Modern Economy, 2013, 4, 627-632
http://dx.doi.org/10.4236/me.2013.49067 Published Online September 2013 (http://www.scirp.org/journal/me)
Estimating the New Keynesıan Phillips Curve by Quantile
Regression Method for Turkey
Çiğdem Boz
Department of Economics, Maltepe University, Maltepe, Turkey
Email: cigdemboz@maltepe.edu.tr
Received July 25, 2013; revised August 25, 2013; accepted September 4, 2013
Copyright © 2013 Çiğdem Boz. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
New Keynesian Phillips Curve based on nominal rigidities and rational expectations is a widely used structural model
of inflation dynamics in the analysis of monetary policy. It postulates that current inflation is determined by expected
inflation and by the real marginal costs. This study uses the Quantile Regression Method (QRM) to present the New
Keynesian Phillips Curve (NKPC) estimation for Turkey instead of Generalized Method of Momentum (GMM). This
method identifies differences in response of the inflation to changes in explanatory variables at various points of in-
flation.
Keywords: Quantile Regression; New Keynesian Phillips Curve; Turkish Economy
1. Introduction
The New Keynesian Phillips Curve (NKPC) which is
based on nominal rigidities and rational expectations is a
widely used structural model of inflation dynamics in the
analysis of monetary policy. It postulates that current
inflation is determined by expected inflation and by the
real marginal costs as the driving variable. Despite it has
a commonly accepted theoretical background, there have
been controversial results regarding its empirical valid-
ity1. In the literature, the Generalized Method of Mo-
mentum (GMM) has been extensively used to estimate
NKPC in order to avoid endogeneity bias caused by ex-
pected inflation, since it is likely to produce imprecise
and biased estimates2. One of the GMM assumptions
specifies that the coefficients are evaluated when the
level of inflation is at the mean of the distribution condi-
tional on its explanatory variables. In this paper, we
would like to contravene this assumption and examine
the response of the inflation rate through different quan-
tiles of its distribution.
Turkish economy has experienced high inflation peri-
ods especially before the adoption of Inflation Targeting
(IT) regime in 2002, later on the inflation rate gradually
decreased. Although the inflation rate is relatively low
and stable in comparison to the past, they range from
29.7% to 6.2% between 2002 and 2012. This trend leads
us to think over that the marginal effects of explanatory
variables on the inflation rate across its distribution could
be different. In order to analyze these effects at various
points of the inflation rate, we estimate the hybrid ver-
sion of the NKPC employing Quantile Regression (QR)
that takes into account endogeneity issues. Findings from
our estimations show that the marginal effects of ex-
planatory variables on the inflation rate through its dis-
tribution are varying. When the inflation rate is low, the
backward looking term is significant, notwithstanding
forward looking term is insignificant. But when the infla-
tion rate is high, the significance of forward looking term
dominates the backward looking term. In addition, the
significance of output gap and exchange rates increases
for high inflation. It reflects that the inflation rate is rela-
tively more driven by lagged inflation when the inflation
rate is low, but on the contrary, it is relatively more dri-
ven by the policy rate and forming of economic agents’
inflation expectations when the inflation rate is high.
1Gali and Gertler (1999) and Gali, Gertler and Lopez Solido (2001) find
that the pure NKPC where inflation is a function of expected future
inflation and real marginal costs, is good approximation of inflation
dynamics in both the US and Europe. However, Roberts (2001)
p
rovides evidence against the NKPC with only forward looking
elements using GMM, although in contrast to Fuhrer (1997) he finds
there to be clear role for forward looking behavior.
2As a solution for this problem, Linde suggests FIML but this method
has not been used extensively.
The following section provides the overview of the
literature on the NKPC. Emprical analyses and findings
are described in the third section. The final section con-
C
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cludes the paper.
2. Evolution of the Phillips Curve and
Literature on NKPC
The relationship between inflation and real variables is
very important for understanding the effects of monetary
policy. The Phillips curve, one of the most famous rela-
tionships in macroeconomics, is concerned with this is-
sue. In 1958, A. W. Phillips’s work demonstrated that
lower unemployment leads to higher wages. Following
the influential contribution from Samuelson and Solow,
the Phillips Curve was interpreted by many orthodox
Keynesians as implying a stable long-run trade-off which
offered the authorities a menu of possible inflation-un-
employment combinations for policy choice [1]. The idea
of a stable trade-off between inflation and output was
challenged independently by Milton Friedman and Ed-
mund Phelps who both denied the existence of a perma-
nent (long-run) trade-off between inflation and unem-
ployment. In other words, expectations augmented PC
was vertical at the natural rate of employment.
However by the late 1960s and early 1970s, both infla-
tion and unemployment had begun to increasing, and this
phenomenon named as stagflation, discredited Friedman
and Phelp’s view. The economists of New Classical
School which is the dominant paradigm in 1970s, went
further and claimed that fiscal or monetary policies could
have no impact on output or employment in short-run
and either long-run as a consequence of rational expecta-
tions together with instantaneous market clearing as-
sumptions. Yet, this policy ineffectiveness proposition
conflicted with the empirical evidence on the efficiacy of
monetary policies on real variables.
As a reaction to this proposition, in 1990s, New
Keynesian models based on prices and wages rigidities
and rational expectations have been widely acknowl-
edged. In order to explain the effects of nominal vari-
ables on real variables, New Keynesian Phillips Curve
(NKPC) which is based on Taylor [2], Rotemberg [3]
and Calvo [4], was suggested. According to the NKPC,
current inflation is expressed as a function of expected
future inflation and real marginal costs. The prior theo-
ries concerning inflation dynamics, neoclassical Phillips
Curve, assume flexible prices and rational expectations
in a microfounded framework. But the predictions of this
model conflicted with the realities; data about the real
effects of money are much stronger than what this model
implies. To be able to explain the stronger nominal ef-
fects on real variables the NKPC stressed the role of
staggered wage and price setting of forward looking in-
dividuals and firms by the use of microfoundations with
optimizing rational agents [5]. In other words, since the
empirical results of VAR analysis implies that the
changes in nominal variables have persistent effects on
real variables, a new consensus emerged about the use of
the NKPC for theoretical analysis of monetary policy in
the past decade.
While theoretically appealing, empirical evidence on
the NKPC is far from decisive. There are a number of
studies which provide evidence in favor of the NKPC,
while the others provide against it. Gali and Gertler [6]
and Gali et al. [7] examine the NKPC for the US econ-
omy find that expected inflation is almost always impor-
tant in determining current inflation. Gali et al. [8] have
similar results for the euro area. Sbordone [9] and Amato
and Gerlach [10] also suggest that the baseline for-ward-
looking NKPC provides a reasonably good description of
US and European inflation dynamics.
Nevertheless, there are studies which emphasize that
forward-looking specifications are not sufficient to cap-
ture inflation persistence (Fuhrer and Moore [11], Rob-
erts [12] and Roberts [13], Rudd and Whelan [14,15] and
Stock Watson [16]). Ball [17] demonstrates that the
model yields the surprising result that announced, credi-
ble disinflations lead booms rather than recessions. Fuh-
rer and Moore [11] argue that it cannot explain why in-
flation is so persistent. Mankiw [18] emphasizes that it
cannot explain why shocks to monetary policy have a
delayed and gradual effect on inflation. According to him,
these problems may arise from the same source; “al-
though the price level is sticky in this model, the inflation
rate can change quickly”. In other words, in the NKPC,
price stickiness is not translated into inflation stickiness,
hence the inflation level can be changed instantaneously
in sharp contrast with empirical patterns.
As a consequence, Gali and Gertler [6] extended
Calvo’s theoretical framework to the so-called hybrid
NKPC (HNKPC) by allowing for a fraction of firms that
set prices according to a backward looking rule-of thumb.
The work of Gali and Gertler made an important contri-
bution to reconciling the NKPC with the data. The hybrid
formulation was able to generate more inflation persis-
tence than the usual NKPC.
However, empirical estimates of the hybrid model also
have yielded conflicting results and interpretations. On
one hand, Fuhrer [19] finds the forward-looking compo-
nent in inflation to be essentially unimportant. Roberts
[13] compares several PC specifications and obtains a
large backward-looking component on US data. Estrella
and Fuhrer [20] also document the poor fit of a purely
forward-looking PC. Jondeau and Le Bihan [21] estimate
hybrid model for major euro countries and US using both
GMM and ML estimation procedures. They found that
forward-lookingness of the inflation dynamics is not al-
tered by the choice of the forcing variable. In contrast, it
is strongly affected by the lag and lead structure of infla-
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t
tion. Henzel and Wollmershaeuser [22] provide evidence
in favor of the hybrid NKPC for selected euro zone
countries, the US and the UK. They find that in com-
parison with the rational expectations approach, back-
ward-looking behavior turns out to be more relevant for
most countries in their sample. Carriero [23] tests the
NKPC without having to estimate its structural parametre
and he concludes that according to simple Wald test it
does not exist as a combination of price stickiness and
firm’s backwardness which is consistent with the US
data and this might be due to the failure of the joint hyp-
thesis of rational expectations. On the other hand, he
stresses that the idea of forward looking price setting
behavior should not be entirely disregarded. Söderlind et
al. [24] show, in a calibrated model, that a large back-
ward-looking component is needed to replicate the auto-
correlation patterns of inflation and output. Jean-Baptiste
[25] estimates the NKPC for United Kingdom using sur-
vey forecasts of inflation. He finds that, survey-based
inflation forecasts make the Phillips Curve predomi-
nantly forward looking and the rational expectations as-
sumption of the agents can be misleading. Roeger and
Herz [26] propose to test the purely backward-looking
Phillips curve and the purely forward-looking Phillips
curve against a hybrid Phillips curve via their implica-
tions for cumulative output effects of monetary policy
shocks. Their empirical evidence is consistent with the
forward-looking model. Chorteas et al. [27] examine the
asymmetry of the response of inflation across quantiles.
They estimate a hybrid NKPC employing two stage
quantile regression. Their results suggest that the re-
sponse of inflation is asymmetric across different quan-
tiles of distribution. When inflation is high, the forward
looking component is significant and dominates the
backward-looking component.
So, it is clear that the evidence from the studies on the
relevancy of the NKPC is mixed and most of the studies
investigated it for developed countries. Among the stud-
ies which investigate the inflation dynamics in Turkey,
Yazgan and Yilmazkuday [28] provide supporting evi-
dence for conventional NKPC and refuting evidence for
the hybrid NKPC from 1988 to 2003 data.
The most current study for Turkey made by Saz [29]
and he found strong empirical evidence speaking for the
conventional NKPC as well for the hybrid NKPC in
Turkey using their own newly constructed measure for
marginal costs, the marginal cost index.
3. Empirical Analysis
3.1. Model and Data
Several papers have provided tests of the NKPC via
GMM. Gali and Gertler [6], Gali, Gertler and Salido [7,8]
and Sbordone [9] have provided estimates of the NKPC
clearly supporting the theory that inflation rate responds
to expected inflation and real marginal costs. GMM es-
timates of the models suggest that forward looking term
is dominant which means the coefficient on expected
inflation rate substantially exceeds the coefficient on
lagged inflation rate, moreover, lagged inflation is stati-
cally insignificant. On the other hand, Rudd and Whelan
[14,15], Stock and Watson [16] and Nason and Smith [30]
found that forward-looking term plays a very limited role
in explaining inflation dynamics. Because of these em-
pirical results, and the inflation rate is generally written
as a linear combination of the expected inflation, lagged
inflation and real marginal costs which is called Hybrid
NKPC.
11
πππ
d
tftt btt
Ey


 (1)
where (πt) is inflation rate, (Etπt+1) is the expected infla-
tion rate, (πt1) is the lagged inflation and reflects
the marginal costs.
d
t
y
Quantile Regression Method (QRM) which is intro-
duced by Koenker and Basset [31] enables us to estimate
the effects of explanatory variables on inflation rate
through its distribution3. This method has an asymmetric
loss function which is based on minimization of asym-
metrically weighted sum of absolute errors4.

min 1
tt
t
V
t
 

(2)
where ζt is the error term for πtt
X
reflects
π
ttt
 and π
ttt
X
 . πt is inflation rate,
Xt is the matrix of all explanatory variables and β is the
coefficient vector. In quantile regression, results are a
function of τ. The τvalue below 0.50 (τ < 0.45) implies
more weights on negative residuals, on the other extreme,
the τ value above 0.50 (τ > 0.55) implies more weights on
positive residuals. Qunatile regression also includes as a
special case of Least Absolute Deviation (LAD) model,
when τ = 0.50.
The quantile regression coefficient (say γf) tells us that
for every one unit change in expected inflation will
change inflation rate as the value of coefficient at a spe-
cific quantile (τ), when Equation (2) is minimized with
respect to β. The conditional quantile function of πt at a
specific quantile of τ given Xt may be defined as;


*
1*
πtt t
qXXF
 (3)
Which can be rewritten as
3Koenker and Basset (1978) ran a simple Monte Carlo experiment and
show how the empirical variance of the median, compared to the vari-
ance of the mean, is delicately higher under the normal distribution, but
it is much lower under all the other distributions taken into considera-
tion.
4As the quantile regression uses absolute values instead of squares it is
also more robust and less sensitive to outliers.
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630


*
1*
111 1
ππ,π,ππ
d
tttt tfttbt
qE yEF
 

(4)
QRM is inconsistent and might have to be replaced by
the TSQR since the NKPC is likely to have an endogene-
ity problem arises from possible correlation of error
terms with the expected inflation. In the first step we
estimated an OLS regression of πt+1 and d
t
y
on an in-
strument set. In the second step, we replaced πt+1and d
t
y
with their fitted values then estimate the hybrid NKPC
using quantile regression5.
The hybrid NKPC model is shown in Equation (1), but
since Turkey is a small-open economy, exchange rate (et)
also has an impact on inflation rate. We can extend the
NKPC as follows;
11
πππ
d
tfttbttt
Ey



Copyright © 2013 SciRes. ME
t
e
(5)
The data used in this study are inflation rate, expected
inflation rate, output gap and nominal exchange rate
which are covering the period 2002q1-2012q3. Inflation
rate is the quarterly change of Consumer Expectation
Price Index which is derived from inflation expectations
for 12 months period and output gap proxies the marginal
cost and calculated by HP Filters which these variables
are seasonally adjusted with TRAMO-SEATS. The no-
minal exchange rate series were calculated as the Turkish
lira value of the official basket (1 USD + 0.77 EUR) of
the Central Bank of the Republic of Turkey (CBT) prior
to the 2001 crisis6. For the GMM estimates, the instru-
ment variables are the three lags of inflation, three lags of
inflation expectations, two lags of output gap a done lag
of exchange rate. In addition, for the effects of 2008 cri-
sis dummy variables are used for the period of 2009q2-
2010q1.



:
:
min π
1π
tt
tt
tt
ttyX t
tt
ttyX
VX
X




 
(6)
3.2. Results
The estimations of the NKPC for Turkey over 2002-2012
are presented below. According to our OLS and GMM
estimations all variables are significant. The QRM esti-
mations shows the effects of explanatory variables on in-
flation rate through its distribution.
Estimation Results
2002: Q1-2012: Q3
γf γb λ δ
OLS 0.27** 0.39* 0.13** 0.10*
GMM 0.40* 0.62* 0.21* 0.16*
0.150.17 0.24 0.12 0.07
0.200.23 0.12 0.07 0.05
0.250.23 0.12 0.07 0.05
0.300.21 0.43** 0.15** 0.08**
0.350.19 0.39** 0.12 0.06
0.400.17 0.46** 0.14** 0.06
0.450.25 0.52* 0.11** 0.07***
0.500.22 0.54* 0.13*** 0.08**
0.550.24 0.52* 0.14 0.10*
0.600.24 0.52* 0.15* 0.11*
0.650.28 0.49* 0.13** 0.13*
0.700.26 0.51*** 0.14** 0.14*
0.75 0.35*** 0.47* 0.19* 0.12*
0.80 0.36*** 0.48* 0.19* 0.11*
QRM
0.85 0.39*** 0.42* 0.20* 0.10**
*1%, **5%, ***10%. Coefficient variances are computed using Huber-Sand-
wich method. The sparsity function is estimated through Siddiqui mean
fitted method using the bandwidth method of Hall-Sheather.
The QRM results demonstrate that the marginal effects
of explanatory variables on inflation rate through its dis-
tribution is varying. When the inflation rate is low, the
backward looking term is significant, notwithstanding
forward looking term is insignificant. But when the infla-
tion rate is high, the significance of forward looking term
dominates the backward looking term. In addition, the
significance of output gap and exchange rates increases
for high inflation. It reflects that inflation rate is rela-
tively more driven by lagged inflation when the inflation
rate is low, but on the contrary, it is relatively more dri-
ven by the policy rate and forming of economic agents’
inflation expectations when the inflation rate is high. The
importance of backward-looking component through whole
quantiles can be explained by the imperfect credibility of
the monetary authority.
5Kim and Muller (2004) presented the asymptotic properties of two
stage quantile regression estimators with random regressors, where the
first stage is based on quantile regressions with the same quantile as in
the second stage, which ensures robustness of the estimation procedure.
They show that TSQR estimators based on OLS predictions are con-
sistent. Thus, we use past values of inflation and marginal costs as in-
struments in the context of the NKPC.
6Prior to adoption of euro, the official basket of the CBRT consisted o
f
1 USD and 1.5 DEM. Indeed, 0.77 is obtained by dividing 1.5
b
y
1.955821, which is the DEM equivalent of one euro.
Thus our results for Turkey Phillips curve suggest that
it becomes purely backward-looking at the low inflation
quantiles while it becomes hybrid one at high quantiles.
4. Conclusions
The empirical evidence on the efficiency of monetary
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policies on real variables discredited the policy ineffec-
tiveness proposition of New Classical paradigm and New
Keynesian models based on nominal rigidities have been
widely acknowledged in 1990s. New Keynesian Phillips
Curve which presents a model of inflation dynamics,
postulates that current inflation is determined by ex-
pected inflation (forward-looking behavior) and the real
marginal costs. By the contributions of Gali and Getrler
[6] a hybrid NKPC which includes backward component
is suggested.
Despite it has a commonly accepted theoretical back-
ground, the evidence from the studies on the relevancy of
the NKPC is mixed. While some studies provide the evi-
dence supporting the NKPC, there are also studies which
have evidence against it.
In this paper, the Quantile Regression Method (QRM)
is used to estimate the New Keynesian Phillips Curve
(NKPC) for Turkey. By this method, it is aimed that to
identify differences in response of the inflation to
changes in explanatory variables at various points of in-
flation. For the period of 2002q1-2012q3, we find that
the backward-looking component appears to be the sig-
nificant variable at all inflation quantiles and it is espe-
cially influential at low levels. In other words, Phillips
curve is purely backward-looking at these quantiles. One
explanation for this might be the imperfect credibility of
the monetary authority. Impact of the forward-looking
inflation terms becomes more significant when the infla-
tion increases and it dominates the backward-looking
term at high inflation quantiles. In addition, the signifi-
cance of output gap (marginal cost) and exchange rates
increases for high inflation. These findings support the
hybrid New Keynesian Phillips curve for Turkish econ-
omy over 2002-2012.
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