Economics Letters 90 (2006) 260 – 265 www.elsevier.com/locate/econbase
On the aggregation of eurozone data E.M. Bosker T Utrecht School of Economics, Vredenburg 138, 3511 BG, Utrecht, The Netherlands Received 1 December 2004; received in revised form 13 June 2005; accepted 16 August 2005 Available online 27 December 2005
Abstract Constructing eurozone aggregates is common practice in empirical studies. This study shows that the choice of aggregation method does not only matter on a theoretical basis. A brief study on eurozone money demand indicates the empirical importance of choosing the correct aggregation method as different aggregates give substantially different outcomes. D 2005 Elsevier B.V. All rights reserved. Keywords: Aggregation; Money demand; Eurozone JEL classification: C82; C32; E41
1. Aggregation methods Constructing aggregate eurozone data from the underlying national series is common practice in empirical studies. Past research has acknowledged the importance of the choice of aggregation method and several methods have been proposed. A good review of four possible aggregation methods used in the literature focusing on aggregating the level series is given in Winder (1997). Winder (1997) concludes in favour of using fixed base period exchange rates because that avoids the problem of introducing an unwanted component, the (de-) appreciation of the exchange rate, in the growth rate series. Moreover a useful property of the
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P constructed aggregate level series, xEU ¼ i xit =eiT , is that the corresponding growth rate series is a t weighted average of each country’s own growth rate, with weights being the respective current shares of the countries in the aggregate series, i.e. X X X xit =eiT xit1 =eiT Dxit =eiT X xi =ei EU DxEU i i t t1 T ¼ i ¼ i Dln xit ð1Þ Dln xt i EU EU EU EU xt1 xt1 xt1 xt1 i where x t is the series to be converted from local currency into the common currency, e t the exchange rate, i.e. units of local currency per unit of common currency and T the fixed base year. In two papers on constructing aggregate eurozone data Beyer et al. (2000, 2001) suggest a different aggregation method. They construct aggregate growth rates using variable weights, X xit1 =eit1 Dln xit ; ¼ Dln xEU t EU xt1 i
ð2Þ
aggregating each country’s own growth rate using the corresponding shares of that country in the total aggregate of the previous period as weights. 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, the level series are obtained by cumulating backwards starting from a given value at the end of the sample period. They prefer this method arguing that aggregating levels using a fixed base period leads to distorted aggregate series because it depends crucially on the choice of base year. Given the substantial relative price-changes due to currency de- and revaluations, using for instance 1979 as base year would lead to aggregate series that are different from the aggregate series constructed using 1999 as base year. Their method has the nice properties that sub-aggregates (regional and temporal) also aggregate correctly and that aggregating a ratio of two variables is equal to taking the ratio of each variable aggregated separately. When aggregating the level series using fixed base period weights, this property holds for the level series but not for the growth rate series. To better compare the method of Beyer et al. (2000, 2001) to the method proposed by Winder (1997), I rewrite (2) as: X Dxi =ei X xit1 =eit1 i X xit1 =eit1 Dxit t t1 ¼ i Dln x ¼ Dln xEU t t i EU EU EU x x x x t1 t1 t1 t1 i i i X X xit =eit1 xit1 =eit1 i X ¼ i : i xt1 =eit1
ð3Þ
i
Comparing this to Eq. (1), one immediately sees that whereas in Eq. (1) a fixed base year is chosen for the whole sample period, in Eq. (3) this fixed base year is each year set at the previous year. Hereby variable weight growth rate aggregation does take exchange rate effects into account without introducing an unwanted component in the aggregate series. This gives it an advantage over fixed weight level aggregation as this method is unable to properly take exchange rate changes into account and depends crucially on the chosen base year.
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2. Aggregation and eurozone money demand To illustrate the importance of using the appropriate aggregation method not only theoretically but also empirically, this section uses aggregates constructed by the two different methods discussed in Section 1 in an empirical study on eurozone money demand. The prominent role for money in the monetary policy of the ECB, it is one of its dtwo pillarsT, relies crucially on the existence of a stable relationship between money holdings and the price level. The existence of a stable money demand equation is typically assessed in the context of standard economic theories of money demand. In the empirical literature on money demand one commonly finds the following money demand equation in log–linear form: md ¼ a þ by þ c1 il þ c2 is þ dDp;
ð4Þ
where lowercase letters indicate variables in logs, a, b, c 1, c 2, and d are coefficients and D is the difference operator. m d denotes real money holdings, p the price level and y the real gross domestic product (GDP). The long-term interest rate, i l , is a proxy for the return on assets alternative to money, and the short-term interest rate, i s , a proxy for the return on assets included in the definition of money. Finally Dp denotes the GDP deflator, a proxy for the return on goods alternative to money. The standard econometric framework when estimating Eq. (4) is a time series setup. As all variables in Eq. (4) are found to be non-stationary, the money demand equation is usually estimated using cointegration techniques, where the Johansen (1995) framework is mostly used in recent studies (e.g. Brand and Cassola, 2000; Vlaar, 2004). All these studies need to construct aggregate eurozone data and, with the only exception being Artis and Beyer (2004), who use variable weight growth rate aggregation, they all construct their aggregates using the fixed weight level aggregation method. To assess the impact of the chosen aggregation method, here eurozone aggregates are constructed using fixed weight level aggregation (dfixed aggregatesT) and variable weight growth rate aggregation (dvariable aggregatesT). Using quarterly national data on M3, GDP, the 3-month interest rate, the 10-year interest rate on government bonds and exchange rates for all twelve eurozone countries1 from 1979 to 2002, fixed and variable aggregates for all variables in Eq. (4) are constructed. The fixed weight level aggregation uses the 1999 fixed conversion rates (for Greece 2001) to convert the series from local currency into euro. As the differences between the two aggregation methods are best illustrated by the formulas in Eqs. (1) and (3), Fig. 1 shows the difference between the two resulting aggregate growth rate series for GDP and M3 and between the resulting level series of inflation and the two interest rates. Fig. 1 shows that this difference gets smaller, and eventually goes to zero over the sample period. This is as expected, compare Eqs. (1) and (3), as the two series should move very close together when the difference between the current and chosen fixed base year exchange rate is small. This exactly happened because of the gradual convergence of the exchange rates to the fixed euro conversion rates. The size of the differences between the two constructed aggregates is substantial, ranging from several percentages for the inflation series, to several tenths of a percentage for real GDP. Because most of the Euro-12 countries experienced substantial currency de- and/or appreciations, fixing the exchange rate at 2001 results in the seven (three) countries, that had a depreciating (appreciating) currency, being dunderrepresentedT (doverrepresentedT) in the aggregate eurozone series. 1
Data available upon request.
E.M. Bosker / Economics Letters 90 (2006) 260–265 .002
.006
.000
.004
-.002
.002
-.004
.06 .05 .04 .03 .02 .01 .00 -.01
.000
-.006
-.002
-.008
-.004
-.010
-.006
-.012 80 82 84 86 88 90 92 94 96 98 00 02 real M3
263
80 82 84 86 88 90 92 94 96 98 00 02 real GDP
80 82 84 86 88 90 92 94 96 98 00 02 Inflation
.005
.002 .000 -.002 -.004 -.006 -.008 -.010 -.012
.000 -.005 -.010 -.015 -.020 -.025 80 82 84 86 88 90 92 94 96 98 00 02 LR interest rate
80 82 84 86 88 90 92 94 96 98 00 02 SR interest rate
Fig. 1. The difference between the two approaches (variable minus fixed). Note: Going from upper left to lower right the graphs represent differences between the two aggregation methods for real M3, real GDP, inflation, long-term bond yield and shortterm interest rate.
The convergence of the exchange rates makes these effects more evident at the beginning of the sample period. All aggregate series, regardless of aggregation method, are found to be nonstationary. Therefore the Johansen (1995) framework to find cointegrating relations between variables is used to obtain results regarding the existence of a stable money demand function. As a cointegrating rank of three was indicated by formal tests, Table 1 shows the estimation results for the three long run relations2 and corresponding short run adjustments for both the variable and the fixed aggregates (for the complete details of the estimation procedure see Bosker, 2003). The results obtained using the two different aggregates differ substantially in some crucial aspects. First the variable aggregates result shows a (significant) negative long run relation between the long-term interest rate and real money holdings, which is also found by Artis and Beyer (2004) using variable aggregates. This is as expected as an increase in the long-term interest rate makes alternatives to money more attractive, hereby decreasing real money holdings. The fixed aggregates result on the contrary suggests a (insignificant) positive relation between the same two variables, which seems highly unlikely. Second the variable aggregates result accepts the homogeneity of the Fisher equation, suggesting a onefor-one long run relation between inflation and the long run interest rate. The fixed aggregates result suggests a smaller effect of the long run interest rate on inflation (Brand and Cassola (2000) also find this result using fixed aggregates). Third and arguably the most important difference, is the difference in result regarding the impact of deviations from the long run money demand equation on inflation, i.e. the short run adjustment term of inflation regarding the first cointegrating relation. The variable aggregates result finds a significant positive effect of money holdings in excess of the long run money demand equation on inflation, hereby justifying the monetary targeting strategy employed by the ECB. The fixed 2
Identification of the cointegrating space (accepted at a 5% level) is guided by economic theory in that the first cointegrating vector represents a money demand equation, the second the Fisher equation and the third the expectations theory of the interest rate. Furthermore only a deterministic constant is allowed for in the cointegrating space.
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Table 1 Estimates of the long-run relations and the short-run adjustments for both aggregates Variable
Long run relations
Short run adjustments
Money demand
Fisher equation
Yield spread
Dp is il y md
0 0 0.84 [0.31] 1.27 [0.05] 1
1 0 1 0 0
0 1 1 0 0
0.10* 0.01 0.01 0.01 0.10*
0.17* 0.09* 0.08* 0.03 0
0.02 0.08 0.02 0.13* 0
Fixed Dp is il y md
Money demand 0 0 0.30 [0.21] 1.52 [0.04] 1
Fisher equation 1 0 0.51 [0.06] 0 0
Yield spread 0 1 1 0 0
0.03 0.08* 0.03 0.08* 0.09*
0.24* 0.07* 0.05* 0.02 0
0.09 0.19* 0.01* 0.12* 0
Note: standard deviations in brackets, * denotes significance at 5% level.
aggregates result on the contrary finds an insignificant negative effect, which would shed (serious) doubts on the effectiveness of the ECB’s strategy. The rest of the estimation results do not differ much between the two aggregates and are as expected. For example both find a positive relation between output and money holdings and accept the stationarity of the yield spread.
3. Conclusions This paper compares two different aggregation methods suggested in the literature to construct Eurozone aggregates from the underlying national series. Besides more clearly showing the theoretical difference between the two methods, a short empirical study on Eurozone money demand shows that the estimation results differ substantially using one or the other aggregation method. Especially the opposing conclusions regarding the effectiveness of the ECB’s monetary targeting strategy make it clear that the choice of aggregation method matters not only theoretically but also empirically.
Acknowledgements Jean-Pierre Urbain, Franz Palm, Peter Vlaar and Harry Garretsen are acknowledged for their discussions and helpful comments.
References Artis, M., Beyer, A., 2004. Issues in money demand: the case of Europe. Journal of Common Market Studies 42, 717 – 736. Beyer, A., Doornik, J.A., Hendry, D.F., 2000. Reconstructing aggregate euro-zone data. Journal of Common Market Studies 38, 613 – 624.
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Beyer, A., Doornik, J.A., Hendry, D.F., 2001. Reconstructing historical euro-zone data. Economic Journal 111, 308 – 327. Bosker, E.M., 2003. Eurozone money demand: time series and dynamic panel results, Dutch Central Bank, WO research memoranda No. 750. Brand, C., Cassola, N., 2000. A money demand system for the euro area, European Central Bank. Working Paper 39. Johansen, S., 1995. Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press, Oxford. Vlaar, P.J.G., 2004. Shocking the eurozone. European Economic Review 48 (1), 109 – 131. Winder, C.C.A., 1997. On the construction of European area-wide aggregates – a review of the issues and empirical evidence. Irving Fisher Committee of Central-Bank Statistics, IFC Bulletin, vol. 1, pp. 15 – 23.
