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© 2014 Nicolaus Copernicus University. All rights reserved.  
http://www.dem.umk.pl/dem 

D Y N A M I C  E C O N O M E T R I C  M O D E L S  
DOI: http://dx.doi.org/10.12775/DEM.2014.003  Vol. 14 (2014) 51−70 

Submitted October 20, 2014  ISSN 
Accepted December 23, 2014 1234-3862 

Mariola Piłatowska, Aneta Włodarczyk, 
Marcin Zawada*  

The Environmental Kuznets Curve in Poland  
– Evidence from Threshold Cointegration Analysis 

A b s t r a c t. The article aims to look at the long-run equilibrium relationship between per 
capita greenhouse gas emissions and per capita real GDP (EKC hypothesis) in an asymmetric 
framework using the non-linear threshold cointegration and error correction methodology for 
Polish economy during the period 2000 to 2012 (quarterly data). To test the robustness of the 
results the additional explanatory variable (per capita energy consumption) is added to the 
EKC model. The EKC hypothesis is tested using threshold autoregressive (TAR) and momen-
tum threshold autoregressive (MTAR) cointegration method. Moreover, the threshold error 
correction model (TECM) is implemented in order to examine both the short-run and the 
long-run Granger-causal relationship between per capita greenhouse gas emissions and per 
capita income. We found strong evidence in favour of the EKC hypothesis for the Polish case 
and additionally we confirmed that adjustment of deviations toward the long-run equilibrium 
is asymmetric. 

K e y w o r d s: Environmental Kuznets Curve, greenhouse gas emission, energy consump-
tion, growth, threshold cointegration, Granger causality.  

J E L Classification: C24, Q43, Q50. 

                                                 
* Correspondence to: Mariola Piłatowska, Nicolaus Copernicus University, Department of 

Econometrics and Statistics, 13A Gagarina Street, 87-100 Toruń, Poland, e-mail: mari-
ola.pilatowska@umk.pl; Aneta Włodarczyk, Czestochowa University of Technology, Faculty 
of Management, 19B Armii Krajowej Street, 42-201 Czestochowa, Poland, e-mail: 
aneta.w@interia.pl; Marcin Zawada, Czestochowa University of Technology, Faculty of 
Management, 19B Armii Krajowej Street, 42-201 Czestochowa, Poland, e-mail: marcinzawa-
da04@gmail.com.  



Mariola Piłatowska, Aneta Włodarczyk and Marcin Zawada  

DYNAMIC ECONOMETRIC MODELS 14 (2014) 51–70 

52

Introduction  

 The harmful effects of climate change made policy makers become in-
creasingly interested in reducing greenhouse gas (GHG) emissions using 
different policy tools such as environmental taxation and regulation impos-
ing the increased use of renewable energy. At the international level various 
steps are taken to motivate countries to reduce the emissions of GHG, e.g. 
the Kyoto Protocol or the EU energy and climate obligations for member 
countries. The problem of how the pollutants relate to the economy has been 
the subject of intense research in the last decades. One of the main develop-
ments in understanding the link between the environment and economy was 
the environmental Kuznets curve (EKC). The term 'environmental Kuznets 
curve' was coined almost simultaneously by Shafik and Bandyopadhyay 
(1992), Grossman and Krueger (1995) and Panayotou (1993). It refers by 
analogy to the inverted U-shaped relationship between the level of economic 
development and the degree of income inequality formulated by Kuznets 
(1955). The EKC hypothesis says that environmental degradation increases 
with per capita income during the early stages of economic growth, and then 
declines with per capita income after arriving at a threshold1. Hence, the 
relationship between income per capita and some types of pollutants is ap-
proximately an inverted U-shaped.  
 There is a wide stream of researches that has employed cointegration 
techniques to examine the relationship between per capita income and some 
types of pollutants, among others, Aspergis and Payne (2009), Halicioglu 
(2009), Soytas and Sari (2009), Ang (2009), Soytas et al. (2007). However, 
empirical results are mixed and not conclusive to give policy recommenda-
tions that can be applied across countries. The common feature of these stud-
ies was the linear approach and symmetric cointegration which may be 
a possible reason for ambiguous results. It has been suggested more recently 
(Balke and Fomby, 1997; Enders and Granger, 1998; Enders and Siklos, 
2001) that the adjustment of deviations toward the long-run equilibrium need 
not be symmetric and reverting each period. To our knowledge, there are 
a very few studies that use non-linear (threshold) cointegration techniques 
for testing the EKC hypothesis, e.g. Fosten et. al. (2012), Esteve and Tamarit 
(2012).  
 This paper aims to look at testing the EKC hypothesis for the presence of 
threshold cointegration between per capita greenhouse gas emissions and per 

                                                 
1 See Stern (2004), Coondoo and Dinda (2002), Dinda (2004), Luzzati and Orisni (2009), 

Halicioglu (2009) for extensive review surveys of studies which tested the EKC hypothesis.  



The Environmental Kuznets Curve in Poland – Evidence from Threshold... 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 51–70 

53

capita income for the Polish economy during the period 2000 to 2012 (quar-
terly data). This approach will allow for a different speed of adjustment to 
the long-run equilibrium depending on whether emissions of greenhouse gas 
are above or below the EKC. Additionally, another explanatory variable is 
added, i.e. energy consumption, to test the robustness of the results. The 
standard EKC hypothesis and its extended version including energy con-
sumption will be tested using threshold autoregressive (TAR) and momen-
tum threshold autoregressive (MTAR) cointegration method of Enders and 
Granger (1998) and Enders and Siklos (2001). We will also concentrate on 
the short-run and long-run causal relationship between per capita greenhouse 
gas emissions and per capita income using threshold error correction models 
(T-ECM) and momentum threshold error correction model (M-TECM). To 
our knowledge, there is no such study that uses this approach for the case of 
Poland as if the EKC hypothesis is concerned.   
 The remainder of this paper is organized as follows. Section 2 presents 
the environmental Kuznets curve. Section 3 describes the methodology em-
ployed in the analysis. Section 4 describes the data and reports the empirical 
results. Section 5 concludes.   

1. The Environmental Kuznets Curve 

 In classical approach to modelling the relationship between environmen-
tal degradation and income level the following quadratic function with the 
turning point occurring at a maximum pollutant level is used (Agras and 
Chapman, 1999):     

,2
210 tttt GDPGDPEP    (1) 

where tEP  – emissions of some pollutant (per capita), tGDP  – real income 

(per capita), both variables are in logarithms, ,1  ,2 0 – estimated param-

eters, t  error term that may be serially correlated.  
 Based on the parameter values we may conclude about the shape of envi-
ronmental pollution and income linkage. If 01   (or 01  ) while 02  , 
then the function (1) is a monotonically increasing (decreasing) according to 
linear function behavior. Otherwise, if 01   and 02  , an inverted  
U-shape describes the situation when the pollution level increases as a coun-
try develops until this development reaches a turning point and after that the 
rising incomes are accompanied by decreasing environmental degradation. 
The turning point value is approximated by following relation (Stern, 2004): 



Mariola Piłatowska, Aneta Włodarczyk and Marcin Zawada  

DYNAMIC ECONOMETRIC MODELS 14 (2014) 51–70 

54

 .2/exp 21 TPGDP  (2) 

 In the EKC literature the more sophisticated functional form is also taken 
into consideration with the third order polynomial for income factor (Dinda, 
2004): 

.3
3

2
210 ttttt GDPGDPGDPEP    (3) 

 Similarly to the EKC model (2), the parameter estimates in equation (3) 
indicate the direction and character of the relationship between environmen-
tal pollutant and income. In the case of ,03  ,02   01   and 00   
the N-shaped function is monotonically increasing with two possible turning 
points. In the case of opposite signs of cubic polynomial parameters, namely 

,03   ,02   01   and ,00   an inverse-N shape is more accurate for 
describing analyzed relationship.  
 In order to capture the effect of technological progress on pollution 
emission level the deterministic time trend (squared time trend)  and some 
additional variables tX  that may affect tEP  can be included in equation (1) 
or (3).  
 In our empirical research of the long-run relationship between green-
house gas emissions and economic growth first the standard EKC model (1) 
is assumed and further the EKC model with energy consumption )( tE  as 
additional variable is considered to test the robustness of results. In the latter 
case the model takes the form:  

ttttt EGDPGDPEP   2
210 , (4) 

where   − estimated parameter. 

2. Methodology 

 The concept of cointegration implicitly assumes linearity and symmetry, 
what means that the adjustment of the deviations towards the long-run equi-
librium is made instantaneously at each period and increases or decreases of 
the deviations are corrected in the same way. However, the cointegration 
tests and their extensions are misspecified if adjustment is asymmetric. To 
take the property of asymmetry into account, Enders and Siklos (2001) de-
veloped the concept of threshold cointegration. This is indeed an extension 
of residual-based two-stage estimation as developed by Engle and Granger 
(1987). The differences between them consist in the formulation of linearity 
and non-linearity from their second stage of unit root test.  



The Environmental Kuznets Curve in Poland – Evidence from Threshold... 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 51–70 

55

 Extracting from the long-run relationship (1) or (4) the disturbance term  

t (first stage), in the second stage we focus on the coefficient estimates of  

1  and 2  (adjustment parameters) in the following regression:  

  
r

i titittttt II
11211 ,)1(   (5) 

where t  is a white noise disturbance.  

The Heaviside indicator function tI  is defined to depend on the lagged val-

ues of the residuals t : 
















1

1

0

1

t

t
t if

if
I  (6)  

or on the lagged changes in t : 
















1

1

0

1

t

t
t if

if
I  (7) 

where   is a threshold value.  
Equations (5)-(6) are referred to as the TAR model (threshold autoregressive 
model, Enders and Sikolos, 2001), while equations (5) and (7) are named the 
MTAR model (momentum-threshold autoregressive model; see Enders and 
Granger, 1998).  
 Petruccelli and Woolford (1984) proved that the necessary and sufficient 
conditions for the stationarity of residuals  t  from the EKC model are 

,01   02   and 1)1)(1( 21    for any threshold value   (Enders 

and Siklos, 2001). If these conditions are satisfied, 0t  can be considered 

as the long run equilibrium value of the sequence. If t  is higher than the 

long-run equilibrium, the adjustment is ,11 t  but if t  is lower than the 

long-run equilibrium, the adjustment is .12 t  Therefore, the equilibrium 
error behaves like a threshold autoregressive process (TAR). The MTAR 
model – according to Enders and Granger (1998) – is especially valuable 
when adjustment is asymmetric as the deviations t  exhibit more 'momen-
tum' in one direction than in the other. Hence, the TAR model allows to ex-
amine whether the positive deviations  )0( t  from the long-run equilibri-
um have different effects on the behavior of emissions than do the negative 
deviations ),0( t  while the MTAR model allows to display various 
amounts of autoregressive decay depending on whether the series is increas-



Mariola Piłatowska, Aneta Włodarczyk and Marcin Zawada  

DYNAMIC ECONOMETRIC MODELS 14 (2014) 51–70 

56

ing or decreasing (Fosten et al., 2012). There is no prescribed rule as to 
whether to use the TAR or MTAR model, but it is recommended to select 
the best adjustment mechanism (TAR or MTAR) using the AIC (Akaike 
Information Criterion) or SBC (Schwarz Bayesian Criterion) information 
criteria (Enders, Chumrusphonlert, 2004).  
 In general, the threshold value   governing the asymmetric behavior is 
unknown and has to be estimated along with the values of  adjustment pa-
rameters 1  and .2  In our studies we follow Enders and Siklos (2001) and 
Yau and Nieh (2009) by employing Chan’s (1993) methodology2 of search-
ing the consistent estimates of threshold value. However, in many economic 
applications this value is set to zero, ,0  and then the cointegrating vector 
coincides with the attractor ( 0t ). 
 Once the threshold value   is obtained and the TAR or MTAR models 
are estimated, then testing for threshold cointegration can be performed. 
First, the null hypothesis of no cointegration 0: 210  H  is tested, and 
when it is rejected, then the null hypothesis of symmetric adjustment 

210 :  H  is verified. To test the null hypothesis of no threshold cointe-

gration, Enders and Siklos (2001) proposed the   statistics which is the F  

statistics. As the distribution of   is non-standard, appropriate critical 

values were tabulated by Enders and Siklos (2001) and later modified by 
Wane et al. (2004). In the presence of cointegration (rejection of  

),0: 210  H  the null hypothesis 210 :  H  of symmetric adjustment 
can be tested using the standard F  statistics. When the adjustments coeffi-
cients are equal (symmetric adjustment), equation (5) converges the standard 
ADF test. Rejecting both the null hypotheses of 021    and 21    
implies the existence of threshold cointegration with asymmetric adjustment. 
For instance, if the null of symmetric adjustment is rejected and 21   , 

then it implies that positive deviations (above threshold) of emissions from 
the long-run EKC tend to revert quickly towards equilibrium, whereas nega-
tive deviations of emissions (below threshold) tend to persist. Hence, it sug-
gests faster convergence for positive deviations of emissions (above thresh-

                                                 
2 The Chan's method to find the consistent estimate of the threshold value arranges the 

values 1t  or 1 t  in ascending order, excludes the smallest and largest 15 percent, and 

the parameter that yields the smallest sum of squared residuals over the remaining 70 percent 
is the consistent estimate of the threshold. 



The Environmental Kuznets Curve in Poland – Evidence from Threshold... 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 51–70 

57

old) than negative deviations (below threshold) from the long-run EKC rela-
tionship. 
 Given the threshold cointegration is found, the next step proceeds with 
the Granger-causality test using the advanced threshold error correction 
model (TECM) or momentum-threshold error correction model (M-TECM) 
by Enders and Granger (1998) and Enders and Siklos (2001). The threshold 
ECM is expressed as the following:  

,2

111
1211

321

tit

q

i
iit

q

i
iit

q

i
ittjt vGDPGDPEPZZY  













    (8) 

or when additional variable tE  is included 

,
4

321

1
`

2

111
1211

tit

q

i
i

it

q

i
iit

q

i
iit

q

i
ittjt

vE

GDPGDPEPZZY






























 (9) 

where in equation (8) and (9):  2,, tttjt GDPGDPEPY  , and 

11 ˆ 

  ttt IZ   and  ,ˆ)1( 11 


  ttt IZ   tI – Heaviside indicator function de-

termined by (6) or (7), 1ˆ t  is obtained from the estimated long-run relation-

ship (1) or (4), and tv  is a white noise disturbance.  
 Based on the equation (8) and (9) the Granger-causality tests are em-
ployed. The long-run causality is determined by the significance of adjust-
ment parameters 1  and .2 To test short-run causality (or weak causality) 

the joint significance of all the coefficients i  of ,itEP  i  of ,itGDP  i  

of 2
itGDP  or i  of itE   is examined using the Wald F  test. It is also 

desirable to check whether this two sources of causation (short and long-run) 
are jointly significant. This can be done by providing the Wald F  statistics 
for the interactive terms, i.e. the   terms and the explanatory variables (e.g. 

,0: 10  iH  ).0: 20  iH  The joint test indicates which variables 
bear the burden of short-run adjustment to re-establish long-run equilibrium, 
given a shock to the system (Asafu-Adjaye, 2000; Mehrara et al., 2012). 
This is referred to as the strong Granger causality test.  
  



Mariola Piłatowska, Aneta Włodarczyk and Marcin Zawada  

DYNAMIC ECONOMETRIC MODELS 14 (2014) 51–70 

58

3. Empirical Results  

3.1. Data Source 

 The data used in this study consist of greenhouse gas emissions ( tEP ) (in 
tons of CO2 equivalent per capita), real gross domestic product per capita  
( tGDP ) and energy consumption3 ( tE ) in kilo of oil equivalent  per capita in 
Poland. The quarterly data for GDP are obtained from the Central Statistical 
Office (www.stat.gov.pl) of Poland, while annual data describing green-
house gas emissions and energy consumption in Poland were obtained from 
the Eurostat database.  
 To obtain the real GDP some transformations were made, i.e. quarterly 
nominal GDP data were transformed by the authors into real GDP in 2005 
prices using GDP deflator. Since the GDP data were characterized by signif-
icant quarterly seasonality, the TRAMO procedure of Gretl software was 
applied to adjust it seasonally. The frequency of real GDP series is quarterly, 
however, the greenhouse gas emissions and energy consumption data are 
only available at annual frequency. Therefore, we interpolated annual data to 
quarterly frequency by employing the Denton-Cholette method (Sax, Stei-
ner, 2013) in the R software. The sample period is from 2000:Q1 to 
2012:Q4. All variables are employed with their natural logarithms form to 
reduce heteroscedasticity and to obtain the growth rate of the relevant varia-
bles by their differenced logarithms.  
 

a) annual data 
 

b) disaggregated data to quarterly frequency 

Figure 1. Energy use (in kg of oil equivalent per capita) in Poland in the period 
2000–2012 – for annual data and disaggregated data to quarterly frequ-
ency 

                                                 
3 Energy consumption covers: consumption by the energy sector itself; distribution and 

transformation losses; final energy consumption by end users (see epp.eurostat.ec.europa.eu, 
Eurostat glossary).  

2200

2300

2400

2500

2600

2700

2000 2002 2004 2006 2008 2010 2012

kg
 o

f 
oi

l 
eq

u
iv

al
en

t

520

540

560

580

600

620

640

660

680

20
00

Q
1

20
01

Q
1

20
02

Q
1

20
03

Q
1

20
04

Q
1

20
05

Q
1

20
06

Q
1

20
07

Q
1

20
08

Q
1

20
09

Q
1

20
10

Q
1

20
11

Q
1

20
12

Q
1

kg
 o

f 
oi

l 
eq

u
iv

al
en

t



The Environmental Kuznets Curve in Poland – Evidence from Threshold... 

DYNAMIC ECONOMETRIC MODELS 14 (2014) 51–70 

59

a) annual data 
 

b) disaggregated data to quarterly frequency 

Figure 2. Greenhouse gas emissions (in tons of CO2 equivalent per capita) in Poland 
in the period 2000–2012 – for annual data and disaggregated data to quar-
terly frequency 

a) seasonally unadjusted 
 

b) seasonally adjusted 

Figure 3. GDP (in PLN per capita, in 2005 prices) in Poland, 2000:Q1–2012:Q4 

 The evolution of time series data (original and disaggregated) employed 
in our analysis is shown in Figure 1–3. 

3.2. Cointegration Analysis with Asymmetric Adjustment 

 Before performing cointegration analysis, we use the Augmented Dick-
ey-Fuller Generalized Least Squares (ADF-GLS; Elliot et al., 1996) and 
Kwiatkowski-Phillips-Schmidt-Shinn (KPSS; Kwiatkowski et al., 1992) 
tests to identify the order of integration for each variable. In Table 1, the 
ADF-GLS tests show that the unit root hypothesis cannot be rejected at any 
significant level for each variable in levels. Further investigations of the unit 
root hypothesis indicate that the first differenced variables are stationary at 
least at the 10% level of significance. We also apply the KPSS unit root test 
based on the null hypothesis of stationarity (or no unit root). The results 
show that the null hypothesis of stationarity is rejected at least at the 10% 
significance level. Hence, all series are found to be integrated of order I(1).  

9,8

10

10,2

10,4

10,6

10,8

11

2000 2002 2004 2006 2008 2010 2012

to
n

n
es

 o
f 

C
O

2
eq

u
iv

al
en

t

2,3

2,4

2,5

2,6

2,7

2,8

20
00

Q
1

20
01

Q
1

20
02

Q
1

20
03

Q
1

20
04

Q
1

20
05

Q
1

20
06

Q
1

20
07

Q
1

20
08

Q
1

20
09

Q
1

20
10

Q
1

20
11

Q
1

20
12

Q
1

to
n

n
es

 o
f 

C
O

2
eq

u
iv

al
en

t

4000

5000

6000

7000

8000

9000

10000

20
00

Q
1

20
01

Q
1

20
02

Q
1

20
03

Q
1

20
04

Q
1

20
05

Q
1

20
06

Q
1

20
07

Q
1

20
08

Q
1

20
09

Q
1

20
10

Q
1

20
11

Q
1

20
12

Q
1

P
L

N

4000

5000

6000

7000

8000

9000
20

00
Q

1

20
01

Q
1

20
02

Q
1

20
03

Q
1

20
04

Q
1

20
05

Q
1

20
06

Q
1

20
07

Q
1

20
08

Q
1

20
09

Q
1

20
10

Q
1

20
11

Q
1

20
12

Q
1

P
L

N



Mariola Piłatowska, Aneta Włodarczyk and Marcin Zawada  

DYNAMIC ECONOMETRIC MODELS 14 (2014) 51–70 

60

Table 1. The results of unit root tests  

 
Variables 

Levels  Differences 
ADF-GLS KPSS  ADF-GLS KPSS 

EPt –1.522 [3]  0.463 [2]*  –5.246 [3]*** 0.073 [2] 
GDPt 0.041 [4] 1.218 [4]***  –2.307 [4]** 0.139 [4] 
GDP2t –0.144 [5] 1.217 [4]***  –1.676 [5]* 0.132 [4] 

Et –0.957 [2] 1.548 [2]***  –5.368 [2]*** 0.110 [2] 
Note: (***), (**), (*) in ADF-GLS tests respectively indicate the rejection of the null hypothesis that 
series has a unit root at 1%, 5% and 10% levels of significance, while in KPSS tests indicate the rejection 
of the null hypothesis that series is stationary. The numbers inside the brackets are the optimum lag 
lengths determined using AIC in ADF-GLS tests and the bandwidth is used using the Newey-West meth-
od in KPSS tests.   

 Table 2 contains cointegration test results of the standard long-run EKC 
in the form (1) and Table 3 – long-run EKC including energy consumption 
in the form (4), when considering threshold (TAR) and momentum adjust-
ment (MTAR). The tables report values of the adjustment coefficients 1  

and 2 , the  statistics for the null hypothesis of no cointegration (a unit 

root in t ) against the alternative of cointegration with asymmetric adjust-
ment. The F-test  is used to test whether the adjustment back to long-run 
equilibrium is symmetric 21   .  

 It can be seen that all coefficients 21,   have negative signs and are 
significant at least at 10% significance level. The necessary and sufficient 
conditions for cointegration hold in the case of all TAR and M-TAR models 
because the null hypothesis 0: 210  H  is rejected (at 5% significance 
level)4 – see Table 2. Using the standard F-statistics for the restriction 

210 :  H  it is shown that asymmetric cointegration is strongly significant 
only in the TAR model with ,0169.0  whereas in the TAR model with 

0  the support for asymmetric cointegration is only at 10% significance 
level. This evidence favors that the adjustment back to equilibrium between 
greenhouse gas emissions )( tEP  and gross domestic product )( tGDP  is non-
linear. For choosing the more appropriate adjustment process (TAR or  
M-TAR) we will follow Enders and Chumrusphonlert's (2004) advice in 
using AIC or SBC to select the best adjustment mechanism. The reported 
SBC for each model shows that the TAR model with threshold value 

0169.0  is more appropriate adjustment mechanism (the minimum SBC 
is in bold in Table 2).   

                                                 
4 It is worth noting that this null hypothesis is also rejected when critical values from 

Wane et al. (2004) are taken.  



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Table 2. Results of TAR and M-TAR Enders-Siklos (E-S) test for cointegration  on 
the standard EKC model  

 1 2  
(1=2=0) 

F 
(1=2) 

Lag SBC LB(4) 

TAR 
=0 

–0.124 
(–2.372)** 

–0.199 
(–5.036)*** 

12.76*** 3.075 
[0.087]* 

5 –387.6 5.15 
[0.273] 

M-TAR 
=0 

–0.125 
(–2.489)** 

–0.191 
(–4.804)*** 

11.722*** 1.722 
[0.197] 

5 –386.1 6,5 
[0.165] 

TAR 
=–0.0169 

–0.119 
(–2.939)** 

–0.222 
(–5.500)*** 

15.184*** 6.236 
[0.017]** 

5 –390.9 4.74 
[0.315] 

M-TAR 
=0.0023 

–0.148 
(–2.925)** 

–0.179 
(–4.536)*** 

10.722*** 0.416 
[0.522] 

5 –384.6 5.35 
[0.253] 

Note: *** (**) (*) indicate significance at 1% (5%) (10%) level. Critical values for  statistics from 
Enders, Siklos (2001). T-statistics for in  parentheses. p-values in brackets. LB(4) for Ljung-Box statis-
tics. The lag length is selected such that the AIC is minimized.   

Table 3.  Results of TAR and M-TAR Enders-Siklos (E-S) test for cointegration  on 
the EKC model including energy consumption  

 1 2  
(1=2=0) 

F 
(1=2) 

Lag SBC LB(4) 

TAR 
=0 

–0.104 
(–3.249)** 

–0.056 
(–2.20)* 

5.83* 2.155 
[0.149] 

2 –488.06 6.91 
[0.141] 

M-TAR 
=0 

–0.071 
(–2.683)* 

–0.072 
(–2.325)* 

4.537 0.002 
[0.961] 

2 –485.77 7.26 
[0.123] 

TAR 
=0.0097 

–0.115 
(–3.516)** 

–0.055 
(–2.237)* 

6.616** 3.462* 
[0.069] 

2 –489.40 6.67 
[0.155] 

M-TAR 
=8.8E-05 

–0.064 
(–2.36)* 

–0.082 
(–2.74)** 

4.74 0.34 
[0.563] 

2 –486.13 0.03 
[0.999] 

Note: ** (*) indicate significance at 5% (10%) level. Critical values for  statistics from Enders, Siklos 
(2001). T-statistics for  in parentheses. p-values in brackets. LB(4) for Ljung-Box statistics. The lag 
length is selected such that the AIC is minimized.   

 We can see in Table 2 that the point estimates 1  and 2  suggest faster 
convergence for the deviations from long-run EKC equilibrium when they 
are below the threshold ( 0169.0t ) than when they are above the 

threshold because 21   . We see that about 22% of the deviation from 

equilibrium is corrected in the next period when emissions are falling, com-
pared to about 12% when they are rising. This means that short-run adjust-
ment towards the EKC equilibrium reverts more quickly when the green-
house gas emissions are decreasing (below the threshold) and tends to persist 
more when the greenhouse gas emissions are increasing (above the thresh-
old). While the opposite result might be expected, this evidence should not 
be surprising when we look at the Poland's energy profile. Heavy reliance on 



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coal makes Poland a relatively carbon-intensive economy, compared to the 
IEA Europe average. The large-scale transition of the Polish energy sector, 
which is characterised by ageing infrastructure5, to a low-carbon economy 
requires huge long-term investments and an adequate policy and regulatory 
framework. Therefore, from a short run perspective the potential reduction 
of greenhouse gas emissions should be rather combined with the energy 
efficiency improvements.  
   

 
Figure 4. The fitted values of the estimated EKC results for greenhouse gas emis-

sions 

Table 4. Estimated parameters of long-run EKC equation 

Variable 
Estimates of parameters 

(t-statistics) 

Constant 
–53.298 

(–4.228)*** 
–23.041 

(–2.444)** 

GDPt 
12.225 

(4.280)*** 
4.345 

(1.978)* 

GDP2t 
–0.688 

(–4.255)*** 
–0.255 

(–2.065)** 

Et  
0.863 

(7.639)*** 
Note: *** (**) (*) indicate significance at  1% (5%) (10%) level. T-statistics for  in parentheses. Estimated 
parameters for equation (1) and (4). 

                                                 
5 Nearly half of today's operating capacity of the Polish energy sector is older than 30 

years. See: Energy Policies of IEA Countries. Poland (2011).  



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 Having established the TAR cointegration in the long-run relationship 
for greenhouse gas emissions, it is now justified to analyse the estimation 
results (Table 4) and the implications for the EKC hypothesis. We can see 
that in terms of the coefficients described in the EKC relation (1), we have 

,00   01   and ,02   which implies the inverted U-shaped function. 
 The fitted values of greenhouse gas emissions for the observed values of 
real GDP are displayed in Figure 4. This results show the strong evidence in 
favour of the EKC hypothesis. The turning point in the observed range of 
real GDP for greenhouse gas occurs at PLN7218.8 per capita which corre-
sponds to around 2007Q2.   
 The addition of energy consumption )( tE  to the standard EKC model 
has not affected the results in terms of the presence of asymmetric cointegra-
tion (Table 3), i.e. in the TAR framework (with )0097.0  the asymmetric 
cointegration is observed but only at 10% significance level when critical 
values from Enders and Siklos (2001) are used. Moreover, the non-linear 
relationship remains significant and correctly signed ( 1  and 2  are nega-
tive), suggesting the relationship is reasonably robust (see Table 3). Howev-
er, when critical values from Wane et al. (2004) are taken, then the null hy-
pothesis of non-cointegration )0:( 210  H  cannot be rejected. Hence, 
the results behind the threshold cointegration for the EKC model with energy 
consumption are rather weak and should be treated with caution.  
 Also the point estimates 1  and 2  differ with regard to the speed of 
adjustment process and direction of convergence for deviations above and 
below the threshold value when compared to the standard EKC model (Table 
2). Now, faster convergence for deviations (from the long-run EKC) above 
the threshold than for those below the threshold is observed. We can see 
(Table 3) that about 12% of the deviation from equilibrium is corrected 
when emissions are above the threshold  ),0097.0( t  compared to 

only 5.5%  when they are below the threshold ).0097.0( t  Therefore, 
the short-run adjustment towards the long-run equilibrium reverts more 
quickly when emissions are increasing (above the threshold) and tends to 
persist when emissions are decreasing (below the threshold). This result is 
quite the opposite to that obtained for the standard EKC model what may 
indicate that energy consumption )( tE is an important determinant of green-
house gas emissions. The faster correction for deviations in emissions, if 



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DYNAMIC ECONOMETRIC MODELS 14 (2014) 51–70 

64

they are too high, indicates that in the presence of environmental regulation6 
the pressure to reduce them into their long-run levels was occurred. Howev-
er, these emissions reductions were to a large extent achieved through the 
restructuring of Polish industry and energy efficiency improvements.   

3.3. Threshold Error Correction Models 

 The positive finding of cointegration with TAR adjustment justifies es-
timation of threshold error correction model (8) and (9) and testing the 
Granger causality7. The T-ECM models are estimated for changes in green-
house gas emissions )( tEP  and gross domestic product ),( tGDP  assum-
ing the estimates of threshold values obtained in previous step, i.e. 

0169.0    − in model (8) and 0097.0  − in model (9) (see also Ta-
ble 2 and 3). The T-ECM for the tE  is not estimated since the energy con-
sumption is added into the standard EKC model to test the robustness of the 
results.  
 Based on equations (8) and (9), the Granger causality tests are employed 

to verify whether all the coefficients of ,itEP  itGDP   or 2
itGDP  (or 

itE   in eq. (9)) are jointly statistically different from zero based on 

a standard F-test (Wald test) and/or whether the coefficients ( 21,  ) of the 
error correction term are significant. To determine the appropriate lag 
lengths we apply the SBC criterion, and empirically find that the lag lengths 
are equal: ,221  qq  .332  qq  Table 5 presents estimates of the error 
correction parameters along with Wald F test statistics regarding Granger 
causality.   
 We will first interpret the results for the T-ECMs and then for T-ECMs 
including tE  (Table 5).  
 While the adjustment speed on the exceeding or underlying threshold 
level in the T-ECM model for tEP  has the 'right' direction ( 1  and 2  have 
a negative sign and are significant) by acting to eliminate deviations from 
the long-run equilibrium, the T-ECM model for tGDP  adjusts to the 

                                                 
6 Regulation on air pollution has become increasingly stringent, including international 

protocols such as the Oslo Protocol, the Kyoto Protocol and the EU energy and climate obli-
gation for member countries.  

7 The T-ECM for 2
tGDP  is run, but not reported because it has little useful economic in-

terpretation (results are available from authors on request).  



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'wrong' direction ( 1  has a positive sign) for one regime, and additionally 

parameters 1  and 2  are insignificant. In the tEP  model the adjustment 
speed responds faster in the lower regime (emissions below the threshold 
value) than in the higher regime with increasing deviations from the long-run 
equilibrium (emissions above the threshold value). This is consistent with 
the results in Table 2. Now, the greenhouse gas emissions converge to their 
long-run equilibrium at the rate of 13.2% with a deviation below the thresh-
old and at a lower rate of  9.3% with a deviation above the threshold.  

Table 5. Estimates of threshold error correction model (T-ECM) and the Wald F 
statistics for Granger causality  

 T-ECM   T-ECM including  Et   
 EPt   GDPt   EPt   GDPt   

1 
 –0.093*  
(–2.021) 

 0.046 
 (0.693) 

–0.081 
(–1.012) 

 –0.015  
(–0.141) 

2 
 –0.132**  
(–2.610) 

 –0.073  
(–1.008) 

 –0.022 
(–0.357) 

 –0.163*  
(–1.961) 

     

H0: i=0 1.328 [0.280]  1.519 [0.227]  
H0: i==0 2.028 [0.111]  1.308 [0.286]  
H0: i==0 2.952** [0.032]  1.209 [0.324]  
     

H0: i=0 1.386 [0.262] 0.562 [0.643] 1.622 [0.202] 1.000 [0.404] 
H0: i==0 2.059 [0.106] 0.489 [0.744] 1.387 [0.259] 0.750 [0.565] 
H0: i==0 3.039** [0.029] 0.786 [0.542] 1.293 [0.292] 1.894 [0.133] 
     

H0: i=0  5.626** [0.007]  1.162 [0.325] 
H0: i==0  3.796** [0.018]  1.056 [0.380] 
H0: i==0  4.487** [0.009]  3.367** [0.029] 
     

H0: i=0   3.857** [0.031] 0.129 [0.879] 
H0: i ==0   2.674* [0.062] 0.187 [0.904] 
H0: i ==0   2.572* [0.069] 2.012 [0.130] 
LB(3) 2.60 [0.457] 1.60 [0.659] 2.66 [0.448] 1.95 [0.583] 
BIC  –395.72  –362.00  –387.32 –360.22 

Note: *** (**) (*) indicate significance at 1% (5%) (10%) level. t-statistics for 1, 2 in parentheses.  
p-values for Wald statistics in brackets. LB(3) for Ljung-Box statistics along with p-values.   

 The results of the Granger causality tests show that there is no short-run 
causality running from real tGDP  (and square of tGDP ) to ,tEP  but there is 
an unidirectional short-run causality from greenhouse gas emissions to per 
capita real .tGDP  This can be interpreted as the non-rejection of  0:0 iH   

and 0:0 iH   in the tEP  equation and rejection of 0:0 iH   in the 

tGDP  equation (see Table 5, 2nd and 3rd column). Besides, the strong 



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DYNAMIC ECONOMETRIC MODELS 14 (2014) 51–70 

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long-run causality running from per capita real GDP (and square of real 
GDP) to greenhouse gas emissions is found in the regime below the thresh-
old value of −0.00169 (rejection of ,0: 20  iH  0: 20   iH ). The 

results for the tGDP  equation suggest reverse long-run causality running 
from greenhouse gas emissions to per capita real GDP (rejection of 

0: 10   iH  and 0: 20  iH ). This implies that deviations from the 
long-run EKC are corrected not only by movements in greenhouse gas emis-
sions but also by movements in per capita real GDP.  
 In the T-ECM model for tEP , including energy consumption (Table 5, 

4th column), the parameters 21,   are correctly signed, but statistically in-
significant8. Nonetheless, it is worth noting that the correction back to equi-
librium is faster in regime above the threshold value of 0.0097 (since 

)21    unlike the results obtained in the T-ECM not including energy 

consumption where faster convergence to equilibrium occurred in the regime 
below the threshold. This means that the addition of energy consumption 
into the T-ECM changed the response of greenhouse gas emissions to error 
correction. The manifested influence of energy consumption to reduce 
greenhouse gas emissions should be rather attached to the promotion of 
technological progress and the energy efficiency improvements, but not the 
large-scale transition to low-carbon economy, as has already been men-
tioned.  
 Further, there is neither short-run Granger causality (or weak causality) 
nor long-run causality from tGDP  to tEP  in the T-ECM including energy 

consumption (the non-rejection of null hypotheses ,0i  ,01  i  

,02  i  ,0i  ,01   i 02   i  in Table 5, 4th column). The 
non-significance of the F-statistics for GDP indicates that it is exogenous in 
the system. However, there exists the short-run and long-run causality from 
energy consumption to greenhouse gas emissions (the rejection of null hy-
potheses: ,0i  01  i  and  02  i  in the tEP  model including 

).tE  This evidence suggests that energy consumption has an effect on 
greenhouse gas emissions and bears the burden of short-run adjustment to 
restore long-run equilibrium after a shock to the system. In the T-ECM for 
                                                 

8 This finding should be rather attached to the effect of small sample and reduction of de-
grees of freedom in the estimated threshold error correction models due to bigger number of 
variables and lagged terms in comparison to previous TAR estimations (see Table 2 and 3). 
Therefore the results in Table 5 should be interpreted with caution and validated on the larger 
sample.  



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tGDP  (including energy consumption) the rejection of 0: 20   iH  
suggests the unidirectional long-run causality from greenhouse gas emis-
sions to real GDP in regime below the threshold value of 0.0097. The results 
from causality analysis based on the T-ECM (including energy consumption) 
indicate that re-establishing of the long-run equilibrium is carried out by the 
interaction of greenhouse gas emissions and energy consumption, but the 
long run effect of GDP is rather weak.  

Conclusions 

 The paper has aimed to investigate the EKC hypothesis for the case of 
the Polish economy during the period 2000-2012. We tested for the presence 
of threshold cointegration between per capita greenhouse gas emissions and 
per capita income (real GDP). Moreover, to test the robustness of the results, 
we considered the standard EKC hypothesis with the addition of per capita 
energy consumption to the model. To address such an issue, we applied the 
threshold cointegration model which allows the nonlinear adjustment to the 
long-run equilibrium.  
 In the case of the standard EKC relationship, the results of threshold 
cointegration indicate that per capita greenhouse gas emissions and per capi-
ta real GDP are cointegrated with an asymmetric adjustment process. Ad-
justments towards the long-run equilibrium revert more quickly when emis-
sions are below the threshold value and tend to persist more when emissions 
are above the threshold value. The evidence of long persistence of adjust-
ments to the equilibrium in higher regime (emissions above the threshold) 
may be explained by the specific of Polish energy sector, namely heavy reli-
ance on coal. As a consequence, the transition to a low-carbon economy will 
require huge long-term investments and an adequate policy and regulatory 
framework. Therefore, from a short run perspective the reduction of emis-
sions should be rather combined with the energy efficiency improvements. 
With regard to the Granger causality tests the results are following. In the 
lower regime the bidirectional long-run causality between per capita real 
GDP and per capita greenhouse gas emissions is found. The short-run dy-
namics suggests that there is no causal relationship from real GDP to green-
house gas emissions but there is an unidirectional Granger causality from 
greenhouse gas emissions to real GDP.  
 Our results find strong evidence in favour of the EKC hypothesis with 
per capita greenhouse gas emissions having an inverse U-relation with real 
GDP per capita. The evidence suggests that the turning point in the observed 
range of real GDP for greenhouse gas emissions occurred at PLN7218.8. As 



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DYNAMIC ECONOMETRIC MODELS 14 (2014) 51–70 

68

a consequence, a decoupling between the two variable appears, i.e. the 
growth of emissions of some pollutant is slower than the economic growth.  
 The addition of energy consumption to the standard EKC model has not 
affected the results in terms of the presence of asymmetric cointegration but 
has changed the direction of convergence for deviations above and below the 
threshold value. Namely, adjustment towards long-run equilibrium is faster 
in the higher regime (emissions above the threshold) than in the lower re-
gime (emissions below the threshold). This mean that in the presence of 
environmental regulation the pressure to reduce emissions into their long-run 
levels is observed. However, it should be emphasized that the abatement of 
emissions is rather achieved through the restructuring of Polish industry, 
promoting technological progress and energy efficiency improvements, but 
not the large-scale transition to low-carbon economy. The results of Granger 
causality tests indicate that there is no short-run causality from real GDP to 
greenhouse gas emissions. However, there is short and long-run causality 
from energy consumption to greenhouse gas emissions. Besides, the unidi-
rectional long-run causality from greenhouse gas emissions to real GDP in 
regime below the threshold value is observed. The results from causality 
analysis indicate that re-establishing of the long-run EKC is carried out by 
the interaction of greenhouse gas emissions and energy consumption, but the 
long run effect of GDP is rather weak.  

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Mariola Piłatowska, Aneta Włodarczyk and Marcin Zawada  

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Ekologiczna krzywa Kuznetsa dla Polski  
− analiza progowej kointegracji 

Z a r y s  t r e ś c i. Artykuł przedstawia analizę relacji długookresowej między emisją gazów 
cieplarnianych w przeliczeniu na mieszkańca a realnym PKB w przeliczeniu na mieszkańca 
(hipoteza EKC, ekologiczna krzywa Kuznetsa)  z wykorzystaniem podejścia progowej (asy-
metrycznej) kointegracji i modelu korekty błędem dla polskiej gospodarki w okresie 2000-
2012 (dane kwartalne). Standardowy model EKC został rozszerzony o zużycie energii w celu 
zbadania wpływu dodatkowych zmiennych na wyniki. Hipoteza EKC była sprawdzana 
z wykorzystaniem progowych modeli autoregresyjnych (TAR i MTAR). Ponadto, dla zbada-
nia krótkookresowej i długookresowej przyczynowości Grangera między emisją gazów cie-
plarnianych w przeliczeniu na mieszkańca a realnym PKB w przeliczeniu na mieszkańca 
zastosowano progowy model korekty błędem. Otrzymane wyniki dostarczają istotnych dowo-
dów na rzecz hipotezy EKC dla przypadku Polski oraz wskazują, że tymczasowe odchylenia 
od ścieżki długookresowej równowagi EKC są korygowane w asymetryczny sposób. 

S ł o w a  k l u c z o w e: ekologiczna krzywa Kuznetsa, emisja gazów cieplarnianych, zużycie 
energii, wzrost gospodarczy, kointegracja progowa, przyczynowość w sensie Grangera.   


