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The purpose of this paper is to evaluate threshold effects in the persistence of South
African aggregate inflation data
Journal of Financial Economic Policy
Threshold effects and inflation persistence in South Africa
Andrew Phiri
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Andrew Phiri, (2012),"Threshold effects and inflation persistence in South Africa", J ournal of Financial
Economic Policy, Vol. 4 Iss 3 pp. 247 - 269
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Threshold effects and in?ation
persistence in South Africa
Andrew Phiri
Department of Economics and Management Sciences,
School of Economics, North West University, Potchefstroom, South Africa
Abstract
Purpose – The purpose of this paper is to evaluate threshold effects in the persistence of South
African aggregate in?ation data.
Design/methodology/approach – The conventional approach for assessing the degree of
persistence within an in?ation process is via its integration properties. This study makes use of
univariate threshold autoregressive (TAR) models and associated unit root testing procedures to
investigate the integration properties of the in?ation data. Out-of-sample forecasts are further
performed for the TAR models and their linear counterparts.
Findings – The empirical results con?rm threshold effects in the persistence of all employed
aggregated measures of in?ation, whereas such asymmetric effects are ambiguous for disaggregated
in?ation measures. None of the observed series is found to be stationary in their levels. The
out-of-sample forecasts for all TAR models outperform their linear counterparts.
Practical implications – Given the scope of the study, the empirical analysis provides insight with
concern to the performance of in?ation subsequent to the adoption of the in?ation target regime in
South Africa. Of particular interest are the low persistence levels observed at in?ation rates of below
4.7 and 4.4 percent for core and CPI in?ation, respectively, as both these aggregated measures of
in?ation play an essential role in guiding monetary policy conduct within the economy. The overall
?ndings imply that on an aggregate level, the South African Reserve Bank’s (SARB’s) current in?ation
target of 3-6 percent encompasses a non-stationary in?ation range and thus proves to be restrictive on
monetary policy conduct.
Originality/value – The paper ?lls in an important gap in the academic literature by evaluating
asymmetric effects in the integration properties of in?ation, at both aggregated and disaggregated
levels, for the exclusive case of South Africa.
Keywords South Africa, Monetary policy, In?ation, Macroeconomics, Money supply, Credit,
Time-series models, Single equation models, Single variables, Mathematical and quantitative methods,
De?ation, Business ?uctuations and cycles, Monetary economics, Central banking
Paper type Research paper
1. Introduction
In the ?eld of practical macroeconomic analysis, policy formulators are primarily
concerned with the behavioural characteristics of macroeconomic variables as they
converge towards a described or desired equilibrium steady-state. Macroeconomic
shocks and associated policy directives implemented in response to such shocks often
result in unprecedented ?uctuations in macroeconomic variables, which under
Inconsistent or irregular occurrence, lead to temporary shifts of these macroeconomic
variables from their steady-states. With reference to monetary policy conduct, in?ation
bears no exception to this rule. Following a particular shock to the in?ation process,
monetary policy actions would ensure that shocks to in?ation only exhibit temporary
The current issue and full text archive of this journal is available at
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JEL classi?cation – C22, C2, E31, E3, E52, E5
In?ation
persistence in
South Africa
247
Journal of Financial Economic Policy
Vol. 4 No. 3, 2012
pp. 247-269
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576381211245971
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effects, and consequentially, monetary authorities may aspire to randomly ?uctuate
in?ation around a certain mean or steady-state target (Chiquiar et al., 2010). Any
observed deviations of in?ation from its mean or steady-state are assumed to be an
outcome of persistence. The notion of in?ation persistence depicts that in the event of a
shock to the macroeconomy, in?ation may nonpermanently deviate from its long-run
equilibrium state. In?ation persistence, in this sense, provides a rather convenient
measure of the speed of convergence on the adjustment of in?ation towards its
steady-state equilibrium following the occurrence of an economic shock. The quicker
in?ation adjusts back to its established equilibrium, the less persistent in?ation is
assumed to be.
In monetary policy jargon, the aforementioned translates to a less persistent
in?ation process being preferred by Reserve Banks since this implies that in?ation will
adjust less resiliently to its equilibrium level in the presence of a macroeconomic shock.
The higher the speed at which in?ation converges back to its equilibrium after an
economic shock, the less complicated the central bank’s task of maintaining price
stability (Darvas and Varga, 2006). High in?ation persistence ultimately presents itself
as a major challenge for monetary policy and is believed to have been the underlying
factor behind the failure of a number of stabilization programmes (Moreno and Villar,
2009). Therefore, an in?ation process exhibiting low levels of persistence re?ects a
macroeconomic environment in which policymakers are presumptuously able to
“effectively” control prevailing or intended in?ation levels. In maintaining low levels of
persistence in the in?ation process, monetary authorities may be regarded as
enhancing their policy obligation of credibility.
An important aspect pertaining to the measurement of in?ation persistence is found
in its integration properties. Stationarity is considered important from the perspective
of macroeconomic modeling, since monetary authorities and macroeconomic model
builders tend to dwell on the assumption of the in?ationary process assuming a
stationary data-generating process (DGP). In view of a non-stationary variable having
in?nite variance and crossing the estimated mean infrequently, in?ation targeting is
meaningless when in?ation is established to contain a unit root (Halunga et al., 2009).
When in?ation behaves as a random-walk process, then the best forecast of the
following year’s in?ation is the most recent observed in?ation and the predictability of
in?ation never tends to an average value. It is standard practice for empirical works
pertaining to in?ation persistence to diagnose the integration properties of a univariate
autoregressive (AR) function of in?ation by using a “na? ¨ve” technique as proposed by
Andrews and Chen (2001). This method entails that if the sum of AR coef?cients
(SARC) is greater than or equal to unity, then the observed in?ation series is assumed
to contain a unit root, i.e. shocks to in?ation are permanent and the series never returns
to its original value. Conversely, if the SARC is of a positive integer below unity,
shocks to in?ation will eventually dissipate and the time series will revert to its
equilibrium level.
For instance, Gadzinski and Orlandi (2004) establish that for the European Union, the
Euro area and the USA, the SARC for consumer price index (CPI) in?ation data across
different monetary regimes has being signi?cantly below unity. Similarly, Filardo and
Genberg (2009) ?nd an SARC below unity for Korea, New Zealand and Australia
subsequent to the adoption of in?ation targeting regimes. For non-in?ation targeting
Asian economies, Gerlach and Tillmann (2011) ?nd that the SARC of in?ation has been
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close-to-unity across monetary regimes while for the case of in?ation targeting
economies the same authors establish that the SARC has subsequently dropped
signi?cantly below unity. On the other hand, there also exists a number of empirical
works that apply conventional unit root tests to determine the integration properties of
the observed in?ation series. Typically the results obtained from conventional unit root
tests tend to contradict those obtained using the na? ¨ve technique of Andrews and Chen
(2001). For Euro CPI, O’Reilly and Whelan (2005) ?nd a unit root in the in?ation process
for the period 1970-2002. Benati (2008) is also unable to reject the unit root hypothesis for
the US in?ation subsequent to 1951. With the focus on G7, Latin American, Asian and
African economies, Charemza et al. (2005) establish that between 1951 and 2001,
a stationary in?ation process is more prominent for G7 economies whereas for the
remaining economies, in?ation developed as a non-stationary process. Darvas and
Varga (2006) highlight the possibility of the observed ambiguity concerning the
integration properties of in?ation being attributed to the fact that a linear approximation
of an otherwise nonlinear underlying structure may be poor in capturing the in?ation
dynamics. Cuestas and Harrison (2010) further point out that conventional linear unit
root tests suffer fromimportant power distortions when nonlinearities exist in the DGP.
Recently, there has been a shift of focus in the empirical literature which attempts to
capture the asymmetric behavior of in?ation using a family of threshold econometric
models. Despite linear models providing the standard benchmark for macroeconomic
modeling, publications by Arango and Gonzalez (2001), Gregoriou and Kontonikas
(2009) and Cuestas and Harrison (2010) have shown how the in?ation process can be
best modeled as regime-switching processes. Essentially, regime-switching models
assume that the DGP of a time series can be captured in differing regimes that are
segregated by unique threshold variable point(s). Above and below the identi?ed
threshold level(s), the AR properties of the observed time series are deemed to differ in
statistical composition. In application to measuring in?ation persistence, this presents
an intriguing appeal as the SARC in the DGP of the univariate AR process of in?ation
is incidentally considered the most suitable reduced-form measure of its persistence
(Rangasamy, 2009). In this sense, the segregation of in?ation data into different
regimes allows for the determination of in?ation bandwidths in which the SARC (and
interpretively the persistence in the in?ation process) can be kept at a minimal.
With reference to the case of South Africa, Khadaroo (2005) employs a two-regime
threshold autoregressive (TAR) speci?cation and ?nds low persistence in CPI levels at
rates exceeding 14 percent in?ation. Khadaroo’s (2005) study offers support towards the
SARB in?ation target of 3-6 percent as being an over-restrictive policy strategy in
controlling the in?ation process. More recently, Mourelle et al. (2011) captured the
nonlinear dynamics of South African CPI in?ation within a two-regime smooth
transition AR (STAR) model. The authors ?nd that above rates of 0.84 percent, in?ation
is unstably persistent and therefore bears a risk to being effectively controlled by the
Reserve Bank. Based on the empirical evidence presented in the aforementioned studies,
there would be little reason to doubt the existence of two estimated thresholds in
South African in?ation. It is also noteworthy that while the studies of Khadaroo (2005)
and Mourelle et al. (2011) provide evidence of existing asymmetries in South African
in?ation, the integration properties of the data have not been previously investigated
using formal asymmetric unit root tests. Presented with these circumstances, our study
adopts a three-regime TAR model in preference to other alternatives on the basis of the
In?ation
persistence in
South Africa
249
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model’s ability to simultaneously capture asymmetric behaviour of in?ation and
investigate possible unit roots for higher-order threshold levels, i.e. two threshold points.
Our paper further takes heed of allegations in the literature that are suggestive of a
certain biasness ascribed towards pragmatic studies which fail to account for
persistence associated with disaggregated measures of in?ation. This phenomenon
implies that idiosyncratic shocks tend to disappear when a substantial number of series
are aggregated (Clark, 2006). Our study therefore widens the scope of investigation and
employs higher-order TAR frameworks to quantify and contrast the integration
properties of aggregated as well as disaggregated measures of South African in?ation.
The remainder of the paper is structured as follows. The following section provides
an overview of monetary policy developments in South Africa while Section 3 of the
paper presents the theoretical motivation for the study. Section 4 of the paper formally
outlines methodology used in the paper. The empirical analysis is then conducted in
Section 5 and the paper is concluded in Section 6 by integrating the overall empirical
?ndings of the study with theoretical and policy implications.
2. An overview of monetary policy in South Africa
Sichei (2005) conveniently identi?es ?ve distinct monetary policy regimes adopted by
the SARB following the termination of the Bretton Woods system namely; liquid-asset
based system, mixed system, cost of cash reserves based system with monetary
targeting, repurchase agreement (repo) system with both monetary targeting and
informal in?ation targeting; and a repo system with a formal in?ation target. The ?rst
two monetary policy regimes are representative of conservative Keynesian policies as
employed from the 1960s until the mid-1980s. These regimes were regarded as
ineffective monetary policies on the basis of their non-market approach towards
monetary policy. Following the de Kock Commission’s report in 1986, the SARBdecided
to adopt a pragmatic monetarist approach to policy conduct in which M3 money supply
targets became the anchor of monetary policy in South Africa. However, due to ?nancial
liberalization and other structural changes experienced in South Africa during the
1990s, money supply targeting proved to be an inappropriate means of controlling
in?ation. This was mainly due to instabilities found in the demand for money function
(Nell, 2000). Accordingly, the SARB sought to take a more eclectic approach towards
monetary policy which involved the monitoring of a wide-range of ?nancially related
economic indicators. Following the Asian ?nancial crisis of 1997-1998, an informal
in?ation targeting regime became active policy for the SARB until February 2000.
Entering a new millennium, the SARB decided to shift from its eclectic monetary
policy approachand announcedthe adoption of a formal in?ation target frameworkwith
targets of between 3 and 6 percent set to have been met in 2002. The SARB viewed this
shift as necessary since the eclectic framework created uncertainties and the Reserve
Bank’s decisions were seen to be in con?ict with the stated guidelines for the growth in
money supply and bank credit extension (Muhanna, 2006). The in?ation target mandate
was favoured based on the premise of its transparency and accountability which are
intended to enhance policy credibility as a means of curbing in?ation expectations of
economic agents. Whilst such an in?ation targeting regime may appear feasible for
industrialized economies, concerns have been directed towards whether such a policy
framework is suitable for the South African macroeconomy in face of its more severe
problems such as unemployment and job creation. Take for instance, Kaseeram and
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Contogiannis (2011) who ?nd that the adoption of the SARB’s in?ation target regime has
not being effective in controlling in?ation through the uncertainty channel.
Bonga-Bonga and Kabundi (2010) also establish that shocks to the repo rate do not
produce desirable effects in curbing in?ation through the channel of money demand in
South Africa whilst Gupta and Uwilingiye (2008) demonstrate on howthe Reserve Bank
would have produced lower in?ation rates had monetary authorities shown consistency
in intermediate policy objectives prior to the in?ation target regime. A recent study by
Phiri (2010) further suggests that a mid-range in?ation target of 8 percent is suf?cient in
terms of maximizing economic growth in South Africa. Comert and Epstein (2011) more
formally encompass the aforementioned arguments by putting forth the implication that
the sole manipulation of short-term interest rates is not the most effective policy
instrument for South African monetary authorities. Besides, the forecastability of
in?ation depends on the observed persistence in the in?ation process and Mourelle et al.
(2011) have demonstrated how South African in?ation has been highly persistent
throughout the entire in?ation targeting era.
Despite the current success of the in?ation target regime being, for a greater part of
it, due to its credibility, commentators such as McKinley (2008) have highlighted the
risk that supply shocks pose towards the Reserve Bank in adopting a narrowly de?ned
in?ation target. Initially, the in?ation targeting regime did not begin on a positive note,
as indicated by a target breach of in?ation performance in 2002-2003; caused by a
sudden burst in the out?ow of short-term capital which resulted in a depreciation of the
Rand (Gil-Alana, 2010). Accompanied with the currency depreciation, were sharp
increases in domestic and imported food prices while in the international arena, CPI
in?ation was being further aggravated by increases in world oil prices. Another
noteworthy period depicting signi?cant supply shocks is acquainted with the global
?nancial crisis of 2007-2008 caused by the closing down of major banks in the USA.
This period accounts for the highest in?ation rates experienced in South Africa during
the in?ation targeting period. During both in?ationary periods, the SARB’s response
was reserved towards aggressively manipulating interest rates in fear of further
aggravating macroeconomic instability. However, it was after the 2008 ?nancial crisis
that the SARB began paying more attention to volatility of exchange rates and placing
emphasis on the role of asset prices as a means of ensuring stability in ?nancial
markets and the South African economy as a whole. The policy responses taken by the
SARB have raised concerns as to whether the Reserve Bank may have adopted a
subjective in?ation target mandate intended to restrict aggregate demand yet a
majority of its experienced problems are caused by supply-oriented factors. Overall,
there are a lot of indications as to why acquiring new tools of monetary policy is likely
to be necessary in addressing problems of ?nancial stability, unemployment and
inequality in the South African economy (Comert and Epstein, 2011).
3. Theoretical motivation of the study
From a theoretical perspective, in?ation persistence is often considered as a
post-Keynesian phenomenon and can be derived from models that incorporate
nominal rigidities generating price stickiness. The price formation mechanism that
characterizes these sticky price models have their roots theoretically embedded in the
works of Taylor (1979, 1980) and Calvo (1983). Theoretical models based on price
stickiness are concerned with describing the micro foundational dynamics of in?ation
In?ation
persistence in
South Africa
251
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adjustment in response to various economic shocks and monetary policy actions.
Speci?cally, the dynamic in?ation adjustments have been deemed a theoretically
important component in determining the signi?cance of the recently popularized New
Keynesian Phillips Curve (NKPC) which is fundamentally based on the principles of
price stickiness (Kang et al., 2009). The ability of the NKPC model to ef?ciently analyze
important macroeconomic variables within a monetary policy framework has been what
Brissimis and Magginus (2008) refer to as “[. . .] the closest [theoretical model
framework] there is to standard perfection [. . .] ”. The nature of in?ation dynamics is
arguably the most distinctive feature of the forward-looking NKPCand this bears a close
theoretical relation with the framework of the forward-looking in?ation target monetary
regime (Du Plessis and Burger, 2006). Therefore, the paper intentionally employs the
New Keynesian speci?cation of the Phillips Curve as a baseline model to capture the
level of persistence in the in?ation process. In its basic structural form the NKPC
expresses in?ation as a function of expected future in?ation and some measure of a
?rm’s real marginal costs or excess demand:
p
t
¼ aE
t
p
tþ1
þbx
t
ð1Þ
This traditional structural in?ation equation identi?es two types of persistence
associated with the model’s in?ation dynamics; one being expectations-based in?ation
persistence (i.e. aE
t
p
tþ1
) and the other being extrinsic in?ation persistence (i.e. bx
t
).
Expectations-based in?ation persistence is theorized as a result of the distorted
formation of expected future in?ation. On the other hand, extrinsic in?ation persistence
is determined by the real marginal costs of ?rms or by the output gap of the
macroeconomy. Both expectations-based and extrinsic persistence are categorized as
“inherited” in?ation persistence since in?ation, in both circumstances, inherits its
persistence from the unrelenting movements in its driving variables (Dossche and
Evereart, 2005). In practice, empirical sources of dif?culty concern the characteristics of
the proper measure of the driving variable or excess demand as well as the assumption
concerning an appropriate proxy of expected in?ation (Brissimis and Magginus, 2008).
In consequence of its strictly forward-looking nature, the “traditional” NKPC has
been criticized for being able to generate price stickiness without re?ecting in?ation
inertia which inevitably leads to the unrealistic postulation of complete ?exibility in the
in?ation process. The “traditional” NKPC therefore predicts that once factors that give
rise to high in?ation have passed, in?ation can return to its equilibrium without
suffering a temporary reduction in economic activity (Sheedy, 2010). According to
Karanassou and Snower (2007), this controversial phenomenon of in?ation “jump
behavior” has been labeled “the persistence puzzle”. In an attempt to rectify the much
debated “persistence puzzle” several models address this issue by introducing the
lagged value of in?ation into the NKPC. Fuhrer and Moore (1995) show that a staggered
wage contract model in which agents care about relative wages can account for the
backward-looking component of in?ation. Gali and Gertler (1999) present an alternative
theory in which a fraction of ?rms rely on a rule-of-thumb when setting prices while
Mankiw and Reis (2002) introduce in?ation inertia through information lags in
price-setting mechanisms. Christiano et al. (2005) argue that in times when actual pricing
decisions are made, ?rms continually re-index their prices in line with past in?ation.
All-in-all, these price-setting developments in the New Keynesian in?ation dynamics
have resulted in the formation of a “hybrid” version of the NKPC. The hybrid
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New Keynesian Phillips Curve (HNKPC) incorporates both forward-looking and
backward-looking elements into the New Keynesian framework and is re?ected in the
following structural in?ation equation:
p
t
¼ rp
t21
þaE
t
p
tþ1
þbx
t
ð2Þ
The backward-looking dynamical behavior allows for deviations of observed in?ation
rates fromthe equilibriumto persist due to consecutive prior periods of in?ation (Dossche
and Evereart, 2005). Overall, the general classi?cation of identi?able lag persistence
(i.e. ap
t21
) inthe structural in?ationdynamics is knownas “intrinsic or inherent” in?ation
persistence. The extent to which in?ation determination is dominantly backward-looking
as opposed to forward-looking has been empirically proved in the studies of Sbordone
(2002), Rudd and Whelan (2005), Fuhrer (2007) and Whelan (2007). However, it has been
argued that the obtained results are sensitive to the statistical methods employed and the
observed persistence may be due to the existence of unaccounted structural changes
(Gadea and Mayoral, 2006). Furthermore, Sheedy (2010) highlights a particular danger in
these studies assuming a constant hazard function associated with the in?ation dynamics
of the NKPC. The empirical performance of an estimated nonlinear DSGE model of
in?ation persistence, as demonstrated in the works of Amisano and Tristani (2010)
con?rms the plausibility of these arguments. Theoretically, developments by Charemza
and Makarova (2009) have integrated a nonlinear component into the intrinsic portion of
in?ation in the HNKPC. The motivation behind their theory is prompted by the fact that
the standard HNKPC and other macroeconomic policy models assume stationarity in the
in?ation process where such a presumption may not conform to actual time series data.
Their approach into incorporating nonlinearities within the in?ation process is achieved
by modeling in?ation expectations as a collective function of the expected real marginal
cost or output gap (E
t
x
t
) and an error representative of a monetary shock induced by
policy-makers, i.e. ((2lg
t21
)(p
t21
)). Expected in?ation (E
t
p
tþ1
) within the model is
expressed as:
E
t
p
tþ1
¼ bE
t
x
t
þ ð2lg
t21
Þp
t21
ð3Þ
The parameter measuring the monetary policy effect, l, is bound by the condition
0 , l , 1 and is introduced as a means of ensuring that in?ation strictly ?uctuates
between a stationary I(0) process and a nonstationary I(1). By making use of equations (2)
and (3), monetary policy actions can be contained within the following structural in?ation
equation:
p
t
¼ ð1 2lg
t21
Þp
t21
þbE
t
x
t
ð4Þ
Within the model, the effects of monetary policy on in?ation persistence can be described
as follows. When the policy factor is a non-zero integer, i.e. l – 0, then monetary policy is
effective in the sense of containing in?ation within the limits of being a stationary I(0)
process. On the other hand, when the policy factor is l ¼ 0; then in?ation evolves as
a nonstationary I(1) process and the monetary authorities do not have effective control
over it. Ideally, in?ation persistence would be measured in a multivariate AR model as a
lag between monetary policy shock and the peak response inin?ation. However, given the
possibilityof the in?ationprocess switchingbetween anI(0) andI(1) process, the nonlinear
in?ation mechanism within the described theoretical framework cannot be captured
In?ation
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within a conventional multivariate vector autoregressive (VAR) speci?cation. As
indicated by Batini (2002), a VAR systemwould require all the observed data variables to
be constantly integrated of similar I(0) order thereby giving rise to this empirical
limitation. Based on the available academic literature, an alternative and highly
standardized practice in quantifying the persistence in in?ation is to capture it as an
intrinsic or inherent process within a univariate AR speci?cation. This approach has an
advantage in terms of simplicity and Batini (2002) describes it as:
[. . .] a reduced-form property [analysis] of in?ation that [simultaneously] manifests the
underlying pricing process, the conduct of monetary policy and the expectations formation
process of price-setting agents. Changes in any of these three factors will in?uence the
autocorrelation properties of in?ation [. . .].
Incidentally in?ation in South Africa is largely subject to intrinsic in?ation persistence
and is responsible for aggravating the overall containment of in?ation within the
economy (South African Reserve Bank, 2009). Therefore, this paper’s approach into
capturing the described theoretical nonlinear in?ation dynamics in application to
South African time series data is via a univariate regime-switching econometric
framework.
4. Methodology
4.1 Quantifying in?ation persistence within a three-regime SETAR model
Empirically, in?ation persistence is typically captured as the positive serial correlation
in a univariate AR in?ation model (see Dossche and Evereart, 2005; Darvas and Varga,
2006; Rangasamy, 2009; Sheedy, 2010 for examples):
p
t
¼
X
a
1i
p
t2i
þm
t
ð5Þ
From equation (5), the persistence of in?ation (r) is estimated as the sums of the AR
coef?cients of lag order i (i.e. r
p1
¼
P
a
1i
) and directly measures the sluggishness of
which in?ation responds to external shocks (Hondroyiannis and Lazareto, 2004). The
examination of potential nonlinearities in in?ation persistence is prompted via
Hansen’s (2000) estimation and testing of the TAR model. The extension of linear AR
model equation (5) into a three-regime TAR model is facilitated by determining
whether two supplementary regimes of in?ation coef?cients (i.e. r
p2
¼
P
a
2i
p
t2i
and
r
p3
¼
P
a
3i
p
t2i
) can signi?cantly be accommodated within the AR framework.
Denoting g
i
as a threshold breakpoint and I( · ) as the indicator functions of the TAR
process that segregates the function into different regimes, the encompassing
three-regime TAR model of in?ation is speci?ed as:
p
t
ðgÞ ¼ a
1
þ
X
a
1i
þm
t1
I · ðp
t
# gÞ
þa
2
þ
X
a
2i
þm
t2
I · ðg
1
, p
t
, g
2
Þ
þa
3
þ
X
a
3i
þm
t3
I · ðp
t
. g
2
Þ
ð6Þ
The empirical process is instigated by reducing equation (6) into a two-regime TAR
by assuming g
2
¼ 0, such that initially there exists one threshold estimate point
(i.e. g
1
¼ g). Hansen (2000) suggests that the least squares (LS) estimator of the
threshold g can be attained by minimizing the residual sum of squares (RSS) within
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a search region de?ned by G
1
¼ [g
^
1min
, g
^
1max
]. In attaining a threshold estimate of
g
^
1
, Hansen (2000) has shown that the estimation technique can be extended to the
context of a multiple change point model. The joint LS estimates of double-threshold
points (g
1
, g
2
) are de?ned as the values which jointly minimize the function of RSS (g
1
, g
2
)
given the threshold condition of g
1
, g
2
and a search region G
2
¼ [g
^
2min
, g
^
2max
].
It should be noted that since the ?rst threshold estimate, g
^
1
, is initially obtained from a
sum squares of errors function which ignores the presence of a third regime, then g
^
1
cannot be deemed as an asymptotically ef?cient threshold estimate in a double-threshold
TAR model. Hansen (2000) thereby proposes that an asymptotically ef?cient estimate of
the ?rst threshold value,
r
g
^
1
, can be obtained via a re?nement criterion.
Attributing to the Davies (1987) problem in which inference complexities are
associated with the unknown threshold parameters (g
1
, g
2
), Hansen (2000) suggests the
use of a bootstrap procedure on likelihood-ratio (LR) test statistics in constructing
asymptotically valid p-values. First, the hypothesis of a linear versus a two-regime
process is tested via an LR test statistic denoted as
r
LR
1
(g). The null hypothesis of no
threshold effects is accepted if the
r
LR
1
(g) statistic is of a smaller value when compared
with its associated bootstrapped critical value, c
z
(1 2 a). In such a case, in?ation is
best captured as a linear AR process as given equation (5). However, when
r
LR
1
(g)
. c
z
(1 2 a), a higher-order LR statistic, i.e.
r
LR
2
(g); is then used to test the hypothesis
of a two-regime against an alternative of a three-regime TAR process. If the alternative
hypothesis of a three-regime model is rejected (i.e.
r
LR
2
(g) # c
z
(1 2 a)), then the
singular threshold estimate is applicable whereas when
r
LR
2
(g) . c
z
(1 2 a) then two
re?ned threshold points,
r
g
^
1
and
r
g
^
2
, can be estimated. Once the optimal threshold
values are estimated and validated, the conditional-heteroskedastic covariance matrix
of b from equation (6) is estimated via backward substitution.
4.2 Unit root tests
Given the possibility of linear and nonlinear econometric structures associated with the
time series, three unit root tests are proposed for diagnosing the integration properties
of the time series, namely; the Augmented Dickey-Fuller (ADF), Enders and Granger
(1998) and Bec et al. (2004) unit root tests. Suppose that the both LR statistics fail to
reject their null hypotheses of linearity, this implies that the in?ation processes are best
?t using linear AR models. In this regard, the ADF unit root test is designed to
accommodate linear AR speci?cations and is based on the following test regression:
Dp
t
¼ cp
t21
þ
X
k
j¼1
g
j
Dp
t2j
þ1
t
ð7Þ
Under the null hypothesis of a unit root p
t
is I(1), which implies that c ¼ 0.
The Dickey-Fuller (DF) t-statistic,
DF
w
u
, is then applied in testing the null hypothesis
of c ¼ 0. The test statistic rejects the null hypothesis unit root when the
DF
w
u
statistic is of a lower absolute value compared with the critical values given by
MacKinnon (1996).
The second proposed unit root test has been devised by Enders and Granger (1998)
(E-G hereafter) who generalize the DF methodology to consider the null hypothesis of
a unit root against the alternative of a two-regime TAR model. This unit root test is
applied when one threshold is established within an in?ation series. Formally,
the nonlinear unit root test can be depicted and described in the following speci?cation:
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Dp
t
¼ c
1
p
t21
I · ðp
t21
$ 0Þ þc
2
p
t21
I · ðp
t21
, 0Þ þ1
t
ð8Þ
Where the governing heaviside indicator function used to accommodate possible
asymmetric effects within the AR decay is given as:
I · t ¼ 1 if p
t21
$ 0
0 if p
t21
, 0
ð9Þ
A modi?ed F-statistic (
NDF
w
u
) is used to test the null hypothesis of a unit root
(i.e. c
1
¼ c
2
¼ 0) against the alternative of an otherwise stationary two-regime
process. The hypothesis of a unit root can only be rejected if the
NDF
w
u
statistic is
larger in absolute value in comparison with the critical values as tabulated in Enders
and Granger (1998).
A ?nal scenario may occur in which the null hypotheses of linearity and one
threshold point, which are, respectively, tested by the
r
LR
1
(g) and
r
LR
2
(g) statistics, are
both rejected for a given series. The integration properties of such existing series are
examined through a nonlinear unit root testing procedure proposed by Bec et al. (2004).
Their econometric speci?cation suggests an application of a ?rst difference operator to
Hansen’s (2000) three-regime TAR model. The following condensed auxiliary
nonlinear in?ation function can best represent the above described unit root test:
p
t
¼ a
1
Dp
t21
þc
1
p
t21
þz1
t1
ðif p
t21
# 2g
*
Þ
þa
2
Dp
t21
þc
2
p
t21
þz1
t2
ðif p
t21
j j , g
*
Þ
þa
3
Dp
t21
þc
3
p
t21
þz1
t3
ðif p
t21 j j , g
*
Þ
ð10Þ
Restrictions of g
1
¼ 2g
2
¼ 2g and a
i
# 1, c
i
# 1 are imposed on the parameter
variables of equation (10) to rule out the possibility of explosive behaviour in any
existing unit roots. This also ensures that nonstationarity can only be detected in the
middle regime of signi?cant three-regime processes in which the entire series remains
globally ergodic. Kapetanois and Shin (2006) highlight the importance of a geometric
ergodicity as it implies:
[. . .] the existence of a unique stationary distribution for a [time series] such that [it]
converges to stationarity exponentially fast when it is initialized at an arbitrary ?nite value
[and] further implies B-mixing [coef?cients] with geometric decay [. . .].
Under the null hypothesis of a unit root in the middle regime, i.e. H
0
: a
1
¼ a
2
¼ a
3
;
c
1
¼ c
2
¼ c
3
¼ 0, a unit root process of Dp
t
¼ aDp
t21
þ z1
t
is tested, whereas under
the alternative hypothesis of H
1
: jc
1
j , 1, jc
2
j , 0, jc
3
j # 0, the regression reduces to a
stationary three-regime TAR process. In order to effectively test these described
hypotheses, there must be a singular threshold value of, g
*
which is plugged-into the
unit root test regression. Bec et al. (2004) suggest that the threshold value can be selected
a prior by the econometrician in testing for the unit root hypothesis. The asymptotic
distributions of these unit root tests are derived from Supremum-based tests on
the Wald, Lagrange multiplier (LM) and LR statistics, i.e.
BBC
W
SUP
,
BBC
LR
SUP
and
BBC
LM
SUP
. From these unit root connotations, a time series can only be rendered as a
stationary three-regime process if the above test statistics are of a smaller value in
comparison to their computed critical values.
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5. Data and empirical analysis
Having detailed the empirical procedures in the previous section, this section of the
study presents the application of the described methodology on experimental data.
Given that the objective of the study seeks to substantiate threshold effects in the
in?ation process for periods subsequent to the adoption of the in?ation targeting
mandate, the in?ation data that is collected and analyzed is bound between the monthly
periods of February 2000 and December 2010. The data consist of both aggregated and
disaggregated price indices. The aggregated series consists of the core in?ation index,
the total CPI, the total prices of goods and the total prices of services, with the latter
three series being obtained from the SARB database. The series of core in?ation is
obtained from the Statistics South Africa (SSA) database and by purpose serves to
capture the underlying in?ationary pressures that exclude highly volatile products from
its computation. The CPI data is considered as a plausible aggregated measure of
in?ation for the study since it provides a “[. . .] measure [of] in?ation in the economy so
that macroeconomic policy is based on comprehensive and up-to-date price information
[. . .] ” (Statistics South Africa, 2009). The CPI is constructed using the classi?cation of
individual consumption by purpose (COICOP) for individual components of various
commodities and service products which in aggregation forms the total prices in
commodities and services, respectively. In addition, the individual components of the
COICOP are used as the disaggregated measures of commodities and service in?ation
in this study. Table I provides a more formal decomposition of the aggregated and
disaggregated price indexes used in this study. The estimation results of the aggregated
in?ation data is presented in Table II, whereas those for disaggregated measures of
commodities and services are provided in Tables III-IV. The results of the unit root tests
are reported in Table V, whereas Table VI presents the out-of-sample forecasting
performance of the time series.
As is shown in Table II, the
r
LR
1
(g) statistic manages to reject the null hypothesis of
linear AR processes for all the observed aggregated in?ation data while the
r
LR
2
(g)
statistic cannot reject the hypothesis of a three-regime model for all the series with the
Core in?ation
Total CPI
Total consumer prices of goods Total consumer prices of services
Aggregated measures
Food Housing and utilities
Alcohol and tobacco Household contents, equipment and maintenance
Clothing and footwear Health
Housing and utilities Transport
Disaggregated measures
Household contents, equipment and maintenance Communication
Health Recreation and Culture
Transport Education
Communication Miscellaneous
Recreation and culture
Miscellaneous
Source: Author’s own tabulation
Table I.
Decomposition of the
aggregated and
disaggregated price
indexes
In?ation
persistence in
South Africa
257
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:
4
5
2
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2
0
1
6
(
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)
L
R
s
t
a
t
i
s
t
i
c
s
I
n
?
a
t
i
o
n
t
h
r
e
s
h
o
l
d
s
P
e
r
s
i
s
t
e
n
c
e
m
e
a
s
u
r
e
s
T
i
m
e
s
e
r
i
e
s
r
L
R
1
(
g
)
r
L
R
2
(
g
)
r
g
^
1
r
g
^
2
L
a
g
o
r
d
e
r
r
p
1
¼
P
a
1
i
r
p
2
¼
P
a
2
i
r
p
3
¼
P
a
3
i
C
o
r
e
i
n
?
a
t
i
o
n
6
0
.
6
2
*
*
*
(
0
.
0
0
)
2
4
.
8
4
*
(
0
.
1
)
4
.
7
%
[
3
.
8
%
,
5
.
5
%
]
8
.
5
%
[
7
.
8
%
,
9
.
1
%
]
6
0
.
3
7
1
.
0
0
0
.
8
0
T
o
t
a
l
C
P
I
4
6
.
6
0
*
*
*
(
0
.
0
0
)
2
1
.
2
3
(
0
.
7
)
4
.
4
%
[
3
.
9
%
,
4
.
9
%
]
–
6
0
.
9
2
0
.
9
4
–
T
o
t
a
l
g
o
o
d
s
3
7
.
9
3
*
*
(
0
.
0
0
)
2
9
.
5
1
*
*
(
0
.
0
0
)
3
.
2
%
[
2
.
6
%
,
4
.
1
%
]
8
.
7
%
[
7
.
9
%
,
9
.
6
%
]
6
0
.
7
1
0
.
9
8
0
.
6
0
T
o
t
a
l
S
e
r
v
i
c
e
s
6
6
.
3
7
*
*
*
(
0
.
0
0
)
5
2
.
6
4
*
*
*
(
0
.
0
0
)
2
.
7
%
[
2
.
1
%
,
3
.
5
%
]
7
.
6
%
[
6
.
8
%
,
6
.
4
%
]
6
0
.
8
7
1
.
1
7
0
.
0
1
N
o
t
e
s
:
S
i
g
n
i
?
c
a
n
t
a
t
:
*
*
*
1
,
*
*
5
a
n
d
*
1
0
p
e
r
c
e
n
t
l
e
v
e
l
s
;
t
h
e
b
o
o
t
s
t
r
a
p
p
-
v
a
l
u
e
s
o
f
t
h
e
L
R
t
e
s
t
s
a
r
e
r
e
p
o
r
t
e
d
i
n
(
)
a
n
d
t
h
e
o
p
t
i
m
a
l
l
a
g
l
e
n
g
t
h
o
f
t
h
e
T
A
R
r
e
g
r
e
s
s
i
o
n
s
i
s
s
e
l
e
c
t
e
d
b
y
m
i
n
i
m
i
z
i
n
g
t
h
e
A
I
C
;
t
h
e
9
0
p
e
r
c
e
n
t
c
o
n
?
d
e
n
c
e
i
n
t
e
r
v
a
l
s
o
f
t
h
r
e
s
h
o
l
d
e
s
t
i
m
a
t
e
s
a
r
e
g
i
v
e
n
i
n
[
]
;
t
h
e
O
L
S
s
t
a
n
d
a
r
d
e
r
r
o
r
s
a
r
e
s
i
g
n
i
?
c
a
n
t
f
o
r
t
h
e
c
o
e
f
?
c
i
e
n
t
e
s
t
i
m
a
t
e
s
Table II.
Empirical results
of aggregated measures
of in?ation
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2
1
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4
5
2
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2
0
1
6
(
P
T
)
L
R
s
t
a
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i
c
s
I
n
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a
t
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o
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t
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i
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e
r
i
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s
r
L
R
1
(
g
)
r
L
R
2
(
g
)
r
g
^
1
r
g
^
2
L
a
g
o
r
d
e
r
r
p
1
¼
P
a
1
i
r
p
2
¼
P
a
2
i
r
p
3
¼
P
a
3
i
C
o
m
m
u
n
i
c
a
t
i
o
n
8
.
6
6
(
0
.
4
)
–
–
–
2
1
.
0
4
–
–
H
o
u
s
i
n
g
7
.
0
3
(
0
.
9
)
–
–
–
3
0
.
9
7
–
–
F
o
o
d
1
3
.
6
8
(
0
.
8
)
–
–
–
5
0
.
9
7
–
–
R
e
c
r
e
a
t
i
o
n
1
8
.
2
1
(
0
.
2
)
–
–
–
5
0
.
9
4
–
–
H
o
u
s
e
h
o
l
d
c
o
n
t
e
n
t
s
1
7
.
9
4
(
0
.
2
)
–
–
–
4
0
.
9
3
–
–
C
l
o
t
h
i
n
g
1
8
.
6
8
(
0
.
3
)
–
–
–
3
0
.
9
3
–
–
H
e
a
l
t
h
1
1
.
8
1
(
0
.
7
)
–
–
–
5
0
.
9
2
–
–
A
l
c
o
h
o
l
1
8
.
9
7
(
0
.
2
)
–
–
–
5
0
.
9
1
–
–
T
r
a
n
s
p
o
r
t
3
1
.
0
9
*
*
(
0
.
0
)
1
7
.
4
1
(
0
.
6
)
3
.
7
%
[
2
.
5
%
,
5
.
6
%
]
–
6
0
.
7
3
0
.
7
7
–
M
i
s
c
e
l
l
a
n
e
o
u
s
2
6
.
0
9
*
(
0
.
1
)
2
6
.
2
2
*
(
0
.
1
)
1
.
6
%
[
0
.
1
%
,
2
.
7
%
]
7
.
5
%
[
5
.
4
%
,
8
.
9
%
]
6
0
.
9
0
1
.
0
7
0
.
7
8
N
o
t
e
s
:
S
i
g
n
i
?
c
a
n
t
a
t
:
*
*
*
1
,
*
*
5
a
n
d
*
1
0
p
e
r
c
e
n
t
l
e
v
e
l
s
;
t
h
e
b
o
o
t
s
t
r
a
p
p
-
v
a
l
u
e
s
o
f
t
h
e
L
R
t
e
s
t
s
a
r
e
r
e
p
o
r
t
e
d
i
n
(
)
;
t
h
e
o
p
t
i
m
a
l
l
a
g
l
e
n
g
t
h
o
f
t
h
e
T
A
R
r
e
g
r
e
s
s
i
o
n
s
i
s
s
e
l
e
c
t
e
d
b
y
m
i
n
i
m
i
z
i
n
g
t
h
e
A
I
C
;
t
h
e
9
0
p
e
r
c
e
n
t
c
o
n
?
d
e
n
c
e
i
n
t
e
r
v
a
l
s
o
f
t
h
r
e
s
h
o
l
d
e
s
t
i
m
a
t
e
s
a
r
e
g
i
v
e
n
i
n
[
]
;
t
h
e
O
L
S
s
t
a
n
d
a
r
d
e
r
r
o
r
s
a
r
e
s
i
g
n
i
?
c
a
n
t
f
o
r
t
h
e
c
o
e
f
?
c
i
e
n
t
e
s
t
i
m
a
t
e
s
Table III.
Empirical results of
disaggregated measures
of commodities
In?ation
persistence in
South Africa
259
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
4
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
L
R
s
t
a
t
i
s
t
i
c
s
I
n
?
a
t
i
o
n
t
h
r
e
s
h
o
l
d
s
P
e
r
s
i
s
t
e
n
c
e
m
e
a
s
u
r
e
s
T
i
m
e
s
e
r
i
e
s
r
L
R
1
(
g
)
r
L
R
2
(
g
)
r
g
^
1
r
g
^
2
L
a
g
o
r
d
e
r
r
p
1
¼
P
a
1
i
r
p
2
¼
P
a
2
i
r
p
3
¼
P
a
3
i
M
i
s
c
e
l
l
a
n
e
o
u
s
1
6
.
3
0
(
0
.
7
)
–
–
–
5
0
.
9
6
–
–
H
o
u
s
e
h
o
l
d
c
o
n
t
e
n
t
s
1
4
.
8
9
(
0
.
5
)
–
–
–
6
0
.
9
8
–
–
H
o
u
s
i
n
g
3
4
.
0
3
*
*
(
0
.
0
)
1
9
.
8
8
(
0
.
7
)
0
.
1
%
[
1
.
1
%
,
0
.
6
%
]
6
0
.
9
0
0
.
8
9
C
o
m
m
u
n
i
c
a
t
i
o
n
1
3
5
.
8
6
*
*
*
(
0
.
0
)
2
1
.
2
9
(
0
.
7
)
3
.
2
%
[
2
.
5
%
,
3
.
9
%
]
–
6
0
.
9
3
1
.
0
6
–
R
e
c
r
e
a
t
i
o
n
1
0
7
.
4
1
*
*
*
(
0
.
1
)
1
2
.
1
8
(
0
.
7
)
3
.
3
%
[
2
.
8
%
,
4
.
2
%
]
–
6
0
.
9
7
0
.
2
6
–
H
e
a
l
t
h
4
8
.
1
9
*
*
*
(
0
.
0
)
1
3
.
2
3
(
0
.
0
)
4
.
3
%
[
3
.
4
%
,
5
.
2
%
]
–
1
0
.
4
1
0
.
9
5
–
T
r
a
n
s
p
o
r
t
2
9
.
7
0
*
(
0
.
1
)
3
7
.
3
8
*
*
*
(
0
.
1
)
0
.
9
%
[
0
.
1
%
,
2
.
2
%
]
4
.
4
%
[
3
.
2
%
,
5
.
3
%
]
6
0
.
6
9
2
.
6
1
0
.
6
1
E
d
u
c
a
t
i
o
n
3
5
.
0
4
*
*
*
(
0
.
0
)
2
8
.
5
1
*
*
(
0
.
1
)
6
.
5
%
[
5
.
6
%
,
7
.
7
%
]
7
.
0
%
[
5
.
7
%
,
8
.
2
%
]
3
0
.
1
3
6
.
3
6
0
.
9
7
N
o
t
e
s
:
S
i
g
n
i
?
c
a
n
t
a
t
:
*
*
*
1
,
*
*
5
a
n
d
*
1
0
p
e
r
c
e
n
t
l
e
v
e
l
s
;
t
h
e
b
o
o
t
s
t
r
a
p
p
-
v
a
l
u
e
s
o
f
t
h
e
L
R
t
e
s
t
s
a
r
e
r
e
p
o
r
t
e
d
i
n
(
)
;
t
h
e
o
p
t
i
m
a
l
l
a
g
l
e
n
g
t
h
o
f
t
h
e
T
A
R
r
e
g
r
e
s
s
i
o
n
s
i
s
s
e
l
e
c
t
e
d
b
y
m
i
n
i
m
i
z
i
n
g
t
h
e
A
I
C
;
t
h
e
9
0
p
e
r
c
e
n
t
c
o
n
?
d
e
n
c
e
i
n
t
e
r
v
a
l
s
o
f
t
h
r
e
s
h
o
l
d
e
s
t
i
m
a
t
e
s
a
r
e
g
i
v
e
n
i
n
[
]
;
t
h
e
O
L
S
s
t
a
n
d
a
r
d
e
r
r
o
r
s
a
r
e
s
i
g
n
i
?
c
a
n
t
f
o
r
t
h
e
c
o
e
f
?
c
i
e
n
t
e
s
t
i
m
a
t
e
s
Table IV.
Empirical results of
disaggregated measures
of services
JFEP
4,3
260
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
4
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
L
i
n
e
a
r
t
i
m
e
s
e
r
i
e
s
D
F
w
u
T
w
o
-
r
e
g
i
m
e
t
i
m
e
s
e
r
i
e
s
N
D
F
w
u
T
h
r
e
e
-
r
e
g
i
m
e
t
i
m
e
s
e
r
i
e
s
B
B
C
W
S
U
P
B
B
C
L
M
S
U
P
B
B
C
L
R
S
U
P
F
o
o
d
(
g
o
o
d
s
)
2
1
.
9
1
(
2
2
.
2
5
)
{
2
5
.
0
4
}
T
o
t
a
l
C
P
I
3
.
7
1
(
2
.
7
5
)
C
o
r
e
i
n
?
a
t
i
o
n
1
8
.
3
2
(
1
1
.
3
4
)
1
5
.
1
0
(
1
0
.
0
1
)
1
6
.
6
1
(
1
0
.
6
5
)
C
o
m
m
u
n
i
c
a
t
i
o
n
(
g
o
o
d
s
)
2
2
.
1
4
(
2
8
.
2
3
)
T
r
a
n
s
p
o
r
t
(
g
o
o
d
s
)
2
.
1
6
T
o
t
a
l
g
o
o
d
s
2
5
.
7
2
(
1
0
.
8
5
)
1
9
.
8
0
(
9
.
6
3
)
2
2
.
5
0
(
1
0
.
2
2
)
H
o
u
s
i
n
g
(
g
o
o
d
s
)
2
1
.
1
6
(
2
5
.
6
1
)
H
o
u
s
i
n
g
(
s
e
r
v
i
c
e
s
)
2
.
5
7
T
o
t
a
l
s
e
r
v
i
c
e
s
2
8
.
0
4
(
1
2
.
7
5
)
2
1
.
1
4
(
1
1
.
0
9
)
2
4
.
2
7
(
1
0
.
4
2
)
R
e
c
r
e
a
t
i
o
n
(
g
o
o
d
s
)
2
1
.
4
9
(
2
9
.
4
4
)
C
o
m
m
u
n
i
c
a
t
i
o
n
(
s
e
r
v
i
c
e
s
)
5
.
3
1
(
1
.
8
5
)
M
i
s
c
e
l
l
a
n
e
o
u
s
(
g
o
o
d
s
)
2
3
.
0
9
(
1
5
.
9
6
)
1
7
.
9
2
(
1
3
.
2
5
)
2
3
.
0
9
(
1
4
.
5
2
)
H
o
u
s
e
h
o
l
d
c
o
n
t
e
n
t
s
(
g
o
o
d
s
)
2
2
.
5
3
(
2
6
.
7
5
)
R
e
c
r
e
a
t
i
o
n
(
s
e
r
v
i
c
e
s
)
6
.
3
9
(
2
.
6
4
)
T
r
a
n
s
p
o
r
t
(
s
e
r
v
i
c
e
s
)
4
7
.
9
8
(
3
5
.
6
3
)
{
2
1
.
2
8
}
3
3
.
2
6
(
2
7
.
1
6
)
{
1
1
.
9
4
}
4
3
.
3
6
(
3
1
.
7
8
)
{
1
4
.
3
1
}
C
l
o
t
h
i
n
g
(
g
o
o
d
s
)
2
1
.
7
7
(
2
9
.
0
1
)
H
e
a
l
t
h
(
s
e
r
v
i
c
e
s
)
5
.
8
2
(
2
.
9
4
)
E
d
u
c
a
t
i
o
n
(
s
e
r
v
i
c
e
s
)
5
4
.
8
3
(
3
7
.
4
9
)
{
2
2
.
7
8
}
4
2
.
6
1
(
3
0
.
2
2
)
{
1
5
.
6
9
}
5
2
.
3
8
(
3
2
.
1
8
)
{
1
7
.
9
4
}
H
e
a
l
t
h
(
g
o
o
d
s
)
2
1
.
9
4
(
2
8
.
1
5
)
A
l
c
o
h
o
l
(
g
o
o
d
s
)
2
1
.
9
1
(
2
8
.
8
5
)
M
i
s
c
e
l
l
a
n
e
o
u
s
(
s
e
r
v
i
c
e
s
)
2
.
4
7
(
2
6
.
4
1
)
H
o
u
s
e
h
o
l
d
c
o
n
t
e
n
t
s
(
s
e
r
v
i
c
e
s
)
0
.
5
5
(
2
9
.
5
7
)
1
0
%
2
2
.
5
8
2
.
8
3
1
6
.
1
8
1
5
.
5
9
1
5
.
7
7
5
%
2
2
.
9
0
3
.
6
0
1
8
.
4
1
7
.
6
3
1
7
.
8
9
1
%
2
3
.
5
1
5
.
3
8
2
3
.
0
1
2
1
.
7
6
2
2
.
2
3
N
o
t
e
s
:
T
h
e
t
e
s
t
s
t
a
t
i
s
t
i
c
s
a
s
s
o
c
i
a
t
e
d
w
i
t
h
t
h
e
?
r
s
t
d
i
f
f
e
r
e
n
c
e
s
o
f
t
h
e
t
i
m
e
-
s
e
r
i
e
s
a
r
e
r
e
p
o
r
t
e
d
i
n
(
)
a
n
d
f
o
r
s
e
c
o
n
d
d
i
f
f
e
r
e
n
c
e
s
a
r
e
g
i
v
e
n
i
n
{
}
;
t
h
e
l
a
g
l
e
n
g
t
h
f
o
r
t
h
e
A
D
F
t
e
s
t
s
t
a
t
i
s
t
i
c
i
s
s
e
l
e
c
t
e
d
b
y
m
i
n
i
m
i
z
i
n
g
t
h
e
A
I
C
Table V.
Unit root tests
In?ation
persistence in
South Africa
261
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
4
5
2
4
J
a
n
u
a
r
y
2
0
1
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exception of in?ation in total CPI. Further referring to the results presented in Table II,
it can be seen that a single threshold of 4.4 percent is established for in?ation in total
CPI where above this level a signi?cant higher, close-to-unity SARC is observed.
Between in?ation rates of 4.7 and 8.5 percent, core in?ation exhibits the highest
persistence with the SARC being above unity in this regime, and the lowest SARC is
established at rates below 4.7 percent. Similarly for total goods and total services, the
highest SARC exists in the middle regimes (i.e. between 3.2 and 8.7 percent for total
goods and 2.7-7.6 percent for total services). The lowest SARC for both of these series is
found in the high regimes at in?ation rates of above 8.7 percent for total goods and
7.6 percent for total services. Given these relatively high SARC estimates obtained
from the TAR models, it is tempting to interpret these results as evidence of unit roots
existing in the data series. At this stage, such an interpretation is tentative and
warrants more formal unit root tests to con?rm these preliminary speculations.
The results in Table III present evidence of an aggregation bias in the data, that is, of
lower persistence in individual components of commodity products in comparison with
the total prices of commodities. Approximately, 60 percent of the disaggregated series of
commodities do not contain sums of autoregressive coef?cients (SARC) which can
substantially indicate nonstationary in their processes (i.e. recreation, household
contents, clothing, health, alcohol and transport). The remaining 40 percent of the
commodity series (i.e. communication, housing, food and miscellaneous commodities)
appear to re?ect random walks in their series and have similar SARC to those of their
aggregated counterparts. With regards to asymmetric effects in the data, both of
Hansen’s (2000) LRtest statistics fail to reject the hypothesis of no threshold effects for a
majority of the observed disaggregated series of commodities (i.e. communication,
housing, food recreation, household contents, clothing, health and alcohol). On the other
hand, the hypothesis of a two-regime TAR process is accepted for transport and
a three-regime TAR for miscellaneous commodities. For the case of transport in
commodities, one threshold point is estimated at 3.7 percent of which above this level,
AR ( p) TAR2 ( p) TAR3 ( p)
In?ation measure RMSE MAPE RMSE MAPE RMSE MAPE
Aggregate series
Core in?ation 0.25 0.07 0.17 0.06 0.15 0.05
Total CPI 0.29 0.17 0.19 0.14 N/A N/A
Total goods 0.37 0.14 0.31 0.14 0.29 0.12
Total services 0.88 0.25 0.53 0.18 0.37 0.12
Disaggregate series of commodities
Transport 1.28 1.02 1.09 0.90 N/A N/A
Miscellaneous 0.35 0.19 0.27 0.18 0.20 0.16
Disaggregate series of services
Housing 3.46 1.54 2.44 0.93 N/A N/A
Communication 0.65 0.44 0.62 0.41 N/A N/A
Recreation 3.80 0.35 2.33 0.28 N/A N/A
Health 1.69 0.13 1.09 0.11 N/A N/A
Transport 1.88 0.29 1.45 0.29 1.22 0.26
Education 0.18 0.02 0.17 0.03 0.11 0.02
Note: 120 historic time series observations were used for the out-of-sample forecasts
Table VI.
Out-of-sample forecast
for one-step-ahead
predictions: AR vs TAR
speci?cations
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in?ation exhibits a slightly higher SARC. Two signi?cant thresholds of 1.6 and
7.5 percent are also found for miscellaneous commodities. The highest SARC estimates
for miscellaneous commodities goods are established between 1.6 and 7.5 percent
in?ation rates while the lowest SARC exists at rates above 7.5 percent.
The results displayed in Table IV, display similar evidence of an aggregation bias
with respect to disaggregated measures of services as only housing and transport
services have SARC estimates that are closely emulated with those found in the total
prices of services. The SARC in individual components of services are found to be
generally higher and display more asymmetric effects than for the case of individual
commodity items. This result can be expected since production in the service sectors is
more labour intensive compared to the production of commodities (Lunneman and
Matha, 2005). In particular, Hansen’s (2000) threshold test results indicate that 71 percent
of the series (i.e. housing, communication, recreation, health, transport and education) can
be ?tted into nonlinear TAR processes, while the remaining series of household contents
and miscellaneous services are best represented as linear AR processes. The SARC
estimates associated with household contents, recreation, health, transport, education
and miscellaneous services indicate the possibility of unit roots in these processes.
A singular threshold is identi?ed for each of the following services; housing (0.1 percent),
communication (3.2 percent), recreation (3.3 percent) and health (4.3 percent). Lower
persistence is associated with in?ation in the lower regimes of communication and
health, while lower persistence is found in the higher regimes of housing and recreation.
Two thresholds estimates of 0.9 percent and 4.4 percent are established for transport
with the highest measures of persistence existing in the middle regime of the TAR
process and the lowest persistence being in the high regimes. The SARC estimates
associated with household contents, recreation, health, transport, education and
miscellaneous services indicate the possibility of unit roots in these processes.
In drawing comparisons between the unit root test results shown in Table V with
the SARC estimate results presented through Tables II-IV, the compliance of these
results with concern to the integration properties of disaggregated in?ation measures
produces mixed results. Contrary to the implications drawn from the SARC estimates
for disaggregated items, the unit root tests cannot reject the hypothesis of stationarity
in their levels for only three disaggregated series, i.e. food (goods), transport (goods)
and housing (services). The remainder of the disaggregated series are established to
contain unit roots in their process with transport (services) and education (services)
being the only indices that are found to be integrated of an order high than I(1). The
nonlinear unit root test performed on the aggregated in?ation series show that in their
levels, the null hypothesis of a unit root process in the middle regime (i.e. r
p2
¼
P
a
2i
)
cannot be rejected in their levels by the employed test statistics for all observed series.
Stationary, nonlinear processes are attained for all aggregate series in their respective
?rst differences. It is worth noting that the implied integration properties of the SARC
estimates for the aggregated time series and their associated unit root tests seem to be
in mutual compliance with each other as they are suggestive of existing unit roots in
the middle regimes of the observed processes.
The evaluation of the performance of the nonlinear TAR processes against their
counterpart linear AR processes is presented in an exposition of an out-of-sample
analysis for the observed time series. The objective of these out-of-sample ?t exercises
is to determine whether a nonlinear or linear ?tted time series provides a better
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indication of their predictive ability of the observed time series. In extracting
out-of-sample forecast plots, a “skeleton method” is used to derive the one-step-ahead
forecasts and entails setting the errors of the observed linear and threshold processes
to zero such that an approximation of an expectational function of random variables is
drawn through a function of its expectation (Clements and Smith, 1997). The forecasts
are designed on the premise of assuming that the time series evolves through the
following mapping function:
p
^
tþS
¼ f
^
ðp
t
; p
t21
; . . . ; p
t2ðm21Þ
Þ; uÞ ð11Þ
A prediction function is then designed inorder to extend the observations of the original
time series andis usedto estimate the model encapsulatedwithinthe “skeleton” of the ?tted
model. From equation (11), we de?ne the generic vector of parameters that govern the
shape of the mapping function
^
f ¼ f ð
^
uÞ using the historical time series {p
t
, p
tþ1
, . . . , p
N
},
to obtain the following one-step-ahead (i.e. s ¼ 1) forecasting function:
p
^
Nþ1
¼ f
^
ðp
N2S
; p
N2S21
; . . . ; p
N2S2ðm21Þ
Þ; uÞ ð12Þ
The forecasts for the two-regime and three-regime TARmodel speci?cations are obtained
by substituting the forecasting function given in equation (10) into TAR regressions (3)
and (5). To accommodate threshold effects, the indicator functions incorporated in the
forecasting functions are then revised to x
TAR2
(g
*
1
) ¼ (x
t
0
I.(p
NþS
# g
1
) , x
t
0
I.(p
NþS
.g
1
)) for the two-regime TAR speci?cation; and x
TAR3
(g
*1
, g
*2
) ¼ (x
TAR3
0
I.(p
NþS
# g
1
), x
TAR3
‘ I.(g
1
, p
NþS
# g
2
), x
TAR3
0
I.(p
NþS
. g
2
)) for the three-regime
TAR model in order to produce the forecasts for
NþS
. In assessing the performance of the
forecasts, we estimate the mean absolute percentage error (MAPE):
MAPE ¼
h
1=n
X
n
i¼1
absðð
^
p
t
2p
t
Þ=p
t
Þ
i
*
100 ð13Þ
Where n is the number of forecast periods (i.e. n ¼ 1) and
^
p
t
is the forecast value of p
t
. As
noted by Dacco and Satchell (1999), if the time series is generated by a regime-switching
process, the MAPEof a linear model may be smaller than the MAPEof the true nonlinear
model. Therefore, we also apply the root mean square error (RMSE) for evaluating the
forecast estimates:
RMSE ¼
h
ð1=n
X
n
i¼1
ðð
^
p
t
2p
t
Þ=p
t
Þ
2
i
*
100Þ
1=2
ð14Þ
Table VI presents the results of the of the forecast values for TAR and AR models in
comparison with the original time series. The lower comparative RMSPE and MAPE
values associated with data estimates of the TAR model speci?cations prove that TAR
model estimates provide superior in-sample ?ts when compared with the linear ARmodel
estimates for all observed in?ation series. These results are in coherence with those
presented by Clements and Smith (1997) who observe that TAR speci?cations are more
appropriate in ?tting univariate macroeconomic data in comparison to linear AR
counterparts.
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6. Conclusions
This study sought to investigate asymmetric behaviour in South African in?ation by
exploiting monthly data of four aggregate in?ation indices and 18 disaggregate
components of commodities andservices for the post in?ationtarget periodFebruary2000
to December 2010. In addressing the issue of asymmetry in the South African in?ation
process, this paper has reached three main conclusions. First, the analysis depicts the
presence of an aggregation bias, that is, aggregate in?ation is shown to be more persistent
than a majority of its underlying components. This result re?ects the need for improved
measures of aggregate in?ation if monetary policy is to accommodate the underlying
factors of in?ation in its targeting practices. A similar view is held by the Riskbank in
believing that decision making and communication from a monetary policy standpoint
can be improved by making the operational measures of in?ation more precise.
Second, in view of in?ation persistence having been incorporated in recent
theoretical analysis of monetary policy, the ?ndings of this study also have clear-cut
theoretical implications. Most existing macroeconomic models assume that in?ation
evolves as a linear process and thus anticipate a uniform response of in?ation to
monetary policy shocks. However, our ?ndings suggest that persistence in the in?ation
process is highly asymmetric and this, in turn, implies that the response of in?ation to
policy shocks may not be homogeneous. Our work can be extended by examining
whether an asymmetric in?ation process can be modeled as a stylized fact in
sophisticated models of monetary policy analysis. This development would be
complementary to the existing asymmetric versions of the Phillips Curve and Okun’s
Law speci?cations already incorporated in monetary policy analysis. Moreover, it
would be of interest to evaluate whether these asymmetric models could be used to
produce better in?ation forecasts as a means of enabling monetary authorities to apply
better policy decisions in their attempts to keep in?ation under control.
Lastly, in bridging the obtained empirical results to practical policy conduct, South
African monetary authority efforts may prove ineffective in controlling in?ation within
band-widths de?ned by the middle regimes of the estimated TAR models. Of particular
interest pertaining to the obtained results, are the existing unit roots found between the
rates of 4.7-8.5 percent for core in?ation and for rates of above 4.4 percent for CPI
in?ation. These band-widths are of importance as both of the aforementioned
aggregated measures of in?ation play an essential role in guiding the SARB in their
policy conduct. Within these identi?ed band-widths, in?ation would be best controlled
by focusing on alternative market-based policies that aimat simultaneously in?uencing
the demand as well as the supply-side of the macroeconomy. Only at levels below
4.5-4.7 percent, when the persistence measured in core in?ation and CPI in?ation is
minimal, would the sole use of direct monetary instruments prove to be most effective in
policy conduct.
The policy implications drawn from these results are essentially two-fold. On one
hand, the in?ation target may have to be re-adjusted to accommodate higher and/or
lower target ranges if short-term policy instruments are continued to be relied on for
policy conduct. On the other hand, if the narrow in?ation target of 3-6 percent where to
remain unchanged, the adoption of other market-based policies may prove useful in
ensuring that in?ation remains within its target. On the frontier of such suggested
policies are dual in?ation and employment/output targets and a real exchange rate
targeting frameworks.
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Further reading
Babetskii, I., Coricelli, F. and Horvath, R. (2007), “Measuring and explaining in?ation persistence:
disaggregate evidence on the Czech Republic”, Working Paper Series No. 1, Research
Department, Czech National Bank, Prague, September.
Dickey, D. and Fuller, W. (1979), “Distribution of the estimators for autoregressive time series
with a unit root”, Journal of the American Statistical Association, Vol. 74, pp. 427-31.
Kumar, M. and Okimoto, T. (2007), “Dynamics of persistence in international in?ation rates”,
Journal of Money, Credit and Banking, Vol. 39 No. 6.
About the author
Andrew Phiri is a Lecturer of Finance Theory and Markets. His latest publications were included
in the Journal of Sustainable Development in Africa (2010) and Economics Bulletin (2011) and he
has received invitations from the South African Reserve Bank (SARB) to present his current
research output. Andrew Phiri can be contacted at: [email protected]
In?ation
persistence in
South Africa
269
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doc_350055678.pdf
The purpose of this paper is to evaluate threshold effects in the persistence of South
African aggregate inflation data
Journal of Financial Economic Policy
Threshold effects and inflation persistence in South Africa
Andrew Phiri
Article information:
To cite this document:
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Economic Policy, Vol. 4 Iss 3 pp. 247 - 269
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Threshold effects and in?ation
persistence in South Africa
Andrew Phiri
Department of Economics and Management Sciences,
School of Economics, North West University, Potchefstroom, South Africa
Abstract
Purpose – The purpose of this paper is to evaluate threshold effects in the persistence of South
African aggregate in?ation data.
Design/methodology/approach – The conventional approach for assessing the degree of
persistence within an in?ation process is via its integration properties. This study makes use of
univariate threshold autoregressive (TAR) models and associated unit root testing procedures to
investigate the integration properties of the in?ation data. Out-of-sample forecasts are further
performed for the TAR models and their linear counterparts.
Findings – The empirical results con?rm threshold effects in the persistence of all employed
aggregated measures of in?ation, whereas such asymmetric effects are ambiguous for disaggregated
in?ation measures. None of the observed series is found to be stationary in their levels. The
out-of-sample forecasts for all TAR models outperform their linear counterparts.
Practical implications – Given the scope of the study, the empirical analysis provides insight with
concern to the performance of in?ation subsequent to the adoption of the in?ation target regime in
South Africa. Of particular interest are the low persistence levels observed at in?ation rates of below
4.7 and 4.4 percent for core and CPI in?ation, respectively, as both these aggregated measures of
in?ation play an essential role in guiding monetary policy conduct within the economy. The overall
?ndings imply that on an aggregate level, the South African Reserve Bank’s (SARB’s) current in?ation
target of 3-6 percent encompasses a non-stationary in?ation range and thus proves to be restrictive on
monetary policy conduct.
Originality/value – The paper ?lls in an important gap in the academic literature by evaluating
asymmetric effects in the integration properties of in?ation, at both aggregated and disaggregated
levels, for the exclusive case of South Africa.
Keywords South Africa, Monetary policy, In?ation, Macroeconomics, Money supply, Credit,
Time-series models, Single equation models, Single variables, Mathematical and quantitative methods,
De?ation, Business ?uctuations and cycles, Monetary economics, Central banking
Paper type Research paper
1. Introduction
In the ?eld of practical macroeconomic analysis, policy formulators are primarily
concerned with the behavioural characteristics of macroeconomic variables as they
converge towards a described or desired equilibrium steady-state. Macroeconomic
shocks and associated policy directives implemented in response to such shocks often
result in unprecedented ?uctuations in macroeconomic variables, which under
Inconsistent or irregular occurrence, lead to temporary shifts of these macroeconomic
variables from their steady-states. With reference to monetary policy conduct, in?ation
bears no exception to this rule. Following a particular shock to the in?ation process,
monetary policy actions would ensure that shocks to in?ation only exhibit temporary
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1757-6385.htm
JEL classi?cation – C22, C2, E31, E3, E52, E5
In?ation
persistence in
South Africa
247
Journal of Financial Economic Policy
Vol. 4 No. 3, 2012
pp. 247-269
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576381211245971
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effects, and consequentially, monetary authorities may aspire to randomly ?uctuate
in?ation around a certain mean or steady-state target (Chiquiar et al., 2010). Any
observed deviations of in?ation from its mean or steady-state are assumed to be an
outcome of persistence. The notion of in?ation persistence depicts that in the event of a
shock to the macroeconomy, in?ation may nonpermanently deviate from its long-run
equilibrium state. In?ation persistence, in this sense, provides a rather convenient
measure of the speed of convergence on the adjustment of in?ation towards its
steady-state equilibrium following the occurrence of an economic shock. The quicker
in?ation adjusts back to its established equilibrium, the less persistent in?ation is
assumed to be.
In monetary policy jargon, the aforementioned translates to a less persistent
in?ation process being preferred by Reserve Banks since this implies that in?ation will
adjust less resiliently to its equilibrium level in the presence of a macroeconomic shock.
The higher the speed at which in?ation converges back to its equilibrium after an
economic shock, the less complicated the central bank’s task of maintaining price
stability (Darvas and Varga, 2006). High in?ation persistence ultimately presents itself
as a major challenge for monetary policy and is believed to have been the underlying
factor behind the failure of a number of stabilization programmes (Moreno and Villar,
2009). Therefore, an in?ation process exhibiting low levels of persistence re?ects a
macroeconomic environment in which policymakers are presumptuously able to
“effectively” control prevailing or intended in?ation levels. In maintaining low levels of
persistence in the in?ation process, monetary authorities may be regarded as
enhancing their policy obligation of credibility.
An important aspect pertaining to the measurement of in?ation persistence is found
in its integration properties. Stationarity is considered important from the perspective
of macroeconomic modeling, since monetary authorities and macroeconomic model
builders tend to dwell on the assumption of the in?ationary process assuming a
stationary data-generating process (DGP). In view of a non-stationary variable having
in?nite variance and crossing the estimated mean infrequently, in?ation targeting is
meaningless when in?ation is established to contain a unit root (Halunga et al., 2009).
When in?ation behaves as a random-walk process, then the best forecast of the
following year’s in?ation is the most recent observed in?ation and the predictability of
in?ation never tends to an average value. It is standard practice for empirical works
pertaining to in?ation persistence to diagnose the integration properties of a univariate
autoregressive (AR) function of in?ation by using a “na? ¨ve” technique as proposed by
Andrews and Chen (2001). This method entails that if the sum of AR coef?cients
(SARC) is greater than or equal to unity, then the observed in?ation series is assumed
to contain a unit root, i.e. shocks to in?ation are permanent and the series never returns
to its original value. Conversely, if the SARC is of a positive integer below unity,
shocks to in?ation will eventually dissipate and the time series will revert to its
equilibrium level.
For instance, Gadzinski and Orlandi (2004) establish that for the European Union, the
Euro area and the USA, the SARC for consumer price index (CPI) in?ation data across
different monetary regimes has being signi?cantly below unity. Similarly, Filardo and
Genberg (2009) ?nd an SARC below unity for Korea, New Zealand and Australia
subsequent to the adoption of in?ation targeting regimes. For non-in?ation targeting
Asian economies, Gerlach and Tillmann (2011) ?nd that the SARC of in?ation has been
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close-to-unity across monetary regimes while for the case of in?ation targeting
economies the same authors establish that the SARC has subsequently dropped
signi?cantly below unity. On the other hand, there also exists a number of empirical
works that apply conventional unit root tests to determine the integration properties of
the observed in?ation series. Typically the results obtained from conventional unit root
tests tend to contradict those obtained using the na? ¨ve technique of Andrews and Chen
(2001). For Euro CPI, O’Reilly and Whelan (2005) ?nd a unit root in the in?ation process
for the period 1970-2002. Benati (2008) is also unable to reject the unit root hypothesis for
the US in?ation subsequent to 1951. With the focus on G7, Latin American, Asian and
African economies, Charemza et al. (2005) establish that between 1951 and 2001,
a stationary in?ation process is more prominent for G7 economies whereas for the
remaining economies, in?ation developed as a non-stationary process. Darvas and
Varga (2006) highlight the possibility of the observed ambiguity concerning the
integration properties of in?ation being attributed to the fact that a linear approximation
of an otherwise nonlinear underlying structure may be poor in capturing the in?ation
dynamics. Cuestas and Harrison (2010) further point out that conventional linear unit
root tests suffer fromimportant power distortions when nonlinearities exist in the DGP.
Recently, there has been a shift of focus in the empirical literature which attempts to
capture the asymmetric behavior of in?ation using a family of threshold econometric
models. Despite linear models providing the standard benchmark for macroeconomic
modeling, publications by Arango and Gonzalez (2001), Gregoriou and Kontonikas
(2009) and Cuestas and Harrison (2010) have shown how the in?ation process can be
best modeled as regime-switching processes. Essentially, regime-switching models
assume that the DGP of a time series can be captured in differing regimes that are
segregated by unique threshold variable point(s). Above and below the identi?ed
threshold level(s), the AR properties of the observed time series are deemed to differ in
statistical composition. In application to measuring in?ation persistence, this presents
an intriguing appeal as the SARC in the DGP of the univariate AR process of in?ation
is incidentally considered the most suitable reduced-form measure of its persistence
(Rangasamy, 2009). In this sense, the segregation of in?ation data into different
regimes allows for the determination of in?ation bandwidths in which the SARC (and
interpretively the persistence in the in?ation process) can be kept at a minimal.
With reference to the case of South Africa, Khadaroo (2005) employs a two-regime
threshold autoregressive (TAR) speci?cation and ?nds low persistence in CPI levels at
rates exceeding 14 percent in?ation. Khadaroo’s (2005) study offers support towards the
SARB in?ation target of 3-6 percent as being an over-restrictive policy strategy in
controlling the in?ation process. More recently, Mourelle et al. (2011) captured the
nonlinear dynamics of South African CPI in?ation within a two-regime smooth
transition AR (STAR) model. The authors ?nd that above rates of 0.84 percent, in?ation
is unstably persistent and therefore bears a risk to being effectively controlled by the
Reserve Bank. Based on the empirical evidence presented in the aforementioned studies,
there would be little reason to doubt the existence of two estimated thresholds in
South African in?ation. It is also noteworthy that while the studies of Khadaroo (2005)
and Mourelle et al. (2011) provide evidence of existing asymmetries in South African
in?ation, the integration properties of the data have not been previously investigated
using formal asymmetric unit root tests. Presented with these circumstances, our study
adopts a three-regime TAR model in preference to other alternatives on the basis of the
In?ation
persistence in
South Africa
249
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model’s ability to simultaneously capture asymmetric behaviour of in?ation and
investigate possible unit roots for higher-order threshold levels, i.e. two threshold points.
Our paper further takes heed of allegations in the literature that are suggestive of a
certain biasness ascribed towards pragmatic studies which fail to account for
persistence associated with disaggregated measures of in?ation. This phenomenon
implies that idiosyncratic shocks tend to disappear when a substantial number of series
are aggregated (Clark, 2006). Our study therefore widens the scope of investigation and
employs higher-order TAR frameworks to quantify and contrast the integration
properties of aggregated as well as disaggregated measures of South African in?ation.
The remainder of the paper is structured as follows. The following section provides
an overview of monetary policy developments in South Africa while Section 3 of the
paper presents the theoretical motivation for the study. Section 4 of the paper formally
outlines methodology used in the paper. The empirical analysis is then conducted in
Section 5 and the paper is concluded in Section 6 by integrating the overall empirical
?ndings of the study with theoretical and policy implications.
2. An overview of monetary policy in South Africa
Sichei (2005) conveniently identi?es ?ve distinct monetary policy regimes adopted by
the SARB following the termination of the Bretton Woods system namely; liquid-asset
based system, mixed system, cost of cash reserves based system with monetary
targeting, repurchase agreement (repo) system with both monetary targeting and
informal in?ation targeting; and a repo system with a formal in?ation target. The ?rst
two monetary policy regimes are representative of conservative Keynesian policies as
employed from the 1960s until the mid-1980s. These regimes were regarded as
ineffective monetary policies on the basis of their non-market approach towards
monetary policy. Following the de Kock Commission’s report in 1986, the SARBdecided
to adopt a pragmatic monetarist approach to policy conduct in which M3 money supply
targets became the anchor of monetary policy in South Africa. However, due to ?nancial
liberalization and other structural changes experienced in South Africa during the
1990s, money supply targeting proved to be an inappropriate means of controlling
in?ation. This was mainly due to instabilities found in the demand for money function
(Nell, 2000). Accordingly, the SARB sought to take a more eclectic approach towards
monetary policy which involved the monitoring of a wide-range of ?nancially related
economic indicators. Following the Asian ?nancial crisis of 1997-1998, an informal
in?ation targeting regime became active policy for the SARB until February 2000.
Entering a new millennium, the SARB decided to shift from its eclectic monetary
policy approachand announcedthe adoption of a formal in?ation target frameworkwith
targets of between 3 and 6 percent set to have been met in 2002. The SARB viewed this
shift as necessary since the eclectic framework created uncertainties and the Reserve
Bank’s decisions were seen to be in con?ict with the stated guidelines for the growth in
money supply and bank credit extension (Muhanna, 2006). The in?ation target mandate
was favoured based on the premise of its transparency and accountability which are
intended to enhance policy credibility as a means of curbing in?ation expectations of
economic agents. Whilst such an in?ation targeting regime may appear feasible for
industrialized economies, concerns have been directed towards whether such a policy
framework is suitable for the South African macroeconomy in face of its more severe
problems such as unemployment and job creation. Take for instance, Kaseeram and
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Contogiannis (2011) who ?nd that the adoption of the SARB’s in?ation target regime has
not being effective in controlling in?ation through the uncertainty channel.
Bonga-Bonga and Kabundi (2010) also establish that shocks to the repo rate do not
produce desirable effects in curbing in?ation through the channel of money demand in
South Africa whilst Gupta and Uwilingiye (2008) demonstrate on howthe Reserve Bank
would have produced lower in?ation rates had monetary authorities shown consistency
in intermediate policy objectives prior to the in?ation target regime. A recent study by
Phiri (2010) further suggests that a mid-range in?ation target of 8 percent is suf?cient in
terms of maximizing economic growth in South Africa. Comert and Epstein (2011) more
formally encompass the aforementioned arguments by putting forth the implication that
the sole manipulation of short-term interest rates is not the most effective policy
instrument for South African monetary authorities. Besides, the forecastability of
in?ation depends on the observed persistence in the in?ation process and Mourelle et al.
(2011) have demonstrated how South African in?ation has been highly persistent
throughout the entire in?ation targeting era.
Despite the current success of the in?ation target regime being, for a greater part of
it, due to its credibility, commentators such as McKinley (2008) have highlighted the
risk that supply shocks pose towards the Reserve Bank in adopting a narrowly de?ned
in?ation target. Initially, the in?ation targeting regime did not begin on a positive note,
as indicated by a target breach of in?ation performance in 2002-2003; caused by a
sudden burst in the out?ow of short-term capital which resulted in a depreciation of the
Rand (Gil-Alana, 2010). Accompanied with the currency depreciation, were sharp
increases in domestic and imported food prices while in the international arena, CPI
in?ation was being further aggravated by increases in world oil prices. Another
noteworthy period depicting signi?cant supply shocks is acquainted with the global
?nancial crisis of 2007-2008 caused by the closing down of major banks in the USA.
This period accounts for the highest in?ation rates experienced in South Africa during
the in?ation targeting period. During both in?ationary periods, the SARB’s response
was reserved towards aggressively manipulating interest rates in fear of further
aggravating macroeconomic instability. However, it was after the 2008 ?nancial crisis
that the SARB began paying more attention to volatility of exchange rates and placing
emphasis on the role of asset prices as a means of ensuring stability in ?nancial
markets and the South African economy as a whole. The policy responses taken by the
SARB have raised concerns as to whether the Reserve Bank may have adopted a
subjective in?ation target mandate intended to restrict aggregate demand yet a
majority of its experienced problems are caused by supply-oriented factors. Overall,
there are a lot of indications as to why acquiring new tools of monetary policy is likely
to be necessary in addressing problems of ?nancial stability, unemployment and
inequality in the South African economy (Comert and Epstein, 2011).
3. Theoretical motivation of the study
From a theoretical perspective, in?ation persistence is often considered as a
post-Keynesian phenomenon and can be derived from models that incorporate
nominal rigidities generating price stickiness. The price formation mechanism that
characterizes these sticky price models have their roots theoretically embedded in the
works of Taylor (1979, 1980) and Calvo (1983). Theoretical models based on price
stickiness are concerned with describing the micro foundational dynamics of in?ation
In?ation
persistence in
South Africa
251
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adjustment in response to various economic shocks and monetary policy actions.
Speci?cally, the dynamic in?ation adjustments have been deemed a theoretically
important component in determining the signi?cance of the recently popularized New
Keynesian Phillips Curve (NKPC) which is fundamentally based on the principles of
price stickiness (Kang et al., 2009). The ability of the NKPC model to ef?ciently analyze
important macroeconomic variables within a monetary policy framework has been what
Brissimis and Magginus (2008) refer to as “[. . .] the closest [theoretical model
framework] there is to standard perfection [. . .] ”. The nature of in?ation dynamics is
arguably the most distinctive feature of the forward-looking NKPCand this bears a close
theoretical relation with the framework of the forward-looking in?ation target monetary
regime (Du Plessis and Burger, 2006). Therefore, the paper intentionally employs the
New Keynesian speci?cation of the Phillips Curve as a baseline model to capture the
level of persistence in the in?ation process. In its basic structural form the NKPC
expresses in?ation as a function of expected future in?ation and some measure of a
?rm’s real marginal costs or excess demand:
p
t
¼ aE
t
p
tþ1
þbx
t
ð1Þ
This traditional structural in?ation equation identi?es two types of persistence
associated with the model’s in?ation dynamics; one being expectations-based in?ation
persistence (i.e. aE
t
p
tþ1
) and the other being extrinsic in?ation persistence (i.e. bx
t
).
Expectations-based in?ation persistence is theorized as a result of the distorted
formation of expected future in?ation. On the other hand, extrinsic in?ation persistence
is determined by the real marginal costs of ?rms or by the output gap of the
macroeconomy. Both expectations-based and extrinsic persistence are categorized as
“inherited” in?ation persistence since in?ation, in both circumstances, inherits its
persistence from the unrelenting movements in its driving variables (Dossche and
Evereart, 2005). In practice, empirical sources of dif?culty concern the characteristics of
the proper measure of the driving variable or excess demand as well as the assumption
concerning an appropriate proxy of expected in?ation (Brissimis and Magginus, 2008).
In consequence of its strictly forward-looking nature, the “traditional” NKPC has
been criticized for being able to generate price stickiness without re?ecting in?ation
inertia which inevitably leads to the unrealistic postulation of complete ?exibility in the
in?ation process. The “traditional” NKPC therefore predicts that once factors that give
rise to high in?ation have passed, in?ation can return to its equilibrium without
suffering a temporary reduction in economic activity (Sheedy, 2010). According to
Karanassou and Snower (2007), this controversial phenomenon of in?ation “jump
behavior” has been labeled “the persistence puzzle”. In an attempt to rectify the much
debated “persistence puzzle” several models address this issue by introducing the
lagged value of in?ation into the NKPC. Fuhrer and Moore (1995) show that a staggered
wage contract model in which agents care about relative wages can account for the
backward-looking component of in?ation. Gali and Gertler (1999) present an alternative
theory in which a fraction of ?rms rely on a rule-of-thumb when setting prices while
Mankiw and Reis (2002) introduce in?ation inertia through information lags in
price-setting mechanisms. Christiano et al. (2005) argue that in times when actual pricing
decisions are made, ?rms continually re-index their prices in line with past in?ation.
All-in-all, these price-setting developments in the New Keynesian in?ation dynamics
have resulted in the formation of a “hybrid” version of the NKPC. The hybrid
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New Keynesian Phillips Curve (HNKPC) incorporates both forward-looking and
backward-looking elements into the New Keynesian framework and is re?ected in the
following structural in?ation equation:
p
t
¼ rp
t21
þaE
t
p
tþ1
þbx
t
ð2Þ
The backward-looking dynamical behavior allows for deviations of observed in?ation
rates fromthe equilibriumto persist due to consecutive prior periods of in?ation (Dossche
and Evereart, 2005). Overall, the general classi?cation of identi?able lag persistence
(i.e. ap
t21
) inthe structural in?ationdynamics is knownas “intrinsic or inherent” in?ation
persistence. The extent to which in?ation determination is dominantly backward-looking
as opposed to forward-looking has been empirically proved in the studies of Sbordone
(2002), Rudd and Whelan (2005), Fuhrer (2007) and Whelan (2007). However, it has been
argued that the obtained results are sensitive to the statistical methods employed and the
observed persistence may be due to the existence of unaccounted structural changes
(Gadea and Mayoral, 2006). Furthermore, Sheedy (2010) highlights a particular danger in
these studies assuming a constant hazard function associated with the in?ation dynamics
of the NKPC. The empirical performance of an estimated nonlinear DSGE model of
in?ation persistence, as demonstrated in the works of Amisano and Tristani (2010)
con?rms the plausibility of these arguments. Theoretically, developments by Charemza
and Makarova (2009) have integrated a nonlinear component into the intrinsic portion of
in?ation in the HNKPC. The motivation behind their theory is prompted by the fact that
the standard HNKPC and other macroeconomic policy models assume stationarity in the
in?ation process where such a presumption may not conform to actual time series data.
Their approach into incorporating nonlinearities within the in?ation process is achieved
by modeling in?ation expectations as a collective function of the expected real marginal
cost or output gap (E
t
x
t
) and an error representative of a monetary shock induced by
policy-makers, i.e. ((2lg
t21
)(p
t21
)). Expected in?ation (E
t
p
tþ1
) within the model is
expressed as:
E
t
p
tþ1
¼ bE
t
x
t
þ ð2lg
t21
Þp
t21
ð3Þ
The parameter measuring the monetary policy effect, l, is bound by the condition
0 , l , 1 and is introduced as a means of ensuring that in?ation strictly ?uctuates
between a stationary I(0) process and a nonstationary I(1). By making use of equations (2)
and (3), monetary policy actions can be contained within the following structural in?ation
equation:
p
t
¼ ð1 2lg
t21
Þp
t21
þbE
t
x
t
ð4Þ
Within the model, the effects of monetary policy on in?ation persistence can be described
as follows. When the policy factor is a non-zero integer, i.e. l – 0, then monetary policy is
effective in the sense of containing in?ation within the limits of being a stationary I(0)
process. On the other hand, when the policy factor is l ¼ 0; then in?ation evolves as
a nonstationary I(1) process and the monetary authorities do not have effective control
over it. Ideally, in?ation persistence would be measured in a multivariate AR model as a
lag between monetary policy shock and the peak response inin?ation. However, given the
possibilityof the in?ationprocess switchingbetween anI(0) andI(1) process, the nonlinear
in?ation mechanism within the described theoretical framework cannot be captured
In?ation
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within a conventional multivariate vector autoregressive (VAR) speci?cation. As
indicated by Batini (2002), a VAR systemwould require all the observed data variables to
be constantly integrated of similar I(0) order thereby giving rise to this empirical
limitation. Based on the available academic literature, an alternative and highly
standardized practice in quantifying the persistence in in?ation is to capture it as an
intrinsic or inherent process within a univariate AR speci?cation. This approach has an
advantage in terms of simplicity and Batini (2002) describes it as:
[. . .] a reduced-form property [analysis] of in?ation that [simultaneously] manifests the
underlying pricing process, the conduct of monetary policy and the expectations formation
process of price-setting agents. Changes in any of these three factors will in?uence the
autocorrelation properties of in?ation [. . .].
Incidentally in?ation in South Africa is largely subject to intrinsic in?ation persistence
and is responsible for aggravating the overall containment of in?ation within the
economy (South African Reserve Bank, 2009). Therefore, this paper’s approach into
capturing the described theoretical nonlinear in?ation dynamics in application to
South African time series data is via a univariate regime-switching econometric
framework.
4. Methodology
4.1 Quantifying in?ation persistence within a three-regime SETAR model
Empirically, in?ation persistence is typically captured as the positive serial correlation
in a univariate AR in?ation model (see Dossche and Evereart, 2005; Darvas and Varga,
2006; Rangasamy, 2009; Sheedy, 2010 for examples):
p
t
¼
X
a
1i
p
t2i
þm
t
ð5Þ
From equation (5), the persistence of in?ation (r) is estimated as the sums of the AR
coef?cients of lag order i (i.e. r
p1
¼
P
a
1i
) and directly measures the sluggishness of
which in?ation responds to external shocks (Hondroyiannis and Lazareto, 2004). The
examination of potential nonlinearities in in?ation persistence is prompted via
Hansen’s (2000) estimation and testing of the TAR model. The extension of linear AR
model equation (5) into a three-regime TAR model is facilitated by determining
whether two supplementary regimes of in?ation coef?cients (i.e. r
p2
¼
P
a
2i
p
t2i
and
r
p3
¼
P
a
3i
p
t2i
) can signi?cantly be accommodated within the AR framework.
Denoting g
i
as a threshold breakpoint and I( · ) as the indicator functions of the TAR
process that segregates the function into different regimes, the encompassing
three-regime TAR model of in?ation is speci?ed as:
p
t
ðgÞ ¼ a
1
þ
X
a
1i
þm
t1
I · ðp
t
# gÞ
þa
2
þ
X
a
2i
þm
t2
I · ðg
1
, p
t
, g
2
Þ
þa
3
þ
X
a
3i
þm
t3
I · ðp
t
. g
2
Þ
ð6Þ
The empirical process is instigated by reducing equation (6) into a two-regime TAR
by assuming g
2
¼ 0, such that initially there exists one threshold estimate point
(i.e. g
1
¼ g). Hansen (2000) suggests that the least squares (LS) estimator of the
threshold g can be attained by minimizing the residual sum of squares (RSS) within
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a search region de?ned by G
1
¼ [g
^
1min
, g
^
1max
]. In attaining a threshold estimate of
g
^
1
, Hansen (2000) has shown that the estimation technique can be extended to the
context of a multiple change point model. The joint LS estimates of double-threshold
points (g
1
, g
2
) are de?ned as the values which jointly minimize the function of RSS (g
1
, g
2
)
given the threshold condition of g
1
, g
2
and a search region G
2
¼ [g
^
2min
, g
^
2max
].
It should be noted that since the ?rst threshold estimate, g
^
1
, is initially obtained from a
sum squares of errors function which ignores the presence of a third regime, then g
^
1
cannot be deemed as an asymptotically ef?cient threshold estimate in a double-threshold
TAR model. Hansen (2000) thereby proposes that an asymptotically ef?cient estimate of
the ?rst threshold value,
r
g
^
1
, can be obtained via a re?nement criterion.
Attributing to the Davies (1987) problem in which inference complexities are
associated with the unknown threshold parameters (g
1
, g
2
), Hansen (2000) suggests the
use of a bootstrap procedure on likelihood-ratio (LR) test statistics in constructing
asymptotically valid p-values. First, the hypothesis of a linear versus a two-regime
process is tested via an LR test statistic denoted as
r
LR
1
(g). The null hypothesis of no
threshold effects is accepted if the
r
LR
1
(g) statistic is of a smaller value when compared
with its associated bootstrapped critical value, c
z
(1 2 a). In such a case, in?ation is
best captured as a linear AR process as given equation (5). However, when
r
LR
1
(g)
. c
z
(1 2 a), a higher-order LR statistic, i.e.
r
LR
2
(g); is then used to test the hypothesis
of a two-regime against an alternative of a three-regime TAR process. If the alternative
hypothesis of a three-regime model is rejected (i.e.
r
LR
2
(g) # c
z
(1 2 a)), then the
singular threshold estimate is applicable whereas when
r
LR
2
(g) . c
z
(1 2 a) then two
re?ned threshold points,
r
g
^
1
and
r
g
^
2
, can be estimated. Once the optimal threshold
values are estimated and validated, the conditional-heteroskedastic covariance matrix
of b from equation (6) is estimated via backward substitution.
4.2 Unit root tests
Given the possibility of linear and nonlinear econometric structures associated with the
time series, three unit root tests are proposed for diagnosing the integration properties
of the time series, namely; the Augmented Dickey-Fuller (ADF), Enders and Granger
(1998) and Bec et al. (2004) unit root tests. Suppose that the both LR statistics fail to
reject their null hypotheses of linearity, this implies that the in?ation processes are best
?t using linear AR models. In this regard, the ADF unit root test is designed to
accommodate linear AR speci?cations and is based on the following test regression:
Dp
t
¼ cp
t21
þ
X
k
j¼1
g
j
Dp
t2j
þ1
t
ð7Þ
Under the null hypothesis of a unit root p
t
is I(1), which implies that c ¼ 0.
The Dickey-Fuller (DF) t-statistic,
DF
w
u
, is then applied in testing the null hypothesis
of c ¼ 0. The test statistic rejects the null hypothesis unit root when the
DF
w
u
statistic is of a lower absolute value compared with the critical values given by
MacKinnon (1996).
The second proposed unit root test has been devised by Enders and Granger (1998)
(E-G hereafter) who generalize the DF methodology to consider the null hypothesis of
a unit root against the alternative of a two-regime TAR model. This unit root test is
applied when one threshold is established within an in?ation series. Formally,
the nonlinear unit root test can be depicted and described in the following speci?cation:
In?ation
persistence in
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Dp
t
¼ c
1
p
t21
I · ðp
t21
$ 0Þ þc
2
p
t21
I · ðp
t21
, 0Þ þ1
t
ð8Þ
Where the governing heaviside indicator function used to accommodate possible
asymmetric effects within the AR decay is given as:
I · t ¼ 1 if p
t21
$ 0
0 if p
t21
, 0
ð9Þ
A modi?ed F-statistic (
NDF
w
u
) is used to test the null hypothesis of a unit root
(i.e. c
1
¼ c
2
¼ 0) against the alternative of an otherwise stationary two-regime
process. The hypothesis of a unit root can only be rejected if the
NDF
w
u
statistic is
larger in absolute value in comparison with the critical values as tabulated in Enders
and Granger (1998).
A ?nal scenario may occur in which the null hypotheses of linearity and one
threshold point, which are, respectively, tested by the
r
LR
1
(g) and
r
LR
2
(g) statistics, are
both rejected for a given series. The integration properties of such existing series are
examined through a nonlinear unit root testing procedure proposed by Bec et al. (2004).
Their econometric speci?cation suggests an application of a ?rst difference operator to
Hansen’s (2000) three-regime TAR model. The following condensed auxiliary
nonlinear in?ation function can best represent the above described unit root test:
p
t
¼ a
1
Dp
t21
þc
1
p
t21
þz1
t1
ðif p
t21
# 2g
*
Þ
þa
2
Dp
t21
þc
2
p
t21
þz1
t2
ðif p
t21
j j , g
*
Þ
þa
3
Dp
t21
þc
3
p
t21
þz1
t3
ðif p
t21 j j , g
*
Þ
ð10Þ
Restrictions of g
1
¼ 2g
2
¼ 2g and a
i
# 1, c
i
# 1 are imposed on the parameter
variables of equation (10) to rule out the possibility of explosive behaviour in any
existing unit roots. This also ensures that nonstationarity can only be detected in the
middle regime of signi?cant three-regime processes in which the entire series remains
globally ergodic. Kapetanois and Shin (2006) highlight the importance of a geometric
ergodicity as it implies:
[. . .] the existence of a unique stationary distribution for a [time series] such that [it]
converges to stationarity exponentially fast when it is initialized at an arbitrary ?nite value
[and] further implies B-mixing [coef?cients] with geometric decay [. . .].
Under the null hypothesis of a unit root in the middle regime, i.e. H
0
: a
1
¼ a
2
¼ a
3
;
c
1
¼ c
2
¼ c
3
¼ 0, a unit root process of Dp
t
¼ aDp
t21
þ z1
t
is tested, whereas under
the alternative hypothesis of H
1
: jc
1
j , 1, jc
2
j , 0, jc
3
j # 0, the regression reduces to a
stationary three-regime TAR process. In order to effectively test these described
hypotheses, there must be a singular threshold value of, g
*
which is plugged-into the
unit root test regression. Bec et al. (2004) suggest that the threshold value can be selected
a prior by the econometrician in testing for the unit root hypothesis. The asymptotic
distributions of these unit root tests are derived from Supremum-based tests on
the Wald, Lagrange multiplier (LM) and LR statistics, i.e.
BBC
W
SUP
,
BBC
LR
SUP
and
BBC
LM
SUP
. From these unit root connotations, a time series can only be rendered as a
stationary three-regime process if the above test statistics are of a smaller value in
comparison to their computed critical values.
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5. Data and empirical analysis
Having detailed the empirical procedures in the previous section, this section of the
study presents the application of the described methodology on experimental data.
Given that the objective of the study seeks to substantiate threshold effects in the
in?ation process for periods subsequent to the adoption of the in?ation targeting
mandate, the in?ation data that is collected and analyzed is bound between the monthly
periods of February 2000 and December 2010. The data consist of both aggregated and
disaggregated price indices. The aggregated series consists of the core in?ation index,
the total CPI, the total prices of goods and the total prices of services, with the latter
three series being obtained from the SARB database. The series of core in?ation is
obtained from the Statistics South Africa (SSA) database and by purpose serves to
capture the underlying in?ationary pressures that exclude highly volatile products from
its computation. The CPI data is considered as a plausible aggregated measure of
in?ation for the study since it provides a “[. . .] measure [of] in?ation in the economy so
that macroeconomic policy is based on comprehensive and up-to-date price information
[. . .] ” (Statistics South Africa, 2009). The CPI is constructed using the classi?cation of
individual consumption by purpose (COICOP) for individual components of various
commodities and service products which in aggregation forms the total prices in
commodities and services, respectively. In addition, the individual components of the
COICOP are used as the disaggregated measures of commodities and service in?ation
in this study. Table I provides a more formal decomposition of the aggregated and
disaggregated price indexes used in this study. The estimation results of the aggregated
in?ation data is presented in Table II, whereas those for disaggregated measures of
commodities and services are provided in Tables III-IV. The results of the unit root tests
are reported in Table V, whereas Table VI presents the out-of-sample forecasting
performance of the time series.
As is shown in Table II, the
r
LR
1
(g) statistic manages to reject the null hypothesis of
linear AR processes for all the observed aggregated in?ation data while the
r
LR
2
(g)
statistic cannot reject the hypothesis of a three-regime model for all the series with the
Core in?ation
Total CPI
Total consumer prices of goods Total consumer prices of services
Aggregated measures
Food Housing and utilities
Alcohol and tobacco Household contents, equipment and maintenance
Clothing and footwear Health
Housing and utilities Transport
Disaggregated measures
Household contents, equipment and maintenance Communication
Health Recreation and Culture
Transport Education
Communication Miscellaneous
Recreation and culture
Miscellaneous
Source: Author’s own tabulation
Table I.
Decomposition of the
aggregated and
disaggregated price
indexes
In?ation
persistence in
South Africa
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L
R
s
t
a
t
i
s
t
i
c
s
I
n
?
a
t
i
o
n
t
h
r
e
s
h
o
l
d
s
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e
r
s
i
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t
e
n
c
e
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e
a
s
u
r
e
s
T
i
m
e
s
e
r
i
e
s
r
L
R
1
(
g
)
r
L
R
2
(
g
)
r
g
^
1
r
g
^
2
L
a
g
o
r
d
e
r
r
p
1
¼
P
a
1
i
r
p
2
¼
P
a
2
i
r
p
3
¼
P
a
3
i
C
o
r
e
i
n
?
a
t
i
o
n
6
0
.
6
2
*
*
*
(
0
.
0
0
)
2
4
.
8
4
*
(
0
.
1
)
4
.
7
%
[
3
.
8
%
,
5
.
5
%
]
8
.
5
%
[
7
.
8
%
,
9
.
1
%
]
6
0
.
3
7
1
.
0
0
0
.
8
0
T
o
t
a
l
C
P
I
4
6
.
6
0
*
*
*
(
0
.
0
0
)
2
1
.
2
3
(
0
.
7
)
4
.
4
%
[
3
.
9
%
,
4
.
9
%
]
–
6
0
.
9
2
0
.
9
4
–
T
o
t
a
l
g
o
o
d
s
3
7
.
9
3
*
*
(
0
.
0
0
)
2
9
.
5
1
*
*
(
0
.
0
0
)
3
.
2
%
[
2
.
6
%
,
4
.
1
%
]
8
.
7
%
[
7
.
9
%
,
9
.
6
%
]
6
0
.
7
1
0
.
9
8
0
.
6
0
T
o
t
a
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e
r
v
i
c
e
s
6
6
.
3
7
*
*
*
(
0
.
0
0
)
5
2
.
6
4
*
*
*
(
0
.
0
0
)
2
.
7
%
[
2
.
1
%
,
3
.
5
%
]
7
.
6
%
[
6
.
8
%
,
6
.
4
%
]
6
0
.
8
7
1
.
1
7
0
.
0
1
N
o
t
e
s
:
S
i
g
n
i
?
c
a
n
t
a
t
:
*
*
*
1
,
*
*
5
a
n
d
*
1
0
p
e
r
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e
n
t
l
e
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e
l
s
;
t
h
e
b
o
o
t
s
t
r
a
p
p
-
v
a
l
u
e
s
o
f
t
h
e
L
R
t
e
s
t
s
a
r
e
r
e
p
o
r
t
e
d
i
n
(
)
a
n
d
t
h
e
o
p
t
i
m
a
l
l
a
g
l
e
n
g
t
h
o
f
t
h
e
T
A
R
r
e
g
r
e
s
s
i
o
n
s
i
s
s
e
l
e
c
t
e
d
b
y
m
i
n
i
m
i
z
i
n
g
t
h
e
A
I
C
;
t
h
e
9
0
p
e
r
c
e
n
t
c
o
n
?
d
e
n
c
e
i
n
t
e
r
v
a
l
s
o
f
t
h
r
e
s
h
o
l
d
e
s
t
i
m
a
t
e
s
a
r
e
g
i
v
e
n
i
n
[
]
;
t
h
e
O
L
S
s
t
a
n
d
a
r
d
e
r
r
o
r
s
a
r
e
s
i
g
n
i
?
c
a
n
t
f
o
r
t
h
e
c
o
e
f
?
c
i
e
n
t
e
s
t
i
m
a
t
e
s
Table II.
Empirical results
of aggregated measures
of in?ation
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a
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s
h
o
l
d
s
P
e
r
s
i
s
t
e
n
c
e
m
e
a
s
u
r
e
s
T
i
m
e
s
e
r
i
e
s
r
L
R
1
(
g
)
r
L
R
2
(
g
)
r
g
^
1
r
g
^
2
L
a
g
o
r
d
e
r
r
p
1
¼
P
a
1
i
r
p
2
¼
P
a
2
i
r
p
3
¼
P
a
3
i
C
o
m
m
u
n
i
c
a
t
i
o
n
8
.
6
6
(
0
.
4
)
–
–
–
2
1
.
0
4
–
–
H
o
u
s
i
n
g
7
.
0
3
(
0
.
9
)
–
–
–
3
0
.
9
7
–
–
F
o
o
d
1
3
.
6
8
(
0
.
8
)
–
–
–
5
0
.
9
7
–
–
R
e
c
r
e
a
t
i
o
n
1
8
.
2
1
(
0
.
2
)
–
–
–
5
0
.
9
4
–
–
H
o
u
s
e
h
o
l
d
c
o
n
t
e
n
t
s
1
7
.
9
4
(
0
.
2
)
–
–
–
4
0
.
9
3
–
–
C
l
o
t
h
i
n
g
1
8
.
6
8
(
0
.
3
)
–
–
–
3
0
.
9
3
–
–
H
e
a
l
t
h
1
1
.
8
1
(
0
.
7
)
–
–
–
5
0
.
9
2
–
–
A
l
c
o
h
o
l
1
8
.
9
7
(
0
.
2
)
–
–
–
5
0
.
9
1
–
–
T
r
a
n
s
p
o
r
t
3
1
.
0
9
*
*
(
0
.
0
)
1
7
.
4
1
(
0
.
6
)
3
.
7
%
[
2
.
5
%
,
5
.
6
%
]
–
6
0
.
7
3
0
.
7
7
–
M
i
s
c
e
l
l
a
n
e
o
u
s
2
6
.
0
9
*
(
0
.
1
)
2
6
.
2
2
*
(
0
.
1
)
1
.
6
%
[
0
.
1
%
,
2
.
7
%
]
7
.
5
%
[
5
.
4
%
,
8
.
9
%
]
6
0
.
9
0
1
.
0
7
0
.
7
8
N
o
t
e
s
:
S
i
g
n
i
?
c
a
n
t
a
t
:
*
*
*
1
,
*
*
5
a
n
d
*
1
0
p
e
r
c
e
n
t
l
e
v
e
l
s
;
t
h
e
b
o
o
t
s
t
r
a
p
p
-
v
a
l
u
e
s
o
f
t
h
e
L
R
t
e
s
t
s
a
r
e
r
e
p
o
r
t
e
d
i
n
(
)
;
t
h
e
o
p
t
i
m
a
l
l
a
g
l
e
n
g
t
h
o
f
t
h
e
T
A
R
r
e
g
r
e
s
s
i
o
n
s
i
s
s
e
l
e
c
t
e
d
b
y
m
i
n
i
m
i
z
i
n
g
t
h
e
A
I
C
;
t
h
e
9
0
p
e
r
c
e
n
t
c
o
n
?
d
e
n
c
e
i
n
t
e
r
v
a
l
s
o
f
t
h
r
e
s
h
o
l
d
e
s
t
i
m
a
t
e
s
a
r
e
g
i
v
e
n
i
n
[
]
;
t
h
e
O
L
S
s
t
a
n
d
a
r
d
e
r
r
o
r
s
a
r
e
s
i
g
n
i
?
c
a
n
t
f
o
r
t
h
e
c
o
e
f
?
c
i
e
n
t
e
s
t
i
m
a
t
e
s
Table III.
Empirical results of
disaggregated measures
of commodities
In?ation
persistence in
South Africa
259
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
4
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
L
R
s
t
a
t
i
s
t
i
c
s
I
n
?
a
t
i
o
n
t
h
r
e
s
h
o
l
d
s
P
e
r
s
i
s
t
e
n
c
e
m
e
a
s
u
r
e
s
T
i
m
e
s
e
r
i
e
s
r
L
R
1
(
g
)
r
L
R
2
(
g
)
r
g
^
1
r
g
^
2
L
a
g
o
r
d
e
r
r
p
1
¼
P
a
1
i
r
p
2
¼
P
a
2
i
r
p
3
¼
P
a
3
i
M
i
s
c
e
l
l
a
n
e
o
u
s
1
6
.
3
0
(
0
.
7
)
–
–
–
5
0
.
9
6
–
–
H
o
u
s
e
h
o
l
d
c
o
n
t
e
n
t
s
1
4
.
8
9
(
0
.
5
)
–
–
–
6
0
.
9
8
–
–
H
o
u
s
i
n
g
3
4
.
0
3
*
*
(
0
.
0
)
1
9
.
8
8
(
0
.
7
)
0
.
1
%
[
1
.
1
%
,
0
.
6
%
]
6
0
.
9
0
0
.
8
9
C
o
m
m
u
n
i
c
a
t
i
o
n
1
3
5
.
8
6
*
*
*
(
0
.
0
)
2
1
.
2
9
(
0
.
7
)
3
.
2
%
[
2
.
5
%
,
3
.
9
%
]
–
6
0
.
9
3
1
.
0
6
–
R
e
c
r
e
a
t
i
o
n
1
0
7
.
4
1
*
*
*
(
0
.
1
)
1
2
.
1
8
(
0
.
7
)
3
.
3
%
[
2
.
8
%
,
4
.
2
%
]
–
6
0
.
9
7
0
.
2
6
–
H
e
a
l
t
h
4
8
.
1
9
*
*
*
(
0
.
0
)
1
3
.
2
3
(
0
.
0
)
4
.
3
%
[
3
.
4
%
,
5
.
2
%
]
–
1
0
.
4
1
0
.
9
5
–
T
r
a
n
s
p
o
r
t
2
9
.
7
0
*
(
0
.
1
)
3
7
.
3
8
*
*
*
(
0
.
1
)
0
.
9
%
[
0
.
1
%
,
2
.
2
%
]
4
.
4
%
[
3
.
2
%
,
5
.
3
%
]
6
0
.
6
9
2
.
6
1
0
.
6
1
E
d
u
c
a
t
i
o
n
3
5
.
0
4
*
*
*
(
0
.
0
)
2
8
.
5
1
*
*
(
0
.
1
)
6
.
5
%
[
5
.
6
%
,
7
.
7
%
]
7
.
0
%
[
5
.
7
%
,
8
.
2
%
]
3
0
.
1
3
6
.
3
6
0
.
9
7
N
o
t
e
s
:
S
i
g
n
i
?
c
a
n
t
a
t
:
*
*
*
1
,
*
*
5
a
n
d
*
1
0
p
e
r
c
e
n
t
l
e
v
e
l
s
;
t
h
e
b
o
o
t
s
t
r
a
p
p
-
v
a
l
u
e
s
o
f
t
h
e
L
R
t
e
s
t
s
a
r
e
r
e
p
o
r
t
e
d
i
n
(
)
;
t
h
e
o
p
t
i
m
a
l
l
a
g
l
e
n
g
t
h
o
f
t
h
e
T
A
R
r
e
g
r
e
s
s
i
o
n
s
i
s
s
e
l
e
c
t
e
d
b
y
m
i
n
i
m
i
z
i
n
g
t
h
e
A
I
C
;
t
h
e
9
0
p
e
r
c
e
n
t
c
o
n
?
d
e
n
c
e
i
n
t
e
r
v
a
l
s
o
f
t
h
r
e
s
h
o
l
d
e
s
t
i
m
a
t
e
s
a
r
e
g
i
v
e
n
i
n
[
]
;
t
h
e
O
L
S
s
t
a
n
d
a
r
d
e
r
r
o
r
s
a
r
e
s
i
g
n
i
?
c
a
n
t
f
o
r
t
h
e
c
o
e
f
?
c
i
e
n
t
e
s
t
i
m
a
t
e
s
Table IV.
Empirical results of
disaggregated measures
of services
JFEP
4,3
260
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
4
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
L
i
n
e
a
r
t
i
m
e
s
e
r
i
e
s
D
F
w
u
T
w
o
-
r
e
g
i
m
e
t
i
m
e
s
e
r
i
e
s
N
D
F
w
u
T
h
r
e
e
-
r
e
g
i
m
e
t
i
m
e
s
e
r
i
e
s
B
B
C
W
S
U
P
B
B
C
L
M
S
U
P
B
B
C
L
R
S
U
P
F
o
o
d
(
g
o
o
d
s
)
2
1
.
9
1
(
2
2
.
2
5
)
{
2
5
.
0
4
}
T
o
t
a
l
C
P
I
3
.
7
1
(
2
.
7
5
)
C
o
r
e
i
n
?
a
t
i
o
n
1
8
.
3
2
(
1
1
.
3
4
)
1
5
.
1
0
(
1
0
.
0
1
)
1
6
.
6
1
(
1
0
.
6
5
)
C
o
m
m
u
n
i
c
a
t
i
o
n
(
g
o
o
d
s
)
2
2
.
1
4
(
2
8
.
2
3
)
T
r
a
n
s
p
o
r
t
(
g
o
o
d
s
)
2
.
1
6
T
o
t
a
l
g
o
o
d
s
2
5
.
7
2
(
1
0
.
8
5
)
1
9
.
8
0
(
9
.
6
3
)
2
2
.
5
0
(
1
0
.
2
2
)
H
o
u
s
i
n
g
(
g
o
o
d
s
)
2
1
.
1
6
(
2
5
.
6
1
)
H
o
u
s
i
n
g
(
s
e
r
v
i
c
e
s
)
2
.
5
7
T
o
t
a
l
s
e
r
v
i
c
e
s
2
8
.
0
4
(
1
2
.
7
5
)
2
1
.
1
4
(
1
1
.
0
9
)
2
4
.
2
7
(
1
0
.
4
2
)
R
e
c
r
e
a
t
i
o
n
(
g
o
o
d
s
)
2
1
.
4
9
(
2
9
.
4
4
)
C
o
m
m
u
n
i
c
a
t
i
o
n
(
s
e
r
v
i
c
e
s
)
5
.
3
1
(
1
.
8
5
)
M
i
s
c
e
l
l
a
n
e
o
u
s
(
g
o
o
d
s
)
2
3
.
0
9
(
1
5
.
9
6
)
1
7
.
9
2
(
1
3
.
2
5
)
2
3
.
0
9
(
1
4
.
5
2
)
H
o
u
s
e
h
o
l
d
c
o
n
t
e
n
t
s
(
g
o
o
d
s
)
2
2
.
5
3
(
2
6
.
7
5
)
R
e
c
r
e
a
t
i
o
n
(
s
e
r
v
i
c
e
s
)
6
.
3
9
(
2
.
6
4
)
T
r
a
n
s
p
o
r
t
(
s
e
r
v
i
c
e
s
)
4
7
.
9
8
(
3
5
.
6
3
)
{
2
1
.
2
8
}
3
3
.
2
6
(
2
7
.
1
6
)
{
1
1
.
9
4
}
4
3
.
3
6
(
3
1
.
7
8
)
{
1
4
.
3
1
}
C
l
o
t
h
i
n
g
(
g
o
o
d
s
)
2
1
.
7
7
(
2
9
.
0
1
)
H
e
a
l
t
h
(
s
e
r
v
i
c
e
s
)
5
.
8
2
(
2
.
9
4
)
E
d
u
c
a
t
i
o
n
(
s
e
r
v
i
c
e
s
)
5
4
.
8
3
(
3
7
.
4
9
)
{
2
2
.
7
8
}
4
2
.
6
1
(
3
0
.
2
2
)
{
1
5
.
6
9
}
5
2
.
3
8
(
3
2
.
1
8
)
{
1
7
.
9
4
}
H
e
a
l
t
h
(
g
o
o
d
s
)
2
1
.
9
4
(
2
8
.
1
5
)
A
l
c
o
h
o
l
(
g
o
o
d
s
)
2
1
.
9
1
(
2
8
.
8
5
)
M
i
s
c
e
l
l
a
n
e
o
u
s
(
s
e
r
v
i
c
e
s
)
2
.
4
7
(
2
6
.
4
1
)
H
o
u
s
e
h
o
l
d
c
o
n
t
e
n
t
s
(
s
e
r
v
i
c
e
s
)
0
.
5
5
(
2
9
.
5
7
)
1
0
%
2
2
.
5
8
2
.
8
3
1
6
.
1
8
1
5
.
5
9
1
5
.
7
7
5
%
2
2
.
9
0
3
.
6
0
1
8
.
4
1
7
.
6
3
1
7
.
8
9
1
%
2
3
.
5
1
5
.
3
8
2
3
.
0
1
2
1
.
7
6
2
2
.
2
3
N
o
t
e
s
:
T
h
e
t
e
s
t
s
t
a
t
i
s
t
i
c
s
a
s
s
o
c
i
a
t
e
d
w
i
t
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)
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r
e
g
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v
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n
i
n
{
}
;
t
h
e
l
a
g
l
e
n
g
t
h
f
o
r
t
h
e
A
D
F
t
e
s
t
s
t
a
t
i
s
t
i
c
i
s
s
e
l
e
c
t
e
d
b
y
m
i
n
i
m
i
z
i
n
g
t
h
e
A
I
C
Table V.
Unit root tests
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exception of in?ation in total CPI. Further referring to the results presented in Table II,
it can be seen that a single threshold of 4.4 percent is established for in?ation in total
CPI where above this level a signi?cant higher, close-to-unity SARC is observed.
Between in?ation rates of 4.7 and 8.5 percent, core in?ation exhibits the highest
persistence with the SARC being above unity in this regime, and the lowest SARC is
established at rates below 4.7 percent. Similarly for total goods and total services, the
highest SARC exists in the middle regimes (i.e. between 3.2 and 8.7 percent for total
goods and 2.7-7.6 percent for total services). The lowest SARC for both of these series is
found in the high regimes at in?ation rates of above 8.7 percent for total goods and
7.6 percent for total services. Given these relatively high SARC estimates obtained
from the TAR models, it is tempting to interpret these results as evidence of unit roots
existing in the data series. At this stage, such an interpretation is tentative and
warrants more formal unit root tests to con?rm these preliminary speculations.
The results in Table III present evidence of an aggregation bias in the data, that is, of
lower persistence in individual components of commodity products in comparison with
the total prices of commodities. Approximately, 60 percent of the disaggregated series of
commodities do not contain sums of autoregressive coef?cients (SARC) which can
substantially indicate nonstationary in their processes (i.e. recreation, household
contents, clothing, health, alcohol and transport). The remaining 40 percent of the
commodity series (i.e. communication, housing, food and miscellaneous commodities)
appear to re?ect random walks in their series and have similar SARC to those of their
aggregated counterparts. With regards to asymmetric effects in the data, both of
Hansen’s (2000) LRtest statistics fail to reject the hypothesis of no threshold effects for a
majority of the observed disaggregated series of commodities (i.e. communication,
housing, food recreation, household contents, clothing, health and alcohol). On the other
hand, the hypothesis of a two-regime TAR process is accepted for transport and
a three-regime TAR for miscellaneous commodities. For the case of transport in
commodities, one threshold point is estimated at 3.7 percent of which above this level,
AR ( p) TAR2 ( p) TAR3 ( p)
In?ation measure RMSE MAPE RMSE MAPE RMSE MAPE
Aggregate series
Core in?ation 0.25 0.07 0.17 0.06 0.15 0.05
Total CPI 0.29 0.17 0.19 0.14 N/A N/A
Total goods 0.37 0.14 0.31 0.14 0.29 0.12
Total services 0.88 0.25 0.53 0.18 0.37 0.12
Disaggregate series of commodities
Transport 1.28 1.02 1.09 0.90 N/A N/A
Miscellaneous 0.35 0.19 0.27 0.18 0.20 0.16
Disaggregate series of services
Housing 3.46 1.54 2.44 0.93 N/A N/A
Communication 0.65 0.44 0.62 0.41 N/A N/A
Recreation 3.80 0.35 2.33 0.28 N/A N/A
Health 1.69 0.13 1.09 0.11 N/A N/A
Transport 1.88 0.29 1.45 0.29 1.22 0.26
Education 0.18 0.02 0.17 0.03 0.11 0.02
Note: 120 historic time series observations were used for the out-of-sample forecasts
Table VI.
Out-of-sample forecast
for one-step-ahead
predictions: AR vs TAR
speci?cations
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in?ation exhibits a slightly higher SARC. Two signi?cant thresholds of 1.6 and
7.5 percent are also found for miscellaneous commodities. The highest SARC estimates
for miscellaneous commodities goods are established between 1.6 and 7.5 percent
in?ation rates while the lowest SARC exists at rates above 7.5 percent.
The results displayed in Table IV, display similar evidence of an aggregation bias
with respect to disaggregated measures of services as only housing and transport
services have SARC estimates that are closely emulated with those found in the total
prices of services. The SARC in individual components of services are found to be
generally higher and display more asymmetric effects than for the case of individual
commodity items. This result can be expected since production in the service sectors is
more labour intensive compared to the production of commodities (Lunneman and
Matha, 2005). In particular, Hansen’s (2000) threshold test results indicate that 71 percent
of the series (i.e. housing, communication, recreation, health, transport and education) can
be ?tted into nonlinear TAR processes, while the remaining series of household contents
and miscellaneous services are best represented as linear AR processes. The SARC
estimates associated with household contents, recreation, health, transport, education
and miscellaneous services indicate the possibility of unit roots in these processes.
A singular threshold is identi?ed for each of the following services; housing (0.1 percent),
communication (3.2 percent), recreation (3.3 percent) and health (4.3 percent). Lower
persistence is associated with in?ation in the lower regimes of communication and
health, while lower persistence is found in the higher regimes of housing and recreation.
Two thresholds estimates of 0.9 percent and 4.4 percent are established for transport
with the highest measures of persistence existing in the middle regime of the TAR
process and the lowest persistence being in the high regimes. The SARC estimates
associated with household contents, recreation, health, transport, education and
miscellaneous services indicate the possibility of unit roots in these processes.
In drawing comparisons between the unit root test results shown in Table V with
the SARC estimate results presented through Tables II-IV, the compliance of these
results with concern to the integration properties of disaggregated in?ation measures
produces mixed results. Contrary to the implications drawn from the SARC estimates
for disaggregated items, the unit root tests cannot reject the hypothesis of stationarity
in their levels for only three disaggregated series, i.e. food (goods), transport (goods)
and housing (services). The remainder of the disaggregated series are established to
contain unit roots in their process with transport (services) and education (services)
being the only indices that are found to be integrated of an order high than I(1). The
nonlinear unit root test performed on the aggregated in?ation series show that in their
levels, the null hypothesis of a unit root process in the middle regime (i.e. r
p2
¼
P
a
2i
)
cannot be rejected in their levels by the employed test statistics for all observed series.
Stationary, nonlinear processes are attained for all aggregate series in their respective
?rst differences. It is worth noting that the implied integration properties of the SARC
estimates for the aggregated time series and their associated unit root tests seem to be
in mutual compliance with each other as they are suggestive of existing unit roots in
the middle regimes of the observed processes.
The evaluation of the performance of the nonlinear TAR processes against their
counterpart linear AR processes is presented in an exposition of an out-of-sample
analysis for the observed time series. The objective of these out-of-sample ?t exercises
is to determine whether a nonlinear or linear ?tted time series provides a better
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indication of their predictive ability of the observed time series. In extracting
out-of-sample forecast plots, a “skeleton method” is used to derive the one-step-ahead
forecasts and entails setting the errors of the observed linear and threshold processes
to zero such that an approximation of an expectational function of random variables is
drawn through a function of its expectation (Clements and Smith, 1997). The forecasts
are designed on the premise of assuming that the time series evolves through the
following mapping function:
p
^
tþS
¼ f
^
ðp
t
; p
t21
; . . . ; p
t2ðm21Þ
Þ; uÞ ð11Þ
A prediction function is then designed inorder to extend the observations of the original
time series andis usedto estimate the model encapsulatedwithinthe “skeleton” of the ?tted
model. From equation (11), we de?ne the generic vector of parameters that govern the
shape of the mapping function
^
f ¼ f ð
^
uÞ using the historical time series {p
t
, p
tþ1
, . . . , p
N
},
to obtain the following one-step-ahead (i.e. s ¼ 1) forecasting function:
p
^
Nþ1
¼ f
^
ðp
N2S
; p
N2S21
; . . . ; p
N2S2ðm21Þ
Þ; uÞ ð12Þ
The forecasts for the two-regime and three-regime TARmodel speci?cations are obtained
by substituting the forecasting function given in equation (10) into TAR regressions (3)
and (5). To accommodate threshold effects, the indicator functions incorporated in the
forecasting functions are then revised to x
TAR2
(g
*
1
) ¼ (x
t
0
I.(p
NþS
# g
1
) , x
t
0
I.(p
NþS
.g
1
)) for the two-regime TAR speci?cation; and x
TAR3
(g
*1
, g
*2
) ¼ (x
TAR3
0
I.(p
NþS
# g
1
), x
TAR3
‘ I.(g
1
, p
NþS
# g
2
), x
TAR3
0
I.(p
NþS
. g
2
)) for the three-regime
TAR model in order to produce the forecasts for
NþS
. In assessing the performance of the
forecasts, we estimate the mean absolute percentage error (MAPE):
MAPE ¼
h
1=n
X
n
i¼1
absðð
^
p
t
2p
t
Þ=p
t
Þ
i
*
100 ð13Þ
Where n is the number of forecast periods (i.e. n ¼ 1) and
^
p
t
is the forecast value of p
t
. As
noted by Dacco and Satchell (1999), if the time series is generated by a regime-switching
process, the MAPEof a linear model may be smaller than the MAPEof the true nonlinear
model. Therefore, we also apply the root mean square error (RMSE) for evaluating the
forecast estimates:
RMSE ¼
h
ð1=n
X
n
i¼1
ðð
^
p
t
2p
t
Þ=p
t
Þ
2
i
*
100Þ
1=2
ð14Þ
Table VI presents the results of the of the forecast values for TAR and AR models in
comparison with the original time series. The lower comparative RMSPE and MAPE
values associated with data estimates of the TAR model speci?cations prove that TAR
model estimates provide superior in-sample ?ts when compared with the linear ARmodel
estimates for all observed in?ation series. These results are in coherence with those
presented by Clements and Smith (1997) who observe that TAR speci?cations are more
appropriate in ?tting univariate macroeconomic data in comparison to linear AR
counterparts.
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6. Conclusions
This study sought to investigate asymmetric behaviour in South African in?ation by
exploiting monthly data of four aggregate in?ation indices and 18 disaggregate
components of commodities andservices for the post in?ationtarget periodFebruary2000
to December 2010. In addressing the issue of asymmetry in the South African in?ation
process, this paper has reached three main conclusions. First, the analysis depicts the
presence of an aggregation bias, that is, aggregate in?ation is shown to be more persistent
than a majority of its underlying components. This result re?ects the need for improved
measures of aggregate in?ation if monetary policy is to accommodate the underlying
factors of in?ation in its targeting practices. A similar view is held by the Riskbank in
believing that decision making and communication from a monetary policy standpoint
can be improved by making the operational measures of in?ation more precise.
Second, in view of in?ation persistence having been incorporated in recent
theoretical analysis of monetary policy, the ?ndings of this study also have clear-cut
theoretical implications. Most existing macroeconomic models assume that in?ation
evolves as a linear process and thus anticipate a uniform response of in?ation to
monetary policy shocks. However, our ?ndings suggest that persistence in the in?ation
process is highly asymmetric and this, in turn, implies that the response of in?ation to
policy shocks may not be homogeneous. Our work can be extended by examining
whether an asymmetric in?ation process can be modeled as a stylized fact in
sophisticated models of monetary policy analysis. This development would be
complementary to the existing asymmetric versions of the Phillips Curve and Okun’s
Law speci?cations already incorporated in monetary policy analysis. Moreover, it
would be of interest to evaluate whether these asymmetric models could be used to
produce better in?ation forecasts as a means of enabling monetary authorities to apply
better policy decisions in their attempts to keep in?ation under control.
Lastly, in bridging the obtained empirical results to practical policy conduct, South
African monetary authority efforts may prove ineffective in controlling in?ation within
band-widths de?ned by the middle regimes of the estimated TAR models. Of particular
interest pertaining to the obtained results, are the existing unit roots found between the
rates of 4.7-8.5 percent for core in?ation and for rates of above 4.4 percent for CPI
in?ation. These band-widths are of importance as both of the aforementioned
aggregated measures of in?ation play an essential role in guiding the SARB in their
policy conduct. Within these identi?ed band-widths, in?ation would be best controlled
by focusing on alternative market-based policies that aimat simultaneously in?uencing
the demand as well as the supply-side of the macroeconomy. Only at levels below
4.5-4.7 percent, when the persistence measured in core in?ation and CPI in?ation is
minimal, would the sole use of direct monetary instruments prove to be most effective in
policy conduct.
The policy implications drawn from these results are essentially two-fold. On one
hand, the in?ation target may have to be re-adjusted to accommodate higher and/or
lower target ranges if short-term policy instruments are continued to be relied on for
policy conduct. On the other hand, if the narrow in?ation target of 3-6 percent where to
remain unchanged, the adoption of other market-based policies may prove useful in
ensuring that in?ation remains within its target. On the frontier of such suggested
policies are dual in?ation and employment/output targets and a real exchange rate
targeting frameworks.
In?ation
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Further reading
Babetskii, I., Coricelli, F. and Horvath, R. (2007), “Measuring and explaining in?ation persistence:
disaggregate evidence on the Czech Republic”, Working Paper Series No. 1, Research
Department, Czech National Bank, Prague, September.
Dickey, D. and Fuller, W. (1979), “Distribution of the estimators for autoregressive time series
with a unit root”, Journal of the American Statistical Association, Vol. 74, pp. 427-31.
Kumar, M. and Okimoto, T. (2007), “Dynamics of persistence in international in?ation rates”,
Journal of Money, Credit and Banking, Vol. 39 No. 6.
About the author
Andrew Phiri is a Lecturer of Finance Theory and Markets. His latest publications were included
in the Journal of Sustainable Development in Africa (2010) and Economics Bulletin (2011) and he
has received invitations from the South African Reserve Bank (SARB) to present his current
research output. Andrew Phiri can be contacted at: [email protected]
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