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Threshold effects of in
ation on economic growth in developing countries
Alexander Bick
⁎
Department of Economics, Goethe University Frankfurt, House of Finance H28, Grueneburgplatz 1, 60323 Frankfurt, Germany
a b s t r a c ta r t i c l e i n f o
Article history:
Received 14 July 2008Received in revised form 15 April 2010Accepted 26 April 2010Available online 28 May 2010
Keywords:
Panel threshold modelIn
ation thresholdsEconomic growth
JEL classi
cation:
C51E31O40
This paper introduces a generalized panel threshold model by allowing for regime intercepts. The empiricalapplication to the relation between in
ation and growth con
rms that the omitted variable bias of standardpanel threshold models can be statistically and economically signi
cant.© 2010 Elsevier B.V. All rights reserved.
1. Introduction
A central objective of macroeconomic policies is to foster economicgrowthandtokeepin
ationonalowlevel.Inrecentyearstherehasbeensubstantial empirical work on the relationship between in
ation andgrowth, yet the results have been mixed. Fisher (1993) was the
rst toidentifyanon-linearrelationshipwherelowin
ationrateshaveapositiveimpact on growth which turns negative as in
ation increases. Bruno andEasterly (1998) con
rm the
nding of a negative effect for high in
ationratesbut doubtthe growth-enhancing effectof low in
ation.In linewiththis result, Khan and Senhadji (2001) estimate a threshold of 11% fordeveloping countries where in
ation rates above this threshold areassociated with a signi
cant negative effect on growth, while in
ationrates below 11% do not have any signi
cant impact.This paper sheds new light on the in
ation-growth nexusintroducing a natural extension of Hansen's (1999) panel thresholdmodel by accounting for regime intercepts. The empirical resultscon
rm the importance of including a regime intercept from astatistical and economical perspective. Once the regime intercept isincluded, the threshold, up to which in
ation is growth enhancing,decreases substantially and, more importantly, the negative impact of in
ation above the threshold becomes signi
cant.The paper is structured as follows. The next section brie
y reviewspanel threshold estimation and discusses the role of regime intercepts.Section3introducesthedataandpresentstheestimationresultsforthein
ation-growth nexus. Finally, Section4 concludes.
2. Panel threshold models
Hansen (1999) proposes an estimation and inference strategy forbalanced panels with individual speci
c effects and observations {
y
it
,
q
it
,
x
it
;1
≤
i
≤
N
,1
≤
t
≤
T
}wherethesubscripts
i
and
t
indextheindividualandtime. The equation of interest with one potential threshold
γ
is given by
y
it
=
μ
i
+
β
0
1
x
it
I
ð
q
it
≤
γ
Þ
+
β
0
2
x
it
I
ð
q
it
N
γ
Þ
+
ε
it
with
ε
it
iid
∼
ð
0
;
σ
2
Þ
;
ð
1
Þ
where
I
(·) istheindicatorfunctionandthethresholdvariable
q
it
dividesthe observations into two
’
regimes
’
distinguished by differing regressionslopes
β
1
and
β
2
. The dependent variable
y
it
and
q
it
are both scalar. Thelattermay,buthasnottobeanelementof
x
it
,the
k
-dimensionalvectorof exogenousregressors.
1
Moreover,someelementsof
x
it
canbeconstrainedto have the same impact in both regimes, i.e.
β
1,
j
may be equal to
β
2,
j
forsome
j
a
{1,
…
,
k
}. The individual speci
c effects are eliminated using thestandard
xed-effectstransformationimplyingfortheidenti
cationof
β
1
and
β
2
thattheelementsof
x
it
areneithertime-invariantnoraddinguptoa vector of ones. This latter case applies to regime intercepts which areusually included in each regime in threshold models in pure cross-sectionalortime-seriescontexts.Eveninthepresenceof
xed-effectsitispossible to control for differences in the regime intercepts by includingthem in all but one regime as in the following extension of Eq. (1):
y
it
=
μ
i
+
β
0
1
x
it
I
ð
q
it
≤
γ
Þ
+
δ
1
I
ð
q
it
≤
γ
Þ
+
β
0
2
x
it
I
ð
q
it
N
γ
Þ
+
ε
it
:
ð
2
Þ
Economics Letters 108 (2010) 126
–
129
⁎
Tel.: +49 69 798 33829; fax: +49 69 798 33925.
E-mail address:
bick@wiwi.uni-frankfurt.de.
1
Caner and Hansen (2004) develop instrumental variable estimation for thresholdmodels with endogenous regressors, but only for cross-sectional data.0165-1765/$
–
see front matter © 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.econlet.2010.04.040
Contents lists available at ScienceDirect
Economics Letters
journal homepage: www.elsevier.com/locate/ecolet
Thisformulationassumesthatthedifferenceintheregimeintercepts,represented by
δ
1
, is not individual speci
c but the same for all cross-sections.SinceEq.(2)hasneitherbeenconsideredbyHansen(1999)norany of the numerous studies, e.g. Adam and Bevan (2005), Lensink andHermes(2004)orNautzandScharff(2006),applyinghismethodology,itseems worthwhile to brie
y discuss the role of regime intercepts for theestimation results in the Hansen (1999) framework.
2
For any given threshold
γ
, the slope coef
cients
β
1
and
β
2
can beestimated by ordinary least squares (OLS) using the data after the
xed-effects transformation. In case a regime intercept is included, asinspeci
cation(2),theslopeestimatesforeachregimeareidenticaltothose from a regression using only observations from the respectiveregime which re
ects the orthogonality of the regressors
x
i
I
(
x
i
≤
x
m
)and
x
i
I
(
x
i
N
x
m
).
3
Omission of any variable correlated with at least oneregressor and the dependent variable causes biased estimates, butregime intercepts are a particularly interesting case. First, the bias canbe clearly interpreted. Estimating Eq. (1) in the presence of a regimeintercept in the data generating process results in a bias proportionalto
δ ̂
1
because the orthogonality of the regressors is not preservedanymore. Second, availability of regime intercepts as regressors is notan issue since they are as easily constructed as the regime-dependentexogenous regressors for a given threshold.Biased estimates of the regression slopes have further conse-quencesinthepanelthresholdmodelbecausethethresholdestimatesare also obtained by least squares:
ˆ
γ
= argmin
γ
S
1
ð
γ
Þ ð
3
Þ
where
S
1
(
γ
)isthesumofsquaredresidualsfromestimatingEq.(1)or(2) for a given threshold
γ
. Only by coincidence, these estimates willbe the same for speci
cations (1) and (2) if a regime intercept ispresent in the data generating process. Moreover, unbiased estimatesof
β
1
and
β
2
are crucial for the test of the signi
cance of a thresholdwhich can be represented by the following linear constraint
H
0
:
β
1
=
β
2
:
ð
4
Þ
3. The in
ation-growth nexus
Therelationshipbetweenin
ationandgrowthisinvestigatedforabalanced panel of 40 developing countries through the period from1960 to 2004. As it is standard in the empirical growth literature, theresults on the determinants of long-term economic growth will bebased on
ve-year averages. The equation of interest is given by
Δ
ln
gdp
it
=
μ
i
+
β
1
˜
π
it
I
ð
˜
π
it
≤
γ
Þ
+
δ
1
I
ð
˜
π
it
≤
γ
Þ
+
β
2
˜
π
it
I
ð
˜
π
it
N
γ
Þ
+
ϕ
′
w
it
+
ε
it
;
ð
5
Þ
representing a single threshold model that already includes a regimeintercept.ThedependentvariableisthegrowthrateofGDPpercapita.Thein
ation variable
π̃
serves as the regime-dependent regressor andthreshold variable and is a semi-log transformation of in
ation with
π̃
it
=
π
it
−
l,if
π
it
b
1and
π̃
it
=ln
π
it
,if
π
it
≥
1.In
ationratessmalleronearere-scaled for the sake of continuity. Using in
ation levels in growthregressions implies that the marginal effect of in
ation on economicgrowth is independent of the average level of in
ation whereas the logmodel has the more plausible implication that multiplicative in
ationshocks will have identical effects. The control variables are selected inaccordance with the empirical growth literature, see e.g. Islam (1995) orKhanand Senhadji(2001),andpassed therobustnesstestsinLevineandRenelt (1992), and Sala-i-Martin (1997).
w
it
contains investment as ashare of GDP (
igdp
), population growth (
dpop
), the log of initial incomeper capita of the previous period (
initial
) as well as the growth rate andstandard deviation of terms of trade (
dtot
,
sdtot
).Table 1 presents the results for both speci
cations, i.e. without(column 1) and with (column 2) regime intercepts. The upper panelshows that in both cases the null hypothesis of no threshold can berejected at the 5% signi
cance level, while the presence of one thresholdcannotberejected.Inclusionofaregimeinterceptdecreasesthethresholdestimate(middlepanel)from19%to12%andthelowerboundofthe95%con
dence interval from 11.8% to 5.3%. The most striking point is that inabsence of a regime intercept, in
ation rates below the threshold of 19%have a signi
cant positive effect (0.407) on growth only on the 10%signi
cance level, while the negative impact (
−
0.232) for in
ation ratesabove19%isnotstatisticallysigni
cantatall,comparethelowerpanel.Incontrast, allowing for differences in the regimes
’
intercepts doubles themagnitude(0.785,
−
0.531)andestablishessigni
canceatleastonthe5%level of the marginal impacts of in
ation on growth in both regimes. Theregime intercept
δ̂
1
itself is also signi
cant on the 5% level. Most of theregime-dependent coef
cients are consistent with the implications of standardgrowththeoryandareverysimilarforbothspeci
cations.Theresults from the speci
cation with a regime intercept are in line withthose by Khan and Senhadji (2001), despite that, similarly to Fisher
(1993), low in
ation rates (less than 12%) are associated with asigni
cant positive effect on growth.
4
2
For a detailed review of the general estimation and inference strategy and thetreatment of multiple thresholds the reader is referred to Hansen (1999).
3
The exact algebraic expressions for the coef
cient estimates of both speci
cationsare given in the appendix which also lists the modi
cations needed in the setupconsidered by Hansen (1999) to allow for regime intercepts as in Eq. (2).
Table 1
In
ation-growth nexus in developing countries.No regime intercepts Regime interceptsTest for the number of thresholds:
p
-value
H
0
:
No threshold (K=
0
)
0.013 0.025
H
0
:
At most one threshold (K
=1
)
0.252 0.642Threshold estimates and con
dence intervals
γ̂
19.16% 12.03%95% con
dence interval [11.82%, 20.48%] [5.29%, 20.48%]Coef
cient estimates:
∆
ln g
dp
it
=
μ
i
+
β
1
π̃
it
I
(
π̃
it
≤
γ
)+
δ
1
I
(
π̃
it
≤
γ
)+
β
2
π̃
it
I
(
π̃
it
N
γ
)+
ϕ
′
w
it
+
ε
it
Regime-dependent regressors
β ̂
1
0.407* 0.785***(0.214) (0.281)
δ ̂
1
−
1.985**(1.000)
β ̂
2
−
0.232
−
0.531**(0.146) (0.245)
Regime-independent regressorsinitial
−
3.353***
−
3.341***(0.563) (0.567)
igdp
0.031 0.021(0.041) (0.042)
dpop
−
0.814***
−
0.646**(0.306) (0.307)
dtot
0.014 0.002(0.028) (0.028)
sdtot
−
0.054**
−
0.052**(0.020) (0.020)Notes: Standard errors are given in parentheses, */**/*** indicate the 10%/5%/1% signi
cancelevels.Similarlyto Hansen(1999), eachregime has tocontain atleast 5%of allobservations.
1000 bootstrap replications were used to obtain the p-values to test for the number of thresholds.Byconstruction,thecon
denceintervalsforthethresholdestimatescanbehighlyasymmetric. The likelihood ratio statistics and critical values for determining the number of thresholdsareavailablefromtheauthoruponrequest.ThedatasetandanextensionofBruceHansen'sprogramthataccountsfor regime interceptscanbe downloaded fromthe author'swebsite: http://www.wiwi.uni-frankfurt.de/profs/fuchs/bick.html.
4
The results of Khan and Senhadji (2001) are not exactly comparable to thosepresented here for two reasons. First, they use an unbalanced panel of more than 100developing countries from 1960 to 1998. Second, they introduce continuity at thethresholdwhich,thoughnotexplicitlystated,isnothingelsebutanonlinearrestrictiononregime intercepts:
Δ
ln
gdp
it
=
μ
i
+
β
1
ð
˜
π
it
γ
Þ
I
ð
˜
π
it
≤
γ
Þ
+
β
2
ð
˜
π
it
γ
Þ
I
ð
˜
π
it
N
γ
Þ
+
ϕ
′
w
it
+
ε
it
:
Note that the setup in Hansen (1999), with and without regime intercepts, implies a
discontinuity at the threshold and refers to balanced panels.127
A. Bick / Economics Letters 108 (2010) 126
–
129
From a policy perspective, choosing the correct speci
cation, i.e.controlling for differences in the regime intercepts, has importantimplications. First, the point estimate and lower bound of the con
denceinterval from which onwards in
ation is harmful for growth are bothsubstantially lower. Second, the detrimental impact for in
ation ratesabove the threshold turns signi
cantly and doubles in magnitude. Third,keeping in
ation below the threshold has a stronger bene
cial effect.
4. Conclusion
This paper revisits the relationship between in
ation andeconomic growth for developing countries using a generalization of Hansen's (1999) panel threshold model. Regime intercepts areintroduced and the potential bias of omitting these readily availableregressors for both, regression slope and threshold estimates, isdiscussed. The regime intercept is signi
cant in the in
ation-growthnexus and affects the results in important ways.
Acknowledgments
I thank Bruce Hansen and Dieter Nautz for helpful comments andsuggestions. Stephanie Kremer provided excellent research assis-tance. Financial support by the Monetary Stability Foundation isgratefully acknowledged.
Appendix A
A.1. Coef
cient estimates
Without loss of generality assume that
T
=1;
μ
i
=
μ
∀
i
=1,
…
,
N
;
x
is scalar and
x
1
b
x
2
b
…
b
x
m
b
x
m
+1
b
…
b
x
N
and the threshold is known at
γ
=
x
m
s.t. (1) and (2) boil down to
y
i
=
˜
μ
+
˜
β
1
x
i
I
ð
x
i
≤
x
m
Þ
+
˜
β
2
x
i
I
ð
x
i
N
x
m
Þ
+
ε
i
ð
6
Þ
and
y
i
=
μ
+
β
1
x
i
I
ð
x
i
≤
x
m
Þ
+
δ
1
I
ð
x
i
≤
x
m
Þ
+
β
2
x
i
I
ð
x
i
N
γ
Þ
+
ε
i
:
ð
7
Þ
The coef
cient estimates for speci
cation (7) are given by
ð
ˆ
μ
ˆ
β
1
ˆ
δ
1
ˆ
β
2
Þ
=1
N
−
m
∑
N i
=
m
+ 1
y
i
−
ˆ
β
2
1
N
−
m
∑
N i
=
m
+ 1
x
i
1
m
∑
mi
= 1
x
i
y
i
−
1
m
∑
mi
= 1
x
i
1
m
∑
mi
= 1
y
i
1
m
∑
mi
= 1
x
2
i
−
1
m
∑
mi
=1
x
i
h i
2
1
m
∑
mi
= 1
y
i
−
ˆ
β
1
1
m
∑
mi
= 1
x
i
−
ˆ
μ
1
N
−
m
∑
N i
=
m
+ 1
x
i
y
i
−
1
N
−
m
∑
N i
=
m
+ 1
x
i
1
N
−
m
∑
N i
=
m
+ 1
y
i
1
N
−
m
∑
N i
=
m
+ 1
x
2
i
−
1
N
−
m
∑
N i
=
m
+ 1
x
i
h i
2
0BBBBBBBBBBBBBBBBB@1CCCCCCCCCCCCCCCCCA
ð
8
Þ
and can be expressed for speci
cation (6) in the following way
ˆ
˜
μ
ˆ
˜
β
1
ˆ
˜
β
2
0BB@1CCA
=
ˆ
μ
ˆ
β
1
ˆ
β
2
0BBB@1CCCA
+
∑
N i
=
m
+ 1
x
2
i
∑
mi
=1
x
i
2
−
m
∑
mi
= 1
x
2
i
h i
∑
N i
=
m
+ 1
x
i
2
∑
mi
= 1
x
2
i
+
∑
N i
=
m
+ 1
x
2
i
∑
mi
=1
x
i
2
−
N
∑
mi
= 1
x
2
i
h i
∑
mi
= 1
x
i
∑
N i
=
m
+ 1
x
i
2
−
ð
N
−
m
Þ
∑
N i
=
m
+ 1
x
2
i
∑
N i
=
m
+ 1
x
i
2
∑
mi
= 1
x
2
i
+
∑
N i
=
m
+ 1
x
2
i
∑
mi
=1
x
i
2
−
N
∑
mi
= 1
x
2
i
h i
−∑
N i
=
m
+ 1
x
i
∑
mi
=1
x
i
2
−
m
∑
mi
= 1
x
2
i
h i
∑
N i
=
m
+ 1
x
i
2
∑
mi
= 1
x
2
i
+
∑
N i
=
m
+ 1
x
2
i
∑
mi
=1
x
i
2
−
N
∑
mi
= 1
x
2
i
h i0BBBBBBBBBBBBBBBB@1CCCCCCCCCCCCCCCCA
ˆ
δ
1
ð
9
Þ
where
β ̂
1
,
β ̂
2
and
δ ̂
1
are taken from (8). Note that in the presence of a
xed effect,
μ̂
and
ˆ ˜
μ
would correspond to the estimate of the average
xedeffect.
A.2. Regime intercepts in the panel threshold model
ThesetupinHansen(1999)hastobeextendedtoallowforregimeinterceptsasinEq.(2).First,thenullhypothesistotestforthesigni
canceof thethresholdhastobeextendedby
δ
1
=0.Second,thederivationoftheasymptoticdistributionofthethresholdestimatenowreliesontheadditionaltechnical assumption that
δ
1
→
0 as
N
→
∞
. It means that the difference in the intercepts between the two regimes is
’
small
’
relative to sample sizewhich is completely analogous to the assumption regarding the slope coef
cients, namely that (
β
2
−
β
1
)
→
0 as
N
→
∞
. Third, the proof in theappendixnowreliesonthefollowingtwoexpressionstakingtheregimeinterceptasanadditionalregressorintoaccount:
θ
’
=((
β
2
−
β
1
)
’
−
δ
1
)and
z
’
it
=(
x
’
it
1)
C
.
128
A. Bick / Economics Letters 108 (2010) 126
–
129
References
Adam, C.S., Bevan, D.L., 2005. Fiscalde
cits andgrowthin developing countries. Journalof Public Economics 89, 571
–
597.Bruno, M., Easterly, W., 1998. In
ation crisis and long-run growth. Journal of MonetaryEconomics 41, 3
–
26.Caner, M., Hansen, B.E., 2004. Instrumental variable estimation of a threshold model.Econometric Theory 20 (5), 813
–
843.Fisher, S., 1993. The role of macroeconomic factors in growth. Journal of MonetaryEconomics 32, 485
–
512.Hansen, B.E., 1999. Threshold effects in non-dynamic panels: estimation, testing, andinference. Journal of Econometrics 93, 345
–
368.Islam, N., 1995. Growth empirics: a panel data approach. Quarterly Journal of Economics 110 (4), 1127
–
1170.Khan, M.S., Senhadji, A.S., 2001. Threshold effects in the relationship between in
ationand growth. IMF Staff Paper 48 (1), 1
–
21.Lensink, R., Hermes, N., 2004. The short-term effects of foreign bank entry on domesticbankbehaviour:doeseconomicdevelopment matter?JournalofBanking&Finance28, 553
–
568.Levine, R., Renelt, D., 1992. A sensitivity analysis of cross-country growth regressions.The American Economic Review 82 (4), 942
–
963.Nautz, D., Scharff, J., 2006. In
ation and relative price variability in the Euro area:evidence from a panel threshold model.
Deutsche Bundesbank Discussion Paper
14/06.Sala-i-Martin, X., 1997. I just ran two million regressions. The American EconomicReview 87, 178
–
183.129
A. Bick / Economics Letters 108 (2010) 126
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129

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