Estimating the New Keynesian Phillips Curve by Quantile Regression Method for Turkey

doi:10.4236/me.2013.49067

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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: [email protected]

Received July 25, 2013; revised August 25, 2013; accepted September 4, 2013

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)

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-

Ç. BOZ

628

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-

Ç. BOZ 629

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.

πππ

tftt btt







 (1)

where (πt) is inflation rate, (Etπt+1) is the expected infla-

tion rate, (πt‒1) is the lagged inflation and reflects

the marginal costs.





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



 









(2)

where ζt is the error term for πtt





 reflects

ttt









 and π

ttt







 . 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;









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.

Ç. BOZ

630







111 1

ππ,π,ππ

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

on an in-

strument set. In the second step, we replaced πt+1and d

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;

πππ

tfttbttt







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

ttyX t

ttyX





















 



 (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

1 USD and 1.5 DEM. Indeed, 0.77 is obtained by dividing 1.5

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

Ç. BOZ 631

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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doi:10.2307/1913643