Since the seminal works of Nelson and Plosser (1982), who have shown
that relevant macroeconomic variables exhibit stochastic trends
and are only stationary after differencing, and
Engle and Granger (1987), who introduced the concept of
cointegration, the (vector) error correction model, (V)ECM, is the
dominant econometric framework for money demand analysis. If a
certain set of conditions about the number of cointegration
relations and exogeneity properties is met, the following single
equation error correction model (SE-ECM) can be used to estimate
money demand functions:
In practice, the number of cointegration relations and the exogeneity of certain variables cannot be considered as known. Therefore, the VECM is often applied. In this framework, all variables are assumed to be endogenous a priori, and the imposition of a certain cointegration rank can be justified by statistical tests. The standard VECM is obtained from a vector autoregressive (VAR) model:
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(11.8) |
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(11.9) |
The cointegration framework is only appropriate if the relevant variables are actually integrated. This can be tested using unit root tests. When no unit roots are found, traditional econometric methods can by applied.
We use quarterly data from 1990:1 until 2002:3 for our empirical
analysis. The data is not seasonally adjusted and taken from
Datastream (gross national product at 1993 prices and
long-term interest rate
) and from Bank Indonesia (money stock
M2
and consumer price index
). In the following, logarithms
of the respective variables are indicated by small letters, and
denotes logarithmic real balances. The data is
depicted in Figure 11.1.
In the first step, we analyze the
stochastic properties of the variables. Table
11.1 presents the results of unit root tests for
logarithmic real balances , logarithmic real GNP
,
logarithmic price level
, and logarithmic long-term interest
rate
. Note that the log interest rate is used here
while in the previous section the level of the interest rate has
been used. Whether interest rates should be included in logarithms
or in levels is mainly an empirical question.
Variable | Deterministic terms | Lags | Test stat. | 1/5/10% CV |
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c, t, s, P89c (98:3) | 2 |
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-4.75 / -4.44 / -4.18 |
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c, t, s, P89c (98:1) | 0 |
![]() |
-4.75 / -4.44 / -4.18 |
![]() |
c, t, s, P89c (98:1) | 2 |
![]() |
-4.75 / -4.44 / -4.18 |
![]() |
c, s | 2 |
![]() |
-3.57 / -2.92 / -2.60 |
Because the time series graphs show that there seem to be structural breaks in real money, GNP and price level, we allow for the possibility of a mean shift and a change in the slope of a linear trend in the augmented Dickey-Fuller test regression. This corresponds to model (c) in Perron (1989), where the critical values for this type of test are tabulated. In the unit root test for the interest rate, only a constant is considered. According to the test results, real money, real GNP and price level are trend-stationary, that is they do not exhibit a unit root, and the interest rate is also stationary. These results are quite stable with respect to the lag length specification. The result of trend-stationarity is also supported by visual inspection of a fitted trend and the corresponding trend deviations, see Figure 11.2. In the case of real money, the change in the slope of the linear trend is not significant.
Now, let us denote centered seasonal dummies , a step dummy switching from zero
to one in the respective quarter
, and an impulse dummy having value one only in the
respective quarter
. Indonesian money demand is then estimated by OLS using the reduced form
equation (11.4) (
- and
-values are in round and square parantheses,
respectively):
The implied income elasticity of money demand is 0.47/(1-0.53) = 1 and the
interest rate elasticity is -0.13/(1-0.53) = -0.28. These are quite reasonable magnitudes.
Equation (11.10) can be transformed into the following error correction representation:
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|
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(11.10) |
Stability tests for the real money demand equation (11.10)
are depicted in Figure 11.3. The CUSUM of squares test
indicates some instability at the time of the Asian crises,
and the coefficients of lagged real money and GNP seem to change
slightly after the crisis. A possibility to allow for a change in
these coefficients from 1998 on is to introduce two additional
right-hand-side variables: lagged real money multiplied by the
step dummy and GNP multiplied by
.
Initially, we have also included a corresponding term for the interest
rate. The coefficient is negative (-0.04) but not significant (
-value: 0.29),
such that we excluded the term from the regression equation.
The respective
coefficients for the period 1998:3-2002:3 can be obtained by
summing the coefficients of lagged real money and lagged real
money times step dummy and of GNP and GNP times step dummy,
respectively. This reveals that the income elasticity stays
approximately constant (0.28/(1-0.70)=0.93) until 1998:02 and
((0.28+0.29)/(1-0.70+0.32)=0.92) from 1998:3 to 2002:3 and that the
interest rate elasticity declines in the second half of the sample
from -0.13/(1-0.70)=-0.43 to -0.13/(1-0.79+0.32)=-0.21:
It can be concluded that Indonesian money demand has been
surprisingly stable throughout and after the Asian crisis given
that the Cusum of squares test indicates only minor stability
problems. A shift in the constant term and two impulse dummies
that correct for the different break points in real money and real
output are sufficient to yield a relatively stable money demand
function with an income elasticity of one and an interest rate
elasticity of -0.28. However, a more flexible specification shows
that the adjustment coefficient increases and that the
interest rate elasticity decreases after the Asian crisis.
In the next section, we analyze if these results are
supported by a fuzzy clustering technique.