MODELING THE DEMAND FOR M3 IN THE UNIFIED GERMANY Ju ¨rgen Wolters, Timo Tera ¨svirta, and Helmut Lu ¨tkepohl* Abstract —An error correction model for the demand for real M3 money is constructed for the period of 1976–1994 with real GNP, the GNP deflator, as well as a short-term and a long-term interest rate as explanatory variables. Quarterly, seasonally unadjusted data are used in estimating the model. It is found that there is a clear structural break due to the German unification in 1990. On the other hand, once this structural break is accounted for, a stable relation is found which resists a series of specification tests. These include a number of recent tests of parameter constancy and linearity. Our specification is at variance with findings reported by some other researchers, notably the Deutsche Bundesbank. I. Introduction I N 1975 the German Bundesbank started targeting money balances. Central bank money was then used as an indicator of monetary policy. In 1988 the Bundesbank changed the monetary indicator. Since then money growth targets based on inflation targets and forecasts of potential output and velocity growth have been fixed for M3. In conducting such a policy a stable demand function for money is an important prerequisite. Therefore it is not surprising that the stability of a demand function for M3 has been discussed extensively since the emergence of the German monetary union (GMU) on July 1, 1990. However, only a few empirical studies analyze the stability of structural M3 demand functions after the GMU. They all use error correction models to account for the nonstationarity of the variables and to separate long-run and short-run behavior. Tullio et al. (1996) is the only study presenting clear evidence for an unstable demand function after the GMU. Hansen and Kim (1995), Issing and To ¨dter (1995), Deutsche Bundesbank (1995a), as well as Scharnagl (1996) all conclude that a more or less stable long-run relation between real M3 money, real gross national or gross domestic product, and an interest rate or an interest rate differential does exist. Moreover, in its monthly report of July 1995 the Deutsche Bundesbank reports a cointegration relation between nominal M3, nominal gross domestic product (GDP), and a bond yield with very similar coeffi- cients before and after the GMU. A Lagrange multiplier test does not reject the null hypothesis of constant long-run coefficients. A relationship with even more convincing test results exists if the difference between financial wealth and nominal GDP is included in the equation as an additional explanatory variable. 1 Financial wealth is also included in a money demand relation by Kole and Meade (1995), who also claim stability for their long-run relation. Hansen and Kim (1995) and the Deutsche Bundesbank (1995b) use seasonally adjusted data whereas Kole and Meade (1995), Scharnagl (1996), Issing and To ¨dter (1995), and Deutsche Bundesbank (1995a) work with seasonally unadjusted observations and model the seasonality in the long-run relation by including seasonal dummies. Because after the GMU only M3 data for the unified Germany are available, the latter two papers adjust the level of M3 and gross national product (GNP) by multiplying the series with a constant factor in the preunification period. The main objective of this study is to shed more light on the stability issue. We argue that all the previously men- tioned studies raise questions which we shall address in more detail in section V. In our analysis we will use seasonally unadjusted and untransformed data. Seasonal fluctuations are a major source of variation in economic time series. Therefore it seems more reasonable to model these fluctuations instead of eliminating them, especially when these fluctuations are different for different variables. In particular, if there are possible structural breaks in a variable, as will be the case here, standard seasonal adjust- ment procedures may distort the structure of the original series. This is because the usual adjustment procedures based on moving averages may smooth a structural break over a longer period. Our aim is to specify and estimate error correction models for real M3 for the period from 1976(1) to 1994(2), which includes the GMU. The starting period is chosen such that only the period of monetary targeting by the Bundesbank is covered. We analyze possible instabilities as well as nonlin- earities using recently developed tests based on smooth transition regression (STR) models (e.g., Granger and Tera ¨svirta (1993, chap. 7)). Furthermore we will also compare our final model to those presented in the aforemen- tioned studies and argue that our model is superior to its competitors. The paper is organized as follows. In the next section the data and some of their basic properties are discussed in some detail. In section III the number of cointegration relations is considered using Johansen’s systems approach (Johansen (1995)). The results are used in the search for an adequate conditional error correction model in section IV, where several single-equation methods are applied. In section V a comparison with competing models is performed and sec- tion VI concludes. Received for publication April 4, 1996. Revision accepted for publica- tion July 25, 1997. * Freie Universita ¨t Berlin, Stockholm School of Economics, and Hum- boldt Universita ¨t Berlin, respectively. Financial support by the DFG, Sonderforschungsbereich 373, is grate- fully acknowledged. The second author also acknowledges support from the Swedish Research Council for Letters and Social Sciences. We are grateful to Kirstin Hubrich and Uwe Hassler for helping with the computations. Comments by David Hendry, Neil Ericsson, Kirstin Hu- brich, James Stock, and three anonymous referees have resulted in several improvements of the analysis and the exposition. An earlier version of the paper was presented at the ESEM 96 in Istanbul. 1 There may be a problem related to the interpretation of this relationship. If three variables are enough to form a stationary linear relation, what does it mean in a single equation context that another nonstationary variable is included in that relation? [ 399 ]  1998 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/003465398557636 by guest on 05 May 2021