A.C. Arize et al. International Review of Economics and Finance 8 1999 399–420 403
the system converges to the long-run equilibrium implied by Eq. 1, with convergence being assured when l is between 0 and 21. In addition, the value of l depends on
the normalization of the cointegrating vector Arize Darrat, 1994.
3. Empirical results
3.1. The data and the unit root tests The data for this study are taken from the International Monetary Fund’s IMF
International Financial Statistics in the case of 11 countries, and the data for Taiwan
are drawn from the Taiwan Financial Statistics and Taiwan Financial Monthly. All the data used in this article are annual observations of the variables, and the estimation
period is 1961 through 1996. The sample period is determined by the availability of consistent measures of the aggregate in question.
3
For each of the 12 countries, we have more than 30 observations, so that the problems of using small samples are
arguably minimized. In addition, it is, now known from the studies by both Hakkio and Rush 1991 and Campbell and Perron 1991 that the ability of cointegration
tests to detect cointegration is a function of total sample length and not a function of data frequency. That is, using annual data over 1961–1996 is just as good as using
quarterly or monthly data over the sample period.
Data on prices Consumer Price Index, 1980 5 100, exchange rate domestic price of U.S. dollar and the narrow and broad money stock were compiled from various
issues of the IMF’s International Financial Statistics. The consumer price index of each country is used to measure inflation. The real exchange rate was created by multiplying
the U.S. consumer price index by the domestic exchange rate and then deflating by the domestic consumer price index. The proxy for foreign exchange-rate risk was
obtained from a time-varying measure of real exchange-rate volatility.
4
The U.S. lending rate is used as a proxy for the foreign interest rate. This can be justified on
the grounds following Wickens 1972. Because cointegration tests require a certain stochastic structure of the time series
involved, the first step in the estimation procedure is to determine if the variables are stationary or nonstationary in levels. The common practice is to use the augmented
Dickey-Fuller ADF test and the 90 confidence intervals for the largest autoregres- sive root. The intervals are constructed using Stock’s 1991 procedure.
However, a number of authors i.e., Perron, 1989 have pointed out that the standard ADF test is not appropriate for the variables that may have undergone structural
changes. To examine the stationarity of variables with a structural break, we use the recursive version of the Banerjee et al. 1992 test. The latter test is based on asymp-
totic-distribution theory, which treats break dates as unknown a priori. The results are given in the Appendix Table A1.
5
The null hypothesis of a unit root is tested against the alternative of stationarity and is investigated for real money balances, real GDP, the inflation rate, the official
exchange rate, foreign interest rate and foreign exchange-rate risk. The lag structures were determined on the basis of a t-test following a procedure proposed by Ng and
Perron 1995. The results in Table A1 suggest that, while it is reasonable to conclude
404 A.C. Arize et al. International Review of Economics and Finance 8 1999 399–420
that the null hypothesis of a unit root i.e., nonstationarity is accepted for the vari- ables, some caution is necessary. It is thus assumed that these series are integrated
of order one.
3.2. Structural break Given that we have I1 variables, an Ordinary Least Squares OLS equation
linking some of these variables will not be a mere spurious regression only if the I1 variables are cointegrated. A possible reason for the failure to find cointegration using
the Engle and Yoo 1987 methodology
6
may be due to structural instability in the long-run relationship given in Eq. 1, especially since their test for linear cointegration
presumes that the parameters of the equation are time-invariant and is therefore inappropriate during a period undergoing institutional changes. Gregory and Hansen
1996 propose extensions of the ADF test that allow for a regime shift in either the intercept or the entire coefficient vector. As Gregory and Hansen 1996, p. 101 noted,
their residual-based tests “are useful in helping lead an applied researcher to a correct model specification.” A major advantage of this procedure is that it allows one to
search for a break at an unknown shift point and to test for cointegration. Here, we imposed a priori, as well as estimated endogenously the breakpoints.
7
The results of applying the Gregory and Hansen 1996 method are summarized in Table 1. It presents the test statistics for cointegration at the estimated breakpoints
and, for comparison, the test statistics achieved for pre-selected breakpoints. The timing of the structural break is shown in years and expressed in proportion to the
sample sizes.
Three key points are highlighted by the results. First, the endogenously estimated break dates vary across countries and real balances. Second, for most of the countries
i.e., 9 out of 12 the results show that the variables bear a stationary relationship after accounting for a structural break. This finding suggests that there is a long-run
equilibrium relationship among either real M1 or real M2, real income, inflation and openness variables in at least nine out of 12 countries. The null hypothesis of no
cointegration with structural change is not rejected in Morocco, South Africa and the Philippines. However, the absolute values of the calculated Gregory and Hansen
1996 test statistic for the three countries are close to the 10 critical values, although not significant. The lack of cointegration may simply be the product of the low
power of the test for samples below 50 Gregory Hansen, 1996, p. 110 when the autocorrelation coefficient is close to one. Finally, in general, the pre-selected
breakpoints are not statistically significant.
3.3. Multivariate cointegration A system-based cointegration procedure has been developed by Johansen 1988,
1992 to test for the presence or absence of long-run equilibria among the variables in Eq. 1. The optimality of this technique has been shown by Phillips 1991 in terms
of symmetry, unbiasedness and efficiency properties. It should be preferred over other estimators because it does not suffer from problems associated with normalization
A.C. Arize et al. International Review of Economics and Finance 8 1999 399–420 405
Table 1 Gregory and Hansen 1996 tests for regime shifts
Estimated Imposed time break
Estimated breakpoint
Countries Variables
73 79
85 breakpoint
test statistic Asia
India M1,y,p,e
2 5.04
2 5.19
2 3.86
1978 [0.52] 2
7.22 M2,y,p,e
2 5.27
2 5.38
2 4.61
1979 [0.48] 2
5.38 Korea
M1,y,p,e,s φ
2 5.11
2 3.74
2 4.58
1976 [0.38] 2
7.72 M2,y,p,e,s
φ 2
4.00 2
4.98 2
5.26 1978 [0.44]
2 5.42
Malaysia M1,y,p,e,r
f
2 4.65
2 5.99
2 5.09
1974 [0.36] 2
6.31 M2,y,p,e,r
f
2 4.51
2 4.18
2 4.49
1988 [0.79] 2
5.24 Philippines
M1,y,p,e 2
3.02 2
5.85 2
4.96 1981 [0.54]
2 6.24
M2,y,p,e 2
4.64 2
4.68 2
3.99 1975 [0.37]
2 5.24
Singapore M1,y,p,e,s
φ 2
3.88 2
5.49 2
5.01 1978 [0.42]
2 6.01
M2,y,p,e,s φ
2 4.57
2 5.75
2 5.03
1980 [0.48] 2
6.37 Sri Lanka
M1,y,p,e 2
3.02 2
5.85 2
4.96 1981 [0.56]
2 6.25
M2,y,p,e 2
4.64 2
4.68 2
3.99 1975 [0.38]
2 5.24
Taiwan M1,y,p,e,s
φ 2
4.44 2
6.46 2
4.70 1976 [0.50]
2 6.73
M2,y,p,e,r
f
2 5.47
2 6.47
2 5.92
1979 [0.51] 2
6.47 Thailand
M1,y,p,e,s φ
2 2.54
2 3.90
2 3.62
1983 [0.61] 2
4.26 M2,y,p,e,s
φ ,r
f
2 7.21
2 7.18
2 6.49
1983 [0.61] 2
8.41 Africa
Ghana M1,y,p,e,r
f
2 4.55
2 5.17
2 4.28
1980 [0.56] 2
5.33 M2,y,p,e,r
f
2 4.43
2 5.20
2 4.47
1980 [0.56] 2
5.32 Morocco
M1,y,p,e,r
f
2 4.55
2 4.67
2 4.96
1976 [0.41] 2
6.01 M2,y,p,e
2 2.49
2 2.80
2 4.28
1985 [0.68] 2
4.28 S. Africa
M1,y,p,e,s φ
2 3.88
2 5.49
2 5.01
1978 [0.42] 2
6.01 M2,y,p,e,s
φ ,r
f
2 4.51
2 4.18
2 4.49
1988 [0.73] 2
5.24 Tunisia
M1,y,p,e 2
3.38 2
5.85 2
4.97 1981 [0.54]
2 6.25
M2,y,p,s φ
2 4.16
2 5.30
2 4.73
1979 [0.45] 2
5.30 The critical values at the 10 level are 25.75 for m 5 3 i.e., for India, m is 3 and for Singapore, m
is 4 and 26.17 for m 5 4. The critical values are from Table 1 of Gregory and Hansen 1996. There are no critical values for m 5. The imposed time breaks represent oil price shocks and the Plaza
Accord of 1985.
Johansen, 1995, and it is robust to departures from normality Cheung Lai, 1993; Johansen, 1995 and heteroskedasticity MacDonald Taylor, 1991; Johansen, 1995.
Furthermore, Johansen 1995 points out that the power of the Johansen test is better than that of the residual-based tests. The test utilizes two likelihood-ratio LR test
statistics for the number of cointegrating vectors: namely, the trace and the maximum eigenvalue l-max statistics. To perform the test, the conditioning vector includes
the step and impulse or spike dummy variables where applicable.
8
Similar dummies are included in the studies by Hoffman et al. 1995, p. 322 and Hendry and Doornik
1994, pp. 11–13. Optimal smallest order lag length of the Vector Autoregression VAR was
determined by a LR test and the F-version of the Breusch and Godfrey statistic for
406 A.C. Arize et al. International Review of Economics and Finance 8 1999 399–420
serial correlation.
9
After deciding the lag length in the VAR, we then followed the procedure in Johansen 1995 to test the joint hypothesis of both the rank order and
the deterministic components. The presence of a significant cointegration vector or vectors indicates a stable relationship among the relevant variables.
Table 2 reports the estimated the l-max and trace test statistics and their attendant critical values. These estimated test statistics have been adjusted by Reinsel and Ahn
scaling factor discussed in Cheung and Lai 1993. For space reasons, we report only tests for the null hypotheses r 5 0 and r 1. To facilitate an appropriate interpretation
of our results, we also report the results with and without shift or step dummies.
10
Focusing on the l-max test results, the null hypothesis tested is that there is no cointegrating vector, r 5 0 and the null hypothesis of at most one cointegrating vector
H
o
: r 1 is not rejected in any country except the real M1 and real M2 results for Singapore and Ghana, respectively.
11
In each of the 12 cases, we can reject the hypothesis of no cointegration. Thus, a stable demand for real money balances real M1 and real M2 exists during the period
for each country.
12
We also tested for evidence of cointegration among real money balances, real income and expected inflation, and the results not reported here show
that there is no evidence of cointegration in both real M1 and real M2 equations of Korea, Malaysia, Morocco and Tunisia. These results suggest that the openness vari-
ables are important in the MDF of these countries in order for cointegration to be achieved.
3.4. Long-run equilibrium estimates Given the relatively small sample available and the presence of one cointegrating
relationship in the results of each country, we estimate and test the coefficients of Eq. 1 using two alternative approaches, the dynamic ordinary least squares DOLS
estimator of Stock and Watson 1993 and the fully modified ordinary least-squares FM-OLS estimator of Phillips and Hansen 1990.
13
The former allowed the inclusion of the dummies mentioned earlier, whereas the latter procedure does not allow these
dummies. Examining the results reported in Table 3 enables us to determine to what degree these estimates are affected by the inclusion of dummies.
Focusing on the results obtained from the FM-OLS estimator, the hypothesis that MDF is homogenous of degree one with respect to the price level is tested first with
only the traditional variables and second with both the traditional and openness variables. These results are reported in Table 3. With only the traditional variables
i.e., without openness variables this hypothesis is rejected in 12 i.e., five cases for real M1 and seven cases for real M2 out of 24 cases. With both the traditional and
openness variables included, the hypothesis is rejected in only seven i.e., four cases for real M1 and three cases for real M2 out of 24 cases. This latter finding showing
that only seven are rejected and the cointegration results discussed above lend credence to the importance of the openness variables in the MDF of LDCs.
Given that employing the DOLS procedure yielded similar results on price homoge- neity, a possible question is: What are the implications of a price elasticity different
from unity? The first implication of a price elasticity greater than unity is that a 1
←
→
A.C. Arize
et al.
International
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and Finance
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407 Table 2
Testing for cointegration using Reinsel and Ahn’s 1992 small-sample correction Maximum likelihood rank tests
M 1
M 2
l -Max
l -Max9
Trace Trace9
l -Max
l -Max9
Trace Trace9
Country r 5
r 1
r 5 r
1 r 5
r 1
r 5 r
1 r 5
r 1
r 5 r
1 r 5
r 1
r 5 r
1 Asia
India 37.40
17.24 37.24
20.42 67.25
29.84 65.49
28.25 59.69
19.64 85.68
25.99 Korea
24.18 18.22
39.39 19.11
59.07 34.89
72.07 32.69
34.59 19.31
71.52 36.95
Malaysia 37.26
16.79 31.97
16.77 83.59
46.33 76.54
44.57 36.30
17.64 78.71
42.41 Philippines
55.30 11.17
55.59 16.24
72.75 17.45
80.66 25.07
61.06 9.84
75.92 14.86
Singapore 80.08
30.76 132.60
52.51 33.12
15.81 41.48
26.37 68.29
35.17 87.97
46.49 Sri Lanka
33.18 18.95
33.99 14.03
65.37 32.18
55.81 21.83
49.44 21.66
88.54 39.10
Taiwan 67.29
20.97 67.23
26.04 101.70
34.38 104.6
37.33 29.85
16.38 31.05
24.52 62.73
32.88 74.68
43.63 Thailand
35.60 16.91
60.32 24.72
37.10 16.07
44.75 22.35
81.87 44.77
103.39 58.64
Africa Ghana
31.18 18.75
73.32 42.14
43.46 33.28
110.4 66.93
Morocco 39.80
23.46 88.16
48.35 25.02
14.65 48.45
23.43 S. Africa
32.08 19.45
74.67 42.42
37.69 24.75
95.12 57.42
Tunisia 48.91
10.33 47.75
20.86 65.13
16.23 72.68
24.93 38.68
20.77 64.30
25.62 Critical values
95 27.42
21.12 48.88
31.54
a
90 24.99
19.02 45.70
28.78 95
33.64 27.42
70.49 48.88
b
90 31.02
24.99 66.23
45.70 95
39.83 33.64
95.87 70.49
c
90 36.84
31.02 91.40
66.23 The test statistics are adjusted for degrees of freedom following Reinsel and Ahn 1992 and the critical values are taken from Pesaran and
Pesaran 1997 unrestricted intercepts and no trends in VAR model. l-Max9 and Trace9 show test statistics when step dummines are included.
a
Number of variables 5 4.
b
Number of variables 5 5.
c
Number of variables 5 6.
→
A.C. Arize
et al.
International
Review of
Economics
and Finance
8 1999
399–420 Table 3
Estimates of the cointegrating relationships Tests
Tests Zero price level
Zero price level Phillips and Hansen 1990 estimates
elasticity Stock and Watson estimates
elasticity Traditional
With Without
Traditional With
Without variables
Openness variables openness openness variables
Openness variables openness openness
variables variables variables variables
Country y
p e
s φ
r
f
y p
e s
φ r
f
Asia India
M1 0.83
2 0.01
0.01 0.99
1.02 0.99
2 0.01
0.02 1.03
1.31 [17.26]
[2.01] [3.06]
[0.07] [0.18]
[11.09] [2.60]
[3.28] [1.03]
[1.36] M2
1.77 2
0.01 2
0.01 1.15
1.13 1.79
2 0.01
2 0.01
0.94 1.30
[35.07] [2.52]
[3.59] [1.20]
[1.04] [32.75]
[1.96] [4.23]
[0.52] [1.82]
Korea M1
0.95 2
0.01 2
0.01 2
0.20 1.06
0.90 0.92
2 0.01
2 0.01
2 0.24
1.12 0.86
[44.87] [0.95]
[6.10] [13.97]
[0.65] [0.50]
[19.71] [2.70]
[2.11] [10.24]
[0.73] [0.99]
M2 0.96
0.01 0.01
2 0.36
2.02 1.44
0.74 0.01
0.01 2
0.52 1.39
1.36 [12.43]
[0.04] [1.30]
[6.78] [5.70]
[1.19] [10.29]
[1.05] [2.53]
[8.67] [1.76]
[0.95] Malaysia
M1 1.25
0.01 0.14
2 0.02
1.26 1.54
1.19 0.02
0.17 2
0.02 1.30
1.21 [49.14]
[2.76] [1.91]
[3.78] [1.32]
[1.64] [20.50]
[3.30] [1.54]
[2.07] [0.96] [0.38]
M2 1.54
2 0.02
2 0.28
2 0.01
1.21 1.74
1.62 2
0.02 2
0.15 2
0.01 1.16
1.18 [81.92]
[5.17] [5.24]
[3.59] [1.09]
[3.78] [61.90]
[4.04] [2.94]
[3.62] [0.39] [0.82]
Philippines M1 0.58
2 0.01
0.01 0.90
1.04 0.63
2 0.01
0.02 0.92
0.95 [5.65]
[2.53] [1.60]
[0.83] [0.88]
[15.19] [2.62]
[3.29] [0.70]
[0.76] M2
0.89 2
0.01 0.03
1.32 1.37
1.39 2
0.03 0.01
1.04 1.21
[5.60] [3.38]
[5.61] [1.66]
[5.44] [5.45]
[5.75] [2.74]
[0.22] [2.62]
Singapore M1
0.73 2
0.01 2
0.21 0.02
1.08 1.06
0.74 2
0.01 2
0.21 0.02
1.20 1.16
[32.05] [7.40]
[6.32] [2.82]
[1.11] [0.85]
[22.36] [1.96]
[4.71] [1.73]
[3.73] [2.34]
M2 1.36
2 0.01
0.26 2
0.06 0.88
0.84 1.29
2 0.01
0.18 2
0.02 0.83
0.63 [16.88]
[1.74] [2.20]
[2.56] [0.90]
[1.12] [20.40]
[3.13] [2.08]
[2.04] [1.14]
[1.54] Sri Lanka
M1 0.58
2 0.01
0.01 0.75
1.14 0.56
2 0.01
0.01 0.48
1.11 [8.44]
[0.99] [2.64]
[1.40] [2.14]
[8.96] [2.58]
[2.32] [3.41]
[1.48] M2
0.97 0.01
0.01 0.02
1.10 0.70
0.01 0.01
0.69 1.07
[9.24] [0.57]
[1.74] [3.67]
[1.09] [5.39]
[1.14] [1.89]
[1.19] [0.55]
Taiwan M1
1.50 2
0.01 2
0.01 0.05
1.16 0.95
1.43 2
0.03 2
0.01 0.06
0.96 0.67
[83.43] [5.13]
[3.25] [2.46]
[1.53] [0.40]
[50.69] [10.56] [5.63]
[3.83] [0.18]
[2.03] continued
←
→
A.C. Arize
et al.
International
Review of
Economics
and Finance
8 1999
399–420
409 Table 3
Continued Tests
Tests Zero price level
Zero price level Phillips and Hansen 1990 estimates
elasticity Stock and Watson estimates
elasticity Traditional
With Without
Traditional With
Without variables
Openness variables openness openness variables
Openness variables openness openness
variables variables variables variables
Country y
p e
s φ
r
f
y p
e s
φ r
f
Asia Taiwan
M2 1.56
2 0.01
2 0.03
2 0.01
1.02 0.62
1.58 20.01 20.02 2
0.02 0.99
0.49 [56.89]
[4.02] [7.47]
[2.05] [0.34]
[2.87] [76.85]
[9.34] [4.88]
[3.94] [0.22] [3.00]
Thailand M1
0.81 2
0.01 2
0.03 2
0.02 0.62
0.64 0.75 20.01 20.04
2 0.03
0.73 0.67
[24.40] [2.04]
[3.31] [1.42]
[7.51] [4.98]
[27.42] [2.38]
[2.27] [3.18]
[2.49] [7.41]
M2 1.49
2 0.01
0.04 0.02 20.01
1.05 1.22
1.56 20.01 0.09
0.04 2
0.03 0.97
1.10 [83.42]
[2.51] [8.37]
[2.45] [1.48]
[0.90] [2.93]
[326.5] [12.79] [46.9] [53.60]
[30.15] [1.35] [1.10]
Africa Ghana
M1 1.17
2 0.01
2 0.01
2 0.02
0.98 0.95
1.12 20.01 20.01 2
0.02 1.08
0.95 [15.30]
[2.21] [10.8]
[3.70] [0.95]
[6.02] [10.79]
[0.41] [4.13]
[2.22] [1.65] [4.77]
M2 1.40
2 0.01
2 0.01
2 0.01
0.97 0.96
1.77 0.01 20.01
2 0.02
1.00 0.95
[17.64] [1.70]
[8.84] [1.78]
[1.35] [5.77]
[12.06] [1.18]
[3.10] [2.25] [0.23]
[6.79] Morocco
M1 1.37
0.04 2
0.02 2
0.02 1.51
1.06 1.34 20.01 20.04
2 0.02
1.49 0.60
[21.59] [0.95]
[1.88] [3.55]
[6.36] [0.50]
[17.79] [0.18]
[3.72] [3.34] [4.96]
[1.55] M2
1.38 2
0.01 0.02
1.58 1.33
1.52 20.01 20.02 1.21
1.16 [24.41]
[1.24] [1.85]
[9.31] [3.72]
[39.88] [2.77]
[1.77] [1.88]
[1.48] S. Africa
M1 0.88
2 0.03
0.13 0.08
1.43 1.17
0.59 20.04 0.15
0.19 0.99
1.19 [6.65]
[3.59] [5.13]
[1.77] [4.82]
[4.48] [4.27]
[6.13] [5.97]
[5.29] [0.05]
[3.56] M2
1.54 2
0.02 0.06
2 0.09 20.02
0.91 1.11
1.70 20.01 20.05 2
0.11 2
0.03 1.02
1.11 [9.68]
[2.14] [1.91]
[2.29] [2.12]
[0.96] [2.84]
[8.21] [3.51]
[1.76] [1.82]
[3.59] [0.16] [1.72]
Tunisia M1
0.99 0.01
2 0.32
0.47 0.58
0.84 0.01 20.58
0.78 0.57
[18.17] [0.14]
[2.09] [2.26]
[3.59] [16.83]
[3.47] [2.11]
[0.93] [1.58]
M2 1.27
2 0.01
2 0.04
0.99 1.02
1.25 20.01 2
0.03 1.00
1.04 [58.56]
[0.72] [1.90]
[0.08] [0.24]
[45.15] [2.27]
[2.32] [0.03]
[2.28] The numbers in brackets below the individual coefficient estimates are the absolute values of t-statistics. For testing price homogeneity, we report
the estimated coefficient on the price level variable, in addition, to the t-statistic to test whether this coefficient is different from 1. Significant at the conventional levels.
410 A.C. Arize et al. International Review of Economics and Finance 8 1999 399–420
increase in the price level and money balances leads to a different level of real money balances. Assuming that M2 is chosen as the monetary target by the monetary
authorities in Korea, our results imply that a 1 increase in the price level leads to a 2.02 increase in the demand for nominal M1. A possible explanation for this may
be that, as the price level, increases the real cost of transactions experienced by economic agents also rises. This is different from the results reported for nominal
balances in the United States. For instance, Arize and Darrat 1994 reported a price elasticity of less than one for the U.S. economy. Our results for Korea’s M2 suggest
that to control inflation under 10, the growth rate of M2 should be 29.8, assuming the economy grows at 10 per year.
14
Finally, as Hafer and Kutan 1994 noted, if the demand for money is a demand for real balances, a price elasticity inconsistent
with unity should cast doubt on whether the reported relationship is indeed a function of the money demand.
The long-run real income elasticities are also reported in Table 3 for real M1 and real M2, respectively. For the FM-OLS, the long-run elasticity of money demand with
respect to real GDP has the expected positive signs in all countries. They range from 0.58 Sri Lanka to 1.50 Taiwan for real M1 and 0.89 Sri Lanka to 1.77 India
for real M2. For the DOLS method, real income is positive and significant in all cases and ranges from 0.56 to 1.43 for real M1, whereas for real M2, the range is from 0.70
to 1.96. This implies a fairly large response of real money balances to changes in real income. A test of whether long-run real income elasticities of the demand for real
money balances is unity indicates that this hypothesis is rejected in most of the countries, a verdict that is corroborated by the work of Aghevli et al. 1979. This
finding implies that, as income rises, velocity tends to decline. Although there are exceptions, it can be argued that there is absence of economies of scale in money
holdings in LDCs.
The sign, magnitude and significance of the long-run elasticity of money demand with respect to inflation is consistent with previous studies i.e., Zilberfarb, 1988 and
range from 20.01 to 20.03 for real M1 and 20.01 to 20.02 for real M2. For real M1, we do not believe that the positive sign in the case of Malaysia is credible. For the
DOLS method, the range is 20.01 to 20.04 for real M1; however, significantly positive coefficients are obtained for Malaysia and Tunisia. For real M2, the inflation coeffi-
cients in India, Korea, Sri Lanka, Ghana and Thailand are negative but nonsignificant.
An appealing aspect of the results is that exchange rate is statistically significant in all countries except Tunisia’s broad MDF. For real M1, it has a negative sign in
seven countries and ranges from 20.01 to 20.21, whereas the sign is positive in India, Malaysia, the Philippines, Sri Lanka and South Africa 0.01 to 0.14. For real M2, it
has a negative sign in four countries 20.01 to 20.28 and a positive sign in six countries 0.01 to 0.26. The DOLS estimates are similar to those of the FM-OLS
method. It is worth mentioning that the effect of exchange rate on real money balances is largely positive i.e., consistent with the Arango and Nadiri 1981 hypothesis when
it is the broad MDF and negative when it is the narrow MDF.
15
For the FM-OLS method, foreign exchange-rate risk enters significantly into the long-run real M1 equations for Korea, Singapore, Taiwan and Thailand. The coefficient
A.C. Arize et al. International Review of Economics and Finance 8 1999 399–420 411
Table 4 Speed of adjustments and mean time lags for adjustments of real balances [estimates from Phillips and
Hansen 1990 procedure] Mean time lags for adjustments of real balances
Speed of adjustments
M1 M2
Country M1
M2 y
p e
s φ
r
f
y p
e s
φ r
f
Asia India
2 0.47
2 0.27
0.01 1.90
1.87 0.81
1.19 1.24
Korea 2
0.73 2
0.19 0.21
1.47 1.46
1.50 0.70
1.83 1.81
1.99 Malaysia
2 0.69
2 0.41
0.23 0.80
0.95 0.78
1.77 1.86
2.50 1.84
Philippines 2
0.49 2
0.31 0.39
2.16 2.23
1.96 2.06
2.14 Singapore
2 0.73
2 0.29
0.06 1.36
1.26 1.35
0.14 2.39
2.70 2.36
Sri Lanka 2
0.65 2
0.36 1.38
0.54 0.52
1.13 1.07
1.02 Taiwan
2 0.61
2 0.56
1.28 0.95
0.97 0.92
1.33 1.54
1.56 1.57
Thailand 2
0.37 2
0.73 0.01
1.84 1.96
1.82 0.22
1.26 1.25
1.26 1.28
Africa Ghana
2 0.66
2 0.59
1.20 1.25
1.25 1.24
0.91 1.27
1.27 1.26
Morocco 2
0.41 2
0.29 2.42
2.34 2.48
2.38 2.70
2.61 2.66
South Africa 2
0.54 2
0.54 0.52
2.01 1.91
1.76 0.79
1.19 1.52
0.78 1.15
Tunisia 2
0.35 2
0.43 0.01
2.47 1.11
0.59 1.31
1.31 Absolute values.
on the risk measure is 20.20 for Korea and 20.02 for Thailand. These results support the Akhtar and Putnam 1980 hypothesis, whereas the estimates for Singapore 0.02
and Taiwan 0.05 are consistent with the Zilberfarb 1988 hypothesis of a positive effect of exchange-rate risk on real money balances. For real M2, the foreign exchange
risk variable is statistically significant in five countries. The estimated coefficients are 2
0.36, 20.06, 0.02, 20.09 and 20.04 for Korea, Singapore, Thailand, South Africa and Tunisia, respectively. These results are similar to those obtained using the DOLS
estimates. For the FM-OLS method, the foreign interest rate variable is significantly negative,
and the semi-elasticity is about 20.02 in the long-run real M1 equations for Malaysia, Ghana and Morocco. For the real M2 equations, the long-run semi-elasticity is about
2 0.01 in Malaysia, Taiwan, Thailand and Ghana, and 20.02 in South Africa. These
results are consistent with those reported for the DOLS estimator. 3.5. Speed of adjustment and mean time lags
This section provides information on the speed of adjustment to equilibrium and identifies how quickly real balances respond to changes in the determinants. Table 4
reports the coefficient of the error-correction term and the mean time lag of each explanatory variable.
16
These results were obtained by estimating Eq. 2 for each of the 12 countries.
17
The speed of adjustment is represented by the absolute value of the error-correction term, which can be interpreted as the change in real money balances per year that is
attributed to the disequilibrium between the actual and equilibrium levels.
412 A.C. Arize et al. International Review of Economics and Finance 8 1999 399–420
For both real M1 and real M2, there is considerable inter-country variation in the adjustment speed to the last period’s disequilibrium. In the case of real M1, the
coefficient of the error-correction term ranges from a low of 0.35 for Tunisia to a high of 0.73 for Korea, whereas for real M2, the range from a low of 0.29 for Singapore
and Morocco to a high of 0.73 for Thailand. For example, in Singapore and Morocco, only about 29 of adjustment occurs in a year, whereas the figure is 73 for Thailand.
Our results imply that the adjustment of real money balances to changes in the regressors may take about three years in Singapore and Morocco to a little below
one and a half years in Thailand. This indicates the existence of market forces in the monetary sector that operate to restore long-run equilibrium after a short disturbance.
Three points are worthy of mention. First, our results are not consistent with the hypothesis of an instantaneous adjustment of the rate of growth of real money balances
to departure from their equilibrium value in the previous period. Second, our rela- tively large speeds of adjustment suggest that the predictive content of the relation-
ship between real balances and their determinants have not deteriorated over time. Finally, because M2 contains a savings component, the speed of adjustment is below
that of M1.
18
The mean time shows that the average time lag for adjustment of real money balances to changes in each independent variable. The results suggest that the mean
lag for adjustment of real money balances to changes in real income is approximately one year in almost all cases. In the case of inflation, it takes about two years in the
majority of the countries when the model is real M1, except for Malaysia, Sri Lanka and Taiwan, where it is about a year. For real M2, it takes more than one year in all
countries and close to three years in Morocco.
Given the open nature of LDCs, another interesting aspect of our study is that the average time lag for the adjustment of real money balances to changes in the openness
variables is fairly short.
19
For the majority of the countries, the mean time lags for exchange rate, foreign exchange risk and foreign interest rate are below two years
for both real M1 and M2.
20
In sum, the response of real money balances to changes in real income is similar to the response to changes in the “openness” variables.
3.6. Choice of a monetary aggregate Our results are directly relevant to concerns about which monetary aggregate best
determines the long- and short-run effects of monetary policies in LDCs. Our empirical results provide evidence in support of either M1 or M2 as the preferred monetary
aggregate. Our results, however, provide more evidence against M1 than M2. There are more reasons against relying on M1 as “a measure with which the long-run
economic effects of monetary policy actions on major macroeconomic variables, such as prices and real income could be gauged” Hafer Kutan, 1994, p. 943. This is
because more real M1 estimated equations showed structural instability using the Gregory and Hansen 1996 procedure and also failed the price homogeneity test. In
addition, some of the estimated coefficients of the inflation variable are positive and statistically significant in the real M1 equations. It is worth mentioning that our finding
is consistent with those of Aghevli et al. 1979, pp. 812–813, who found that either
A.C. Arize et al. International Review of Economics and Finance 8 1999 399–420 413
M1 or M2 can be used to achieve the objective of price stability. Our findings also support the conclusion by Chowdhury 1997, p. 407 that the appropriate MDF for
Thailand is real M2. Like Bahmani-Oskooee and Rhee 1994, our results point to real M1 as the appropriate MDF for Korea.
Concerning the short-run dynamics, the results favor both M1 and M2. First, we employed Sargan’s likelihood criterion recommended in Pesaran and Pesaran 1997,
pp. 364–367. The results of this measure favor both M1 and M2. For example, Sargan’s criterion chose M2 for Malaysia, the Philippines, Sri Lanka, Thailand, Singapore and
Morocco, whereas for India, Korea, Taiwan, Ghana, South Africa and Tunisia, it chose M1.
Second, following the procedure outlined in Baye and Jensen 1995, pp. 645–647, we found that the estimated slope coefficient of a three-year moving average of M2
growth is positive and larger in size than those obtained using M1 growth in six out of 12 countries i.e., India, South Africa, Tunisia, Morocco, Taiwan and Ghana,
whereas in the other six countries, this procedure favored M1. These results imply that if the objective of the monetary authorities is the achievement of greater price
stability, then either M1 or M2 can be used as a monetary target.
4. Conclusions
