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2019 Volume 72, Issue 3
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Authors:
::
:
P
AVLOS
S
TAMATIOU
Department of Accounting and Finance, Western Macedonia University of Applied Sciences, Kozani, Greece
C
HAIDO
D
RITSAKI
Department of Accounting and Finance, Western Macedonia University of Applied Sciences, Kozani, Greece
THE
PHILLIPS
CURVE:
UNEMPLOYMENT
DYNAMICS
AND
NAIRU
ESTIMATES
OF
POLAND’S
ECONOMY
A
BSTRACT
The purpose of this paper is to investigate the relationship between inflation and unemployment
rate, in the case of Poland over the period 19922017, within the Phillips curve context. For the
longterm equilibrium relationship and the causal relationship of the examined variables, the
Autoregressive Distributed Lag (ARDL) technique developed by Pesaran et al. (2001) and the
causality approach of Toda and Yamamoto (1995) are applied, as the most appropriate for the
sample size and the integration of the variables. The results of the study revealed that there is a
long run relation between unemployment rate and the inflation rate for Poland, for the
aforementioned period. In addition, the causality results indicated a unidirectional relationship
between unemployment rate and inflation rate, with direction from unemployment to inflation.
Finally, to forecast the model variables, the impulse response functions and the variance
decomposition method are applied. The results for a 10year forecasting period indicated that
shocks in unemployment rate cause a decrease on inflation rate for the first years, followed by a
steady increase for the remaining years. Policy implications are then explored in the
conclusions.
Keywords
KeywordsKeywords
Keywords: Inflation, Unemployment, NAIRU, Phillips Curve, Poland, Autoregressive Distributed Lag Cointegration Test, Toda
Yamamoto Causality Test, Variance Decomposition, Impulse Response Function
JEL Classification
JEL ClassificationJEL Classification
JEL Classification: C22, C32, E31, E50
R
IASSUNTO
La curva di Phillips: dinamiche di disoccupazione e stime Nairu dell’economia polacca
Il fine di questo studio è analizzare la relazione tra inflazione e tasso di disoccupazione in
Polonia nel periodo 19922017, nel contesto della curva di Phillips. Per testare la relazione di
lungo periodo e la relazione causale delle variabili esaminate è stata applicata la tecnica ARDL
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(Autoregressive Distributed Lag) di Pesaran et al. (2001) e quella con approccio di causalità di
Toda e Yamamoto (1995), considerate le più appropriate per dimensione del campione e
integrazione delle variabili. I risultati degli studi evidenziano che c’è una relazione di lungo
periodo tra tasso di disoccupazione e inflazione in Polonia, nel periodo considerato. Inoltre, i
risultati di causalità indicano una relazione unidirezionale tra tasso di disoccupazione e
inflazione, con direzione disoccupazione verso inflazione. Infine per fare previsioni sulle
variabili del modello, sono state applicate le funzioni di risposta agli impulsi e il metodo di
scomposizione della varianza. I risultati di previsione a 10 anni indicano che gli shock nel tasso di
disoccupazione causano un decremento sul tasso di inflazione per i primi anni, seguito da un
incremento costante nei successivi. Le implicazioni politiche sono esposte nelle conclusioni.
1. I
NTRODUCTION
The observed inverse relationship between unemployment and inflation, first discovered by
William Phillips (1958) on his article “The Relationship between Unemployment and the Rate of
Change of Money Wage Rates in the United Kingdom, 1861 to 1957”, has come to be known as the
Phillips curve. Since then, unemployment and inflation as economic concepts have been a
central topic in macroeconomics. These two concepts are considered as key factors in the
process of economic development of every country. All government programs are conducted
focusing on policies that keep on stable price levels and low unemployment rates.
However, the failure to explain economic phenomena of the crisis of 1970s had created serious
doubts about the validity of Phillips curve. The Phillips curve idea was openly criticized by the
Monetarist school, among them Milton Friedman. Friedman (1968) argued that there is only
short run tradeoff between the inflation rate and the unemployment rate, but for the long run
he introduced the concept of the NAIRU (NonAccelerating Inflation Rate of Unemployment).
NAIRU is defined as the rate of unemployment when the rate of inflation is stable. Therefore,
the long run Phillips curve is vertical and there is no tradeoff between unemployment and
inflation (see Phelps 2006).
In 2017, unemployment rate in Poland reached the lowest level in the country’s postcommunist
history, as youth employment picks up. Even during the recent financial crisis of 20072008,
increasing growth rates helped Polish economy to respond in the difficult conditions of the
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global economy. The purpose of this paper is to examine the existence of Phillips curve in Poland
using annual time series data for the period 1992 2017.
Most of the previous relevant studies examine the tradeoff relationship between inflation and
unemployment rate on the developed countries. The focus on the developing countries,
regarding the Phillips curve is relatively recent. The structure of the paper is as follows: Section 2
presents the literature. Section 3 analyzes the theoretical framework. Section 4 presents
correlations between the two variables. Section 5 describes data and methodology. Empirical
results are discussed in section 6. Concluding remarks are given in the final section.
2. L
ITERATURE REVIEW
An extensive and expanding volume of both theoretical and empirical studies exists on the
relationship between inflation and unemployment across developed and developing countries,
over varying sample periods and different econometric approaches. However, the issue still
remains controversial for the policy makers. The results seem to vary from country to country
due to the different structure of their domestic economies and the continuous changes in
economic conditions.
Changes in monetary conditions are often believed to have a significant impact on real economic
variables, such as output and employment, through the classical Phillips curve relationship
(Vermeulen 2017). Among prominent economists who support the existence of the Phillips
curve are Samuelson and Solow (1960). Samuelson and Solow (1960) examined the relationship
between the rate of inflation and unemployment rate for a twentyfive year period (1934 to 1958)
for the case of the United States (US). The results of their study revealed an inverse relationship
between inflation and unemployment. It is worth mentioning that these researchers were the
first who championed the Phillips curve as a policy tool.
In addition, Gordon (1971) confirmed Phillips relation in the US using macroeconomic data for
the pre1970s and the post1970s periods.
The fact that there exists an inverse relationship between unemployment and inflation was
criticized by Phelps (1967) and Friedman (1968). Phelps (1967) and Friedman (1968) supported
that as the Phillips curve shifts over time, the equilibrium rate of unemployment is independent
from the rate of inflation. Therefore there is only short run tradeoff between inflation and
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unemployment rate. For the long run they introduced the concept of NAIRU (NonAccelerating
Inflation Rate of Unemployment). NAIRU refers to a level of unemployment, below which
inflation rises. The stability of original Phillips curve was disputed in the early 1970s, where the
US economy faced high inflation and unemployment rate simultaneously (stagflation). Later,
other researchers argued against the Phillips hypothesis (Lucas, 1976; Okun, 1975).
Contrary to Friedman (1968) and Phelps (1967), Modigliani and Tarantelli (1976) argued that no
“natural” unemployment rate exists and that the Phillips curve does not disappear in the long
run. Modigliani and Tarantelli (1976) argued that the Phillips curve shifts upward and become
steeper every contract renewal.
Lucas (1976) argued that could be a tradeoff relationship between unemployment and inflation
under the condition that the workers do not expect the policymakers to create an artificial
situation of high inflation combined with low unemployment. In a different case, employees
would predict high inflation and an increase in wages would be possible. In such a case, high
unemployment and high inflation could coexist, which is known as “Lucas Critique” (see also
Zaman et al., 2011; Dritsaki and Dritsaki, 2012).
In 1975, Okun commented that “Phillips curve has become an unidentified flying object” (p.
353)”. However, in the 1990’s, Phillips curve came to the front giving mixed results. Alogoskoufis
and Smith (1991) supported empirically the “Lucas Critique”. On the other hand, Fisher and
Seater (1993), King and Watson (1994) and Fair (2000) find a long run inflation unemployment
tradeoff.
Marcelino and Mizon (1999) examined the relationship between wages, prices, productivity,
inflation and unemployment in Italy, Poland and the UK between the 1960’s and the early
1990’s. They investigated the labor markets of these countries and found that there are
significant changes in the structures of the relationships between wagesprices and
unemploymentinflation for the period 197980. They concluded that although there are
important changes in the labor markets of the examined countries, taking into account a greater
degree of flexibility, there are no common characteristics among them.
Recent advances in data analysis methods allow a more in depth examination of the Phillips
curve hypothesis. Schreiber and Wolters (2007) investigated the relationship between
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unemployment and inflation, using a vector autoregressive model (VAR) and a vector error
correction model (VECM), for the case of Germany over the period 19772002. Their study
revealed a negative relationship between unemployment and inflation, both in the short and in
the long run, for the examined period.
Del Boca et al. (2008) examined the existence of Phillips curve in Italy using data covering the
period 19782000. The results of the study showed that a tradeoff relationship exists only
during low inflation and stable aggregate supply. Del Boca et al. (2008) captured the effects of
structural changes and asymmetries on the estimated parameters of alternative Phillips
equations using the Kalman filter.
A similar study, conducted by Russell and Banerjee (2008), examined the Phillips curve
hypothesis assuming nonstationarity in the series. They found that there is a positive relation
between inflation and unemployment rate in the short run for the case of US during the period
19522004.
Islam et al. (2011) used the ARDL bound approach to examine the existence and stability of
Phillips curve for North Cyprus using data covering the period 19782007. The results of their
analysis showed the existence of Phillips curve both in the short and in the long run. In addition,
a stable relation is confirmed.
Karahan et al. (2012) investigated the relationship between unemployment and inflation for
Turkey over the period 20062011. The ARDL bounds tests indicated that, in the short run,
unemployment has a negative impact on inflation. However, the results did not reveal any causal
relation between the two variables in the long run supporting the views of Friedman (1967) and
Phelps (1967), not advocating the “hysteresis effect”.
Dritsaki and Dritsaki (2012) investigated the Phillips curve hypothesis in Greece using data for
the period 19802010. Their results revealed a long run relationship and a causal relationship
between unemployment and inflation. In addition, their results showed that shocks in inflation
cause a reduction on unemployment for the first years, following by a slight rise for the
remaining years.
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T
ABLE
1

Summary of Recent Empirical Studies
Authors Study Period and
Area Main Methods Main Results
Schreiber and
Wolters (2007)
Germany
19772002 VAR and VECM
A
negative relationship
between unemployment
and inflation, both in the
short and in the long run
Del Boca et al.
(2008)
Italy
19782000
structural
changes and
asymmetries
using Kalman
filter
A tradeoff relationship
exists only during low
inflation and stable
aggregate supply
Russell and
Banerjee
(2008)
United States
19952004
Nonstationarity
models with
GMM
A
positive relation between
inflation and
unemployment rate in the
short run
Islam et al.
(2011)
North Cyprus
19782007
ARDL bounds
test
E
xistence of stable Phillips
curve, both in the short and
in the long run
Karahan et al.
(2012)
Turkey
20062011
ARDL bounds
test
N
o causal relation between
inflation and
unemployment in the long
run
Dritsaki and
Dritsaki (2012)
Greece
19802010
Johansen
cointegration
and VECM
A
long run causality
relation between
unemployment and
inflation
Shocks in inflation cause a
reduction on
unemployment
Nikulin (2015)
Poland and other
5 new EU
members
20022013
Panel data
techniques
A
n increase of productivity
in Poland in comparison to
Czech Republic is greater
than an increase of wages in
Poland in comparison to
Czech Republic
The productivity in Poland
in relation to Hungary and
Estonia has been growing
slower than the wages in
Poland in comparison to
Hungary and Estonia
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Nikulin (2015) examined the relationships between wages, labor productivity and
unemployment for Poland and other 5 new EU members (using Poland as benchmark) for the
period 20022013. The results of the study revealed that the relations among the examined
variables in the new EU member countries are diversified. More specific, the results showed that
an increase of productivity in Poland in comparison to Czech Republic is greater than an
increase of wages in Poland in comparison to Czech Republic. In addition, the productivity in
Poland in relation to Hungary and Estonia has been growing slower than the wages in Poland in
comparison to Hungary and Estonia. The lower productivity in Poland could be a reason for
greater dynamic of productivity growth in the country.
3. C
ORRELATION BETWEEN INFLATION AND UNEMPLOYMENT
In this section, we present correlations between the two variables. The correlation matrix and
the graphs of inflation rate and unemployment rate for the period 19922017 are following.
The inverse relationship between inflation and unemployment is most obvious during the
period 19982008. This correlation is the evidence which is traditionally associated with Phillips
curve hypothesis and significantly different from zero (see Table 2).
T
ABLE
2

Correlation Matrix (19922017)
INF
INFINF
INF
UN
UNUN
UN
INF
INFINF
INF
1.000 0.195 (0.072)*
UN
UNUN
UN
0.195 (0.072)* 1.000
Note: * indicates significance at 10% level of significance, pvalues in
parentheses.
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F
IGURE
1

Inflation Rate for Poland (period 19922017)
F
IGURE
2

Unemployment Rate for Poland (period 19922017)
4. M
ATERIALS AND METHODS
4.1 Data
The variables that are used in this study are inflation (INF) expressed as percentage change of
average consumer prices, and unemployment (UN) expressed as a percentage of civilian labor
force. The sample data of this study is 19922017. Data are gathered from economic databases of
10
0
10
20
30
40
50
92 94 96 98 00 02 04 06 08 10 12 14 16
INF
4
8
12
16
20
24
92 94 96 98 00 02 04 06 08 10 12 14 16
UN
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International Monetary Fund (IMF) and Annual MacroEconomic Database (AMECO). Figure 3
plots the actual and forecast values of inflation and unemployment rates.
F
IGURE
3

Actual and Forecast Values of the Inflation and Unemployment (INFF and UNF
Denote Forecast Values of Inflation and Unemployment Rate Respectively)
The descriptive statistics for all variables are shown in Table 3.
T
ABLE
3

Descriptive Statistics
INF
INFINF
INF
UN
UNUN
UN
Mean
MeanMean
Mean
9.201962 12.27308
Median
MedianMedian
Median
3.596000 11.50000
Maximum
MaximumMaximum
Maximum
43.00000 20.00000
Minimum
MinimumMinimum
Minimum
0.933000 5.000000
Std. Dev.
Std. Dev.Std. Dev.
Std. Dev.
12.25142 4.299633
Skewness
SkewnessSkewness
Skewness
1.540673 0.326658
Kurtosis
KurtosisKurtosis
Kurtosis
4.139750 2.134451
Jarque
JarqueJarque
Jarque

Bera
BeraBera
Bera
11.69320 1.273996
Observations
ObservationsObservations
Observations
26 26
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4.2 Econometric Methodology
After presenting the descriptive statistics for the variables, the paper involves into the following
objectives:
• The first is to examine the stationarity of the variables using the Augmented Dickey
Fuller test (ADF) (1979), the Phillips Perron test (PP) (1988) as well as the test proposed
by Kwiatkowski et al. (KPSS) (1992).
• If the variables are integrated of order one then Johansen’s (1998) cointegration test is
the most appropriate to be used. In the case that the variables do not have the same
integration order, Pesaran et al. (2001) cointegration test is the most appropriate.
The Johansen’s cointegration method, except the integration I(1) of the variables,
requires a large number of observations in order to give robust results. In this study we
apply the ARDL approach.
• The third is to estimate the long run and short run relationship between the variables of
the examined model.
• The fourth step is to check the causal relationship between the variables using a dynamic
vector error correction model (VECM). In this paper, the TodaYamamoto (1995)
causality technique is applied.
• The fifth aim is to estimate the variance decomposition analysis and impulse response
functions using Choleski technique.
4.2.1 Unit Root Tests
We begin our analysis by checking the stationary properties of the variables included in the
study. We apply the tests suggested by DickeyFuller (ADF) (1979), PhillipsPerron (PP) (1988)
and Kwiatkowski et al. (KPSS) (1992). In all these tests, the null hypothesis is that the variable
contains a unit root (i.e., it is not stationary).
4.2.2 Autoregressive Distributed Lag (ARDL) Cointegration Analysis
The purpose of this paper is to investigate the relationship between unemployment and inflation
in the case of Poland, within the Phillips Curve context. For this reason, this study employs the
AutoRegressive Distributed Lag (ARDL) analysis of cointegration, developed by Pesaran and
Shin (1999) and extended by Pesaran et al. (2001) (see also Dritsaki and Stamatiou 2018).
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The ARDL approach has a number of advantages over traditional cointegration methods, such as
Engle and Granger (1987), Johansen (1988), and Johansen and Juselius (1990), as noted below: i)
it provides consistent estimates regardless of whether the variables are integrated I(0) or I(1), ii)
all variables of the models assumed to be endogenous, iii) it is more efficient for small sample
data, iv) it allows that the variables may have different lag lengths, v) in addition, the bounds of
ARDL approach can distinguish and eliminate autocorrelation and endogeneity problems
between dependents and independents variables, vi) finally, a dynamic error correction model
can be derived from the ARDL method through a simple linear transformation (Harris and
Sollis, 2005; Jalil and Ma, 2008) (see also Dritsakis and Stamatiou, 2016; Stamatiou and
Dritsakis, 2014).
The autoregressive distributed lag (ARDL) cointegration technique as a general vector
autoregressive (VAR) model of order p is shown below:
( , )
t t t
L INF UNGAP
=
(1)
where L
t
is a column vector composed of the two variables.
The ARDL models that are used in this study are the following:
01 11 1 21 1 1 2 1
1 0
p q
t t t i t i i t i t
i i
UNGAP UNGAP INF UNGAP INF
β δ δ α α ε
− − − −
= =
∆ = + + + ∆ + ∆ +
∑ ∑
(2)
02 12 1 22 1 1 2 2
1 0
p q
t t t i t i i t i t
i i
INF INF UNGAP INF LUNGAP
β δ δ α α ε
− − − −
= =
∆ = + + + ∆ + ∆ +
∑ ∑
(3)
where ∆ denotes the first difference operator, β is constant and ε
1t
, ε
2t
are the “well behaved”
random disturbance terms. The error terms assumed to be independently and identically
distributed.
The optimal values for the maximum lags, p and q, will be determined by the minimum values of
criteria Akaike (AIC), Schwarz (SIC) and HannanQuinn (HQC) in accordance with the
following models:
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01 1 2 1
1 0
p q
t i t i i t i t
i i
UNGAP UNGAP INF
β α α µ
− −
= =
= + + +
∑ ∑
(4)
02 1 2 2
1 0
p q
t i t i i t i t
i i
INF INF UNGAP
β α α µ
− −
= =
= + + +
∑ ∑
(5)
where UNGAP
t
and INF
t
are the dependent variables, β is constant, α
1i
and α
2i
are the long terms
and (p, q) are the optimal lag lengths of the ARDL model. Under the equations (2) and (3), the
null and alternative hypotheses are as follow:
0 11 21
: 0
H
δ δ
= =
i.e., there is no cointegration among the variables
1 11 21
: 0
H
δ δ
≠ ≠
i.e., there is cointegration among the variables
and
0 12 22
: 0
H
δ δ
= =
i.e., there is no cointegration among the variables
1 12 22
: 0
H
δ δ
≠ ≠
i.e., there is cointegration among the variables.
According to Pesaran et al. (2001) the null hypothesis is tested by conducting an Ftest for the
joint significance of the coefficients of the lagged levels of the variables.
Two sets of critical values, for a given level significance, have been calculated by Narayan (2005).
Narayan (2005) critical bounds are more appropriate for small samples. The lower bound is
based on the assumption that all variables including in the model are I(0), and the upper bound
is based on the assumption that all of the variables are I(1).
The null hypothesis of no cointegration is rejected when the Fstatistic exceeds the upper
critical bound value. If the calculated Fstatistic is lower than the critical value of lower limit, we
accept the null hypothesis. The cointegration test is inconclusive when the Fvalue is between
the lower and the upper limit of critical bounds (Pesaran et al., 2001).
Once cointegration is confirmed, the next step is to proceed with the estimation of the long run
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coefficient of the ARDL model using equations (6) and (7):
01 11 21 1
1 0
p q
t t i t i t
i i
UNGAP UNGAP INF e
β δ δ
− −
= =
= + + +
∑ ∑
(6)
02 12 22 2
1 0
p q
t t i t i t
i i
INF INF UNGAP e
β δ δ
− −
= =
= + + +
∑ ∑
(7)
This study also estimates a dynamic error correction model (ECM) to investigate the short run
dynamics of the respective variables towards the long run equilibrium. The ECM integrates the
short run coefficient with the long run coefficient without losing long run information.
The dynamic unrestricted ECM is depicted in equations (8) and (9), as shown below:
01 1 2 1 1
1 0
p q
t i t i i t i t t
i i
UNGAP UNGAP INF ECM
β α α λ ε
− − −
= =
∆ = + ∆ + ∆ + +
∑ ∑
(8)
02 1 2 2 1
1 0
p q
t i t i i t i t t
i i
INF INF UNGAP ECM
β α α λ ε
− − −
= =
∆ = + ∆ + ∆ + +
∑ ∑
(9)
where ECM
t1
is the error correction term.
The coefficient of ECM
t1
should be negative and statistically significant. This coefficient
indicates the speed of adjustment to the long run equilibrium after a short run shocks.
4.2.3 Diagnostics Tests of the Model
One of the most important and crucial assumptions in the bounds testing (ARDL) approach is
that the error terms of equations (2) and (3) have to be serially independent and normally
distributed. So, in order to check the validity and reliability of the estimation results, several
diagnostics are performed. The diagnostic tests include JarqueBera normality test, ARCH test
for heteroscedasticity, BreuschGodfrey Serial Correlation (LM) test and Ramsey RESET
specification test.
4.2.4 Stability Tests of the Model
The existence of cointegration does not necessarily imply that the estimated coefficients of the
model are stable. Therefore, in order to check that all parameters used in each of the models are
sufficiently stable, the cumulative sum (CUSUM) and the cumulative sum of squares
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(CUSUMSQ) proposed by Brown et al. (1975) are applied. These tests are also suggested by
Pesaran et al. (2001) for measuring the parameter stability.
4.2.5 TodaYamamoto Causality Analysis
The objective of our study is to identify the causality relations between inflation and
unemployment rates for the case of Poland, using data covering the period 19922017. In this
paper, we employ the TodaYamamoto (1995) and the Modified Wald (MWALD) causality
techniques in order to find out the direction of causality between the two variables.
TodaYamamoto (1995) test:
•
Ignores the condition of stationary or cointegration of the series to test the causality.
•
Uses a standard vector autoregressive (VAR) model in the levels of the variables
(rather than in the first differences as in Granger’s test) minimizing, in this way, the
risks associated with the possibility of the wrong specification of the integration order
of the variables, or the presence of cointegrated vector among them.
•
Minimizes the distortion of the test’s sizes as a result of pretesting (Giles 1997,
Mavrotas and Kelly 2001).
Toda and Yamamoto (1995) procedure can improve the power of Granger causality test. The
procedure makes valid estimation of the parameters even the VAR system is not cointegrated.
Toda and Yamamoto (1995) develop a different approach based on a level VAR model. The steps
of the procedure are shown below:
• We begin with the specification of integration order of the series. If the order is
different we get the maximum (dmax).
• We create a level VAR model.
• We define the appropriate lag order (k) of the VAR model using the Likehood Ratio
(LR), Akaike Information Criterion (AIC), Schwarz Information Criterion (SC), Final
Prediction Error (FPE) and HannanQuinn (HQ) Information Criterion.
• If series have the same integration order then we continue with the Johansen
cointegration approach. Otherwise, we employ ARDL bounds test proposed by
Pesaran et al. (2001).
• Regardless the presence of a cointegrated vector among the series, we continue with
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the investigation of the causality relations between them.
• We apply Granger causality and Modified Wald (MWALD) techniques for the
significance of parameters on the following equations:
max max
0 1 2 1 2 1
1 1 1 1
k d k d
t i t i j t j i t i j t j t
i j k i j k
INF a INF a INF UNGAP UNGAP
µ β β ε
− − − −
= = + = = +
= + + + + +
∑ ∑ ∑ ∑
(10)
max max
0 1 2 1 2 2
1 1 1 1
k d k d
t i t i j t j i t i j t j t
i j k i j k
UNGAP UNGAP UNGAP INF INF
ϕ γ γ δ δ ε
− − − −
= = + = = +
= + + + + +
∑ ∑ ∑ ∑
(11)
where k is the optimal lag length on the initial VAR model and dmax is the maximum integration
order in VAR model.
In equation (10),
t
UNGAP
causes
t
INF
if
0
1
≠
i
β
, for all i. Similarly, in equation (11),
t
INF
causes
t
UNGAP
if
0
1
≠
i
δ
for all i.
4.2.6 Impulse Response Function (IRF) and Variance Decomposition Method (VDM)
The vector error correction tests provide little evidence on the dynamic properties of the model,
since they show only the causality relations of the endogenous variables during the examined
period. So, we continue with the forecast error variance decomposition (FEVD) in order to test
the strength of causal relationship between inflation and unemployment.
The variance decomposition method (VDM) shows the percentage of variability of a variable of
the VAR model over the variable itself, as well as the system variables. The VDM indicates the
impulse, the innovation or the shock of each variable of the system to the others (including
itself), providing an indication of these relationships which can be described as “out of sample”
causality tests (Kling and Bessler, 1985).
In addition, the impulse response functions (IRF) is an alternative way of variance
decomposition method (VDM) and describes the reaction of the system due to shocks in
variables that parameterizes the dynamic behavior of it (Stamatiou and Dritsakis, 2019). These
shocks are expressed using the standard deviations of the disturbance terms (Dritsaki and
Dritsaki, 2013). The IRF allows us to understand the possible effects of a random disorder of an
equation of the system on the endogenous variable of the equation itself, as well as on the other
endogenous variables of the system.
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5.
E
MPIRICAL RESULTS
5.1 Unit Roots Tests
The preliminary stage of the study is to define the integration order for each time series. We
apply ADF by Dickey and Fuller (1979), PP by Phillips and Perron (1988) as well as KPSS by
Kwiatkowski et al. (1992) test. The results of these tests are presented in Table 4.
T
ABLE
4

Unit Root Analysis
Variable
VariableVariable
Variable
ADF
ADFADF
ADF
PP
PPPP
PP
KPSS
KPSSKPSS
KPSS
C
CC
C
C,T
C,TC,T
C,T
C
CC
C
C,T
C,TC,T
C,T
C
CC
C
C,T
C,TC,T
C,T
INF
INFINF
INF
5.49(0)
***
2.76(0)
8.38[9]
***
4.71[10]
***
0.57[3]
***
0.18[3]
***
UNGAP
UNGAPUNGAP
UNGAP
3.23(1)
**
3.15(1)
2.06[2]
2.03[2]
0.75[3]
0.81[3]
∆INF
INFINF
INF
3.38(0)
**
4.55(0)
***
3.33[2]
**
4.54[2]
***
0.69[2]
***
0.15[1]
***
∆UNGAP
UNGAPUNGAP
UNGAP
4.29(1)
**
4.18(1)
**
3.15[3]
**
3.27[3]
**
0.06[2]
***
0.05[2]
***
Notes: *** and ** show significant at 1% and 5% levels respectively, the numbers within
parentheses followed by ADF statistics represent the lag length of the dependent variable used
to obtain white noise residuals, the lag lengths for ADF equation were selected using Schwarz
Information Criterion (SIC), Mackinnon (1996) critical value for rejection of hypothesis of unit
root applied, the numbers within brackets followed by PP and KPSS statistics represent the
bandwidth selected based on Newey West (1994) method using Bartlett Kernel, C Constant, T
Trend, ∆ First Differences.
The unit root analysis results (see Table 4) revealed that INF is stationary in levels in all the test
that were applied which means that INF is integrated I(0), while UNGAP is stationary in first
differences which means that UNGAP is integrated I(1). So, we examine the long run
relationship of the variables using the ARDL bounds test.
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5.2 ARDL Cointegration Analysis
In order to estimate the parameters of equations (2) and (3), we select the optimal values of p
and q lags by the minimum value of Final Prediction Error (FPE), Akaike Information Criterion
(AIC), Schwarz Information Criterion (SIC), HannanQuinn Criterion (HQC), and Likelihood
Ratio (LR). The results of these criteria are presented in Table 5.
T
ABLE
5

Var Lag Order Selection Criteria (Max=4)
Lag
LagLag
Lag
LogL
LogLLogL
LogL
LR
LRLR
LR
FPE
FPEFPE
FPE
AIC
AICAIC
AIC
SIC
SICSIC
SIC
HQC
HQCHQC
HQC
0 120.994 NA 246.091 11.181 11.280 11.204
1 84.501 63.034 12.871 8.227 8.524 8.297
2 70.298 21.948* 5.156 7.299 7.795* 7.416
3 67.024 4.465 5.673 7.365 8.060 7.529
4 60.019 8.279 4.565* 7.092* 7.985 7.302*
Notes: * indicates lag order selected by the criterion.
The ARDL bound test is sensitive to lag length, so we use the Akaike Information Criterion to
determine the optimal lag length in equations (4) and (5). AIC showed that optimal lag length in
these equations is (2, 4) and (1, 0) respectively. Table 6 shows the cointegration results using
ARDL bounds test.
F
IGURE
4

Optimal Lag Length in Eq. (4) and Eq. (5) Respectively
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6

The Results of ARDL Cointegration Test
Bounds testing to cointegration
Bounds testing to cointegrationBounds testing to cointegration
Bounds testing to cointegration
Diagnostic tests
Diagnostic testsDiagnostic tests
Diagnostic tests
Estimated models
Estimated modelsEstimated models
Estimated models
Optimal
OptimalOptimal
Optimal
lag
laglag
lag
F
FF
F

stat.
stat.stat.
stat.
X
XX
X
2
22
2NOR
NORNOR
NOR
X
XX
X
2
22
2ARCH
ARCHARCH
ARCH
X
XX
X
2
22
2RESET
RESETRES ET
RESET
X
XX
X
2
22
2SERIAL
SERIALSERIAL
SERIAL
F
FF
F
UNGAP
UNGAPUNGAP
UNGAP
(UNGAP/IN
(UNGAP/IN(UNGAP/IN
(UNGAP/IN
F
FF
F)
))
)
(2, 4) 2.93 0.41 1.16[1] 10.3[1] 0.33[2]
F
FF
F
INF
INFINF
INF
(INF
(INF(INF
(INF/
//
/UNGAP
UNGAPUNGAP
UNGAP)
))
)
(1, 0) 15.41*** 1.20 0.02[1] 4.57[2] 2.77[2]
Significant level
Significant levelSignificant level
Significant level
Lower bounds
Lower boundsLower bounds
Lower bounds
Upper bounds
Upper boundsUpper bounds
Upper bounds
I(0) I(1)
10%
3.02 3.51
5%
3.62 4.16
2.5%
4.18 4.79
1% 4.94 5.58
Notes: The optimal lag length is determined by AIC. [ ] is the order of diagnostic tests. Critical
values are collected from Narayan (2005). *** show significant at 1% level.
The results of Table 6 indicate that, in equation (3), the calculated F statistic (15.41) exceeds the
upper bound critical value (5.58) at 1% level of significance. Findings confirm that there is a long
run relationship between inflation rate and unemployment in Poland.
Within the cointegration test results, a number of standard diagnostic tests were applied in
order to check the robustness of the model. The ARDL model fulfills the assumptions of
normality, autoregressive conditional heteroskedasticity (ARCH), functional forms and serial
correlation.
5.3 Long Run and Short Run Estimates
Table 7 presents the results of long and short run relationship between the variables in our
model.
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T
ABLE
7

Long Run and Short Run Results
Variables
VariablesVariables
Variables
Coefficient
CoefficientCoefficient
Coefficient
T
TT
T



statistic
statisticstatistic
statistic
Long run analysis
Long run analysisLong run analysis
Long run analysis
Dependent variable=INF
Dependent variable=INFDependent variable=INF
Dependent variable=INF
t
tt
t
Constant
ConstantConstant
Constant
0.13
0.25
INF
INFINF
INF
t
tt
t

1
11
1
0.81
23.76***
UNGAP
UNGAPUNGAP
UNGAP
t
tt
t

0.30

1.78*
R
RR
R
2
22
2
0.96
F
FF
F



Statistic
StatisticStatistic
Statistic
296.3***
D
DD
D



W
WW
W
2.04
Short run analysis
Short run analysisShort run analysis
Short run analysis
Dependent variable=
Dependent variable=Dependent variable=
Dependent variable=∆INF
INFINF
INF
t
tt
t
Constant
ConstantConstant
Constant

0.01

0.03
∆
INF
INFINF
INF
t
tt
t

1
11
1
0.92
4,18***
∆
UNGAP
UNGAPUNGAP
UNGAP
t
tt
t

0.49

2.02*
ECM
ECMECM
ECM
t
tt
t

1
11
1

0.86

3.57***
R
RR
R
2
22
2
0.59
F
FF
F



Statistic
StatisticStatistic
Statistic
6.45***
D
DD
D



W
WW
W
1.86
Notes: *** and ** show significant at 1% and 10% levels respectively. ∆ denotes the first
difference operator.
From the above table we see that, in the long run equation of INF, a decrease 1% of
unemployment will cause an increase 0.30% of inflation. The ECM
t1
is negative and statistically
significant which implies a long run relationship between the examined variables. This means
that in the short term the deviations from the long run equilibrium are adjusted by 86% every
year.
The DW statistic is 2.04 which confirms that the model is not spurious. The R squared is 0.96
implying that 96% variations in the dependent variable are explained by the model and the rest
by the error term. In addition, the computed Fstatistic (296.3) clearly rejects the null
hypothesis that the regressors have zero coefficients.
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5.4 Diagnostics Tests
As illustrated in the tables below, the model passes the tests regarding normality (JarqueBera),
serial correlation (LM) heteroscedasticity (ARCH) and specification (Ramsey RESET). The
results of all the diagnostics tests for the long run and short run equations are displayed in Table
8 and 9 respectively.
T
ABLE
8

Diagnostics Tests (Long run)
Diagnostics
Tests X
2
Normal X
2
Serial X
2
ARCH X
2
Reset
1.19 3.08[2] 0.00[1] 3.86[2]
Notes: Numbers in brackets are lags for ARCH and Serial tests and fitted terms for Reset test.
T
ABLE
9

Diagnostics Tests (Short run)
Diagnostics
Tests X
2
Normal X
2
Serial X
2
ARCH X
2
Reset
1.45 3.24[2] 0.03[1] 0.08[1]
Notes: Numbers in brackets are lags for ARCH and Serial tests and fitted terms for Reset test.
The diagnostics tests further strengthen and confirm the reliability and validity of our
estimation results.
5.5 Instability Tests
It is obligatory to ensure the dynamic stability of any model having autoregressive structure. A
graphical representation of Recursive Residuals, CUSUM and CUSUMSQ statistics are provided
in Figures 5, 6, 7, 8. If the plots of the Recursive Residuals and CUSUM tests lie inside the critical
bounds at 5% level of significance it would signify the parameter constancy and the model
stability.
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F
IGURE
5

Plots of CUSUM and CUSUMSQ (Long Run)
F
IGURE
6

Plots of Recursive Residuals (Long Run)
F
IGURE
7

Plots of CUSUM and CUSUMSQ (Short Run)
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F
IGURE
8
–
Plots of Recursive Residuals (Short Run)
From the above figures we can see that the straight lines are crossed by CUSUMSQ and
Recursive Residuals in the long run model and by CUSUMQ in the short run model. According to
the test results for the given regression, we conclude that all the coefficients are not stable over
the sample period.
5.6 TodaYamamoto Causality Test
The objective of our study aims to identify the causal relationships between unemployment rate
and inflation. Table 10 presents the results on Toda and Yamamoto (1995) causality testing
according to equations (10) and (11). In Table 4 the unit root tests confirm that the maximum
integration order (dmax) for the selected variables is 1. In addition, Table 5 suggests that the
optimal lag length (k) is 4.
T
ABLE
10
–
Results of Toda and Yamamoto Causality Test
Dependent
Dependent Dependent
Dependent
Variables
VariablesVariables
Variables
MWALD Test
MWALD TestMWALD Test
MWALD Test
Causality Inference
Causality InferenceCausality Inference
Causality Inference
INF
INFINF
INF
t
tt
t
UNGAP
UNGAPUNGAP
UNGAP
t
tt
t
INF
INFINF
INF
t
tt
t
8.63* (0.07)
UNGAP
t
INF
t
UNGAP
UNGAPUNGAP
UNGAP
t
tt
t
2.44 (0.65)
Notes: * show significant at 10% level, pvalues in parentheses.
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As reported in Table 10, the results provide evidence of a unidirectional causal relationship
between inflation (INF) and unemployment rate (UNGAP) at 10% level of significance, with
direction from unemployment rate to inflation (see Figure 9). The knowledge about the
direction of causality will help policy makers to trace out policies for sustainable economic
growth in Poland.
F
IGURE
9
–
Causality Relation for Poland
5.7 Impulse Response and Variance Decomposition Analysis
Figure 10 plots the impulse responses of unemployment tare (UNGAP) and inflation rate (INF)
over a horizon of 10 years. Standard errors are calculated by the Monte Carlo method, with 100
repetitions (of ± 2 standard deviations).
Impulse responses suggest that shocks in inflation rate (INF) have a negative impact on the
variable itself in the first and in the last 3 years (under investigation), whereas there is a
stabilization of inflation rate over the middle 4 years. Regarding unemployment rate (UNGAP),
Figure 10 suggests that shocks in UNGAP have a positive impact on the variable itself in the first
and in the last 2 years (under investigation), whereas there is a negative impact over the middle 6
years.
In addition, shocks in unemployment rate (UNGAP) cause a decrease on inflation rate (INF)
over the first 4 years followed by an increase of the following 5 years.
Finally, shocks in inflation rate (INF) cause a slight increase on unemployment rate (UNGAP)
over the first 2 years followed by a slight decrease for the next 2 years and a steady increase for
the next 4 years.
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The results from variance decompositions analysis are shown in Figure 11 and in Tables 11 and
12.
F
IGURE
10
–
Impulse Response Function
F
IGURE
11
–
Variance Decomposition
1
0
1
2
3
1 2 3 4 5 6 7 8 9 10
Response of INF to INF
1
0
1
2
3
1 2 3 4 5 6 7 8 9 10
Response of INF to UNGAP
2
1
0
1
2
1 2 3 4 5 6 7 8 9 10
Response of UNGAP to INF
2
1
0
1
2
1 2 3 4 5 6 7 8 9 10
Response of UNGAP to UNGAP
R
e
s
p
o
n
s
e
t
o
C
h
o
l
e
s
k
y
O
n
e
S
.
D
.
I
n
n
o
v
a
t
i
o
n
s
±
2
S
.
E
.
40
0
40
80
120
1 2 3 4 5 6 7 8 9 10
Percent INF variance due to INF
40
0
40
80
120
12345678910
Percent INF variance due to UNGAP
40
0
40
80
120
1 2 3 4 5 6 7 8 9 10
Percent UNGAP variance due to INF
40
0
40
80
120
12345678910
Percent UNGAP variance due to UNGAP
Variance Decomposition ± 2 S.E.
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T
ABLE
11
–
Variance Decomposition Approach (a)
Variance Decomposition
Variance Decomposition Variance Decomposition
Variance Decomposition
of
ofof
of
INF
INFINF
INF
Period
PeriodPeriod
Period
S.E.
S.E.S.E.
S.E.
INF
INFINF
INF
UNGAP
UNGAPUNGAP
UNGAP
1 1.851092 100.0000 0.000000
(0.00000) (0.00000)
2 2.032596 99.57451 0.425485
(5.73882) (5.73882)
3 2.051394 99.57446 0.425544
(5.89426) (5.89426)
4 2.127657 97.17003 2.829966
(7.11311) (7.11311)
5 2.168589 96.51680 3.483199
(6.99101) (6.99101)
6 2.195758 96.24136 3.758637
(7.25811) (7.25811)
7 2.236009 94.46359 5.536409
(7.52897) (7.52897)
8 2.263882 92.16782 7.832184
(8.48662) (8.48662)
9 2.293080 90.95009 9.049912
(9.20659) (9.20659)
10 2.305266 90.70356 9.296444
(9.37690) (9.37690)
From Table 11 we observe that a significant percentage of the variance of inflation rate (99.57%)
is explained by inflation innovations in the short run (in a horizon of two years). On the other
hand, the percentage of variance of unemployment rate (UNGAP) is, in the short run, 0.42%. In a
longer horizon of 10 years the percentage of variance of INF is falling at 90.70, while the
percentage of variance of UNGAP is increased at 9.29%.
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12
–
Variance Decomposition Approach (b)
Variance Decomposition
Variance Decomposition Variance Decomposition
Variance Decomposition
of UNGAP
of UNGAPof UNGAP
of UNGAP
Period
PeriodPeriod
Period
S.E.
S.E.S.E.
S.E.
INF
INFINF
INF
UNGAP
UNGAPUNGAP
UNGAP
1 0.906835 18.39250 81.60750
(13.8542) (13.8542)
2 1.599316 14.67072 85.32928
(14.9858) (14.9858)
3 1.979140 18.18667 81.81333
(16.9247) (16.9247)
4 2.251889 32.09485 67.90515
(18.1969) (18.1969)
5 2.352473 37.45516 62.54484
(18.1715) (18.1715)
6 2.420825 35.37986 64.62014
(18.4028) (18.4028)
7 2.549667 34.44883 65.55117
(18.6819) (18.6819)
8 2.702437 36.06916 63.93084
(18.8363) (18.8363)
9 2.820433 38.18643 61.81357
(18.9872) (18.9872)
10 2.867711 39.41225 60.58775
(18.9546) (18.9546)
In addition, Table 12 indicates that a steady percentage of the variance of unemployment rate
(UNGAP) (85.32%) is explained by unemployment innovations in in a horizon of two years
(short run). On the contrary, the percentage of variance of INF is, in the short run, 14.67%. In a
longer horizon of 10 years the percentage of variance of UNGAP is falling at 60.58%, while the
percentage of variance of INF is increased at 39.41%.
6.
C
ONCLUSIONS AND POLICY IMPLICATIONS
This study represents an attempt to investigate the hypothesis referred by Phillips curve in the
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case of Poland, using data covering the period 19922017. In 2017 unemployment rate in Poland
hit a 25 year low, as youth employment picks up. The labor market of the country remains
resilient in relation to the impact of the global financial crisis of 20072008. It is important to be
mentioned that low unemployment rates are due to the intense business activity of international
companies (such as “Gillette International”, “Dell Computers”, “Fujitsu”, “P & G”, etc.) through
the investment incentives provided by the Polish government (Special Economic Zones (SEZs)).
On the other hand, low unemployment rates can have important implications for monetary
policy (Altig et al., 1997). Although the numbers may be impressive, behind them is the labor
supply which is under pressure from immigration, the low workforce participation rate and
government policies such as raising the retirement age. Poland's central bank estimates that the
unemployment rate is already lower that the rate which puts upward pressure on wages.
The results of this paper, based on the bounds testing for cointegration, confirm that the
inflationunemployment hypothesis exists in Poland. Μore specifically, the long run estimates
show that a decrease 1% of unemployment will cause an increase 0.30% of inflation. In addition,
the causality results based on TodaYammamoto analysis (1995) reveal that there is a
unidirectional causality relationship between unemployment rate and inflation, with direction
from unemployment rate to inflation. Finally, the impulse response functions revealed that, in
the short run, a decrease in inflation rate has a positive effect on unemployment rate. On the
other hand, an increase in unemployment rate has a negative effect on inflation rate.
The finding, that a stable Phillips curve exists for Poland, opens opportunities for the central
bank to adopt monetary policies that would keep inflation and unemployment at political and
social acceptable rates. Polish government, as a matter of necessity and concern, should
continue or improve the macroeconomic policies for a sustainable economic framework that will
enhance the domestic output, while continuing controlling inflation.
This study provides strong empirical existence of Phillips curve in Poland, both in the short and
long run. Based on the findings of this study, one could forecast the future trend for the next ten
years. The study recommends that the Polish government should pay attention to its findings in
order to tackle unemployment issue, and encourages it to conduct active labor market programs
to reduce unemployment level through the creation of productive and labor intensive projects
(the replace of foreign labor with local labor could be the starting point).
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Policy makers should continue improving the agricultural sector in order to increase the supply
in farm products and other essential of life. This fact will reduce price level, generate
employment and reduce the level of inflation in the economy. In 2017, employment in
agriculture accounted almost 11% of total employment in Poland, ranking as the fourth country
in EU after Romania (25,8%), Bulgaria (18,2%) and Greece (11,1%) (AMECO, 2018). It’s worth
mentioning that Poland’s volume of exports of agricultural products has quadrupled since 2004
(accession time in the EU) till today.
The results of the paper agree with these of Islam et al., 2011, who found that a stable Phillips
curve exists for the case of North Cyprus for the period 19782007. Policy makers could make
use of this paper for their future policymaking decisions which would stabilize the price level by
controlling inflation and at the same time, living within an unemployment rate consistent with
inflation (Islam et al., 2011).
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Altig, D., T. Fitzgerald and P. Rupert (1997), Okun’s Law Revisited: Should We Worry About Low
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AMECO (2018), Annual Macroeconomic Database, European Commission.
Brown, R.L., J. Durbin and J.M. Evans (1975), “Techniques for Testing the Constancy of
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Del Boca, A., M. Fratianni, F. Spinelli and C. Trecroci (2008), “The Phillips Curve and the Italian
Lira 18611998”, Working Paper s 0908, University of Brescia, Department of Economics.
Dickey, D.A. and W.A. Fuller (1979), “Distributions of the estimators for Autoregressive Time
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Dritsaki, C. and M. Dritsaki (2013), “Phillips Curve Inflation and Unemployment: An Empirical
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Econometrics, 3(1/2), 2742.
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