of the first cointegrating vector, when the cointegrating spaces are identified as in the two cases with the highest p-value in Table 15. Table 16a Testing for the equivalence of the long run money demand relation Specification
Identified Countries (same money demand)
Test statistic, χ 2 (dgf)
___________________ ___________________________________ _________________ (m-p,y,il ), (il ,is ), (il ,∆p) (AU,BE,GE,FR,IT,NL) 130.34 [0.000], χ 2 (22) (m-p,y,il ), (il ,is ), (il ,∆p)
(AU,BE,GE,FR,IT,NL),IER(m-p,y,∆p)
131.31 [0.000], χ 2 (24)
Note: p-values in brackets
Table 16b Testing for the equivalence of the term structure Specification
Identified Countries (same term structure)
Test statistic, χ 2 (dgf)
___________________ ___________________________________ _________________ (m-p,y,il ), (il ,is ), (il ,∆p) (AU,BE,GE,FR,IT,NL) 34.88 [0.006], χ 2 (17) (m-p,y,il ), (il ,is ), (il ,∆p)
(AU,BE,GE,FR,IT,NL),IER(m-p,y,∆p)
38.46 [0.005], χ 2 (19)
Note: p-values in brackets
The equivalence of the first cointegrating vector, representing a long run money demand equation, is clearly rejected in both cases. The two cases in Table 16b, where the equality of the cointegrating vector representing the term structure is tested across six countries, are shown to illustrate that the increase in degrees of freedom (by imposing more restrictions) can lead to an increase in the significance level at which the null hypothesis can be accepted (p-values). However, note that also in this case the null hypothesis cannot be accepted at a 1% level. 5.2
Interpreting the results
Adopting a Panel VECM framework in order to verify the existence of a long run money demand equation leads to results that are a bit twofold. Using the GK-2002 test for common cointegrating rank clearly indicates a common cointegrating rank of three. As in the time series case, the variables included in the analysis of the money demand equation (real M3, real GDP, the long and short term interest rates and inflation), share three long run relations. This finding reinforces the choice for a dynamic panel method that allows for a cointegrating rank larger than one. Applying a dynamic panel method that restricts the number of possible long run relations, e.g. a residual based testing procedure,
- 47 -
seems inappropriate. Tests for the equivalence of the cointegrating spaces of the countries included in the Panel VECM clearly show that (group-wise) homogeneity of these cointegrating spaces is rejected. This indicates differences in the long run relationships between the countries (or groups of countries) in the eurozone. However, this finding per se does not give an indication as to whether a long run money demand equation exists for each country and more specifically if these money demand relations are similar for some (groups of) countries in the eurozone. To be able to draw meaningful conclusions about long run money demand, the cointegrating spaces of each of the countries have to be identified in such a way that one of the three cointegrating vectors specifies a long run money demand equation. This identification poses several problems. The number of possible combinations of (over)identifying restrictions is quite large and testing only one combination already requires a substantial amount of computational time. To restrict the number of possibilities, attention is confined to specifications that are reasonable from an economic perspective (see Condition 1). This, however, does not result in the acceptance of a common specification across the countries of the eurozone. Also when leaving some countries´ cointegrating space unidentified and allowing for differing identifications per country, an identification of a long term money demand equation for each of the ´identified´ countries can not be found. Not surprisingly a homogeneous money demand equation, which could have been accepted due to the increase in degrees of freedom obtained by imposing this extra restriction, is clearly rejected. The effect of national differences in financial structures and markets and country specific structural breaks seems to have an influence on the specific long run relations that are shared by the five variables included in the analysis for each eurozone member country respectively. However, as no specification for the cointegrating spaces is found that can be accepted when tested for, the Panel VECM framework does not yet provide quantitative results by which the effectiveness of the ECB´s monetary policy can be assessed11. Based on the test results it is tempting to say that differences across the countries in the eurozone do exist with respect to long run money demand, confirming earlier panel results by Golinelli and
11 This problem might be the result of modelling the higher order dynamics by only including the first lagged differences for all countries in the panel (ki = 1, see p.33), possibly resulting in autocorrelation in the residuals. The AIC indeed suggests differing short term dynamics when looking at the individual countries, the HQ criterion on the other hand indicates that including only one lag for each country may not be so bad. Allowing for country specific short term dynamics may be able to filter out the country specific effects more effectively, leaving only the ´core´ relations. This, and also allowing for country specific deterministic components (this might change the distribution of the test statistics!), may lead to better quantitative results, but is left to future research.
- 48 -
Pastorelli (2000). Not being able to quantify these differences12 is a major drawback of the Panel VECM framework, as it does not allow for specific comments and/or suggestions in order to take account of these differences13. Direct implications for the ECB´s monetary policy are difficult to indicate. However the difference in the long term relations between the countries that comprise the eurozone, as shown by the differences in their cointegrating spaces, may have an effect on the results that are obtained from the time series analysis using the aggregate series. Some care has therefore to be taken when basing policy decisions on the results obtained from the aggregate analysis. Dedola et al. (2000) and Golinelli and Pastorello (2001) both claim, based on not very rigorous results obtained using residual based testing procedures, that the results obtained from the area-wide aggregates are still useful. In case of Johansen type estimation procedures the impact of using aggregates, constructed from individual series that share different long run relations on the disaggregated level, is not yet clear. Identifying the impact of these differences is therefore an important issue to be looked at in future studies on eurozone money demand.
12 This may also be due to poor size/power of the test given the (relatively) large N-dimension and the number of variables included. However the problem of finding quantitative results remains valid also when using ´smaller´ panels, only a panel consisting of ´D-mark´-countries (see footnote 12) provides quantitative results. This may be viewed as an indication that cross-country differences are a more important reason for the lack of quantitative results, however to be sure simulations need to be performed. 13 Evidence from tests using ´smaller´ panels consisting of subgroups of eurozone countries also shows difficulties finding an identification for each of the cointegrating spaces. Only when focusing on ´the D-mark´ area, consisting of Germany, Austria and the Netherlands, a (common) identification is found. Subsequent tests on the cointegrating vector representing the long run money demand equation reject a common relation for the three countries. This results indicates differences w.r.t. the long run money demand equation even for these three countries that can be said to have a similar history regarding monetary policy.
- 49 -
6
CONCLUSIONS
One of the ´pillars´ of the ECB´s monetary policy aimed at the maintenance of price stability in the medium term, is a prominent role for the amount of money held as inflation is believed to be a monetary phenomenon in the long run. This prominent role for money is based on the assumption that a stable relation exists between money and inflation. This paper tries to verify the existence of such a stable relation using two different econometric methods. First a time series framework is used, a choice very common in recent research on money demand. To allow for the use of a time series approach, eurozone wide aggregates have to be constructed in order to have data series that are long enough to be able to obtain meaningful estimation results. The choice of aggregation method is important as it is shown in section 4 that the estimation results depend on it. The thorough discussion of different aggregation methods in section 3, shows that variable weight growth rate aggregation is the best method to obtain eurozone wide aggregates. This method takes historical exchange rate movements into account without introducing an unwanted exchange rate effect in the aggregated series. The estimation results obtained using the aggregates constructed by this method, see section 4, give clear evidence that a long run money demand equation exists for the eurozone, and that this relation has been quite stable over the past few years. Besides a long run money demand equation, also evidence in favour of the expectations theory of the term structure and the Fisher equation is found. The actual coefficients of the long run money demand equation confirm economic theory, i.e. a positive effect of an increase in real GDP and a negative effect of an increase in the long term interest rate on the amount of money held. More importantly, the effectiveness of the ECB´s monetary targeting strategy is confirmed as a (de-)increase in money holdings (below) above the actual ´equilibrium´ amount, as indicated by the long run money demand equation, leads to a (de-) increase in inflation. The second econometric framework used is that of the (relatively new) dynamic panel data setup. This setup does not call for a specific aggregation method. All national series are used by itself, which allows for the exploitation of commonalities across the countries in the eurozone and also takes country specific effects into account. A thorough discussion of available dynamic (nonstationary) panel methods, leads to the choice for the Panel VECM setup. The Groen and Kleibergen (2002) test is used to verify the number of long run relations that are shared by the countries in the eurozone. As in the time series case, three long run relations are found. A finding that strengthens the argument against using a test procedure that restrict the number of long run relatio ns. A subsequent test for the homogeneity of these three long run relations across all (or within groups of) countries is rejected, indicating differences in each of the countries´ long run relations.
- 50 -
However only one of these long run relations represents a long run money demand equation. To be able to identify and perform tests on the long run money demand equation only, the Groen and Kleibergen (2002) procedure is adapted. Results show difficulties in finding an appropriate identification for each of the country specific long run relations that can be said to correspond to a priori beliefs based on economic theory. The Panel VECM setup seems to be affected too much by potential misspecifications imposed by the panel setup for some specific countries and country specific shocks (evident when looking at the graphs in Appendix B, e.g. Finland´s GDP, Italy´s M3). These country specific effects are of much less influence in the time series analysis as they are ´aggregated´ away when constructing the eurozone wide aggregates. Finding clear quantitative results on which the effectiveness of the monetary targeting strategy of the ECB can be assessed, is difficult. The evidence, obtained from the Panel VECM results, gives the overall impression that differences in the long term money demand equation are likely to exist across the countries of the eurozone. The problem is that the approach is unable to quantify these differences which makes it difficult to draw conclusions about the (differences in) effectiveness of the ECB´s monetary targeting strategy across the individual member countries of the eurozone. As quantifying these differences can be of importance with respect to the effect of the ECB´s monetary policy, looking for other (newer) dynamic nonstationary panel methods or different specification(s) of the Panel VECM (see footnote 10), that are able to give clearer (quantitative) evidence constitutes a possible direction for future research. The results from the time series analysis give very clear quantitative results about the effectiveness of the ECB´s monetary targeting strategy, confirming its effectiveness with respect to maintaining price stability in the eurozone and thereby strengthening the credibility of the ECB´s monetary policy. These results however are based on aggregates that, by construction (statistical averaging effect), dampen the impact of country specific shocks. Moreover these results might be influenced by the differences in long run relations found for the individual national variables. Finding the exact influence of aggregation on the estimation results from a Johansen-type estimation procedure is of importance to the ECB, as it bases its monetary policy on these aggregate results and constitutes another possible direction for future research.
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APPENDIX A THE DATA Table A1 Country Codes Code ____ AU BE ES FI FR GE GR IER IT NE PT LU
Country ___________ Austria Belgium Spain Finland France Germany Greece Ireland Italy Netherlands Portugal Luxembourg
Data Sources Nominal and real GDP Table A2 Nominal and real GDP, data sources Country
Period
Source
______ AU
_____________ 1979.1 – 2002.4
_________________ OECD, QNA 2003.1
BE
1980.1 – 2002.4 1979.1 – 1979.4 1979.1 – 2002.4 1979.1 – 2002.4 1979.1 – 2002.4 1979.1 – 2002.4 1979.1 – 2002.4 1997.1 – 2002.4 1979.1 – 1996.4 1979.1 – 2002.4 1979.1 – 2002.4 1986.1 – 2002.4 1979.1 – 1985.4 1985 – 2002 1979 – 1984
OECD, QNA 2003.1 ECB OECD, QNA 2003.1 OECD, QNA 2003.1 OECD, QNA 2003.1 ECB ECB OECD, QNA 2003.1 Economic Outlook 69 OECD, QNA 2003.1 OECD, QNA 2003.1 OECD, QNA 2003.1 Economic Outlook 69 ECB Economic Outlook 72
ES FI FR GE GR IER IT NE PT LU
Seasonally Adjusted (SA) / Non-Seasonally Adjusted (NSA) ___________________________ NSA, adjusted using Multiplicative X12-ARIMA SA SA SA SA SA, adjusted for unification SA NSA, adjusted using Multiplicative X12-ARIMA SA SA SA SA
Quarterly nominal and real GDP series in levels for each of the twelve Euro-countries. All series are in millions of euro using the irrevocable conversion rates as set by the ECB on December 31st 1998. Whenever two sources are given, the older series is multiplicatively added to the newer series, using the quarterly growth rates in the older series to ´update´ the newer series, e.g. x1985.4,new = x1986.4,new ×
- 55 -
x1985.4,old /x1985.4,old. As most available series were seasonally adjusted (SA), the series for Ireland and Austria, which were only available non seasonally adjusted (NSA), are seasonally adjusted using the multiplicative X12-ARIMA method (see Findley et al. 1998). The multiplicative X12-ARIMA method is chosen as the ECB also uses this method for its published data. 1995 is taken as the base year for the GDP series. For Luxembourg only yearly data are available so these data are made into quarterly data using the Lisman-method. The data obtained from Economic Outlook are semi-annual and are also transformed into quarterly data. Short term interest rates Quarterly short term interest rates expressed in yearly return for each of the twelve Euro-countries for the period 1979.1 – 2002.4. For 1979.1 – 2000.4 3-month interest rates for all countries are obtained from the BIS (Bank of International Settlements) database. For the period 2001.1 – 2002.4, the 3month euro-deposit rate is used for all countries. Long term bond yields Quarterly long term bond yields expressed in yearly return for each of the twelve Euro-countries for the period 1979.1 – 2002.4. 10-year interest rates on government bonds (or a proxy) for 1979.1 – 2000.4 are obtained from the BIS database and for 2001.1 – 2002.4 these are taken from Datastream. M3 M3 data for each of the twelve Euro-countries for the period 1979.1 – 2002.4. A monthly series for each country is obtained from the European Central Bank (ECB) database. The series are in millions of euro using the irrevocable conversion rates of December 31st 1998. The monthly series are converted into quarterly series taking the average of the three corresponding months for each quarter. Then the quarterly series are seasonally adjusted using the multiplicative X12-ARIMA method (see Findley et al. 1998). The German series is corrected for the effect of the unification by first regressing the growth rates on a dummy for 1990.3 (see Fagan and Henry, 1998; Beyer et al., 2001; Wesche, 1997). The effect was found to be 8.1% with a standard error of 0.98. Using this estimated effect the growth rate of 1990.3 is corrected by subtracting the unification effect. These corrected growth rates are then used to calculate back the series in lo glevels (and levels). Exchange rates Exchange rates of each of the twelve Euro-countries against the ECU/EURO for the period 1979.1 – 2002.4. A monthly series is obtained from the Dutch Central Bank – FM database for each country. These series are converted into quarterly series taking the average of the three corresponding months
- 56 -
for each respective quarter. For the period 1999.1 – 2002.4 the irrevocable conversion rates as set by the ECB are used (for Greece from 2001.1 on). Data Analysis In this section a thorough inspection of the data used in our estimation of the money demand equation (2) is presented. For each of the twelve Euro-countries graphs are given in Appendix B for the series as represented in (2) and descriptive statistics for these series are given in first differences to be able to give a meaningful comparison between the countries; the results for inflation and interest rates are only shown in levels. As we do not yet have the series for the GDP-deflator and real M3, we construct the GDP-deflator series for each country respectively by dividing the nominal GDP series by the real GDP series and the real M3 series for each country respectively as the M3 series divided by the GDPdeflator series. We also transform all variables, except long and short term interest rates, in logs as specified in (2) and take first differences of the GDP-deflator series to construct the inflation series ∆p. The inflation series is thereafter multiplied by four to make it compatible to the two interest rate series. For the same reason of compatibility, the long run bond yield and the short term interest series are divided by one hundred. Real M3 (md -p) Table A3.1 Descriptive statistics for quarterly real M3 (md -p) growth rates AU BE ES FI FR GE _________ _________ _________ __________ __________ __________ Mean 0.69 0.73 0.92 0.96 0.70 0.87 Median 0.81 0.74 0.89 1.24 0.85 0.88 Maximum 3.87 4.34 4.54 5.10 2.36 4.04 Minimum -5.59 -3.31 -1.64 -6.45 -2.17 -1.72 Std. Dev. 1.18 1.40 0.94 2.11 0.98 1.02 GR IER IT LU NE PT _________ _________ _________ __________ __________ __________ Mean 1.02 1.22 0.27 0.72 1.16 0.92 Median 0.94 0.93 0.20 0.96 1.16 0.96 Maximum 6.11 7.98 3.41 17.04 3.67 8.44 Minimum -3.26 -5.28 -4.04 -16.85 -1.14 -4.33 Std. Dev. 1.88 2.77 1.26 3.19 1.07 1.86
As can be seen from Figure B1.1. in Appendix B and Table A3.1, all real M3 show an upward trending behaviour. The average quarterly growth rate (multiplied by four to express them in yearly rates) ranges from 1.08% for Italy to 4.88% for Ireland. The growth rate in Spain deviates the least
- 57 -
from its average over the period. The graph for Luxembourg shows an extraordinary decline during the end of the nineties followed by a recline of almost the same magnitude. Real GDP (y) Table A3.2 Descriptive statistics for quarterly real GDP (y) growth rates AU BE ES FI FR GE _________ _________ _________ __________ __________ __________ Mean 0.55 0.50 0.65 0.65 0.51 0.48 Median 0.69 0.49 0.61 0.65 0.53 0.37 Maximum 2.04 4.12 2.84 4.09 1.55 3.28 Minimum -1.31 -1.37 -1.03 -2.29 -0.65 -2.71 Std. Dev. 0.74 0.82 0.70 1.32 0.51 0.97 GR IER IT LU NE PT _________ _________ _________ __________ __________ __________ Mean 0.39 1.29 0.49 1.12 0.59 0.63 Median 0.47 1.07 0.53 0.93 0.70 0.75 Maximum 9.92 6.88 2.33 3.17 2.67 3.87 Minimum -7.09 -1.95 -1.03 -0.30 -2.37 -3.64 Std. Dev. 2.77 1.55 0.59 0.94 0.82 1.41
As Figure B1.2 clearly shows, most series show a smooth increase in real GDP over the sample period. Only Portugal and Greece show a less smooth increase over the years although being seasonally adjusted. The average quarterly growth rates range (multiplied by four to express them in yearly rates) from 1.56% for Greece to 5.16% for Ireland. As expected from Figure B1.2 the standard deviation of the growth rate is the highest for Greece. Inflation ∆p (growth rate GDP-deflato r) Table A3.3 Descriptive statistics for quarterly inflation, ∆p, in yearly returns AU BE ES FI FR GE _________ _________ _________ __________ __________ __________ Mean 2.72 3.01 6.66 4.40 3.96 2.43 Median 2.48 2.64 6.20 3.62 2.36 2.33 Maximum 10.54 15.92 16.76 25.08 13.27 8.48 Minimum -0.84 -10.40 -0.41 -6.99 -0.02 -1.75 Std. Dev. 2.09 2.99 3.75 5.08 3.54 2.07 GR IER IT LU NE PT _________ _________ _________ __________ __________ __________ Mean 12.74 5.73 7.24 3.55 2.46 11.08 Median 12.40 4.36 5.78 2.95 2.27 8.52 Maximum 38.07 19.39 22.15 11.61 10.11 31.33 Minimum -1.17 -8.55 0.21 -0.88 -5.76 -0.57 Std. Dev. 7.50 5.00 5.50 2.74 2.60 7.94
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As expected the inflation rate for Germany is on average the lowest (2.43%) followed by the Netherlands and Austria. Greece has experienced the highest (12.74%) inflation on average. From the graphs it can be seen that all series show a convergence to low levels of inflation. Note that the graph of Luxembourg, in Figure B1.3, is very smooth due to the formation of the quarterly data out of yearly series. Short term interest rate Table A3.4 Descriptive statistics for quarterly short term interest rates in yearly returns AU BE ES FI FR GE _________ _________ _________ __________ __________ __________ Mean 6.02 7.89 11.19 9.13 8.66 5.86 Median 5.36 7.90 12.60 9.93 8.27 5.13 Maximum 12.20 16.64 22.69 16.52 23.44 12.59 Minimum 2.60 2.60 2.60 2.60 2.60 2.60 Std. Dev. 2.41 3.84 5.08 4.48 4.61 2.45 GR IER IT LU NE PT _________ _________ _________ __________ __________ __________ Mean 15.96 9.17 11.24 7.89 6.20 13.05 Median 17.81 9.42 11.37 7.90 5.68 14.39 Maximum 25.91 18.38 20.47 16.64 13.02 27.01 Minimum 3.04 2.60 2.60 2.60 2.60 2.60 Std. Dev. 5.94 4.20 5.08 3.84 2.59 6.54
As can be expected from the inflation series, Germany has on average the lowest short term interest rate (5.86%) and Greece the highest (15.96%). Looking at the individual series the main observation in Figure B1.4 is the convergence of all series to the same low value of short term interest rate (they are actually the same since the introduction of the euro). Furthermore many countries show a period of higher short term interest rates during the beginning of the nineties. Long term bond yield Table A3.5 Descriptive statistics for quarterly long term bond yield in yearly returns AU BE ES FI FR GE _________ _________ _________ __________ __________ __________ Mean 7.21 8.53 11.20 9.76 8.90 6.84 Median 7.16 8.27 11.74 11.10 8.72 6.70 Maximum 11.17 13.81 17.80 14.75 16.86 10.61 Minimum 4.00 4.07 4.10 4.06 3.94 3.85 Std. Dev. 1.61 2.72 4.09 3.15 3.37 1.53
- 59 -
GR IER IT LU NE PT _________ _________ _________ __________ __________ __________ Mean 15.93 9.92 11.25 8.17 7.18 16.13 Median 17.11 9.10 11.28 7.78 6.88 19.17 Maximum 25.91 19.03 21.21 13.13 11.72 32.24 Minimum 4.71 4.00 4.09 4.00 3.97 4.04 Std. Dev. 6.08 3.97 4.45 2.53 1.82 8.11
Looking at Figure B1.5 and B1.4, the movement of the long term interest rate shows great similarity with the short term interest rate, but the series are a bit smoother. This is intuitive as the long term interest rates are more determined by the long run fundamentals in the economy, which do not change that rapidly over time. Again Germany has the lowest long term interest rate on average (6.84%) and the highest long term interest rate (16.13%) can be found for Portugal. Exchange rates Table A3.6 Descriptive statistics for quarterly exchange rate growth rates until fixed euro conversion rates are used. (all series until 1999.1 except Greece 2000.1) AU BE ES FI FR GE _________ _________ _________ __________ __________ __________ Mean -0.36 0.02 0.71 0.13 0.16 -0.31 Median -0.24 -0.08 0.42 -0.07 -0.02 -0.22 Maximum 1.29 4.87 9.46 10.92 4.80 1.25 Minimum -3.26 -3.36 -5.49 -6.12 -3.08 -3.23 Std. Dev. 0.94 1.13 2.31 2.63 1.08 0.91 GR IER IT LU NE PT _________ _________ _________ __________ __________ __________ Mean 2.19 0.20 0.67 0.02 -0.26 1.43 Median 1.58 0.07 0.38 -0.08 -0.19 0.95 Maximum 20.04 4.98 9.30 4.87 1.40 12.77 Minimum -2.69 -3.90 -4.93 -3.36 -3.72 -2.29 Std. Dev. 3.12 1.47 2.08 1.13 0.94 2.38
Looking at the graphs in Figure B1.6 and the descriptive statistics in Table A3.6 it is cle ar that for most countries their currencies have depreciated a lot with respect to the euro. Only the Dutch Guilder, the German Mark and the Austrian Shilling have appreciated on average over the sample period. Also the Belgian Franc has a period in which it appreciates with respect to the euro, but at the beginning of the sample period it depreciated a lot in a few years time. The Austrian Shilling appreciated the most on average and the Greek Drachma depreciated the most on average.
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APPENDIX B FIGURES Figure B1.1 Quarterly real M3 (md -p) series in loglevels 11.9
12.5
11.8
12.4
13.2
12.3
11.7
11.4 11.2
13.0
12.2
11.6
11.0 12.8
12.1 11.5
10.8
12.0
11.4
12.6
11.9
11.3
11.8
11.2
11.7
11.1
10.6 12.4
11.6 80 82 84 86 88 90 92 94 96 98 00 02
10.4
12.2 8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 9 8 00 0 2
LN_AU
10.2 8 0 8 2 8 4 8 6 88 9 0 9 2 9 4 9 6 9 8 0 0 0 2
LN_BE
13.9
14.2
13.8
14.1
13.7
14.0
L N_FI
11.6
11.4 11.2
11.4
11.0
13.9
13.6
8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 98 0 0 0 2
L N_ ES
11.2
10.8
13.8 13.5
11.0
13.7
13.4
13.6
13.3
13.4
13.1
13.3 80 82 84 86 88 90 92 94 96 98 00 02
10.4 10.2
13.5
13.2
10.6
10.8 10.6
10.0
10.4 8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 9 8 00 0 2
LN_FR
9.8 8 0 8 2 8 4 8 6 88 9 0 9 2 9 4 9 6 9 8 0 0 0 2
LN_GE _ADJ
13.5
12.2
11.6
12.6
12.0 11.9
13.3
LN_I ER
12.8
12.1 13.4
11.4
12.4 11.2
11.8
12.2
11.7
13.2
11.0
11.6
12.0
11.5
13.1
11.3 80 82 84 86 88 90 92 94 96 98 00 02
11.6 8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 9 8 00 0 2
L N_IT
Note:
10.8
11.8
11.4 13.0
8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 98 0 0 0 2
LN_G R
10.6 8 0 8 2 8 4 8 6 88 9 0 9 2 9 4 9 6 9 8 0 0 0 2
L N_ LU
8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 98 0 0 0 2
L N_ NE
LN_PT
going from upper left to lower right the graphs represent the series for country AU, BE, ES, FI, FR, GE, GR, IER; IT, LU, NE, PT
Figure B1.2 Quarterly real GDP (y) in loglevels 10.9
11.0
11.9
10.5
10.8
10.9
11.8
10.4
11.7
10.3
11.6
10.2
11.5
10.1
11.4
10.0
10.7
10.8
10.6 10.7 10.5 10.6
10.4
10.5
10.3 10.2
11.3
10.4 80
82
84
86
88 90
92
94
96
98
00
02
9.9
11.2 80
82
84
86
88
LN_AU
90
92
94
96
98
00
02
9.8 80
82
84
86
88
LN_ BE
12.8
13.2
12.7
13.1
12.6
13.0
12.5
12.9
12.4
12.8
90
92
94
96
98
00
02
10.2
84
86
88 90
92
94
96
98
00
02
92
94
96
98
00
02
94
96
98
00
02
94
96
98
00
02
9.6 9.4 9.2 9.0
9.7 80
82
84
86
88
90
92
94
96
98
00
02
8.8 80
82
84
86
88
LN_G E
12.4
90
10.2
9.8
LN_FR
12.5
88
9.8
12.6 82
86
10.0
12.7
80
84
10.1
9.9
12.2
82
LN_FI
10.0
12.3
80
L N_ES
90
92
94
96
98
00
02
80
82
84
86
88
LN_G R
11.5
10.2
8.4
11.4
10.1
11.3
10.0
11.2
9.9
11.1
9.8
11.0
9.7
12.3
92
LN_I ER
8.6
8.2
90
8.0 12.2 7.8 12.1
7.6
12.0
7.4 80
82
84
86
88 90
92
L N_IT
Note:
10.9
94
96
98
00
02
9.6
10.8 80
82
84
86
88
90
92
L N_LU
94
96
98
00
02
9.5 80
82
84
86
88
90
92
94
96
98
00
02
L N_NE
going from upper left to lower right the graphs represent the series for country AU, BE, ES, FI, FR, GE, GR, IER; IT, LU, NE, PT
80
82
84
86
88
90
92
LN_PT
- 61 -
Figure B1.3 Quarterly inflation ∆p in yearly returns (growth rate GDP deflator) .12
.20
.20
.10
.15
.16
.08
.10
.06
.05
.28 .24 .20
.12
.16 .12
.08 .04
.08
.00 .04
.02
-.05
.00
-.10
.00
-.02
-.15
-.04
80
82
84
86
88
90
92
94
96
98
00
02
.04 .00 -.04
80
82
84
86
88
DLN_AU_YR
90
92
94
96
98
00
02
-.08 80
82
84
86
88
DLN_BE_YR
.14
.10
.12
90
92
94
96
98
00
02
82
84
86
88
92
94
96
98
00
02
96
98
00
02
96
98
00
02
94
96
98
00
02
94
96
98
00
02
94
96
98
00
02
.20 .15
.3
.10
90
DLN_FI_YR
.4
.08 .06
.08
80
DLN_ES_YR
.10 .2
.06
.04
.05 .1
.04
.02
.00
.02
.0
.00
.00 -.02
-.02 80
82
84
86
88
90
92
94
96
98
00
02
-.05
-.1 80
82
84
86
88
DLN_FR_YR
90
92
94
96
98
00
02
-.10 80
82
84
86
88
DL N_ GE_ YR
.24
.12
.20
.10
90
92
94
96
98
00
02
.12
-.02 80
82
84
86
88
90
92
94
96
98
00
02
92
94
.16 .12
.00
.08 -.04
.04
-.08
-.04
.00
80
82
84
86
88
DL N_ IT_YR
Note:
90
.20
.02
.00
88
.24
.04
.04
.00
86
.28
.12
.04
84
.32
.08
.06
.08
82
DLN_ IER_YR
.08
.16
80
DL N_GR_ YR
90
92
94
96
98
00
02
80
82
84
86
88
DLN_L U_YR
90
92
94
96
98
00
02
80
82
84
86
88
DLN_NE_YR
90
92
94
DLN_PT_YR
going from upper left to lower right the graphs represent the series for country AU, BE, ES, FI, FR, GE, GR, IER; IT, LU, NE, PT
Figure B1.4 Quarterly short term interest rate in yearly returns .14
.18
.24
.16
.12
.18 .16
.20
.14 .10
.14 .16
.12
.08
.10
.06
.12
.12
.08
.10 .08
.08
.06 .04
.06 .04
.04
.02
.02 80
82
84
86
88
90
92
94
96
98
00
02
.04
.00 80
82
84
86
88
SR_AU
90
92
94
96
98
00
02
.02 80
82
84
86
88
SR_ BE
90
92
94
96
98
00
02
80
82 84
86
88
SR_ES
.24
.14
.30
.20
.12
.25
.16
.10
.20
.12
.08
.15
.08
.06
.10
.04
.04
.05
.00
.02
.00
90
92
SR_FI
.20
.16
.12
.08
80
82
84
86
88
90
92
94
96
98
00
02
80
82
84
86
88
SR_FR
90
92
94
96
98
00
02
.04
.00 80
82
84
86
88
SR_G E
.24
92
94
96
98
00
02
80
82 84
86
88
SR_G R
.18 .16
.20
90
90
92
SR_ IER
.14
.30
.12
.25
.10
.20
.08
.15
.06
.10
.04
.05
.14 .16
.12
.12
.10 .08
.08
.06 .04
.04
.00
.02 80
82
84
86
88
90
92
SR_I T
Note:
94
96
98
00
02
.02 80
82
84
86
88
90
92
SR_LU
94
96
98
00
02
.00 80
82
84
86
88
90
92
94
96
98
00
02
SR_NE
going from upper left to lower right the graphs represent the series for country AU, BE, ES, FI, FR, GE, GR, IER; IT, LU, NE, PT
80
82 84
86
88
90
92
SR_PT
- 62 -
Figure B1.5 Quarterly long term bond yield in yearly returns .12
.14
.11 .12 .10 .09
.10
.18
.16
.16
.14
.14
.12
.12 .10
.08 .08
.10
.07
.08
.06
.08
.06
.06
.06
.05 .04
.04
.04
.04 .03
.02 80
82
84
86
88
90
92
94
96
98
00
02
.02 80
82
84
86
88
LR_AU
.11
.16
.10
.14
.09
.12
.08
.10
.07
.08
.06
.06
.05
.04
.04
.02
.03 82
84
86
88
90
92
92
94
96
98
00
02
.02 80
82
84
86
88
90
LR_BE
.18
80
90
94
96
98
00
02
.12
98
00
02
80
82 84
86
88
90
92
94
96
98
00
02
94
96
98
00
02
94
96
98
00
02
L R_ FI
.28
.20
.24
.16
.12
.08 .12 .04
.08 .04 82
84
86
88
90
92
94
96
98
00
02
.00 80
82
84
86
88
90
L R_GE
.14
96
.16
80
.20
94
.20
LR_FR
.24
92
LR_ES
92
94
96
98
00
02
80
82 84
86
88
LR_ GR
90
92
LR_I ER
.12
.35
.11
.30
.10 .16
.10
.12
.08
.08
.06
.04
.04
.25
.09 .08
.20
.07
.15
.06 .10 .05 .05
.04 .00
.02 80
82
84
86
88
90
92
94
96
98
00
02
.03 80
LR_I T
Note:
82
84
86
88
90
92
94
96
98
00
02
.00 80
82
84
86
88
90
LR_ LU
92
94
96
98
00
02
80
LR_NE
82 84
86
88
90
92
LR_PT
going from upper left to lower right the graphs represent the series for country AU, BE, ES, FI, FR, GE, GR, IER; IT, LU, NE, PT
Figure B1.6 Quarterly exchange rates in local currency per euro 19
47
2.6
46
2.5
45
2.4
18 17
44
7.0
6.5
2.3
6.0
43 16
2.2
42
15
41
2.0
40
14
38 80
82 84 86 88 90
92 94
96 98 00 02
1.8 80
82 84 86 88 90
AU
92 94 96 98 00 02
170
360
7.0
160
320
6.6
.80
240
130
6.4
.76
200
120 6.2
100
120
5.8
90
80
80 80
82 84 86 88 90
92 94
96 98 00 02
.68
40 80
82 84 86 88 90
FR
92 94 96 98 00 02
.64 80 82 84 86 88 90 92 94 96 98 00 02
ES
2400
.72
160
110
6.0
5.6
FI
.84
280
140
80 82 84 86 88 90 92 94 96 98 00 02
GE
7.2
150
4.5 80 82 84 86 88 90 92 94 96 98 00 02
BE
6.8
5.0
1.9
39 13
5.5
2.1
80 82 84 86 88 90 92 94 96 98 00 02
GR
I ER
47
2.9
220
46
2.8
200
45
2.7
44
2.6
1800
43
2.5
1600
42
2.4
41
2.3
40
2.2
39
2.1
2200 2000
180 160 140
1400 1200 1000
38 80
82 84 86 88 90
92 94 IT
Note:
96 98 00 02
120 100 80
2.0 80
82 84 86 88 90
92 94 96 98 00 02 LU
60 80 82 84 86 88 90 92 94 96 98 00 02 NE
going from upper left to lower right the graphs represent the series for country AU, BE, GE, FI, FR, ES, GR, IER; IT, LU, NE, PT
80 82 84 86 88 90 92 94 96 98 00 02 PT
