Download The Demand for Money in Switzerland 1936±1995

The Demand for Money in Switzerland 1936 ±1995
Petra Gerlach-Kristen *
1. INTRODUCTION
Switzerland has gone through a range of monetary regimes in the last two centuries. As a
member of the Latin Monetary Union,1 which had been founded in 1865, the country
had adhered to the gold standard since 1878. Due to World War I, the gold standard collapsed, but parities were reestablished after the end of the war, and a de-facto gold standard was fully operational from 1929 onwards. In the aftermath of the Depression, the
Swiss Franc rate was devalued in 1937 (Yeager, 1976, and Schmid, 1969). At the end
of World War II, Switzerland joined the Bretton Woods system of fixed exchange rates
and remained on fixed rates until January 1973. Up to that date, thus, the Swiss Franc
had mainly had a fixed exchange rate. In 1973 the exchange rate was let float and M1
targeting was introduced. This regime came to an end in 1978 when, after a prolonged
and, in the event, sharp appreciation of the Swiss Franc the Swiss National Bank (SNB)
adopted an exchange rate objective. Switzerland returned to flexible exchange rates already in 1979, when the SNB started to target the monetary base, MB. In 1988, the base
money demand became temporarily unreliable as an indicator since the Swiss Interbank
Clearing system and new bank cash-reserve requirements were introduced, so that instead, short-term interest rates were used to guide monetary policy (Rich, 1996). There
was a return to the MB targeting system, which lasted until late 1999, when the SNB announced a policy framework which increasingly emphasized inflation.
Beside the numerous changes in the monetary policy regime, a second interesting feature is that Switzerland has historically been a financial center with comparatively lax
regulations of capital flows, which exposes the demand for money to external shocks.
Certainly, events like the World Wars and the expectation of Switzerland's departure
from the Bretton Woods system might have triggered large capital inflows, while its
abandonment of the gold standard and financial deregulation elsewhere in the world in
the 1980 s could have caused outflows. One obvious question thus is what impact these
events had on the stability of Swiss money demand. In particular, did the change from a
fixed to a flexible exchange-rate system in 1973 lead to a large change in the demand for
money?
*
University of Basel, WWZ, Petersgraben 51, CH-4001 Basel. E-mail: [email protected].
I thank Peter Kugler, Stefan Gerlach, Carlos Lenz, seminar participants at the University of Basel
and an anonymous referee for helpful comments.
1.
Together with France, Belgium, Italy and later Greece.
Schweiz. Zeitschrift für Volkswirtschaft und Statistik
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Surprisingly, these questions have not been addressed in great detail in the literature.
An exception are Heri and Kugler (1988), who consider how the economy reacted to
monetary disequilibria under the two exchange-rate systems and who find different adjustment patterns. Other papers using data covering the 1973 break are Lambelet and
Nilles (1987) and Fischer and Peytrignet (1990), who do however not focus on the
shift in exchange regime, and Heri (1988) and Kohli (1989), who examine the determinants of money supply under and after the fixed exchange-rate system.
The present paper studies the stability of the demand for money in Switzerland from
1938 to 1990. The main finding is that there is little evidence of instability in the moneydemand function.
The paper is organized as follows. Section 2 gives a selective review of the literature
on Swiss money demand. We describe the main themes in the literature and summarize
the parameter estimates. Section 3 describes and compares the different data sets. Section 4 performs Augmented Dickey-Fuller tests for stationarity and Johansen tests for
cointegration and develops an error-correction model of money demand. In Section 5
we sum up and conclude.
2. REVIEW OF THE LITERATURE
As noted above, the demand for money in Switzerland has been studied by a number of
authors. More than half of the studies reviewed here start in 1973 or later, that is after
the end of the fixed exchange-rate system. Schelbert-Syfrig (1967) is apparently the
first comprehensive study on money demand in Switzerland, and, using data from 1931
to 1963, it finds a stable demand function. Rich (1997) provides a detailed description of
the conduct of monetary policy from the 1970 s onwards. The paper considers a model
with lagged effects of monetary policy and derives feedback rules for optimal policy.
Lags are also treated in Rötheli (1988 and 1990), who uses a Pascal specification and,
assuming that money is exogenous, investigates its impact on inflation. Heri (1988) and
Kohli (1989) argue that while the exogeneity approach is appropriate for the period of
monetary targeting, under exchange or interest-rate targeting money is endogenous.
Fischer (1993) examines whether money in Switzerland is exogenous and cannot confirm this hypothesis. Fischer and Peytrignet (1990) treat money as endogenous and
find that M3 is not a superior measure of money. Peytrignet and Stahel (1998) compare the performance of short-run models of money growth (using M2) and inflation
(using M3) and conclude that the model involving M3 appears more stable.
Heri and Kugler (1988) perform a cointegration analysis to assess the mechanisms
of adjustment to monetary disequilibria under fixed and floating exchange rates and
show that in the former case money supply, and in the latter interest rates, react to disequilibria. Heri (1988) studies whether money behaves as a buffer stock, which would
make money demand statistically unstable, and finds evidence for this. Fischer and
Peytrignet (1991) test whether parameter instability in the Swiss money-demand func-
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THE DEMAND FOR MONEY IN SWITZERLAND 1936±1995
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tion is due to mis-specification caused by shifting monetary regimes as suggested by the
Lucas critique. They reject this hypothesis. Chowdhury (1995) specifies a money-demand function which includes the exchange rate and a foreign interest rate in order to
appropriately model Switzerland as a small open economy. Dueker and Fischer
(1996) model Swiss monetary policy with a Markov switching model, which also includes
the exchange rate.
Table 1 summarizes sample period, data and empirical money demand findings of the
papers referred to above as well as of Lambelet and Nilles (1987) and Boswijk and
Urbain (1997). In the last two columns, we tabulate the estimated income and interestrate elasticities. The lowest income elasticity obtained is 0.12 from Rötheli (1990) using
M1; the highest estimate is 1.80 in Fischer and Peytrignet (1990) using M3. In general, broader monetary aggregates seem to expand faster as income grows and thus to
have higher income elasticities.2 Regarding the interest-rate elasticities, standard interest-rate elasticities (in the regression, the logarithm of the interest rate enters) and
semi-elasticities (ªsemiº since the interest rate is not in logarithms, while money is; denoted with superscript ªsº in Table 1) are presented. We distinguish between the return
on non-monetary assets (measured by bond yields) and the return on money (measured
by deposit rates). The former captures the cost of holding money, the latter the return on
broad monetary aggregates. The bond-yield elasticities range from 0.81 (Peytrignet
and Stahel, 1998) to 0.31 (Fischer and Peytrignet, 1990), while the deposit elasticities go from 0.31 to 0.26 (both in Chowdhury, 1995). The bond yield semi-elasticities lie between 0.15 (Heri and Kugler, 1988) and 0.01 (both Fischer, 1993, and
Heri and Kugler, 1988), and the deposit semi-elasticities range from 0.15 (Kohli,
1989) to 0.01 (Heri, 1988, and Fischer, 1993). Heri's (1988) and Heri and Kugler's
(1988) estimates of income elasticities and interest rate semi-elasticities differ across exchange-rate systems.
Overall, the results indicate that income increases the demand for real money in Switzerland more than proportionally, while interest rates have a depressing impact on real
money demand.
2.
This may be attributed to money-multiplier effects.
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Table 1 : Selection of literature on Swiss money demand (ordered chronologically)
Author(s)
Sample period
Income elasticities,
money definitions
Interest elasticities,
interest definitions
Schlebert-Syfrig (1967)
1931±1963, Q
0.92
M broad
0.70
bond
Lambelet and Nilles (1987)
1959 ±1984, M
0.92 to 1.06
M narrow
0.08 to 0.05 s bond
0.07 to 0.03 s deposit
Heri (1988)
1965 ±1984, Q
0.96
M1
0.060 s bond
0.04 to 0.01 s deposit
Heri and Kugler (1988)
1965 ±1987, Q
0.48 to 1.12*
M1
Rötheli (1988)
1973 ±1986, Q
0.80 to 1.55
MB, M1
0.06 to 0.02 s
deposit
Kohli (1989)
1959 ±1987, A
1.00 to 1.03
MB
0.15 to 0.06 s
deposit
Fischer and Peytrignet (1990)
1967±1989, Q
1.55 ±1.80
M3
Rötheli (1990)
1973 ±1987, Q
0.12
M1
Fischer and Peytrignet (1991)
1973 ±1989, Q
1.06
M1 + savings deposits
Fischer (1993)
1973 ±1987, Q
0.19 ± 0.23
MB, M1
0.02 to 0.01 s
deposit
Chowdhury (1995)
1973 ±1991, Q
0.88 ± 0.94
MB, M1
0.31 to 0.26
deposit
Dueker and Fischer (1996)
1974 ±1987, M
±
MB
Boswijk and Urbain (1997)
1973 ±1989, Q
1.38
M1 + savings deposits
0.07s bond
0.03 s deposit
Peytrignet and Stahel (1998)
1977±1987, Q
1.039 ±1.685
M2, M3
0.809 to 0.365
bond
0.15 to
0.01 s bond
0.31
bond
0.69 bond
0.05 s deposit
0.51
bond
±
±
Note: A denotes annual, Q quarterly, and M monthly data. MB, M1, and M3 stand for the common
money aggregate definitions, while M narrow and M broad correspond to paper-specific definitions.
The superscript s denotes semi-elasticities. * Heri and Kugler (1988) use nominal income.
3. DATA
We use annual data from 1936 to 1995 to study the demand for money: the period 1936
to 1990 is used for estimation, while the last five years of data are excluded for out-ofsample forecasts. Data on Swiss money demand is available for a longer period of time
(from 1930 on), but as a consequence of the Great Depression, money growth was very
volatile in the early 1930 s. The movements in real money are likely to be due to the economic turmoil in the period rather than to the more traditional factors describing money
demand. We therefore choose to exclude the years 1930 to 1935 from our analysis. We
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THE DEMAND FOR MONEY IN SWITZERLAND 1936±1995
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consider six data sources: Bordo and Jonung (in the following BJ),3 Grüebler (1958,
G), Mitchell (1998, M), the SNB data base …SNB†, the Historical Statistics of Switzerland (1996, HSS) and Homer and Sylla (1991, HS). Graphs 1 and 2 display as an illustration the growth rates of the money supply from M and BJ and the changes of bond
yields from HSS and HS. There are noticeable differences between the series.
Graph 1: Data series in comparison: money growth
Note: Money supply growth from M and BJ.
Even though divergences between the series are readily apparent, correlations are relatively high, ranging from 0.36 to 1. Table 2 shows correlations of the first differences of
the natural logarithms of money supply m from SNB, BJ, M and G, income y from BJ
and M, the price level p from BJ, M and the GDP deflator defl from SNB, and the correlations of the first differences of the bond yields i from BJ, HSS and HS, and the deposit and saving rates idep from HSS.
3.
The data stem from the Bordo-Jonung data base. See Bergman, Bordo, and Jonung (1998) for
a description.
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Graph 2: Data series in comparison: change in bond yields
Note: Changes in bond yields from HSS and HS.
For estimation, we use the data by BJ for income (net national income), prices and the
bond yields. For the money supply, the BJ data from 1936 to 1949 are combined with the
SNB data from 1950, the first data point available, to 1995. Both series consist of M3 in
the periods considered.4 Given the broad definition of money, which includes deposits,
we expect an income elasticity above unity and a positive deposit elasticity. The interest
rate on deposits is from HHS. Finally, in order to check for the influence of capital flows
on the short-run growth rate of real money, we make use of the return on long-term US
government securities from the Federal Reserve Bank of St Louis data service FRED in
Section 4.3.5
4.
5.
The only exception is the data point for 1949, which represents money plus quasi-money.
The data are available on request.
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Table 2: Correlations (sample period, where available, 1936 to 1995)
Variables
Correlations
…mSNB †; …mBJ †
0.512
…mSNB †; …mG †
0.361
…mSNB †; …mM †
0.637
…mBJ †; …mG †
0.922
…mBJ †; …mM †
0.462
…mG †; …mM †
0.702
…yBJ †; …yM †
0.991
…pBJ †; …pM †
0.994
…pBJ †; …deflSNB †
0.939
…pM †; …deflSNB †
0.941
…iBJ †; …iHSS †
0.485
…iBJ †; …iHS †
1
…iHSS †; …iHS †
0.485
dep2
…idep1
HSS †; …iHSS †
0.897
Note: Correlations between the differences of the logarithms of money, income, and prices, and between the differences of the bond yields …i† and deposit interest rate …idep † for the overlapping sample
periods. idep1 denotes the deposit rate, idep2 the savings rate, defl the GDP deflator and ˆ …1 L† the
difference operator. Data series from SNB; BJ; G; M; HS, and HSS.
4. ESTIMATING MONEY DEMAND
4.1 Testing for Unit Roots
Inspection of the data suggests that the different time series might have a unit root.
Since correct inference depends on the stationarity of the data, we perform a unit root
test for money supply, income, prices, real money, the bond yield, the deposit rate, the
Swiss interest-rate spread, which is defined as the bond yield minus the deposit rate and
which for broad monetary aggregates captures the cost of holding money, and the spread
between Swiss and US long-term interest rates.6 Table 3 displays the results of the Augmented Dickey-Fuller tests (including a constant and a time trend) for the sample period 1936 to 1995. The decision on the lag length was taken for each variable individually:
starting with a second-order lag specification, we performed a t-test on the last lag. If it
was insignificant, the model was reestimated with one lag less. We show the test values
for the highest lag order which could not be rejected. The money supply, prices, real
6.
The Swiss-US interest-rate spread is used in Section 4.3
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money, income, the bond yield7, and the deposit interest rate appear to have a unit root
when expressed in level form, while for the interest-rate spread the hypothesis of a unit
root is rejected. Furthermore, the change in the spread between Swiss and US long-term
interest rates appears to have a unit root.8
Table 3: Augmented Dickey-Fuller test (sample period 1936 to 1995)
t-statistics
Level
First difference
Second difference
m
0.836
5.474**
6.649**
p
1.606
5.289**
7.528**
m
1.335
5.209**
6.622**
y
p
1.362
4.489**
8.315**
i
3.874*
6.710**
8.341**
idep
3.270
5.274**
7.838**
spreadCH
5.184**
8.701**
10.004**
spreadCHUS
2.352
2.577
11.770**
Note: The logarithms of money, prices, and income, and the levels of the bond yields, the deposit interest rate, and the Swiss-US interest-rate spread are used. m p denotes real money, spreadCH the Swiss
interest-rate spread defined as i idep, and spreadCHUS the spread between the Swiss bond yields and
long-term US government securities. The test was constructed using a constant, two lags and a trend.
The test values presented are those for the highest significant lag number. * denotes significance of a
5 percent and ** of a 1 percent level.
In formulating the money-demand equation, we therefore treat all variables, with the
exception of the Swiss interest-rate spread, as integrated of order one, this is, we use
them in differenced form. The Swiss interest-rate spread enters in levels.
4.2 Cointegration
As noted in the literature review, it is not obvious which of the variables should be treated as endogenous. Endogeneity may in particular depend on the monetary regime in
operation. Although studying this matter in detail goes beyond the scope of the paper,
in this subsection we study the joint behavior of money, prices, income, and the Swiss interest rates.
Since, due to the evidence of unit roots, variables enter the analysis in differenced
7.
8.
For the bond yield, the unit root hypothesis is rejected in the one-lag formulation. However, the
first lag is significantly different from zero only in a t-test, while an F-test of the hypothesis that
the first and second lag are jointly zero is not rejected. According to this test, we thus should use
the specification without lag. The ADF test value for no lag cannot reject the hypothesis of a unit
root. We therefore treat the bond yield as displaying unit-root characteristics.
Nonetheless, in what follows, we treat this variable as integrated of order 1, since a Phillips-Perron test rejects the hypothesis of a unit root in the changes of the variable.
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form, we estimate a vector error-correction model. In order to determine the number of
cointegrating vectors, representing the long-run relations between the levels of the series,
we perform a Johansen test. However, since money, prices, income, and the time trend all
grow smoothly over time, the Johansen procedure may have difficulties in identifying the
cointegrating vector(s) in a finite sample. In order to reduce the number of variables and
thereby alleviate this problem, we make two a-priori assumptions from monetary theory.
First, we impose that the demand for money is a demand for real balances. Secondly, we
use the interest-rate spread instead of the two individual interest rates.
The smallest system without autoregressive errors has a two-lags specification.9 Table
4 shows the maximum-eigenvalue statistic and the trace statistic for the number of cointegrating vectors. Using the small-sample corrected version of the trace statistics (see
Doornik and Hendry, 1997, 225), we reject the hypothesis of no cointegrating vector
at the five percent significance level and interpret this as evidence for one cointegrating
vector.
Table 4 : Cointegration analysis, sample period 1938 to 1995
Number of cointegrating vectors
Maximum eigenvalue statistic (MES)
MES with small
sample correction
Trace statistic
(TS)
TS with small
sample correction
None
23.87
21.4
49.42**
44.31*
At least one
19.91*
17.85
25.55*
22.91
At least two
5.639
5.055
5.639
5.055
* denotes significance of a 5 percent and ** of a 1 percent level.
Estimates of the cointegrating vector and the feedback parameters from the unrestricted
system are shown in Table 5 a. The -vector contains the long-run coefficients of the
money-demand equation, while the elements of capture the short-run reaction of the
growth rates of real money, income, and the interest-rate spread to past disequilibria. Inspection of these feedback parameters shows a significant role of the Swiss interest-rate
spread in the reaction to monetary disequilibria. However, if we assume that the spread
is the only variable reacting to past level values, the resulting money demand matches
neither previous findings nor theory.10 Due to this finding, and since the literature tends
to find that it is real money growth which adapts to restore equilibrium, we proceed to
restrict the income and spread feedback parameters to zero. Further, we impose no
trend in the cointegrating vector. These restrictions are not rejected (p-value of 16.1 %)
and are shown in Table 5 b.
9.
10.
However, the system with two lags suffers from some non-normality in the errors in the equation
for the interest-rate spread. We choose to disregard this by referring to Hamilton (1994, 298),
who notes that OLS estimators of population parameters are consistent even if the innovations
are non-normal.
Specifically, the long-run interest-rate spread elasticity is positive (1.033).
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Table 5: Cointegration tests, sample period 1938 to 1995
(a) System without restrictions
m
p
y
1.000
trend
spreadCH
0.522
0.473
0.015
m
p
Standard errors of 0.013
m
y
0.004
y
spreadCH
1.661
spreadCH
loglik = 492.348
p
0.027
0.020
0.346
log j
j ˆ 16:977
(b) System with restrictions
m
p
y
1.000
trend
spreadCH
1.259
0.221
Standard errors of m
p
y
spreadCH
0.050
0.073
0.141
m
m
p
trend
Standard errors of p
0.031
y
y
spreadCH
spreadCH
loglik = 489.773
log j
j ˆ 16:889
2 …3† ˆ 5:149 ‰0:161Š
Note: The value of the likelihood function when the system is estimated without restrictions is 492.348.
The income elasticity of real money demand in Table 5 b is 1.259, which lies in the range
of previous findings. The interest-rate spread has a coefficient 0.221 and thus also
matches existing evidence.
With reference to the quantity equation, it is sometimes argued that the income elasticity should be unity. This restriction cannot be imposed on the above system (p-value
of 0.2 %). A reason for this might be that we use the consumer price index (CPI) in the
analysis. The Swiss CPI has an average annual growth rate of 3.3 percent over the period
1936 to 1995, while the GDP deflator rose by 3.7 percent on average. Thus, real money
grows more slowly when using the deflator, implying as smaller income elasticity. The
estimation with real money calculated with the GDP deflator (denoted m defl) and
the same feedback parameter restrictions as in Table 5 b cannot reject unit income elasticity and is shown in Table 6. The spread elasticity is 0.105.
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Table 6: Cointegration test with the GDP deflator, sample period 1938 to 1995
m
defl
y
1.000
1.000
spreadCH
trend
0.105
0.000
Standard errors of m
defl
y
trend
spreadCH
0.046
m
defl
Standard errors of 0.148
m
defl
0.035
y
y
spreadCH
spreadCH
loglik = 497.564
log j
j ˆ 17:157
2 …4† ˆ 5:137 ‰0:274Š
Note: The value of the likelihood function when the system is estimated without restrictions is 500.133.
As a further illustration, we re-estimate the model, using money, prices and the two interest rates separately instead of the real money and the interest-rate spread (Table 7).
The absolute size of the impact of both interest rates is restricted to be equal, the coefficient of the price level is set equal to 1. Under this configuration, income elasticity
rises trivially (to 1.265), as do the elasticities of the interest rates (-0.231 for the bond
yield, 0.231 for the deposit rate). The negative bond-yield elasticity reflects the fact that
a higher bond yield raises the opportunity cost of holding money, while the positive deposit-rate elasticity indicates that an increase in the own return on money increases the
demand for money. These elasticities are in line with theory. The p-value of the system in
Table 6 is 7.2 %, which can be interpreted as evidence that the a-priori restrictions made
in Table 5 are not contradicted by the data and thus justified.
In this section, we have thus established that the data do not reject that money demand is a demand for real balances and that it is the interest-rate spread which matters.
Moreover, the income and interest-rate spread elasticities obtained for the estimated cointegrating vector lie within the range of previous findings.
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Table 7 : Cointegration test with money, prices and the interest rates entering separately,
sample period 1938 to 1995
m
p
1.000
y
1.000
i
1.265
0.231
idep
trend
0.231
Standard errors of m
p
y
i
0.051
0.075
idep
trend
Standard errors of m
0.068
m
p
0.068
p
y
0.015
y
i
i
idep
idep
loglik = 828.572
log j
j ˆ 28:571
2 …7† ˆ 12:984 ‰0:072Š
Note: The value of the likelihood function when the system is estimated without restrictions is 835.064.
4.3 Single-Equation Estimates
Since monetary disequilibria seem to feed into the real money stock, income growth and
the interest-rate spread are weakly exogenous.11 We therefore estimate a single OLS
equation for the demand for real balances using data for 1938 to 1990. From the restricted system in Table 5 b, we construct the error-correction term as
ECt ˆ mt
pt
1:259 yt ‡ 0:221 spreadch;t :
…1†
On the right-hand side of the real money-demand growth equation, we have a constant,
real money growth lagged once and twice, income growth, the Swiss interest-rate spread
in level form, and the change of the Swiss-US interest-rate spread for t; t 1 and t 2,
the once-lagged error-correction term and a trend.12 Table 8 presents the unrestricted
equation.
11.
12.
Ericsson, Hendry and Mizon (1998) discuss the notion of weak exogeneity.
As suggested by the referee, I include the Swiss-US interest-rate spread in the short-run analysis.
I also tried to integrate it into the cointegration analysis, but this approach did not prove successful. The referee also suggested including a short-term Swiss-foreign interest-rate spread and the
exchange rate into the short-run setup, both of which, however, turned out to be insignificant in
all regressions and therefore are suppressed here.
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Table 8: Unrestricted money-demand equation, sample period 1938 to 1990
…mt
pt † ˆ
0:150 ‡ 0:651 …mt
(2.489) (3.973)
0:395 yt
( 2.245)
1
pt 1 †
1
0:187 …mt
( 1.122)
2
pt 2 † ‡ 0:272 yt
(1.667)
‡ 0:149 yt 2 0:036 spreadCH;t ‡ 0:023 spreadCH;t
(0.973)
( 3.484)
(1.253)
‡0:008 spreadCH;t
(0.601)
2
0:001 spreadCHUS;t ‡ 0:009 spreadCHUS;t
( 0.145)
(1.448)
0:014 spreadCHUS;t
( 2.439)
2
0:108 ECt
( 2.016)
R2 ˆ 0:757
F(13, 39) = 9.367 [0.000]
1
1
1
‡ 0:000 trendt ‡ "t
(0.447)
DW = 1.84
RSS = 0.023
Note: denotes the change operator (that is, ˆ …1 L†), EC the error-correction term. t-values in
parentheses. F-test shows (in [] parentheses) the probability that all coefficients jointly equal zero.
The reduced form of the money-demand equation is shown in Table 9.
Table 9: Restricted money demand-equation, sample period 1938 to 1990
…mt
pt † ˆ
0:210 ‡ 0:747 …mt
(5.448) (6.918)
‡0:011 2 spreadCHUS;t
(2.623)
R2 ˆ 0:718
F(5, 47) = 23.898 [0.000]
pt 1 †
1
1
0:502 yt
( 4.097)
0:154 ECt
( 4.671)
1
1
0:037 spreadCH;t
( 4.361)
‡ "t
DW = 1.60
RSS = 0.027
Note: denotes the change operator (that is, ˆ …1 L† and 2 ˆ …1 L†2 ), EC the error-correction
term. t-values in parentheses. F-test shows (in [] parentheses) the probability that all coefficients jointly
equal zero.
Real money growth thus appears to be significantly determined by lagged real money
growth, lagged income growth, the change in the Swiss interest-rate spread, the oncelagged change in the Swiss-US interest-rate spread change, and the lagged error-correction term, the negative coefficient of which indicates that if last period real money demand was relatively high, its growth rate today is reduced. The interest-rate spreads are
shown in a once more differenced form than in Table 8, as they each are significant for
two subsequent periods, with coefficients of similar size but opposite sign.
4.4 Diagnostic Tests
To ascertain that the money-demand equation appropriately captures the dynamics of
real balances, we perform a series of diagnostic tests on it. As a first step, we carry out a
series of tests on the errors. Table 10 shows that the hypotheses of no autocorrelation,
no autoregressive conditional heteroskedasticity, and normality cannot be rejected with
p-values of 8.8 %, 29.8 %, and 37.3 %, respectively. Homoskedasticity cannot be rejected
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PETRA GERLACH-KRISTEN
in a White test using squares (p-value 9.8 %) nor in a White test using squares and crossproducts (10.1 %). Finally, a RESET test does not reveal that the squared real money
growth rate should have been included as a right-hand variable (p-value 24.3 %).
Table 10: Test summary
Test
p-value
AR 1± 2
F(2, 45) =
2.565
[8.8 %]
ARCH 1
F(1, 45) =
1.107
[29.8 %]
Normality
2 (2) =
1.970
[37.3 %]
Xi2
F(10, 36) =
1.792
[9.8 %]
Xi Xj
F(20, 26) =
1.700
[10.1 %]
RESET
F(1, 46) =
1.400
[24.3 %]
Note: AR 1±2 tests for second order autoregression, ARCH for autoregressive conditional heteroskedasticity. Xi2 denotes a White test using squares, Xi Xj a White test using squares and cross-products.
RESET is a test for the correct number of powers.
Graph 3 depicts the one-step forecast values of the demand for real money for 1991 to
1995. The forecasts lie within the 95 % confidence band, which implies that our specification captures money demand beyond the estimation period well.
Graph 3: One-step forecast money demand, 1991 to 1995
Note: Confidence band of  two standard deviations.
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THE DEMAND FOR MONEY IN SWITZERLAND 1936±1995
549
Next, we estimate the equation step-wise. Graph 4 shows the errors of a one-period
ahead forecast (the one-step residuals), which all lie within the recursively constructed
95 % confidence band.
Graph 4: One-step residuals
Note: Confidence band of  two standard errors.
Graph 5 shows sequences of Chow tests of structural stability, with the statistics scaled
by their one-off 1 % critical values.13 The first panel of the Graph shows usual one-step
Chow test, the second breakpoint tests, and the third forecast tests.14 Under the hypothesis of no structural break, the scaled p-values should be smaller than unity for all observations: the plots indicate that this is indeed the case.
13.
14.
1 % represents the chosen significance level, ªone-offº denotes that the critical value has been
scaled to one.
The breakpoint test entails estimating the model using observations 1 to t 1, re-estimating the
model using observations t to T, and comparing the residual sums of squares. The forecast test entails estimating the model using observations 1 to M, re-estimating the model using observations
1 to t …t > M† and comparing the residual sums of squares.
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PETRA GERLACH-KRISTEN
Graph 5 : Chow tests
Note: Chow-test values scaled by their one-off 1 % critical values.
A final test concerns the stability of the individual parameters. Graph 6 shows the recursive coefficient estimates within their confidence bands. The coefficients do not significantly vary as new data is added and thus appear stable.
Overall, the money-demand equation for Switzerland passes the usual tests rather
easily and thus seems to fit the data quite well.
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THE DEMAND FOR MONEY IN SWITZERLAND 1936±1995
551
Graph 6: Recursive coefficients
Note: Confidence bands of  two parameter standard errors.
5. CONCLUSIONS
This paper has studied the demand for money in Switzerland using annual data from
1936 to 1995. While there has been a number of studies on Swiss money demand, no use
had been made before of the available long data series. We start with a vector error-correction system of money supply (M3), prices, income, the bond yield, and the deposit
interest rate, for which we impose real money and the interest-rate spread in order to
reduce the number of variables. One cointegrating vector is found. The feedback parameters can be restricted so that real money adapts to disequilibria. We obtain an income
elasticity of 1.259 and an interest-rate spread elasticity of -0.221. Using the two interest
rates separately in the system, we obtain a negative elasticity of the bond yield and a positive impact of the deposit rate, a result which should be expected given our broad definition of money. As a further variation of the model, using the GDP deflator instead of
the consumer price index, we can impose a unit income elasticity, so that the system
seems to fit the predictions made by the quantity theory. From the system using the CPI
and the interest-rate spread, we construct an error-correction term, which enters a single
money-demand equation of error-correction form. This function includes the spread be-
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PETRA GERLACH-KRISTEN
tween long-term Swiss and US interest rates. It appears stable in a series of tests and
forecasts demand well out of sample.
There are three caveats to be mentioned. First, the confidence band for the money
demand forecast is broad. The 95 % confidence band allows for a deviation of the actual
real money demand growth from the forecasted value of about five percent in both directions. For monetary policy purposes, this confidence band may prove too wide: if a
money growth of, say, three percent was to be targeted, a money demand function which
allows for swings of plus / minus five percent might render this policy impracticable. As a
second point of criticism, it has to be noted that, while central bankers are concerned
with the steering of narrow monetary aggregates, our analysis uses broad money. Even
though there seem to be regularities between broad real money demand and income
and interest rates, these relationships may not carry over to the policy variables the central bank can control. A third caveat is that the feedback parameter of real money is low
(-0.141), which implies that after a shock, adjustment happens only slowly over the coming roughly seven years. Monetary disequilibria are thus protracted.
Summarizing, we are able to identify one money-demand function for Switzerland
over the period 1938 to 1990. Neither World War II nor the change of the exchange rate
regime caused shocks large enough to trigger instability in the demand for money.
Furthermore, more subtle but nonetheless for the financial system important events as
deregulation, improvement of the interbank transaction system or changes in the reserve requirements for commercial banks do not appear to have led to significant breaks
in money demand.
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SUMMARY
This paper studies money demand in Switzerland. While the existing literature typically
analyzes post-1973 data, this study uses data covering six decades. We test for cointegration in a system incorporating money, prices, income, a bond yield and a deposit rate,
and find evidence of a single cointegrating vector which feeds into the real money stock.
Income and interest-rate elasticities lie within the range of previous findings. Furthermore, we estimate an error-correction model for the real money stock, which additionally includes the Swiss-US interest-rate spread. This model appears stable in- and outof-sample and passes a number of diagnostic tests.
ZUSAMMENFASSUNG
Dieser Artikel untersucht die Geldnachfrage in der Schweiz. Während in der bestehenden Literatur typischerweise Daten nach 1973 analysiert werden, umfasst diese Studie
sechs Jahrzehnte. In einem System bestehend aus Geld, Preisen, Einkommen, der Obligationenrendite und dem Anlagezins testen wir auf Kointegration und finden den Hinweis auf einen kointegrierenden Vektor, der die reale Geldmenge bestimmt. Einkommens- und Zinselastizitäten liegen im Bereich früherer Resultate. Wir schätzen
ausserdem ein Error-Correction-Modell für die reale Geldmenge, das zusätzlich die
schweizerisch-amerikanische Zinsdifferenz einschliesst. Dieses Modell scheint in- und
out-of-sample stabil zu sein und besteht eine Reihe von Diagnosetests.
RESUME
Cette contribution Øtudie la demande de monnaie en Suisse. Contrairement à la littØrature existante qui analyse d'habitude des donnØes apr›s 1973, cette Øtude utilise des
donnØes couvrant six dØcennies. Nous recherchons des relations de cointØgration dans
un syst›me comprenant la masse monØtaire, les prix, le revenu, le rendement des obligations et le taux d'intØr†t de dØpôts et nous trouvons qu'un seul vecteur de cointØgration
dØtermine la masse monØtaire rØelle. Les valeurs des ØlasticitØs par rapport au revenu et
au taux d'intØr†t correspondent aux dimensions trouvØes dans des Øtudes antØrieures.
En outre, nous estimons un mod›le de correction des erreurs pour la masse monØtaire
rØelle incluant la diffØrence des taux d'intØr†t suisse et amØricain comme variable additionnelle. Ce mod›le semble stable aussi bien in-sample que out-of-sample et passe une
variØtØ de tests diagnostics.
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