Available online at www.sciencedirect.com
Journal of Policy Modeling 30 (2008) 363–376
Evidence of a nonlinear relationship between
inflation and inflation uncertainty: The case of the four
little dragons
Shyh-Wei Chen a,∗ , Chung-Hua Shen b,1 , Zixiong Xie b
b
a Department of Economics, Tunghai University Taichung 407, Taiwan, ROC
Department of Money and Banking, National Chengchi University Mucha, Taipei 116, Taiwan, ROC
Received 1 May 2006; received in revised form 13 September 2006; accepted 10 January 2007
Available online 18 May 2007
Abstract
Using a nonlinear flexible regression model for four economies in east Asia, we re-examine two hypotheses in light of the causal relationship between inflation and inflation uncertainty. The first, proposed by
Friedman [Friedman, M. (1977). Nobel lecture: Inflation and unemployment. Journal of Political Economy,
85, 451–472], postulates that increased inflation raises inflation uncertainty. Conversely, the second, put
forth by Cukierman and Meltzer [Cukierman, A., & Meltzer, A. (1986). a theory of ambiguity, credibility, and inflation under discretion and asymmetric information. Econometrica, 54, 1099–1128], propounds
that a high level of inflation uncertainty leads to a higher rate of inflation. Here, except for Hong Kong,
overwhelming statistical evidence is found in favor of Friedman’s hypothesis. The nonlinearity displays a
U-shaped pattern, strongly implying that, indeed, a high rate of inflation or deflation results in high inflation
uncertainty. At the same time, however, convincing evidence is found for Cukierman–Meltzer’s hypothesis
in favor of all four economies. Although Taiwan has an inverted U-shape, Hong Kong, Singapore and South
Korea show a positive relation, thus agreeing with Cukierman–Meltzer’s hypothesis.
© 2007 Society for Policy Modeling. Published by Elsevier Inc. All rights reserved.
JEL classification: C22; E31
Keywords: Inflation; Inflation uncertainty; Nonlinear; Flexible regression model
∗
Corresponding author. Tel.: +886 4 23590121x2922; fax: +886 4 23590702.
E-mail addresses: [email protected], [email protected] (S.-W. Chen), [email protected]
(C.-H. Shen).
1 Tel.: +886 2 29393091x81020; fax: +886 2 29398004.
0161-8938/$ – see front matter © 2007 Society for Policy Modeling. Published by Elsevier Inc. All rights reserved.
doi:10.1016/j.jpolmod.2007.01.007
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S.-W. Chen et al. / Journal of Policy Modeling 30 (2008) 363–376
1. Introduction
Whether a country should adopt a tighter monetary policy in periods of high inflation has long
been a contentious issue. On the one hand, adopting a tight monetary policy, for example, may
raise the interest rate, and therefore, hinder economic growth; on the other hand, by not adopting
a tight monetary policy, the efficiency of price mechanism collapse in allocating resources. This
uncertainty with regard to monetary policy in the face of high inflation is often cited as a major
source of the costs of inflation. Therefore, how the inflation rate and inflation uncertainty are
linked has been a major concern of policy-makers and researchers alike throughout much of the
past three decades. Okun (1971) is credited as having been the first to argue the point, contending
that countries that experience a higher inflation rate also have larger standard deviation in terms
of inflation.
Among the raft of discussions on the inflation rate and inflation uncertainty, one of the major
issues is the causal link between them. In his Nobel lecture, Friedman (1977) underscored the
potential effects of increased inflation on inflation uncertainty in that it can reduce public welfare
and even output growth. That is, when faced with a higher inflation rate, individuals become
uncertain about the stance of future monetary policy. Because they do not know if policy makers
will arrest the inflation rate at that time or later, they postpone their decision concerning savings
and investment. Accordingly, the real value of future nominal payments is unknown, and thus is
believed to have adverse effects on the efficiency of resource allocation and the level of real activities. Ball (1992) reconfirmed Friedman’s hypothesis and provided a theoretical foundation for the
same notion of a uni-directional positive relationship between inflation and inflation uncertainty.
Providing counterevidence against Friedman’s hypothesis, Cukierman and Meltzer (1986)
asserted that there is reverse causation, that is, higher inflation uncertainty increases the rate
of inflation. While monetary authority may object to inflation, they likely do not pass up away
opportunity to stimulate the economy even with surprise inflation. Authorities may have a greater
tendency to engage in discretionary policy, and as a result, the public is left in the dark as far as
monetary policy goes; this then creates an incentive for central bankers to act opportunistically
in an attempt to secure higher short-term economic growth. The lack of a strong commitment to
controlling the inflation rate, derived from uncertainty with regard to the policy, in place produces
inflationary bias in equilibrium. Thus, inflation uncertainty causes the inflation rate to rise.1
The policies associated with to these two contradictory hypotheses are similar but are not
completely the same. With respect to the Friedman hypothesis, his prediction may typically
occur when there are unexpected shocks that raise the current rate of inflation. These create
uncertainty about whether the authority is willing to accept a temporary reduction in output that
would normally accompany a deflationary policy. To minimize the harmful impact of the high
inflation rate and the resulting increased inflation uncertainty, policy-makers are urged to maintain
“regime certainty”, which means that future inflation could be certain if agents are sure about the
characteristics of the current policy regime. In this situation, the pattern of inflation structure is
less emphasized. Therefore, the mis-allocation of savings and investment can be avoided. Thus,
there must be a strong commitment to stabilizing inflation before being concerned about economic
growth when there are unexpected inflation shocks. For example, during a stagflation period, if
there are unexpected oil shocks, policy-makers should not swing between the policies which
1 By contrast, Holland (1995) made the case that inflation uncertainty has a negative impact on the inflation rate owing
to the central bank’s stabilizing policy.
S.-W. Chen et al. / Journal of Policy Modeling 30 (2008) 363–376
365
tighten and policies which do not tighten monetary spending as this would create the inflation
uncertainty. Instead, during this period, to firmly show the intention of the policy is important so
as to minimize inflation uncertainty and therefore the inflation rate.
With respect to the Cukierman and Meltzer hypothesis, it supports in an economy when the
authority focuses its policy more on economic growth than on inflation. To reduce inflation
uncertainty and the subsequent high inflation rate in this situation, policy-makers should not
put extra stress on the weight of economic growth over inflation stability. This is particularly
difficult for most emerging economies because inflation stability has the first priority de jure but
de facto it does not. To show the strong commitment that the inflation rate is the chief target,
the monetary authority should continuously publicize inflation reports by tracing the patterns of
inflation. That is, they must simply be sure about the current policy regime in each period as just
one of the policy responses under Friedman’s hypothesis is not enough because there would still
be uncertainty about the structure of the inflation process within each regime. This uncertainty
can be lessened only if policy-makers have decided the priority of the goals when a conflict
occurs.
Not surprisingly, empirical studies of these hypotheses have provided mixed, if not contradictory, results. Grier and Perry (1998), Tevfik and Perry (2000), Fountas (2001) and Apergis
(2004), for example, have all found support for Friedman’s hypothesis. Contrast this with Engle
(1982), Bollerslev (1986), Cosimano and Janse (1988) and Hwang (2001), who have all rejected
that notion, asserting that a high rate of inflation does not necessarily imply a high variance in
inflation. As for Cukierman–Meltzer’s hypothesis, Baillie, Chung, and Tieslau’s (1996) evidence
from studying data for three countries with high-inflation firmly supports it. See also Apergis’s
(2004) paper for supporting evidence and Hwang (2001) for counter-evidence.
Despite the abundance of studies on the types of relationships between inflation and inflation
uncertainty most researchers have used the GARCH type models of Engle (1982) and Bollerslev
(1986). A major weakness of these is that they assume a specific functional form before any
estimations are made. But, here, we have no reason whatsoever to exclude other possible functional
forms, linear or nonlinear, to describe such a relation. In this study, we revisit the hypothesis of
Friedman’s and that of Cukierman and Meltzer in conjunction with Hamilton’s (2001) flexible
regression model by using data for four Asian countries, i.e., Taiwan, Hong Kong, Singapore,
and South Korea. The flexible regression model is a fully parametric model which allows us
to simultaneously detect not only linear but also nonlinear relationships in the data and has the
advantage of not requiring us to pre-specify the functional form.
By using the flexible regression model, we obtain new findings. As for the Friedman hypothesis,
our empirical results reveal that the data for Taiwan, Singapore and South Korea uphold Friedman’s
hypothesis in a nonlinear way, with the patterns of the effects of inflation on inflation uncertainty
being U-shaped. Such a nonlinear pattern suggests that inflation uncertainty increases in both
inflationary and deflationary periods, results which have not been previously detected by using
the GARCH models. However, when we use data for Hong Kong, Friedman’s hypothesis is
not supported. When the Cukierman–Meltzer hypothesis is tested, all four of these economies,
however, do support the hypothesis but in a nonlinear way, which will be discussed shortly. Hence,
bi-directional causality between the inflation rate and inflation uncertainty exists for Hong Kong,
Taiwan, Singapore and South Korea.
The organization of this paper is as follows. In Section 2, we review the flexible regression
model of Hamilton (2001) and the nonlinear tests of Dahl and Gonzàle-Rivera (2003). In Section
3, we present our empirical results for the four Asian economies, while in Section 4, we summarize
the conclusions we draw.
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2. Flexible regression model
The flexible regression model is the brainchild of Hamilton (2001) who proposed employing
the concept of a random field as a means to reliably detect the nonlinearity of data. The model is
yt = μ(xt ) + εt ,
(1)
where
μ(xt ) = α0 + ␣ xt + λm(g xt ),
(2)
and where yt and xt are stationary and ergodic processes, respectively. In this model, the symbol denotes the element-by-element multiplication, and m(·) is the outcome of the random field. Model
(1) contains the linear component α0 + ␣ xt and the nonlinear component λm(g xt ), where m(·)
is latent and unseen. Term λ contributes to nonlinearity, while g controls the curvature.
For any choice of x, m(x) is a realization from the random field and is distributed in:
m(x) ∼ N(0, 1),
for
Hk (h) =
where
E[m(x)m(z)] = Hk (h),
Gk−1 (h, 1)/Gk−1 (0, 1) if h ≤ 1,
0
if h > 1,
Gk (h, r) =
h
r
k/2
(r 2 − z2 )
dz
for h ≡ (1/2)[(x − z) (x − z)]1/2 based on the Euclidean distance.
2.1. Estimation
We can infer neither the conditional expectation function μ(xt ) nor the parameter ϑ = (α0 , ␣ ,
σ, g , λ) since m(·) is unseen and latent. Hamilton proposed that Eqs. (1) and (2) be represented
in the GLS form to allow the unobserved part m(x) to be divided into residuals. He rephrased the
model as
⎡ ⎤ ⎡
⎤
⎤
⎡
y1
1 x1
λm(g x1 ) + ε1
⎢ y ⎥ ⎢ 1 x ⎥
⎥
⎢
⎢ 2⎥ ⎢
⎢ λm(g x2 ) + ε2 ⎥
2 ⎥
⎢ ⎥=⎢
⎥ α0 ␣ + ⎢
⎥,
.. ⎥
..
⎢ .. ⎥ ⎢ ..
⎥
⎢
⎣ . ⎦ ⎣.
⎦
⎣
. ⎦
.
yt
1
xT
λm(g xT ) + εT
or
y = X␤ + u.
He then suggested using the maximum likelihood estimate (MLE) with a recursive formulation, like the Kalman filter, to obtain the parameters of ϑ. Being conditional on an nitial set of
parameters, i.e., λ and g, and defining ζ = λ/σ and W(X;␪) = ζ 2 H(g) + IT , the parameters of the
S.-W. Chen et al. / Journal of Policy Modeling 30 (2008) 363–376
367
linear part, i.e., β and σ 2 , can be calculated analytically as
−1
˜
␤(␪)
= [X W(X; ␪)−1 X] [X W(X; ␪)−1 y],
σ̃ 2 (␪) =
(3)
W(X; ␪)−1 [y − X␤(␪)]
˜
˜
[y − X␤(␪)]
,
T
(4)
where IT denotes a T × T identity matrix, and ␪ = (g , ζ) . Thus, we can write the concentrated log
likelihood function as:
T
1
T
T
ln(2π) − ln σ̃ 2 (␪) − ln |W(X; ␪)| − ,
2
2
2
2
2
ˆ , σ̂ , ĝ , ζ̂ by maximizing Eq. (5).
and subsequently we can obtain α̂0 , ␣
η(␪; y, X) = −
(5)
2.2. Nonlinearity test
Given the framework of Eqs. (1) and (2), it is obvious that linearity can be tested by either λ or
the vector g which respectively contribute to nonlinearity and curvature. If the null hypothesis H0 :
λ2 = 0 is rejected, then the nonlinear component λm(g xt ) in Eq. (2) disappears. On the other
hand, if the null hypothesis H0 : g = 0k is rejected, then this is a sign that the individual variable
contributes no nonlinear properties to the model. Hamilton (2001) has proposed a λ-test, called
λEH (g), which is based on the Euclidean distance and the Hessian-type information matrix. The
LM statistic for the nonlinearity test can be calculated as
λEH (g) =
û HT û − σ̃T2 tr(MT HT MT )
(2 tr{[MT HT MT − (T − k − 1)
−1
2 1/2
MT tr(MT HT MT )] })
∼ χ2 (1),
(6)
where
−1
M = IT − X(X X)
X .
Besides this, Dahl and Gonzàle-Rivera (2003) proposed two alternative λ-tests to circumvent
the nuisance problem of g. They are λEOP and λA
OP based on the Minkowski distance. The former
is based on known covariance functions and can be calculated as
λEOP (g) =
T 2 ␬ x̃(x̃ x̃)x̃␬
∼ χ2 (1).
2
␬ ␬
(7)
The latter is based on unknown covariance functions and can be written as
2 2
2 ∗
λA
OP = T R ∼ χ (q ),
where
∗
q =1+
2k+2
j=1
k+j−1
k−1
.
Dahl and Gonzàle-Rivera (2003) also provided the g-test, denoted as gop , which is based on
the Minkowski distance and which has the advantage of being free of the nuisance problem of
the λ parameter under the null. The LM statistic can be expressed as
gop = T 2 R2 ∼ χ2 (k).
(8)
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S.-W. Chen et al. / Journal of Policy Modeling 30 (2008) 363–376
3. Empirical study
3.1. Description of the data and measurement of uncertainty
To investigate the relationship between inflation and inflation uncertainty, we use the monthly
data of the consumer price index (CPI) of the four little dragons of east Asia, i.e., that of Taiwan,
Hong Kong, Singapore and South Korea. The respective sample periods of each of these economies
is January 1980–December 2002; January 1985–July 2003; Januart 1977–July 2003; January
1965–August 2003. The data comes from the AREMOS Economic Statistical Databanks.
First and foremost, we must solve the problem as to how to measure inflation uncertainty.
The approach customarily used is to employ the GARCH-type models. The merit of these is that
inflation uncertainty is automatically constructed from the conditional heteroscedasticity estimate
of a particular GARCH model. Because the flexible regression model cannot generate conditional
variance as effectively as the GARCH model can, a specific measure of inflation uncertainty must
be constructed.2 Following Arize, Osang, and Slottje (2000), we take the measurement of the
moving average standard deviation as our proxy for inflation uncertainty. Accordingly, we define
the measurement of inflation uncertainty as
1/2
m
1
Jt+m =
(Rt+i−1 − Rt+i−2 )2
,
(9)
m
i=1
where R is the natural logarithm of the CPI, and m is the order of the moving average. In this
study, we employ the order m = 7.
3.2. Econometric model
Employing Hamilton’s flexible regression model to ascertain the relationships between the
inflation rate and inflation uncertainty, we focus on two hypotheses. The first is Friedman’s
hypothesis. The other is Cukierman–Meltzer’s hypothesis. In essence, as discussed in the previous
section on model specifications, the empirical models for the two hypotheses are, respectively:
σπt = β0 +
q
βj σπt−j + ϕπt + λσ m(k zt ) + νt ,
(10)
j=1
πt = α0 +
p
αi πt−i + φσπt + λπ m(g xt ) + εt ,
(11)
i=1
where zt = σπt−1 , σπt−2 , . . . , σπt−q , πt , and xt = {πt−1 , πt−2 ,. . ., πt−p , σπt }. The terms πt and
σπt denote inflation and inflation uncertainty, respectively. The terms q and p denote the optimal
lag length as determined by Eqs. (10) and (11), respectively. If the estimate of ϕ in Eq. (10) is
significantly different from zero, then that is clear evidence that, indeed, the inflation rate has
2 A fundamental problem concerning this measurement is that it is a “generated regressor variable” which might
understate true inflation uncertainty. However, Lo and Piger (2003) presented the estimated results of both the generated
and the non-generated variables and found little difference between them. Hamilton’s approach is a trade-off in that the
GARCH models cannot detect the nonlinear relationships between the inflation rate and inflation uncertainty, though
inherently, they do avoid the generated regressor problem.
S.-W. Chen et al. / Journal of Policy Modeling 30 (2008) 363–376
369
Table 1
Results of the optimal lag lengths of the regressors selected on the basis of the SBC
Taiwan
Hong Kong
Singapore
South Korea
σπt−1
σπt−2
σπt−3
σπt−4
−12.588
−12.592a
−12.590
−12.569
−12.547
−12.556a
−12.539
−12.514
−14.540
−14.606a
−14.597
−14.583
−12.654
−12.744a
−12.730
−12.720
πt−1
πt−2
πt−3
πt−4
0.031a
0.039
0.059
0.057
−0.216
−0.211
−0.391a
−0.380
−1.208
−1.306
−1.389a
−1.371
0.418
0.247
0.103a
0.105
a
Note. Denotes the best selection based on the SBC.
a linear effect on inflation uncertainty. By the same token, if the estimate of φ is significantly
different from zero, then inflation uncertainty must understandably have an effect on the inflation
rate. As opposed to a linear relationship between the inflation rate and inflation uncertainty, we
capture the nonlinear relationships by using Hamilton’s flexible regression model. We present the
empirical results in detail in the following paragraph.
Before performing the estimations, we select the optimal lag lengths of the regressors in Eqs.
(10) and (11) based on the Schwarz Bayesian criterion (SBC) rather than the Akaike information
criterion. The reason for this is based on Dahl and Gonzàle-Rivera’s (2003) assertion that “a
moderate number of lags is recommended to guard against dynamic misspecification.” Table 1
presents the results from AR(1) to AR(4). According to the parsimonious principle, the model
which we finally select is based on the minimum value of the SBC. For Eq. (10), the optimal lags
are two for all four economies. As for Eq. (11), the optimal lags for Hong Kong, Singapore and
South Korea are three, while the corresponding value for Taiwan is unity.
3.3. Empirical analyses
3.3.1. Friedman’s hypothesis
Table 2 presents the empirical results of Eq. (10), i.e., Friedman’s hypothesis and the nonlinear
test statistics. Several observations are worthy of mention. First, if the null hypothesis λ = 0 is not
rejected, then regression (10) turns out to be linear since the nonlinear part λσ m(k zt ) disappears.
In the case of Taiwan the p-values of the λEH and the λEOP , and λA
OP statistics are all equal to or
less than 0.001 and hence reject the linear null hypothesis in favor of the nonlinear alternative.
It is reasonable to conclude, therefore, that the relation is nonlinear. The second and equally
important finding is that the linear estimate of πt is equal to 0.00038, which is not significant
at the 5% level; evidently, Friedman’s hypothesis does not hold for the linear relation. The third
note of interest pertains to the nonlinear component since the estimates of the two uncertainties,
σπt−1 and σπt−2 inside zt , i.e., k1 and k2 , are insignificantly different from zero. This means that
two uncertainties play absolutely no role in nonlinearity. By contrast, the nonlinear estimate of
πt inside zt is significantly different from zero, strongly suggesting that nonlinearity is mainly
attributed to the πt variable. The result is evidenced by the linear test gop of which the p-value is
around 0.001, suggesting the rejection of linearliarity.
As reported by Hamilton (2001), given the values of ϑ = {β0 , β1 , β2 , ϕ, ζ, k1 , k2 , k3 , σ}, we
are able to calculate a value for any z of interest, denoted as z* , which represents the econometrician’s inference as the value of the conditional mean μ(z* ) when the explanatory variables take
370
Taiwan
Hong
Kong
Singapore
South
Korea
β0
β1
0.004*** (0.001)
0.001 (4.6e−4)
0.825*** (0.078) −0.030 (0.063)
3.8E–4 (2.2E–4)
1.027*** (0.068) −0.189*** (0.069) −2.5E–5 (1.9E–4)
β2
0.001** (4.4e−4) 1.126*** (0.096) −0.261*** (0.091)
0.003*** (0.001) 1.255*** (0.097) −0.434*** (0.095)
ϕ
2.7E–4 (2.1E–4)
2.6E–4* (1.4E–4)
σ
ζ
0.001*** (7.9E–5)
0.002*** (9.0E–5)
1.025*** (0.303) −43.926 (26.650)
1.027*** (0.203) 97.323 (245.590)
k1
k2
11.872 (22.593)
55.030 (456.070)
5.2E–4*** (3.9E–5) 1.287*** (0.317) 413.886*** (121.436) 331.397** (132.434)
0.001*** (8.2E–5) 0.981*** (0.323) 173.555*** (65.841) 175.302*** (32.954)
k3
λEH
λEOP
λA
OP
gop
0.539*** (0.073) 0.001*** 0.001*** 0.001*** 0.001***
2.383 (2.062)
0.735
0.672
0.027** 0.132
2.245*** (0.351) 0.036** 0.806
0.232*** (0.073) 0.041** 0.671
0.025** 0.001***
0.019** 0.130
Rejection of the null hypothesis at the 1%, 5% and 10% level of significance is indicated by *** , ** and * , respectively. The number in parentheses is the standard error.
S.-W. Chen et al. / Journal of Policy Modeling 30 (2008) 363–376
Table 2
Estimated results from Friedman’s hypothesis
S.-W. Chen et al. / Journal of Policy Modeling 30 (2008) 363–376
371
Fig. 1. Relationship between inflation and inflation uncertainty—Taiwan: (a) Friedman’s hypothesis; (b)
Cukierman–Meltzer’s hypothesis.
on the value represented by z* and when the parameters are known to take on these specified
values.
Fig. 1(a) plots the conditional expectation function with respect to πtTW holding σπTW
and σπTW
t−1
t−2
TW
TW
TW
TW
TW
constant, i.e., the figure plots Ê[μ(σ̄πt−1 , σ̄πt−2 , πt )|YT ] as a function of πt for σπt−1 , σπTW
t−2
TW and Y the given sample observations on σ TW , σ TW ,
,
σ
the sample mean for variable σπTW
T
π
π
π
t
t−2
t−1
t−1
, and πtTW . The solid line is the posterior mean with N = 5000 Monte Carlo draws for the
σπTW
t−2
specification. The dashed lines are the 95% confidence intervals.
Fig. 1(a) displays the U-shaped relation between inflation and inflation uncertainty. It shows
that if the deflation rate increases (πtTW < 0), then deflation uncertainty should similarly increase.
Likewise, if the inflation rate increases (πtTW > 0), then inflation uncertainty should also
increase. Since the slope is asymmetric, inflation uncertainty is more sensitive to inflation in
an inflationary period than in a deflationary one. Another interesting observation is that the
minimum level of inflation is around 0.8%, which suggests that to minimize inflation uncertainty, the best inflation target level for the monetary authority to set is the rate of about
0.8%.
Overall, the linear estimate suggests that higher inflation rates have no effect on inflation
uncertainty because ϕ is not significantly different from zero. However, from the estimate of
the nonlinear component k3 , the inflation rate exerts significantly and has a positive effect on
inflation uncertainty, implying that Friedman’s hypothesis is realized here. This result makes
it unambiguous that we might in fact be making a biased conclusion if we were to ignore the
important nonlinear components of the data.
In the same fashion, the other economies, Singapore and South Korea are in agreement with
Friedman’s hypothesis in both the linear and nonlinear estimates in our specification and also plot
similar U-shaped relationships in Figs. 3(a) and 4(a). By contrast, the lack of statistical evidence
is in favor of Friedman’s hypothesis for Hong Kong. Accordingly, Fig. 2(a) plots a relatively flat
pattern within the 0.0076–0.0084 interval, leading us to assume that weaker relationship between
inflation and inflation uncertainty.
3.3.2. Cukierman–Meltzer’s hypothesis
Table 3 summarizes the results from Eq. (11) and demonstrates the reverse relationship where
higher inflation uncertainty results in a higher rate of inflation (Cukierman–Meltzer’s hypothesis).
372
Taiwan
Hong Kong
Singapore
South Korea
α0
α1
−0.693 (0.592)
−0.266 (0.456)
−0.534 (0.533)
−0.828*** (0.211)
0.019 (0.140)
0.658*** (0.111)
0.777*** (0.113)
0.842*** (0.062)
g2
Taiwan
Hong Kong
Singapore
South Korea
α2
−0.530*** (0.127)
−0.493*** (0.163)
−0.647*** (0.073)
g3
α3
φ
σ
0.433*** (0.127)
0.055 (0.077)
0.060 (0.060)
78.946** (39.416)
38.323 (32.283)
126.262* (72.703)
155.938*** (16.994)
0.860***
0.539***
0.337***
0.243***
g4
***
215.451 (16.251)
0.591*** (0.175)
0.432** (0.162)
1.903*** (0.267)
λEH
λEOP
***
0.839*** (0.185)
0.091 (0.064)
−1.797*** (0.345)
77.892*** (28.032)
399.728*** (38.033)
120.757*** (26.764)
(0.108)
(0.059)
(0.034)
(0.098)
0.004
0.005***
0.002***
0.002***
**
0.028
0.102
0.093*
0.017***
ζ
g1
−0.921 (0.716)
1.511*** (0.416)
1.861*** (0.668)
4.153*** (1.855)
1.157*** (0.067)
0.261** (0.113)
0.210*** (0.092)
0.747*** (0.105)
λA
OP
gop
0.002***
0.001***
0.001***
0.001***
0.024**
0.002***
0.001***
0.002***
Rejection of the null hypothesis at the 1%, 5% and 10% level of significance is indicated by *** , ** and * , respectively. The number in parentheses is the standard error.
S.-W. Chen et al. / Journal of Policy Modeling 30 (2008) 363–376
Table 3
Estimated results from Cukierman–Meltzer’s hypothesis
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Fig. 2. Relationship between inflation and inflation uncertainty—Hong Kong: (a) Friedman’s hypothesis; (b)
Cukierman–Meltzer’s hypothesis.
Again, in the case of Taiwan, first note that the linear null hypothesis is significantly rejected by
the λ test statistics at the 5% level in favor of nonlinearity. Second, the linear estimate of φ is
significantly and positively different from zero, indicating that inflation uncertainty has a linear
effect on the inflation rate.
TW and σ TW are significantly different
Turning to the nonlinear component estimates, those of πt−1
πt
from zero. The results are consistent with the rejection of the linear gop test. Furthermore, Fig. 1(b)
TW on π TW —an inverted U-shape. This points to
displays an interesting pattern of the effect of σπt
t
a nonlinear effect of inflation uncertainty on the inflation rate. Worthy of note too is that below
a specific level of inflation uncertainty σπTW
= 0.012, a positive relation exists between inflation
t
uncertainty and the inflation rate, a clear indication that Cukierman–Meltzer’s hypothesis holds.
When the level of inflation uncertainty is higher than 0.012; however, the pattern shows a negative
relation which is closely in line with Holland’s hypothesis.
In the other three economies, generally speaking, Cukierman–Meltzer’s hypothesis is supported. Also, Figs. 2(b), 3(b) and 4(b) present an graphic representations of Cukierman–Meltzer’s
hypothesis and display an absolutely positive impact of inflation uncertainty on the inflation rate,
which is in keeping with Cukierman–Meltzer’s hypothesis.
Fig. 3. Relationship between inflation and inflation uncertainty—Singapore: (a) Friedman’s hypothesis; (b)
Cukierman–Meltzer’s hypothesis.
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Fig. 4. Relationship between inflation and inflation uncertainty—South Korea: (a) Friedman’s hypothesis; (b)
Cukierman–Meltzer’s hypothesis.
3.4. Empirical illustration and policy discussion
Table 4 presents a summary of the results of our empirical study. First, in the linear estimates, Friedman’s hypothesis is rejected for all four of these economies. After applying a flexible
nonlinear model, we succeed in getting a hold on the nonlinear components which support Friedman’s hypothesis although not for Hong Kong. The relationships between inflation and inflation
uncertainty all have a U-shaped pattern.
Another phenomenon with regard to the U-shaped pattern is that the effect of inflation on
inflation uncertainty is asymmetric. In other words, inflation uncertainty is more sensitive to
inflation in an inflationary period than in a deflationary period. Thus, a firm announcement about
reducing the inflation rate when it is high is more important than increasing the inflation rate when
it is low.
Second, by using the nonlinear inference, all four economies provide overwhelming evidence in
favor of Cuikerman–Meltzer’s hypothesis, implying that inflation increases with inflation uncertainty. Three economies, Hong Kong, Singapore and South Korea, show the positive effect of
inflation uncertainty on inflation. This can be referred to as a politically motivated expansionary
policy. With this type of monetary policy, the authority should be careful about inflation rate.
When the relationship between inflation uncertainty and inflation is visualized, however, Taiwan has a dramatic nonlinear pattern; in fact, it is an inverted U-shaped one. The effect of inflation
uncertainty on inflation is, in general, positive. To be more exact, below a specific (threshold) level
of inflation uncertainty, the results support Cuikerman–Meltzer’s hypothesis; on the other hand,
above the threshold level of inflation uncertainty, Cukierman–Meltzer’s hypothesis is rejected.
Table 4
Summary of the empirical results of the relationship between inflation and inflation uncertainty
Friedman’s hypothesis
Taiwan
Hong Kong
Singapore
South Korea
Cukierman–Meltzer’s hypothesis
Linear
Nonlinear
Pattern
Linear
Nonlinear
Pattern
×
×
×
×
×
U
Flat
U
U
×
×
Inverted-U
Positively sloped
Positively sloped
Positively sloped
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375
4. Conclusions
In this paper, we apply Hamilton’s (2001) flexible regression model to investigate the relationship between inflation and inflation uncertainty for the four dragon economies of east Asia:
Taiwan, Hong Kong, Singapore and South Korea. Two hypotheses are examined. The first, proposed by Friedman (1977), argues that increased inflation raises inflation uncertainty. The other
hypothesis, put fourth by Cukierman and Meltzer (1986), postulated that a high level of inflation
uncertainty leads to a higher rate of inflation. We find overwhelming statistical evidence that
Friedman’s hypothesis holds for theses economies but not for Hong Kong. Thus, a strong commitment to stabilizing the inflation rate should be the first policy that is adopted when there are
inflationary shocks.
Of particular interest, the nonlinearities are U-shaped, implying that higher rates of inflation
and deflation give rise to greater inflation uncertainty. Inflation uncertainty increases in both high
and low inflationary periods. The pattern helps economists identify a target rate of inflation so
that they can minimize inflation uncertainty and reduce economic harm. Thus, policy-makers may
consider adopting the 2% inflation target like that adopted by the Central Bank of New Zealand.
Aside from this, we find evidence to support Cukierman–Meltzer’s hypothesis all four
economies. Three economies, Hong Kong, Singapore and South Korea, display a positive relation in favor of Cukierman–Meltzer’s hypothesis. The implications of this are that the monetary
authority of these three economies put a greater emphasis on growth than on inflation stability.
They prefer to follow a discretionary policy to increase economic growth. Yet, what must be
kept in mind is that, these discretionary expansionary policies should be carefully conducted;
otherwise, when the inflation rate is high, such as when future oil prices go rampant, individuals
think the policy-makers will not curb the inflation rate, and this will create even greater inflation
uncertainty.
By contrast, Taiwan shows an inverted U-shaped trend. The positive relation with respect
to Cukierman–Meltzer’s hypothesis indicates that the monetary authority is more apt to behave
opportunistically to encourage economic growth. This is true for Taiwan but only below a specific
level of inflation uncertainty. Above that level Taiwan’s monetary authority takes on a stabilizing
policy to prevent economic damage brought about by inflation uncertainty. Hence, in Taiwan,
the monetary authority evidently prefers a discretionary policy, with the Taiwan Central Bank
adopting a stabilizing policy to reduce economic harm when inflation uncertainty exceeds its
threshold level.
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