Does fisher hypothesis hold for the East Asian Economies? An application of panel unit root tests.
Ling, Tai-hu ; Liew, Venus Khim-sen ; Wafa, Syed Azizi Wafa Syed Khalid 等
INTRODUCTION
Irving Fisher hypothesized that there should be a long-run
relationship in the adjustment of nominal interest rate corresponding to
changes in expected inflation. If the Fisher hypothesis holds, then
short-term interest rates will be an efficient predictor of future
inflation (Granville and Mallick, 2004). More importantly, the monetary
authority will then be able to influence long-term interest yields in
order to enhance macroeconomic stabilization. Owing to its importance,
the hypothesis has been subjected to rigorous research (Evans and Lewis,
1995; Daniels et al., 1996; Payne and Ewing, 1997; Lee et al., 1998;
Koustas and Serletis, 1999; Cooray, 2002; Fahmy and Kandil, 2003;
Granville and Mallick, 2004, just to name a few). One commonly adopted
method to scrutinize the hypothesis is to examine the stationarity of
the real interest rates. In this respect, if the hypothesis holds, then
the real interest rate should be stationary. Empirical findings obtained
from this approach are abundant but inconclusive thus far; see Cooray
(2003) and Johnson (2006) who provide excellent overviews of the
theoretical and empirical issues on the Fisher effect.
One well-accepted explanation of the contrasting evidence is the
low power of conventional unit root tests with the relatively short span
of data employed (Rapach and Wohar, 2002; Baharumshah et al., 2005). It
is expected that with a longer span of data, the power of test could be
improved, thereby yielding more reliable results. However, long data
sets are normally unavailable. (1) An alternative solution to circumvent
the problem is to perform panel analysis, which has higher power. (2) In
this regard, most of the East Asian economies have a history of about
half a century since independence.
Moreover, by pooling the data, the analysis can consider
cross-country financial markets interactions, which need to be
appropriately dealt with in this era of increasing international markets
globalization and integration. Wu and Chen (1998, 2001) and Holmes
(2002), for instance, demonstrated that by exploiting cross-country
variations of the data in the estimation, panel analysis can yield
higher test power than conventional unit root tests. Owing to its
usefulness, recent studies have adopted panel analysis to investigate
the stationarity of nominal interest rates (for instance, Wu and Chen,
2001) and real interest parity (Holmes, 2002; Baharumshah et al., 2005),
just to mention a few. However, to the best of our awareness, panel
analysis is yet to be applied in the context of the Fisher hypothesis.
This study tests the long-run validity of the Fisher hypothesis using
panel unit root tests. Specifically, this note aims to examine whether
the Fisher hypothesis holds for the East Asian economies. East Asia is a
fascinating economic region which has undergone rapid economic
transformation and experienced spectacular growth over the past four
decades. This study includes ASEAN-5 (Malaysia, Singapore, Taiwan,
Thailand and the Philippines), China, Hong Kong and Taiwan, Japan and
South Korea, which have strong trade and economic relationship. The
intra-regional trade shares of these economies amounted to over one-half
of their total trade in 2005 (United Nations, 2008). The combined
merchandise exports of these East Asian economies amounted to over three
trillion USD, accounting for one-quarter of the world exports in
2005-2006. The extraordinary growth of these economies in the recent
decades and the important roles they play in the international trade
have put East Asia under the spotlight of economic research (see for
instance, Sarel, 1996). Among others, Baharumshah et al. (2005) recently
documented evidence of the real interest rate parity by examining the
stationarity of real interest rate differentials of East Asian
economies. Ling (2008) argues that the existence or non-existence of the
real interest rate parity in these economies can be affected by the
soundness of the Fisher hypothesis. If the hypothesis does not hold,
then the resultant real interest rate differentials will not reflect the
actual international financial linkages. Thus, it is important to verify
the validity of the Fisher hypothesis in the case of these East Asian
economies. To accomplish this task, the stationarity of 10 East Asian
economies' real interest rates are examined using few commonly
adopted panel unit root tests developed by Maddala and Wu (1999), Choi
(2001), and Im et al. (2003).
The remainder of this note is structured as follows: The next
section describes the data and methodology employed in this study. This
is followed by results and interpretation. The final section concludes
this study.
DATA AND METHODOLOGY
This study analyses the stationarity of real interest rates of 10
East Asian economies, namely China, Hong Kong, India, Indonesia, Japan,
Malaysia, Singapore, South Korea, Taiwan, Thailand, and the Philippines.
The sample data, which are obtained from the International Financial
Statistics, Asian Development Bank and Central Banks, span from the
first quarter of 1987 to the third quarter of 2006 (1987:Q1 to 2006:Q3).
Various short-term interest rates are considered, depending on data
availability: deposit rate (China), money market rate (India, Indonesia,
South Korea, Taiwan and Thailand), and 3-Months Treasury bill rate
(Japan, Malaysia and the Philippines). Following Atkins and Coe (2002),
the inflation rate, [[pi].sub.t], is defined as the percentage change of
the quarterly consumer price index multiplied by four. The expected
inflation is then obtained by estimating an autoregressive model for
inflation rate as shown below:
[[pi].sup.e.sub.t] = [[alpha].sub.0] + [k=3.summation over (t-i)]
[[alpha].sub.i][[pi].sub.t-i] + [[eta].sub.t] (1)
where [[pi].sup.e.sub.t] is the expected inflation and
[[pi].sub.t-i] is the inflation rate calculated from the CPI. Expected
inflation rate is defined by [[??].sub.t] = [[pi].sup.e.sub.t].
The real interest rate for each economy, in turn, is obtained by
subtracting the expected inflation rate from the nominal interest rate.
For the Fisher hypothesis to hold, the resultant ex ante real interest
rate should be stationary. To test for stationarity, several panel unit
root tests due to Im et al. (2003), Maddala and Wu (1999) and Choi
(2001) are adopted in this study. For comparison purpose, the
conventional univariate augmented Dickey-Fuller (ADF) and its improved
version known as Generalized Least Squares augmented Dickey-Fuller
(ADF-GLS, due to Elliott et al., 1996; see also Ng and Perron, 2001)
unit root tests are included in this study.
Im et al. (2003) panel unit root test
Im et al. (2003) proposed a t-bar statistic, which is based on the
average of the individual cross-sectional ADF t-statistics, to examine
the unit root hypothesis for panels. (3) In particular, the test is
performed by combining individual unit root tests to derive their panel
counterpart. Im et al. (2003) based their panel unit root test on a
separate ADF test for each cross section (in our case, country) in the
panel. Then the average of the t-statistics of individual ADF statistics
is adjusted to obtain the unit root test statistic for the panel, namely
the t-bar statistic. For a sample of N groups observed over T time
periods, the panel unit root regression of the conventional ADF test is
written as
[DELTA][y.sub.it] = [[alpha].sub.i] + [[beta].sub.i][y.sub.it] +
[[p.sub.t].summation over (j=1)] [[gamma].sub.ij] [DELTA][y.sub.it-j] +
[e.sub.it], i = 1, ..., N, t = 1, ..., T (2)
where [y.sub.it] is the real interest rate, [DELTA][y.sub.it] =
[y.sub.it]-[y.sub.it-1], [[alpha].sub.i], [[beta].sub.I] and
[[gamma].sub.ij] are the parameters to be estimated, and [e.sub.it]
stands for disturbance terms.
The null hypothesis of the Im et al. (2003) test is characterized
as:
[H.sub.0]: [[beta].sub.i]: 0 for all i (3)
against the alternatives that all series are stationary processes
[H.sub.1]: [[beta].sub.i] < 0, i = 1, 2, ..., [N.sub.1];
[N.sub.2] + 2, ..., B (4)
This alternative hypothesis allows for [[beta].sub.i] to differ
across groups and is more general than the uniform alternative
hypothesis, namely [[beta].sub.i] = [beta] < 0 for all i.
To test the hypothesis, Im et al. (2003) proposed a standardized
t-bar statistic given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
where
[bar.[t.sub.NT]] = [N.sup.-1] [N.summation over (i=1)] [t.sub.i],
r([p.sub.i], [[beta].sub.i]) (6)
and [t.sub.i]([p.sub.i], [[beta].sub.i]) is the individual
t-statistic for testing [[beta].sub.i] = 0 for all i. E[[t.sub.i],
r([p.sub.i], 0)| [[beta].sub.i] = 0] and Var[[t.sub.i], T([p.sub.i],
0)[absolute value of [[beta].sub.i] = 0] can be found in Table 2 of Im
et al. (2003). Since E[[t.sub.i], r([p.sub.i], 0)|[[beta].sub.i] = 0]
and Var[[t.sub.i], T([p.sub.i], 0)| [[beta].sub.i] = 0] vary as the lag
length in the ADF regression varies, in practice, we are restricted
implicitly to using the same lag length in all the individual ADF
regressions. Under the null hypothesis, the standardized t-bar statistic
[[psi].sub.t] is asymptotically distributed as a standard normal
distribution, [psi] ~ N(0, 1).
There are several advantages of using the Im et al. (2003) panel
unit root test as compared to previously developed panel-based unit root
tests (Quah, 1992; 1994; Levin and Lin, 1993). First, it takes into
account heterogeneity across countries in two aspects, comprising of
individual-specific effects and different patterns of residual serial
correlations. Second, the proposed t-bar statistics allow for residual
serial correlation and heterogeneity of the dynamics and error variances
across time series data. Therefore, the Im et al. (2003) panel unit root
test is adopted here to examine the validity of the Fisher hypothesis
for the East Asian economies, allowing for heterogeneity and
contemporaneous serial correlations due to financial markets
interactions among these economies.
Maddala and Wu (1999) panel unit root test
Maddala and Wu (1999) proposed a Fisher test statistic solely based
on joining the p-value of the test statistic from the individual unit
root tests. The test is non-parametric and is based on Fisher (1932).
Similar to Im et al. (1997), this test allows for different first-order
autoregressive coefficients and has the same null and alternative
hypothesis in the estimation procedure. The Fisher test statistic,
P([chi]) is written as follows:
P([chi]) = -2 [N.sub.summation over (j=1)] log([pi].sub.j]) (7)
where [[pi].sub.j] is the p-value of the test statistic for j. The
Fisher test statistic p([chi square]) is a chi-squared distribution with
2N degree of freedom.
As pointed out by Maddala and Wu (1999), Fisher test has more
accurate size and better power compared to Levin and Lin (1993).
Moreover, this test provides flexibility in choosing different lag
lengths in each series of ADF regressions. Thus, the usefulness of the
test is that it may reduce the bias due to the lag selection (see
Banerjee, 1999).
Choi (2001) panel unit root test
Choi (2001) extends the Fisher test statistics of Maddala and Wu
(1999) by demonstrating that
Z = 1/[square root of N] [N.summation over (j=1)] [[phi].sup.-1]
([[pi].sub.j) [right arrow] N(0, 1) (8)
where [[phi].sup.-1] is the opposite of the standard collective
distribution function. [right arrow] N (0, 1) refers to asymptotically
distributed as standard normal distribution.
There are several features that distinguish the Choi (2001) test
from above-mentioned panel unit root tests. First, this test is devised
for finite N as well as for infinite N, where N denotes the number of
groups. Second, it is assumed that each series has different types of
non-stochastic and stochastic elements. Third, there is flexibility in
the length of time series whereby each series can appear in different
number of time series. Fourth, this test also deals with problems where
some groups have a unit root and the others do not. Thus, the Choi
(2001) test can be used under more general assumptions than the panel
unit root test of Im et al. (2003) and Levin and Lin (1993). (4)
Moreover, as mentioned by the author, the Choi (2001) test is superior
to that of Maddala and Wu (1999) in terms of finite sample size and
power.
In sum, the fundamental element that differentiates the above three
tests is that the Fisher test (Maddala and Wu, 1999 and Choi, 2001) is
calculated from a combination of the significance levels of the
different tests, whereas the Im et al. (2003) statistic is computed from
a group of test statistics.
Therefore, the Fisher test has the flexibility of using
heterogeneous lag lengths and capability of easing restrictive
assumptions assumed by Im et al. (2003). More importantly, these three
statistics will be computed in this study based on conventional adopted
ADF, as well as ADF-GLS estimation procedures. (5)
RESULTS AND INTERPRETATION
As a preliminary analysis, the ordinary ADF and ADF-GLS univariate
unit root tests are deployed to check the stationarity of the real
interest rates for the sample period (2001:Q1 to 2006:Q3) and the
results are summarized in Table 1. It is evident in Table 1 that the
null hypothesis of non-stationary series can be rejected for China,
Malaysia and Singapore by the ADF test. (6) This is because the
probability value of the t-statistics for the three countries is less
than 0.10, implying that the real interest rates concerned are
stationary at 10 % significance level or better. The implication of this
finding is that there is a long-run relationship between nominal
interest rate and inflation rate in these countries. Hence, the Fisher
hypothesis is valid for these countries. Applying the same principle,
the results suggest that Fisher hypothesis does not hold for other
countries.
In contrast, the ADF-GLS test is able to detect more cases
supportive of the Fisher effect. In particular, the null of
non-stationary series can be rejected at 5% level or better for China,
Hong Kong, Indonesia, Japan, Malaysia, Singapore and Thailand, implying
long-run validity of Fisher hypothesis for these countries. Since the
results from ADF and ADF-GLS are inconsistent, one has to rely on a more
robust test for decision. In this matter, the fact that the ADF-GLS test
provides evidence in favor of the Fisher effect for most countries in
the sample but the ADF test does not is in accordance with previous
discussion in the literature that the ADF-GLS test has more power than
the ADF test in detecting stationarity (Ng and Perron, 2001; Rapach and
Wohar, 2002). As such, relying on results obtained from the ADF-GLS
test, it
(3) Unlike another panel unit root test advocated by Levin et al.
(2002) who imposed the restrictive assumption of homogeneity, Im et al.
(2003) allow for heterogenity across groups and serial correlation
errors across groups. Therefore, it achieves more accurate size and
higher power relative to the Levin et al. (2002) test. By using a Monte
Carlo simulation, Im et al. (2003) showed better finite sample
performances of [[psi].sub.t] in relation to the Levin et al. (2002)
test. may be noted for this moment that Fisher hypothesis hold for all
countries under consideration with the exception of Korea, the
Philippines and Taiwan.
It was mentioned earlier that conventional unit root test such as
the ADF test has a low power when a relatively short span of data is
employed. Therefore, it is possible that a longer period could improve
the results. (7) For the purpose of comparison, we report the results of
examining the longer sample period of data covering the period from
1987:Q1 to 2006:Q3 in Table 2. Based on the ADF test, the null
hypothesis of a unit root is rejected for most of the countries with an
exception of Hong Kong, Indonesia, Japan and Thailand. In other words,
using a longer set of data, the ADF test is able to discover more
evidence favoring the Fisher hypothesis. In addition to the evidence
found earlier (China, Singapore and Malaysia), this time evidence is
also found for South Korea, the Philippines and Taiwan. On the other
hand, the results obtained from the ADF-GLS test suggests that the
non-stationary real interest rate can be rejected for all of the
countries at 10% or even better significance level. Overall the results
from Tables 1 and 2 suggest that the Fisher hypothesis holds better for
a longer set of data. This finding is in accordance with the view that
univariate unit root tests can perform better if they are applied to a
longer set of time series data (Rapach and Wohar, 2002; Baharumshah et
al., 2005).
While the ADF-GLS test is more reliable than the ADF test, it does
not consider financial market interactions across countries, which exist
due to strong trade and investment relationships among these economies.
To circumvent the weakness of these univariate unit root tests, panel
unit root tests are employed. For this purpose, the test statistics of
Im et al. (2003), Maddala and Wu (1999) and Choi (2001) are computed
from both the ADF and ADF-GLS tests. The results for the periods 2001:Q1
to 2006:Q3 and 1987:Q1 to 2006:Q3 are presented in Tables 3 and 4,
respectively. It is observed from these tables that the null hypothesis
of non-stationary series can be rejected at 1% significance level
regardless of the type of unit roots employed. Thus, it can be concluded
that based on panel analysis which allows for the consideration of
cross-country variations, all the East Asian real interest rates are
stationary. Holmes (2002) points out that panel unit root tests work
better than univariate unit root tests in the case of real interest
parity. As such, this study concludes that, as a whole, the Fisher
hypothesis holds for all the 10 countries under investigation based on
panel testing procedures. Recall that in the case of univariate unit
root tests, we need to lengthen the sample data to reveal more evidence
in favor of the Fisher hypothesis. In sharp contrast, empirical findings
of the Fisher hypothesis are obtained from panel unit root tests even
when a shorter sample period was used in our study and the use of a
longer sample provides consistent results. Thus, our findings are in
line with those who found that panel unit root tests are an improvement
over univariate unit root tests for finite data.
CONCLUSION
In general, a long-run relationship between nominal interest rates
and inflation rates for all the East Asian economies under investigation
has been identified by the panel but not the univariate unit root tests.
The finding should come as no surprise as basically, these economies
share quite similar monetary policies over the past few decades.
The key implications of this finding are: first, the validation of
the Fisher hypothesis in these economies will encourage borrowers to
make productive investments that promote economic growth and develop
better banking system (Pill and Pradhan, 1997). Second, the stationarity
finding for real interest rates provides convincing foundation for the
applications of various capital asset pricing models in this region
(Johnson, 2006).
Third, and perhaps more importantly, monetary policy can be used as
an effective tool to influence long-term interest rates in these East
Asian economies (Granville and Mallick, 2004). However, considering the
fact that supportive evidence of the Fisher hypothesis is only obtained
when cross-country interdependence in real interest rates is
incorporated in the estimation, it is expected that monetary policy will
work better with regional collaboration. This would require the
coordination of policy-makers from ministries of finance; the central
banks and the financial market regulators of these economies to develop
a shared vision in their macroeconomic goals (see Sheng and Teng, 2007).
Such collaboration is especially important in combating the recent
global financial crisis and economic downturn. In this respect, the
authorities across East Asia economies had used an array of similar
policies (such as liquidity support, deposit guarantees, and foreign
exchange intervention and swap arrangements) to support their banking
systems and ensure financial stability in response to the global
financial turmoil. According to the Asian Development Bank (2009), these
policies indeed have successfully restored public confidence in the
region's financial systems, and as a result, these economies
managed to make a remarkable recovery (Lipsky, 2009). Nonetheless, to
date, it is still early to safely conclude that crisis is over and as
such, the leaders of China, Japan and South Korea recently emphasized
that it is necessary to reinforce regional collaboration to face the
world economic crisis (AsiaNews, 2009). Perhaps, instead of competitive
interest rate reduction to boost exported-oriented industries during
crisis (Ito, 2009), a more closely coordinated regional exchange rate
mechanism and the establishment of an East Asian regional financial
facility as proposed by the East Asian Study Group (2002) should now be
seriously considered and pursued by the economies in this region to
enhance financial and economic stability.
Acknowledgements
The authors sincerely thank the two anonymous referees and the
Editor, Paul Wachtel, for their insightful comments on the earlier
version of this study. The authors are solely responsible for remaining
errors.
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(1) One exception is the recent work of Granville and Mallick
(2004) who is able to provide evidence supportive of Fisher hypothesis
by employing a century data covering from 1900 to 2000. In contrast,
Rose (1988) is unable to find result in favor of the hypothesis using
shorter span of data from 1892 to 1970 for the US.
(2) Im et al. (1997) demonstrated a substantial increase in power
in panel unit root test, which allows for cross-sectional variation,
even for fairly short time series.
(4) The work of Levin and Lin (1993) is published as Levin et al.
(2002).
(5) Choi (2001) demonstrates the use of ADF-GLS test in his
proposed Fisher test. By applying the Fisher test in the study of
purchasing power parity (PPP), he demonstrated the proposed test is more
powerful than ADF-GLS and t-bar test of Im et al. (2003).
(6) This finding may reflect the fact that these three countries
share quite similar monetary policies in the sense that they had the
experience of fixing their respective currencies against US dollar for
the past few decades, as well as same goals to maintain low inflation
and a stable exchange rate (see Bank for International Settlements,
2006). However, it is too early to base our conclusion on the finding of
ADF test, in which the shortcomings of this test had been discussed
earlier.
(7) Analysis of the longer sample has been included at the
suggestion of one of the reviewers.
TAI-HU LING [1], VENUS KHIM-SEN LIEW [2] & SYED AZIZI WAFA SYED
KHALID WAFA [3]
[1] Labuan School of International Business and Finance, Universiti
Malaysia Sabah, Jatan Sungai Pagar, Labuan 87000, Malaysia.
[2] Department of Economics, Faculty of Economics and Business,
Universiti Malaysia Sarawak, 94300 Kota Samarahan, Sarawak, Malaysia.
[3] School of Economics and Business, Universiti Malaysia Sabah,
8899 Kota Kinabalu, Malaysia.
Table 1: Unit root test results for
individual country (2001:01-2006:03)
Series ADF ADF-GLS
Lag t-Stat Prob. Lag t-Stat Prob.
CH 1 -3.314 ** 0.018 5 -3.087 *** 0.003
HK 1 -2.012 0.281 6 -2.091 ** 0.041
ID 0 -2.152 0.226 0 -2.166 ** 0.033
JP 2 -1.104 0.710 6 -2.595 ** 0.012
KR 0 -1.760 0.397 2 -1.341 0.184
MS 0 -2.628 * 0.092 1 -2.055 ** 0.043
PH 0 -1.905 0.328 4 -1.152 0.253
SG 0 -3.616 *** 0.008 4 -2.065 ** 0.043
TH 0 -2.149 0.227 0 -2.161 ** 0.034
TW 3 -0.723 0.834 7 -0.717 0.476
Note: In all cases, intercept has been included in the
estimation. ***, ** and * denote the rejection of the null
hypothesis of unit root at 1, 5 and 10% significance levels,
respectively. CH, HK, ID, JP, KR, MS, PH, SG, TH and TW denote
China, Hong Kong, Indonesia, Japan, South Korea, Malaysia, the
Philippines, Singapore, Thailand and Taiwan.
Table 2: Unit root tests for individual country (1987:41-2006:43)
Series ADF ADF-GLS
Lag t-Stat Prob. Lag t-Stat Prob.
CH 5 -3.312 * 0.073 1 -3.600 *** 0.001
HK 1 -1.973 0.606 1 -1.806 * 0.075
ID 0 -2.155 0.507 0 -2.182 ** 0.032
JP 4 -2.434 0.360 4 -2.364 *** 0.021
KR 1 -3.477 ** 0.049 0 -2.389 ** 0.019
MS 0 -3.225 * 0.087 0 -2.820 *** 0.006
PH 0 -3.999 ** 0.013 0 -2.591 ** 0.012
SG 0 -3.851 ** 0.019 0 -3.832 *** 0.000
TH 0 -2.744 0.223 0 -2.534 ** 0.013
TW 0 -6.910 *** 0.000 4 -4.070 *** 0.000
Note: In all ** * cases, intercept has been included in the
estimation. ***, and denote the rejection of the null hypothesis
of unit root at 1, 5 and 10% significance levels, respectively.
CH, HK, ID, JP, KR, MS, PH, SG, TH and TW denote China, Hong
Kong, Indonesia, Japan, South Korea, Malaysia, the Philippines,
Singapore, Thailand and Taiwan.
Table 3: Panel unit root tests of 10 countries (2001-2006)
Panel unit root test Computed from
ADF ADF-GLS
Im et al. (2003) -1.9940 *** -1.7213 **
Maddala and Wu (1999) 36.2467 *** 60.7641 ***
Choi (2001) -7.1312 *** -15.4874 ***
Panel unit root test Critical value
1% 5% 10%
Im et al. (2003) -1.960 -1.645 -1.282
Maddala and Wu (1999) 40.289 33.924 30.813
Choi (2001) -1.960 -1.645 -1.282
Note: ***, ** and * denote the rejection of the null hypothesis
of unit root at 1, 5 and 10% significance levels, respectively.
Table 4: Panel unit root tests of 10 countries (1987-2006)
Panel unit root test Computed from
ADF ADF-GLS
Im et at. (2003) -5.1537 *** -2.7575 ***
Maddala and Wu (1999) 72.4849 *** 104.9268 ***
Choi (2001) -14.8187 *** -24.7780 ***
Panel unit root test Critical value
1% 5% 10%
Im et at. (2003) -1.960 -1.645 -1.282
Maddala and Wu (1999) 40.289 33.924 30.813
Choi (2001) -1.960 -1.645 -1.282
Note: ***, ** and * denote the rejection of the null hypothesis
of unit root at 1, 5 and 10% significance levels respectively.
