Money and Banks: Some Theory and Empirical Evidence for Germany
Oliver Holtem¨ ller∗ o November 2002

Abstract This paper contributes to the analysis of the money supply process in Germany during the period of monetary targeting by the Bundesbank from 1975-1998. While the standard money multiplier approach assumes that the money stock is determined by the money multiplier and the monetary base it is argued here that both the money stock and the monetary base are determined endogenously by the optimizing behavior of commercial banks and private agents like households and firms. An industrial organization style model for the money creating sector that describes the money creation process is developed assuming that the main policy variable of the central bank is the money market interest rate. A vector error correction model for the nominal money stock, the monetary base, nominal income, short-term and long-term interest rates, and the required reserve rate is specified, and the interaction between these variables is analyzed empirically. The evidence contradicts the money multiplier approach and supports the presented model of the money creating sector.

JEL Classification: C32, E51, E52 Keywords: Industrial organization approach to banking theory, money multiplier, endogenous money, vector error correction model

∗

This paper is partially based upon the second chapter of the author’s doctoral dissertation (Vector au-

toregressive analysis and monetary policy, Aachen: Shaker, 2002). This version will be published with the title “Money Stock, Monetary Base and Bank Behavior in Germany” in Jahrb¨ cher f¨ r National¨ konomie und u u o Statistik (2003), forthcoming. I thank Helmut L¨ tkepohl and J¨ rgen Wolters for helpful comments. Financial u u support from the Deutsche Forschungsgemeinschaft (SFB 373) is gratefully acknowledged.

1 Introduction
The role of nominal money in the monetary policy transmission process is still an open question. In contemporaneous macroeconomic models that follow a general-equilibrium approach, money is often determined endogenously by a money demand relation without having a direct impact on real variables. The important equations for the development of the real sector in this type of models are an aggregate demand equation, the term structure of interest rates, an inflation-adjustment equation and a monetary policy reaction function, see for example Walsh (1998). On the other hand, money is highly relevant in practiced monetary policy strategies and in empirical macroeconomic models. The growth rate of money plays a prominent role in the first pillar of the European Central Bank’s monetary policy strategy (European Central Bank, 1999a,b), and money growth has been the key element of the Bundesbank’s monetary targeting strategy from 1975 to 1998 (Deutsche Bundesbank, 1995). Econometric models of monetary policy transmission, in which money is explicitly considered, are Br¨ ggemann (2001) and L¨ tkepohl and Wolters (2001) for Germany; an u u overview of monetary policy transmission models for the Euro area is given in Angeloni et al. (2002). Before analyzing the role of money in the monetary policy transmission mechanism, it is necessary to investigate the money supply process. Two conflicting views of money supply can be found in the literature. The older one is the money multiplier approach saying that the money stock is determined by the money multiplier and the monetary base. In general it is assumed in this framework that the monetary base is controlled by the monetary authority. Under certain conditions this implies that the monetary authority can also control the money stock such that money is exogenous in the sense that it is policydetermined. The other view is the so-called “new view” which stresses the importance of commercial banks in the money supply process. According to this view, money is endogenous in the sense that the money stock is not determined by a monetary policy authority but is the result of the optimizing behavior of commercial banks and private agents given the money market conditions set by the monetary policy authority. The purpose of this paper is to analyze the theoretical implications of the exogeneity view and the endogeneity view of money and to compare these implications to empirical evidence for Germany in the period of monetary targeting from 1975 to 1998. The paper is structured as follows. In section 2, the money multiplier approach is discussed, and the development of the money stock in Germany from 1975 to 1998 is analyzed under consideration of the monetary policy strategy of the Deutsche Bundesbank. Afterwards, the “new view” of money supply is briefly reviewed. In section 3, an industrial organization model of the money-creating sector with endogenous money is developed. In section 4, a vector error correction model (VECM) for the nominal money stock, the mon-

1

etary base and related variables is estimated and analyzed. The empirical results are compared to the implications of both the money multiplier approach and the model presented in section 3. Finally, section 5 concludes.

2 The Money Supply Process in Germany from 1975 to 1998
2.1 The Money Multiplier Approach and the “New View” of Money Supply The standard textbook approach explaining the money stock outstanding and its growth rate, is the money multiplier model. Many versions of this model are in use. They have in common that the money stock (M ) is determined by the monetary base (or high-powered money, H) and the money multiplier mm:1 M = mm · H. (1)

The monetary base is controlled by the central bank, and the money multiplier depends on the behavior of the public (constant currency-deposit ratio, d = CU/D), the commercial banks (reserve ratio as a function of interest rates and uncertainty), and the central bank (minimum reserve requirements). These behavioral determinants enter the money multiplier in a nonlinear way. The simplest version of the money multiplier is the following one: The money stock consists of currency in use (CU ) and deposits (D): M = CU + D = mm · H; and the monetary base consists of currency in use and reserves of banks (R): H = CU + R. The (required) reserve rate is r = R/D such that mm = d+1 CU/D + 1 = . CU/D + R/D d+r (2)

If the central bank is able to forecast the money multiplier correctly and is also able to control the monetary base it can control the money stock. Under these circumstances, the money stock is an exogenous variable assuming that the supply of deposits by the public is not restricted such that D = R/r. Exogeneity of the money stock in this context means the ability of the central bank to control the money stock. The money multiplier approach has some important drawbacks: First, the operating target of central banks in the USA and in Europe is not the monetary base but a money market interest rate (federal funds rate, euro overnight index average EONIA). A theory of money supply has to consider this and other institutional details. Second, according to studies of the relationship between the money stock and the monetary base in Germany by Willms (1993) and by Nautz (1998), a stable relationship between the money stock and the monetary base seems not to exist, see also figure 1. The increase of the money multiplier from about 4.5 Insert figThe money multiplier approach is explained in many macroeconomic textbooks. This description benefits from Dornbusch and Fischer (1994).
1

ure 1 about here.

2

to 7.1 shows that the share of the monetary base in M3 has decreased, and that book money created by commercial banks has become more and more important. Therefore, it may be appropriate to model the behavior of banks explicitly instead of reducing it to variations of the money multiplier. In the terminology of Tobin (1967), the money multiplier approach is the “old view” of money supply, while the “new view” interprets financial intermediaries as firms which optimize their portfolios given the optimizing behavior of non-banks. That is, financial intermediaries do not possess the ability to expand deposits without limit like it is assumed in the money multiplier approach above. Thus, the amount of deposits and the money stock are endogenous variables determined by the portfolio selection process of commercial banks and the public. Corresponding to the use of the notion of exogeneity in this paper, endogeneity of money in this context means that the central bank is not able to control the money stock.2 While optimizing their portfolio, banks and non-banks have to consider the conditions set by the central bank. Advocates of the money multiplier approach refuse the new view, and find “no reason to look beyond the balance sheets of commercial banks.” (Meltzer, 1969, p. 39). Albeit weaker and not as explicit as in this quotation, this view can also be found in a more recent work (Meltzer, 1995). The money multiplier approach is also supported by Rasche (1993) who admits “that the algebraic components of the money multiplier, however formulated, vary in response to the economic decisions of both depository institutions and the public” (p. 32) but claims that the variations of the money multiplier are unsystematic, and of short-run nature (p. 47): “Over the longer run, such random movements tend to average out, so that changes in base money are the most important source of changes in transactions money.” 2.2 Monetary Targeting in Germany from 1975 to 1998 The exogeneity or controllability assumption of the money multiplier approach forms the basis of the monetary policy strategy of monetary targeting.3 This strategy has been adopted by the Deutsche Bundesbank from 1975 to 1998. In Deutsche Bundesbank (1995, p. 91 ff.) it is described how the Bundesbank has tried to control the money stock. The Bundesbank refers implicitly to the money multiplier approach and states that its monopoly for bank notes and the minimum reserves requirement imply long-run controllability of the money stock by means of controlling the monetary base. A precondition for an exogenous money stock is a flexible exchange rate. This preconSee also M¨ ller (1993); for an analysis of endogeneity, causation, and their relation see M¨ ller (1998). u u The money multiplier approach does not necessarily imply exogeneity of the money stock. If the money multiplier exhibits unpredictable and endogenous variations, the money stock is endogenous. For reasons of simplicity, it is supposed here that the money stock is exogenous in the money multiplier approach. A money multiplier model with endogenous money can be found in Jarchow (1998), for example.
3 2

3

dition has not been given due to the more or less fixed exchange rates within the European Monetary System (EMS, founded 1979), but the Bundesbank has been able to sterilize interventions on the foreign exchange market like it has been the case in the EMS crisis of September 1992. Nevertheless, as can be seen from figure 2, the Deutsche Bundesbank was not always able to achieve its announced monetary target. In the 24 years of monetary targeting from 1975 to 1998, the observed monetary growth rate deviated from the announced growth rate eleven times. Among others, there are two possible reasons for a deviation of Insert figthe money growth rate from the announced target: first, the Bundesbank has also had other ure 2 about objectives. The money growth rate has not been an ultimate goal but only an intermediate here. target. The ultimate goal has been price stability measured in terms of the inflation rate. In some periods there may have been trade-offs between the announced monetary target, the price stability objective, and other objectives, like the exchange rate. Second, money could be endogenous. That is, the central bank is not able to set the money growth rate as the money multiplier approach or exogeneity view suggests. In a modern open economy with a sophisticated profit-maximizing banking system, a non-banking financial sector, and rapid international capital flows, it is at least questionable whether money is exogenous, see also Desai (1992). The endogeneity view is supported by the explanations of the Bundesbank for the differences between announced target and observed money growth rate since 1992/93. Before 1992/93, the explanations of the Bundesbank for deviations from the money growth rate target were reasons for a more expansive or more restrictive monetary policy than announced. That is, the actions of the Bundesbank have been responsible for the deviations of the exogenous money growth rate from the announced target. Since 1992/93, the explanations refer to unforeseen changes in the demand for money implying that the endogenous money stock has been determined by the demand for money. The following explanations have been given for deviations:4 From 1975 to 1978, the money growth rate was higher than the announced target. The reason was a policy of low interest rates in order to increase the low level of real economic activity. The reasons for the excess money growth from 1986 to 1988 have been the stabilization of exchange rates (DM/US-Dollar, EMS) and provision of liquidity to avoid a recession after the stock market crash in October 1987. In 1993, a flight into currency and into short-term deposits has been the result of the introduction of a withholding tax on interest yields. Therefore, the demand for money increased. In 1995, the only year with a lower money growth rate than the announced target, the demand for money decreased as a consequence of the permission of money market fund shares which have not been part of M3. And in 1996, the money growth rate was too high because of interest rate driven portfolio variations from money capital to time deposits. According to
4

The explanations of the monetary development are taken from von Hagen (1998) and Baltensperger (1998).

4

these explanations, at the end of the period of monetary targeting in Germany, demand side forces have been the reasons for deviations of the money growth rate from the announced target. This supports the endogeneity view.

3 An Industrial Organization Model of the Money-Creating Sector
In the following, the so-called (Freixas and Rochet, 1997) industrial organization approach to banking theory is applied to model the behavior of commercial banks. Central elements are submodels of the credit market and the deposits market. Reduced form equations for the quantity of loans and the quantity of deposits are developed and inserted into the aggregated balance sheet of commercial banks. As a consequence, the monetary base and the money stock are endogenous. Before the details of this model are explained, section 3.1 gives a brief overview of the industrial organization approach to banking theory. 3.1 The Industrial Organization Approach to Banking Theory The definition of a bank in banking theory is mainly the legal definition of a commercial bank in the United States of America (U.S. Banking Act of 1971): banks are financial intermediaries that receive (demand) deposits and originate loans. The models that analyze assets and liabilities as well as its possible dependencies can be divided into subsets.5 One subset is the industrial organization approach. In this subset, a special focus is laid on the structure of the banking market and the competition between banks. The banks are modeled as optimizing agents on the market for loans and the market for deposits. The optimizing behavior is modeled as expected profit maximization, that is banks are risk neutral. This approach can be extended with assumptions about the cost function. Baltensperger (1980) reviews models that consider the costs of real resources, especially labor, and Bofinger (2001) uses a quadratic cost function to model credit default risk. Another subset of models uses the theory of portfolio selection, where banks are assumed to be risk averse, see for example Freixas and Rochet (1997, chapter 8). Two articles, Klein (1971) and Monti (1972), build the basic setup of the industrial organization approach to banking. Three markets (bonds, loans, deposits) and three types of agents (central bank, commercial banks, households/firms) form the main structure. While the bond market is assumed to be perfectly competitive implying that there is only one interest rate for bonds, the loan and the deposits markets are not perfectly competitive. The profit function of an individual banking firm n is: Πn = iS Sn + iL Ln − iD Dn − C (S, L, D) , n n
5

(3)

See for example Santomero (1984), Bhattacharya and Thakor (1993), and Freixas and Rochet (1997) for overviews of banking theory.

5

where Sn , Ln , and Dn are the holdings of bonds (securities), loans, and deposits and iS , iL , n iD are the respective interest rates. The bank decision variables are the interest rate on den posits, the quantity of loans and the quantity of bonds in Klein (1971) and the interest rate on deposits, the interest rate on loans, and the quantity of bonds in Monti (1972). The cost function is not modeled explicitly. If the demand for loans by firms and the supply of deposits by households are specified, the first order conditions of the profit maximization problem can be used to determine the stocks of bank assets and liabilities and the corresponding interest rates. If the demand for loans and the supply of deposits are independent of each other, the cross derivatives of the cost function are zero (∂ 2 C/∂L∂D = ∂ 2 C/∂D∂L = 0), and if no further assumptions about the three markets (loans, deposits, bonds) are made, the decision problem of the bank can be divided into two independent problems: the optimal choice of interest rate/quantity on the loan market and the optimal choice of interest rate/quantity on the deposits market. Freixas and Rochet (1997, p. 60) formulate this model with the quantities of loans and deposits as decision variables and interpret it as “a model with imperfect competition with two limiting cases: N = 1 (monopoly) and N → +∞ (perfect competition)”, where N is the total number of commercial banks. The Monti-Klein model has been expanded in several ways. Dermine (1986) adds bankruptcy risk and deposit insurance and Prisman et al. (1986) analyze uncertainty and liquidity requirements. The result of both papers is that the separability result for loans and deposits breaks down. In the following, a version of the Monti-Klein model with interest rates on loans and deposits as decision parameters of banks is used. 3.2 The Model of the Money-Creating Sector: Market Participants The market participants in this model of the money-creating sector are the central bank, commercial banks and private agents (households/firms). The behavior of the central bank is exogenous. It fixes the interest rate on the money market i. The balance sheet of the central bank consists of central bank credit (CBC) on the assets’ side and currency in use (CU ) and reserves (R) on the liabilities’ side: CBC = CU + R. (4)

The commercial banks are profit-maximizing firms on an oligopolistic banking market. Banks buy loans (L) and sell deposits (D). Their profit function is Πn = iL Ln − iD Dn − i CBCn + i IBPn , n n (5)

6

where iL denotes the interest rate of bank n on loans, iD the interest rate on deposits, and n n IBP the net position on the interbank money market. The balance sheet equation of a commercial bank is Rn + Ln + IBPn = Dn + CBCn such that the net position can be defined as IBPn = Dn · (1 − r) + CBCn − Ln (7) (6)

when it is assumed that banks only hold required reserves (Rn = r·Dn ). The profit function can also be written as Πn = iL Ln + i (1 − r) Dn − i Ln − iD Dn . n n (8)

Commercial banks are price setters and quantity takers on the credit and the deposits market. This type of simultaneous Bertrand competition between banks is discussed in Yanelle (1988, 1989). One problem of simultaneous Bertrand competition is the existence of a competitive equilibrium “because a monopolist in one market automatically becomes a monopolist in the other market“ (Yanelle, 1988, p. XV). If a single commercial bank offers a higher interest rate on deposits than all other commercial banks, it gets all deposits and becomes also a monopolist on the credit market. But in a model with a central bank that offers high powered money at a fixed interest rate there is a second refinancing possibility for commercial banks besides deposits. On this market (the money market), the commercial bank is a price taker. The third group of agents are the households and firms. They have linear demand functions for loans of every bank n: Ln = α0 + α1 · iL + α2 · (iL − iL ) + α3 · Y n −n n with α0 , α2 , α3 > 0, and for deposits of every bank n:6 Dn = β0 + β1 · iD + β2 · (iD − iD ) + β3 · Y n −n n with β0 , β1 , β3 > 0, β2 < 0. (10) α1 < 0 (9)

6 This relationship could also be called supply of deposits. The notion demand for deposits has been chosen in analogy to the credit market.

7

iL and iD are the interest rates on the credit market and the deposits market set by bank n, n n respectively. Y is income and iL and iD are average interest rates of the other banks: −n −n iL −n 1 = N −1
N

iL m m=1 (m=n)

and

iD −n

1 = N −1

N

iD . m m=1 (m=n)

Furthermore , it is assumed that

α0 α1

> i and

β0 β1

> i.

3.3 Equilibrium on the Credit Market As already mentioned, the commercial banks are price setters and quantity takers on the credit market and the deposits market. The quantities of loans and deposits in equilibrium are the results of a price setting game. The following solution of this game is similar to the standard model of a heterogeneous oligopoly in G¨ th (1994). u The first derivative of the profit function (8) of a commercial bank n with respect to the interest rate on the credit market is ∂Πn ∂iL n = Ln + iL · n ∂Ln ∂Ln −i· L L ∂in ∂in

= (α0 + α1 iL − α2 iL + α2 iL + α3 Y ) + iL (α1 − α2 ) − i(α1 − α2 ) n n −n n (11) and the first order condition is: (α0 + α2 iL ) − (α1 − α2 )i + 2(α1 − α2 )iL + α3 Y = 0. −n n The second order condition is satisfied: ∂ 2 Πn ∂iL 2 n = 2(α1 − α2 ) < 0. (13) (12)

By inserting the definition of iL into the first order condition and rearranging we get: −n α0 + iL n =− α2 N −1 N m=1

iL m

− (α1 − α2 )i + α3 Y α2 N −1

2(α1 − α2 ) −

.

(14)

The right-hand side is independent of n, therefore the interest rate on the credit market is the same for all commercial banks: ∀n : iL = iL . n (15)

It follows that the interest rate on the credit market in equilibrium is iL = −
∗

α0 − (α1 − α2 )i + α3 Y . 2α1 − α2 8

(16)

Inserting this interest rate into the demand for loans yields L∗ = α0 + α1 iL + α3 Y n =
2 (α1 − α2 )α3 α0 (α1 − α2 ) α1 − α1 α2 + i+ Y. 2α1 − α2 2α1 − α2 2α1 − α2 ∗

(17)

The aggregated quantity of loans is L = c0 + c1 · i + c2 · Y, where c0 > 0, c1 < 0, c2 > 0 (18)

are the coefficients of the expression for the quantity of loans of a single bank (17) multiplied by N , the number of commercial banks. The quantity of loans depends on the money market interest rate and on the income of the households. 3.4 Equilibrium on the Deposits Market The solution concept on the deposits market is the same as on the credit market. Commercial banks are price setters and quantity takers. The first derivative of the profit function (8) of bank n with respect to the interest rate on the deposits market is: ∂Πn ∂iD n = i · (1 − r) · ∂Dn ∂Dn − Dn − iD · D n D ∂in ∂in

= i · (1 − r) · (β1 − β2 ) − (β0 + β1 iD + β2 (iD − iD ) + β3 Y ) n −n n − iD · (β1 − β2 ). n We get the following first order condition: −(β0 + β2 iD ) + (β1 − β2 )i(1 − r) − 2(β1 − β2 )iD − β3 Y = 0 −n n and the second order condition is satisfied: ∂ 2 Πn ∂iD 2 n = −2(β1 − β2 ) < 0. (21) (20) (19)

In analogy to the credit market, every bank sets the same interest rate on deposits: iD = −
∗

β0 − (β1 − β2 )i(1 − r) + β3 Y 2β1 − β2

(22)

and the demanded quantity of deposits for every bank is:
∗ Dn = β0 + β1 iD + β3 Y ∗

=

2 β0 (β1 − β2 ) β1 − β1 β2 (β1 − β2 )β3 + i(1 − r) + Y. 2β1 − β2 2β1 − β2 2β1 − β2

9

The aggregated quantity of deposits D = d0 + d1 · i(1 − r) + d2 · Y with d0 > 0, d1 > 0, d2 > 0 (23)

depends on the money market interest rate i and on income Y . The coefficients di are again the coefficients of the expression for the individual quantities multiplied by N . 3.5 Monetary Base and Money Stock The aggregated balance sheet of the commercial banks is:
N N

(Rn + Ln + IBPn ) = n=1 n=1

(Dn + CBCn ) .

With Rn = r · Dn and

N n=1 N

IBPn = 0 follows
N N N

Ln = n=1 n=1

Dn − r · n=1 Dn + n=1 CBCn

or H ≡ CBC = L − (1 − r) · D = c0 + c1 i + c2 Y − (1 − r)(d0 + d1 i(1 − r) + d2 Y ). (24) The monetary base H equals central bank credit and it depends on the quantity of loans L =
N n=1 Ln ,

the quantity of deposits D =

N n=1 Dn

and the required reserve rate r.

The monetary base is endogenous. The quantity of central bank lending is a result of the profit maximization of the commercial banks. Aggregating the balance sheet of the banking sector yields the money stock M : L = CU + D ≡ M. (25)

The money stock equals the aggregated quantity of loans, that is, it is determined by its counterparts. In a more detailed model of money supply, the other counterparts of the money stock which are neglected here, could be modeled, too. Neglected major counterparts are net foreign assets of the banking system (F A) and non-monetary liabilities of the banking system (N M L): M (2262.1) = L (5247.7) + FA (262.7) − NML (3005.2) − O (243.0)

Numbers in parentheses are 1998 averages of German M3 and its counterparts in billions of DM, and O denotes other counterparts.7
7

The data is taken from the monthly bulletin of the Deutsche Bundesbank, February 1999, table II.2.

10

3.6 Comparison of Money Multiplier Approach and Money Supply Endogeneity In the money multiplier approach, money is determined by the monetary base and the money multiplier. The monetary base is set exogenously by the central bank, and under the assumptions made here, money is exogenous. In the theory of endogenous money on the other hand, money equals credit demand and the monetary base is a result of the optimal behavior of commercial banks and households. According to the money multiplier approach, changes in income and changes in the money market interest rate should not cause changes in the money stock. However, this statement only holds in the very simple money multiplier model of section 2.1. In more sophisticated models, the money multiplier depends also on interest rates and on income. Therefore, the impact of interest rates and income on the money stock cannot be used to distinguish between the two approaches. However, the effects of changes in the required reserve rate on the monetary base and on the money stock are different in both concepts. Whereas an exogenous monetary base does not depend on changes in the required reserve rate, there is a positive effect on the monetary base in the model of the money-creating sector presented in this section: ∂H = d0 + 2d1 i(1 − r) + d2 Y > 0. ∂r (26)

A higher required reserve rate causes a decrease in the quantity of deposits but does not affect the quantity of loans. The banks ask for more central bank credit to finance the loans.8 The reaction of the money stock on changes in the required reserve rate is different, too. The money multiplier mm depends negatively on the required reserve rate, and so does the money stock, see equation (2). In the model of the money-creating sector with endogenous money, the money stock does not depend on the required reserve rate. A money multiplier equation can also be written in the endogenous money framework: M c0 + c1 i + c2 Y = = mm(Y, i, r). H c0 + c1 i + c2 Y − (1 − r)(d0 + d1 i(1 − r) + d2 Y ) (27)

The interpretation of (27), however, is different from the interpretation of (2). A discussion of the money multiplier approach, the counterparts approach and their relation can also be found in Artis and Lewis (1990).
Regardless of the considered theoretical model, the monetary base will always increase if the required reserve rate is increased, at least in the very short run. This is due to the definition of the monetary base which is the sum of currency in use and reserves. In the money multiplier approach, however, the required reserve rate and the monetary base are assumed to be more or less independent policy variables.
8

11

4 The Econometric Model
4.1 Data and Unit Root Tests Quarterly data for Germany from 1975-1998 is used in the econometric analysis. The variables are denoted as follows: m is the logarithmic money stock M3, h is the logarithmic monetary base, y is logarithmic gross domestic product in current prices, s is a short-term interest rate, is a long-term interest rate, and r is the average required reserve rate. The data is not adjusted for the German unification in 1990 and not seasonally adjusted. Further details can be found in the data appendix. The calculations have been performed with EViews 4.1 and with Mathematica 4.0. Unit root tests show that the endogenous variables can be assumed to be integrated of order one, see table 1. The mean shift in m, h, and y is considered in the unit root tests using a modified Dickey-Fuller type unit root test proposed in Lanne et al. (2002). The results are quite robust to variations of the number of included lagged differences in the test regression.

Table 1: Unit Root Tests, Sample Period: 1975:1-1998:12 Variable m ∆m h ∆h y ∆y ∆ s ∆s r ∆r Lags 1 1 1 1 5 4 1 1 2 1 1 1 Statistic −1.38 −10.37 ∗∗∗ −1.75 −6.96 ∗∗∗ −2.12 −4.32 ∗∗∗ −1.44 −6.50 ∗∗∗ −2.40 −4.33 ∗∗∗ −2.14 −7.82 ∗∗∗ Det. Terms c, sd, t c, sd, di c, sd, t c, sd, di c, sd, t c, sd, di c c c c c, t c Test LLS ADF LLS ADF LLS ADF ADF ADF ADF ADF ADF ADF

Notes: Variable names are described in the text. ADF is the Augmented Dickey-Fuller Test and LLS is the ∗+ test (τint ) proposed by Lanne et al. (2002). The LLS test is used for time series that exhibit a structural break (mean shift) due to the German unification. Deterministic terms are included as indicated in the fourth column: constant (c), seasonal dummies (sd), linear trend (t), impulse dummy (di). Three asterisks denote significance at the 1% level.

12

4.2 Cointegration Analysis An econometric framework that is suited to analyze the relationships between integrated variables is the vector error correction model (VECM):9 k−1 ∆xt = µt + Πxt−1 + i=1 Γi ∆xt−i + ut ,

(28)

where xt is an (p × 1)-vector of endogenous variables, here xt = (mt , ht , yt , t , st , rt ) and thus p = 6; ut ∼ N (0, Σu ) is a p-dimensional error process, and µt contains deterministic terms. Here a constant, centered seasonal dummies (sdit ), and impulse dummies are included: µ t = ν0 + i=1 3 sd νi sdit + i=0 k−1 d νi dt−i ,

(29)

where dt is an impulse dummy variable that is one in the second quarter of 1990 and zero otherwise. The matrix Π can be decomposed into a (p × r)-adjustment matrix α and a (p × r)-matrix containing the cointegration relations: Π = αβ . Here, r denotes the cointegration rank.10 The econometric model (28) differs from the theoretical specification in the following way: first, in addition to the money market interest rate st , the long-term interest rate t is

included such that the empirical analysis can be compared to existing money demand studies. Second, it is assumed that the relations, which determine money stock and monetary base, can be approximated by log-linear simplifications. The lag length k is determined applying information criteria and set to two, k = 2, according to the Hannan-Quinn criterion (HQ). A cointegration rank of two is imposed in the following implying that two stationary linear combinations of the variables exist. This is supported by a cointegration rank test (Johansen, 1995), summarized in table 2. At a significance level of 5%, the hypotheses of at most zero and at most one cointegration relation are rejected while the hypothesis of at most two cointegration relations is not rejected. A cointegration rank of two is also compatible with the theoretical considerations of section 3. Identification of the cointegration vectors can be achieved by imposing linear restrictions: β = (H1 φ1 , H2 φ2 ),
9

(30)

The econometric analysis of vector error correction models is for example described in Johansen (1995), L¨ tkepohl (1993), and L¨ tkepohl (2001). u u 10 r denotes the cointegration rank and rt the required reserve rate. Though this may be confusing, this notation is quite usual in the literature.

13

Table 2: Cointegration Tests, Sample Period: 1975:1-1998:12 H0 r r r r r r =0 ≤1 ≤2 ≤3 ≤4 ≤5 r r r r r r H1 >0 >1 >2 >3 >4 >5 LRtrace 116.12 ∗∗ 77.25 ∗∗ 42.87 18.56 10.12 4.11

Notes: The table shows the Johansen trace statistic used to test the hypothesis of at most r cointegration relations. The lag length of the VAR in levels is k = 2, an unrestricted constant, seasonal dummies and impulse dummies as in equation (29) are included. ∗∗ symbolizes rejection of the null hypothesis at a significance level of 5%.

where the matrices φi contain the unrestricted estimates and H1 and H2 are defined as     1 0 0 0 0 0 1 −1 0 0 0 0     0 0 1 0 0 0 0 0 1 0 0 0     H1 =  0 0 0 1 0 0  and H2 =  0 0 0 1 0 0  . (31)     0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 The restricted cointegrating relations can now be described by the two equations: mt = − β31 yt − β41 t t

− β51 st − β61 rt + ec1t − β52 st − β62 rt + ec2t ,

(32)

mt − ht = − β32 yt − β42

where ec1t and ec2t are the error correction terms which can be interpreted as deviations from the long-run equilibria. These restrictions satisfy the rank criterion given in Johansen and Juselius (1994, Theorem 1) such that they are identifying: rk(H1⊥ H2 ) = rk(H2⊥ H1 ) = 1 ≥ 1. (33)

The just identified cointegration vectors are given in the upper part of table 3. This identification scheme implies that the variables yt , t, st and rt are not cointegrated, which can

be confirmed by testing for the cointegration rank of (yt , t , st , rt ). The hypothesis that the cointegration rank is at most zero is not rejected (LRtrace = 40.86, 5% critical value: 47.21). The required reserve rate measures a policy variable that is assumed to be exogenous, that is, it is assumed that the central bank does not follow a reaction function for setting the required reserve rate. Therefore, the model is now conditioned on the required reserve rate in order to get a slightly more parsimonious model. This transformation into a partial model is supported by testing for weak exogeneity of the required reserve rate: imposing α61 = α62 = 0 in the unconditional model gives a LR test statistic of 0.79 (p-value: 14

Table 3: Long-Run Relations m 1 1 1 1 h y s r 3.97 16.34

just identified cointegrating vectors 0 −0.95 5.14 −2.76 −1 −0.59 10.42 −7.98

overidentified cointegrating vectors, partial system 0 −1.13 3.63 −1.00 0
(0.02) (0.78) (0.43)

−1

0.40
(0.08)

8.99
(1.78)

−6.44
(1.08)

12.25
(1.47)

Notes: Reduced rank estimation of the VECM (28) as described in Johansen (1995) and L¨ tkepohl (2001), u the cointegration rank is two, the number of lags is two. Centered seasonal dummies and impulse dummies according to (29) are included. The estimates reported are the entries of β . Asymptotic standard errors in parentheses. The sample period is 1975:1-1998:4.

0.67).11 Additionally, it cannot be rejected that the coefficient of the required reserve rate in the first cointegration relation is zero (LR test statistic of 2.07, p-value: 0.15). The overidentified cointegration relations in the partial system are given in the lower part of table 3. Abstracting from deterministic terms they can be interpreted as a nominal money demand function mt = 1.13 yt − 3.63 t + 1.00 st + ec1t

(34)

and a money multiplier relation (recall that m, h and y are measured in logarithms) mt − ht = 0.40 yt − 8.99 These two long-run relations imply that ht = 0.73 yt + 5.36 t t

+ 6.44 st − 12.25 rt + ec2t .

(35)

− 5.44 st + 12.25 rt + (ec1t − ec2t ).

(36)

This is a long-run relation between the monetary base and the variables that determine it in the theoretical model of section 3 (yt , st , and rt ). It can be seen that all coefficients including the required reserve rate have the expected signs. The money demand function (34) cannot be compared directly to other money demand studies for Germany. While (34) is a demand function for nominal money, most other studies focus on real money balances. The general result that a stable money demand function can be specified for the unified Germany is among others also supported by Wolters et al. (1998), Br¨ ggemann (2001), and L¨ tkepohl and Wolters (2001). However, a stable relau u tionship between the monetary base and the broad money stock M3 has not been found in
A variable is said to be weakly exogenous if its adjustment coefficients in front of all cointegration relations (ec1,t−1 and ec2,t−1 ) are zero: αi1 = αi2 = 0. For a discussion of (weak) exogeneity and cointegration see Ericsson et al. (1998), partial VECMs are discussed in Harbo et al. (1998).
11

15

other studies. The reason is presumably that the impact of the required reserve rate is modeled explicitly here while Willms (1993) and Nautz (1998), for example, do not include the required reserve rate in the model but use a monetary base that is adjusted for changes in the required reserve rate. 4.3 Adjustment and Short-Run Dynamics The cointegrating vectors do not show the complete information about the relationships between the variables in the system. It is still an open question which variables react on deviations from the long-run equilibria and how innovations or shocks affect the variables. When the cointegrating vectors β are known, the other parameters of the VECM can be estimated by OLS. The adjustment to the long-run equilibria can be characterized by the adjustment parameters that are stored in the matrix α. These parameters are the coefficients of ec1,t−1 and ec2,t−1 in the equations for the first differences. The adjustment parameters are summarized in table 4, where the results of tests on weak exogeneity for each variable can be found, too. These tests suggest that both the long-term and the short-term interest rates are weakly exogenous. Nominal money, the monetary base, and nominal income adjust in direction of the long-run equilibria if equilibrium-deviations occur and are rejected to be weakly exogenous. The table shows also the results of some diagnostic tests for the equations of the VECM. The remaining serial correlation in the monetary base and income equations disappears if the lag length is increased. However, this does not change the qualitative results such that the parsimonious specification with two lags can still be accepted. The non-normality indicated by the Jarque-Bera test for the short-term interest rate is due to two large outliers (1979:4 and 1981:1); after deleting these outliers, the test statistic has a value of 2.41 with p-value 0.30. Overall, it can be supposed that the VECM is well specified. The required reserve rate that does not occur in the money demand function is also not important for the short-run development of the money stock. The coefficients to ∆rt and ∆rt−1 in the equation for the first differences of the money stock are 0.08 (0.35) and −0.33 (−1.29) which are not significant (t-values in parentheses). On the other hand, the coefficient of ∆r is strongly significant in the monetary base equation of the VECM. Its value is 4.34 with a t-value of 6.55 such that the positive impact of the required reserve rate on the monetary base that is predicted from the theoretical model can be confirmed. The coefficient of ∆rt−1 is not significant: −0.24 (−0.32). The reaction of the variables to innovations in other variables can be analyzed with impulse response functions and forecast error variance decompositions. They are calculated

16

Table 4: Adjustment Coefficients (Loading Matrix α) and Diagnostic Tests ∆m ec1,t−1 ec2,t−1 Weak Exogeneity R JB
2

∆h −0.10
(−1.11)

∆y 0.07
(1.36)

∆ −0.00
(−0.05)

∆s −0.04
(−1.67)

−0.15
(−5.01)

0.01
(0.97)

0.14
(4.04)

0.05
(2.69)

−0.01
(−1.96)

0.02
(2.70)

18.21
[0.00]

9.78
[0.02]

8.36
[0.04]

4.48
[0.21]

7.52
[0.06]

0.94 3.93
[0.14]

0.77 1.67
[0.43]

0.94 4.19
[0.12]

0.05 0.25
[0.88]

0.21 131.20
[0.00]

LM(1) LM(4) ARCH(1) ARCH(4) RESET(1)

0.86
[0.36]

2.34
[0.13]

6.94
[0.01]

0.79
[0.38]

1.63
[0.21]

1.13
[0.35]

3.30
[0.02]

9.82
[0.00]

0.78
[0.54]

1.23
[0.30]

0.47
[0.49]

8.03
[0.01]

1.20
[0.28]

0.00
[0.98]

0.02
[0.88]

0.86
[0.49]

5.38
[0.00]

2.31
[0.06]

2.97
[0.02]

0.35
[0.85]

0.35
[0.56]

1.22
[0.27]

0.43
[0.51]

0.20
[0.65]

0.07
[0.79]

Notes: Upper part: coefficients of the error-correction terms in the equation for the variable in the first row. Ratio of coefficient and respective asymptotic standard error in parentheses. Middle part: The test on weak exogeneity is a likelihood ratio test of zero restrictions on α. Weak exogeneity is rejected if the p-value (in brackets) is smaller than 0.05. Lower part: diagnostic tests. JB denotes the Jarque-Bera test for normality, LM(k) the Lagrange multiplier test for serial correlation of the residuals (k lagged residuals included), ARCH(k) the Lagrange multiplier test for autoregressive conditional heteroskedasticity, and RESET(1) the Regression Spec2 ification Error Test considering the second powers of the fitted values from the original regression, R is the adjusted sample multiple correlation coefficient.

from the level representation: xt = µt + A1 xt−1 + A2 xt−2 + ut , (37)

with A1 = Γ1 + Π + I5 and A2 = −Γ1 . Because A1 and A2 are calculated from the VECM representation, the cointegration restrictions and the overidentifying restrictions are imposed on the level coefficients. Now, the impulse responses and their asymptotic standard errors as well as the forecast error variance decompositions can be calculated, see L¨ tkepohl u (1993, Chapter 11). Not all 25 impulse responses are discussed here, only the reaction of the money stock and the monetary base to innovations are of interest here. Figure 3 shows the generalized impulse responses, which do not depend on the ordering of the variables, see Pesaran and Shin (1998). The forecast error variance decompositions in figure 4 confirm that innovations in the monetary base have only a weak impact on the money stock but 17

that innovations in the money stock have a considerable impact on the monetary base. The largest impact on both variables have innovations in the short-term interest rate. Insert figabout The economic scenario can now be described as follows: the interest rates seem to ures 3 and be exogenous with respect to money stock and monetary base. This is supported by tests 4 for weak exogeneity and by the impulse responses of st and t to innovations in mt and here.

ht , which are not significant (not depicted here). Stable demand functions for the money stock and the monetary base exist, in which interest rates play a significant role. Therefore, it can be supposed that the Bundesbank has influenced money stock and monetary base by controlling the short-term interest rate. A stable relationship between money stock and monetary base does also exist. However, the money multiplier approach is strongly rejected. The monetary base adjusts in direction of the equilibrium between these two variables but the money stock does not. Similar results are reported by Brand (2001) who estimates a state space model for interest rates, bank reserves, and the money stock. He concludes that (p. 114 f.) “it would be misleading to view the money supply process in terms of a moneymultiplier model, since interest rates and money are exogenous to bank reserves and not vice versa.”

5 Conclusions
A model of the money-creating sector with endogenous money has been developed. In this model, money equals credit, and the monetary base is determined by the profit-maximizing behavior of commercial banks. The implications of the theoretical model have been tested in the framework of a cointegrated vector autoregressive model. Strong empirical evidence against the money multiplier approach has been found: A stable relationship between the monetary base and the money stock can be specified, but the nominal money stock does not adjust if deviations from this long-run relation occur; the adjustment is done by the monetary base instead. Furthermore, the required reserve rate has not the negative impact on the money stock that is predicted from the money multiplier approach. On the other hand, the empirical evidence is very much in line with an industrial organization style model of the money creating sector. The money stock and the monetary base are determined endogenously after the central bank has set the money market interest rate. While the model of the money creating sector seems to be a better description of the money supply process in Germany than the money multiplier approach, it has still some shortcomings. The money stock is simply set equal to the quantity of loans, which are only one item of the counterparts of M3. There are also other important counterparts like net capital formation, for example, which are neglected here. The main conclusion of this analysis is therefore that the Bundesbank has been able to

18

influence the money stock M3 via interest rate changes to a considerable extent but that the standard textbook money multiplier approach is not appropriate to describe how the Bundesbank has affected the development of M3. Because a stable money demand relation can be specified for the period of monetary targeting in Germany it is reasonable to suppose like for example Brand (2001) that the Bundesbank followed a policy of indirect monetary targeting by changing money market conditions.

19

Data Appendix
M3: End of month money stock M3 (currency in use plus sight deposits of domestic nonbanks at domestic banks in Germany plus time deposits for less than four years of domestic non-banks at domestic banks plus savings deposits at three months’ notice of domestic non-banks at domestic banks in Germany) in billions of DM, seasonally unadjusted. Monthly data (TU0800) from the Compact Disc Deutsche Bundesbank (1998a), continued with data from the monthly bulletin of the Deutsche Bundesbank, table II.2. 1975:01-1990:5 West Germany, and 1990:06-1998:12 Germany, not adjusted for German unification. Quarterly data are end of quarter stocks. Monetary base: sum of currency in use (TU0048), required and excess reserves (TU0062), liabilities of the Deutsche Bundesbank against domestic banks (TU0084) and cash of banks (OU0312), in billions of DM, seasonally unadjusted. Monthly data from the Compact Disc Deutsche Bundesbank (1998a), continued with data from the monthly bulletin of the Deutsche Bundesbank, tables II.2., III.2 and IV.1. Quarterly data are end of quarter stocks. Nominal GDP: Gross domestic product in current prices, in billions of DM, seasonally unadjusted. Quarterly data (WH12011N) for 1975:01-1990:02, West Germany, from Deutsches Institut f¨ r Wirtschaftsforschung (DIW) Berlin (DIW-statfinder: http:// u www.diw-berlin.de) continued with GDP for Germany (GH12011N). Short-term interest rate: Daily money market interest rate, Frankfurt/Main, monthly averages, fractions, monthly data (SU0101) from the Compact Disc Deutsche Bundesbank (1998a), continued with data from the monthly bulletin, table VI.4. Quarterly data are the respective values of the last month in a quarter. Long-term interest rate: Yields on bonds outstanding issued by residents, monthly averages, fractions, monthly data (WU0017) from the Compact Disc Deutsche Bundesbank (1998a), continued with data from the monthly bulletin, table VII.5. Quarterly data are the respective values of the last month in a quarter. Average required reserve rate: Ratio of required reserves (IU3006) and reserve base of banks subject to reserve requirements (IU3156), monthly data from the Compact Disc Deutsche Bundesbank (1998a), continued with data from the monthly bulletin of the Deutsche Bundesbank, table V.2. Quarterly data are the respective values of the last month in a quarter.

20

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Angeloni, I., A. Kashyap, B. Mojon, D. Terlizzese (2002), Monetary transmission in the Euro area: Where do we stand?, Working Paper 114, European Central Bank, Frankfurt/Main. Artis, M. J., M. K. Lewis (1990), Money supply and demand, in: Bandyopadhyay, T., S. Ghatak (Eds.), Current issues in monetary economics, Hemel Hempstead: Harvester Wheatsheaf, pp. 1–62. Baltensperger, E. (1980), Alternative approaches to the theory of the banking firm. Journal of Monetary Economics, Vol. 6, pp. 1–37. Baltensperger, E. (1998), Geldpolitik bei wachsender Integration (1976-1996), in: Deutsche Bundesbank (1998b), S. 475–559. Bhattacharya, S., A. V. Thakor (1993), Contemporary banking theory. Journal of Financial Intermediation, Vol. 3, pp. 2–50. Bofinger, P. (2001), Monetary policy: goals, institutions, strategies, and instruments, Oxford: Oxford University Press. Brand, C. (2001), Money stock control and inflation targeting in Germany: a state space modelling approach to the Bundesbank’s operating procedures and intermediate strategy, Heidelberg: Physica. ¨ Br¨ ggemann, I. (2001), Zum geldpolitischen Ubertragungsmechanismus in Deutschland. u Eine Analyse im Vektorfehlerkorrekturmodell, Aachen: Shaker. Dermine, J. (1986), Deposit rates, credit rates and bank capital. The Monti-Klein model revisited. Journal of Banking and Finance, Vol. 10, pp. 99–114. Desai, M. (1992), Endogenous and exogenous money, in: Newman, P. K. (Ed.), The new Palgrave dictionary of money and finance, London: Macmillan, pp. 762–764. Deutsche Bundesbank (1995), Die Geldpolitik der Bundesbank, Frankfurt/Main: Deutsche Bundesbank. Deutsche Bundesbank (1998a), F¨ nfzig Jahre Deutsche Mark. Monet¨ re Statistiken 1947u a 1998 auf CD-ROM, M¨ nchen: Beck. u Deutsche Bundesbank (Hrsg.) (1998b), F¨ nfzig Jahre Deutsche Mark: Notenbank und u W¨ hrung in Deutschland seit 1948, M¨ nchen: Beck. a u Dornbusch, R., S. Fischer (1994), Macroeconomics, sixth edition , New York: McGrawHill. Ericsson, N. R., D. F. Hendry, G. E. Mizon (1998), Exogeneity, cointegration, and economic policy analysis. Journal of Economic Dynamics & Control, Vol. 16, pp. 370–387. European Central Bank (1999a), The stability-oriented monetary policy strategy of the Eurosystem. Monthly Bulletin, January, pp. 39–50. European Central Bank (1999b), Euro area monetary aggregates and their role in the Eu-

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rosystem’s monetary policy strategy. Monthly Bulletin, February, pp. 29–46. Freixas, X., J.-C. Rochet (1997), Microeconomics of banking, Cambridge: MIT Press. Gebauer, W. (Ed.) (1993), Foundations of European Central Bank policy, Heidelberg: Physica. G¨ th, W. (1994), Markt- und Preistheorie, Berlin: Springer. u Harbo, I., S. Johansen, B. Nielsen, A. Rahbek (1998), Asymptotic inference on cointegrating rank in partial systems. Journal of Economic Dynamics & Control, Vol. 16(4), pp. 388– 399. Jarchow, H.-J. (1998), Theorie und Politik des Geldes I, Zehnte Auflage , G¨ ttingen: Vano denhoek & Ruprecht. Johansen, S. (1995), Likelihood-based inference in cointegrated vector autoregressive models, New York: Oxford University Press. Johansen, S., K. Juselius (1994), Identification of the long-run and the short-run structure. An application to the ISLM model. Journal of Econometrics, Vol. 63, pp. 7–36. Klein, M. A. (1971), A theory of the banking firm. Journal of Money, Credit, and Banking, Vol. 3, pp. 205–218. Lanne, M., H. L¨ tkepohl, P. Saikkonen (2002), Comparison of Unit Root Tests for Time u Series with Level Shifts. Journal of Time Series Analysis, forthcoming. Leschke, M., T. Polleit (1997), Zur Validit¨ t der M3-Konzeption der Deutschen Bundesbank. a Konjunkturpolitik, Vol. 43, pp. 16–42. L¨ tkepohl, H. (1993), Introduction to multiple times series analysis, second edition , Berlin: u Springer. L¨ tkepohl, H. (2001), Vector autoregressions, in: Baltagi, B. (Ed.), Companion to theoretiu cal econometrics, chap. 32, Oxford: Blackwell, pp. 678–699. L¨ tkepohl, H., J. Wolters (2001), The transmission of German monetary policy in the preu Euro period, Working Paper 2001-87, SFB 373, Humboldt-Universit¨ t zu Berlin. a Meltzer, A. H. (1969), Money, intermediation, and growth. Journal of Economic Literature, Vol. 7, pp. 27–56. Meltzer, A. H. (1995), Monetary, credit and (other) transmission processes: a monetarist perspective. Journal of Economic Perspectives, Vol. 9(4), pp. 49–72. Monti, M. (1972), Deposit, credit and interest rate determination under alternative bank objective functions, in: Shell, K., G. P. Szeg¨ (Eds.), Mathematical methods in investment o and finance, Amsterdam: North-Holland, pp. 430–454. M¨ ller, M. (1993), Endogenous money and interest rates in Germany, in: Gebauer (1993), u pp. 35–48. M¨ ller, M. (1998), Endogenit¨ t des Geldes: Eine Untersuchung zum Beitrag des Krediu a tes zur Endogenit¨ t des Geldes am Beispiel der Bundesrepublik Deutschland, Frankfurt: a 22

Haag und Herchen. Nautz, D. (1998), Wie brauchbar sind Multiplikatorprognosen f¨ r die Geldmengensteueu rung der Bundesbank? Kredit und Kapital, pp. 171–189. Pesaran, H. H., Y. Shin (1998), Generalized impulse response analysis in linear multivariate models. Economics Letters, Vol. 58, pp. 17–29. Prisman, E. Z., M. B. Slovin, M. E. Sushka (1986), A general model of the banking firm under conditions of monopoly, uncertainty, and recourse. Journal of Monetary Economics, Vol. 17, pp. 293–304. Rasche, R. H. (1993), Monetary policy and the money supply process, in: Fratianni, M., D. Salvatore (Eds.), Monetary policy in developed economies, Amsterdam: Elsevier, pp. 25–54. Santomero, A. M. (1984), Modeling the banking firm. Journal of Money, Credit, and Banking, Vol. 16, pp. 576–602. Tobin, J. (1967), Commercial banks as creators of money, in: Hester, D. D., J. Tobin (Eds.), Financial markets and economic activity, New York: Wiley, pp. 1–11, reprinted from Carson, D. (Ed.) Banking and monetary studies. Homewood: Richard D. Irwin, 1963. von Hagen, J. (1998), Geldpolitik auf neuen Wegen, in: Deutsche Bundesbank (1998b), S. 439–473. Walsh, C. E. (1998), Monetary theory and policy, Cambridge: MIT Press. Willms, M. (1993), The money supply approach: empirical evidence for Germany, in: Gebauer (1993), pp. 11–34. Wolters, J., T. Ter¨ svirta, H. L¨ tkepohl (1998), Modeling the demand for M3 in the unified a u Germany. The Review of Economics and Statistics, Vol. 80, pp. 399–409. Yanelle, M.-O. (1988), On the theory of intermediation, Dissertation, Rheinische FriedrichWilhelms-Universit¨ t, Bonn. a Yanelle, M.-O. (1989), The strategic analysis of intermediation. European Economic Review, Vol. 33, pp. 294–301.

Dr. Oliver Holtem¨ ller, Humboldt-Universit¨ t zu Berlin, Wirtschaftswissenschaftliche Fakult¨ t, o a a ¨ Sonderforschungsbereich 373, c/o Freie Universit¨ t Berlin, Institut f¨ r Statistik und Okonomea u trie, Boltzmannstr. 20, D-14195 Berlin, phone: +49(0)30-838-56358, fax: +49(0)30-838-54142, EMail: oh@holtem.de.

23

Figure 1: Money Multiplier, Germany, 1975-1998
7.5 7.0 6.5 6.0 5.5 5.0 4.5 75
Notes: Money Multiplier mm =
M H

80

85

90

95

, where M is the money stock M3 and H is the monetary base.

Figure 2: Money Growth Rate and Monetary Target in Germany

10 8 6 4 2

75

77

79

81

83

85

87

89

91

93

95

97

Notes: Thick line: Money growth rate in %, shaded area: announced target (point target from 1975 to 1978, and in 1989, other years: upper and lower bound). From 1975 to 1987, the money stock under consideration has been central bank money, from 1988 to 1998, M3. Up to the complete year 1990, the targets and the realized growth rates are for West Germany. From 1991 on, the targets and the realized growth rates are for united Germany. The data are taken from Leschke and Polleit (1997), and from the monthly bulletin of the Deutsche Bundesbank.

Figure 3: Generalized Impulse Responses of Money Stock and Monetary Base

0.02 0.01 0.00 0.01 2 0.02 0.01 0.00 0.01 2 0.02 0.01 0.00 0.01 2 0.02 0.01 0.00 0.01 2 4 4 4 4

y

m

0.02 0.01 0.00 0.01

y

h

6 s

8 10 12 14 m 0.02 0.01 0.00 0.01

2

4

6 s

8 10 12 14 h

6 {

8 10 12 14 m 0.02 0.01 0.00 0.01

2

4

6 {

8 10 12 14 h

6 h

8 10 12 14 m 0.02 0.01 0.00 0.01

2

4

6 m

8 10 12 14 h

6

8 10 12 14

2

4

6

8 10 12 14

Notes: Generalized impulse responses of money stock (m) and monetary base (h) to innovations in income (y), short-term interest rate (s), and long-term interest rate ( ), calculated from the level representation that is recovered from the VECM. Dashed lines indicate ± 2 asymptotic standard errors.

Figure 4: Forecast Error Variance Decompositions for Money Stock and Monetary Base
Money Stock Monetary Base

1.00 0.80 0.60 0.40 0.20 4

1.00 0.80 0.60 0.40 0.20

8 y 12

16 s {

4

8 h m

12

16

Notes: Generalized forecast error variance decompositions of money stock (m) and monetary base (h), calculated from the level representation that is recovered from the VECM. For m, the upper dark layer depicts the impact of h, and for h, the upper dark layer depicts the impact of m.