



































DYNAMIC ECONOMETRIC MODELS


© 2016 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.2016.004  Vol. 16 (2016) 65−86 

Submitted October 25, 2016  ISSN (online) 2450-7067 

Accepted December 18, 2016 ISSN (print) 1234-3862 

Andrzej Geise, Mariola Piłatowska
*
 

Asymmetries in the Relationship between Economic 

Activity and Oil Prices in the Selected EU Countries 

A b s t r a c t. In this paper the threshold (T-ECM) and linear (ECM) error correction models 

are estimated to examine the short-run and long-run Granger causality in terms of asymmetric 

and symmetric relationship for seven European Union economies (Germany, France, Den-

mark, the Netherlands, Poland, Czech Republic and the whole EU). The relationship between 

production, inflation and oil prices are analyzed in the presence of structural break when both, 

the change in intercept and the change in the slope of the trend function exist. Threshold 

ECMs show the asymmetric response of production and inflation to the changes in oil prices 

in the case of Germany, France, Poland and the EU. For other economies (Netherlands, Den-

mark and Czech Republic) the reaction was rather symmetric. 

K e y w o r d s: short-run asymmetry, threshold cointegration, threshold error correction 

model, Granger causality, oil price shock.  

J E L Classification: C32; E23; E32; Q43. 

Introduction 

 Energy price shocks have important effects not only on economic activi-

ty but also on macroeconomic policy of industrialized countries. It is related 

to the essential meaning of energy in all areas of economic activities. Energy 

                                                 
* Correspondence to: . Andrzej Geise, Nicolaus Copernicus University, Faculty of Eco-

nomic Sciences and Management, 13A Gagarina Street, 87-100 Toruń, Poland, e-mail: 

a.geise@umk.pl; Mariola Piłatowska, Nicolaus Copernicus University, Faculty of Economic 

Sciences and Management, 13A Gagarina Street, 87-100 Toruń, Poland, e-mail: 

mariola.pilatowska@umk.pl. 
 This work was financed from Faculty of Economic Sciences and Management research 

grant no. 2185-E.  



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

66 

is pushing all developed and developing countries to ensure the long-term 

stable energy prices and energy supply. The stable price of energy and inde-

pendent source of imported energy resources are crucial to the economic 

development. Huge and unexpected increases of energy prices can cause the 

inflation to rise and reduce real money balances. These changes have nega-

tive effects on consumption and economic output. 

 The purpose of this paper is to analyze the short- and long-term dynam-

ics of oil prices, production and inflation in the selected EU countries in the 

presence of structural break due to the financial crisis. The potential asym-

metries over the production are investigated, and then we examine the cau-

sality among the oil prices, production and inflation in the context of high 

and low growth regime. 

 First, the threshold cointegration analysis applied in Geise and 

Piłatowska (2014) for 7 European economies is extended to the case of 

structural break due to the financial crisis not only in an intercept but both 

intercept and trend coefficient. These results will be compared to those con-

tained in the mentioned article. 

 Second, the Granger causality among oil prices, production and inflation 

in the selected EU countries (Germany, France, Netherlands, Denmark, Po-

land, Czech Republic and the European Union as well) is examined based on 

the linear ECM and threshold ECM models. In Geise and Piłatowska (2014) 

the relationships among explanatory variables were analyzed by the thresh-

old error correction model with asymmetric adjustment process. Here, the 

relationships between production, inflation and oil prices are analyzed by 

both threshold ECM and linear ECM. When the threshold cointegration oc-

curs, the threshold error correction model with asymmetric adjustment pro-

cess and asymmetric short-run dynamics (T-ECM) is estimated. In other 

cases the linear ECM models are estimated. The threshold model allows us 

to identify the relationships among oil prices, production and inflation ac-

cording to business cycle phases, i.e. the growth phase of the economic busi-

ness cycle is defined as high growth regime (when the deviations from long-

run equilibrium are above the threshold value) and the recession phase is 

related to low growth regime (when the deviations are below the threshold 

value). 

 The concept of a research study is presented in Scheme 1. 

 The plan of this paper is as follows. Section 1 presents short theoretical 

explanations for symmetric and asymmetric reaction of economic activity to 

oil price shocks. Section 2 reviews the methodology applied in this paper. 

Section 3 shows the results of threshold cointegration analysis and presents 



Asymmetries in the Relationship between EconomicActivity and Oil Prices… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

67 

empirical error correction models. Section 4 presents the results of Granger-

causality analysis. The last section concludes. 

 
Scheme 1. Concept of the study the Granger causality among oil prices, production 

and inflation 

1. Asymmetries in the Transmission of Oil Price Shocks 

 The nature of the relationship between oil prices and economic activity 

(symmetric or asymmetric) determines the way of oil prices modelling. It 

helps to understand the magnitude of positive and negative oil price shocks 

impact on economy and select the model of transmission of oil price shocks 

among alternative models. The study of transmission of oil price shocks 

should focus on whether the transmission channel leads to the symmetric or 

asymmetric response of economic activity in the context of oil importing and 

oil exporting countries. 

 Oil price shocks are transmitted to the economic activity by the direct 

supply-side channel. Increases in the prices of crude oil have a direct impact 

on the supply of crude oil and supply of high energy-consuming goods. Con-

sidering oil importing countries in which the production function can be 

expressed as a functional form of input factors (such as labour, capital and 

energy), it turns out that the large fluctuations in economic activity are 

unlikely to observe without a large fluctuation in the variation in energy 

prices. Also, when the smooth production function is assumed,  the symmet-

ric response of output to changes in energy input is observed (Hamilton, 

2008). 

 The direct demand-side channel of oil price shock transmission for oil 

importing countries indicates that the increase of oil prices leads to changes 

in consumer’s purchasing power. These changes are related to the income 

transfer from oil exporting countries to oil importing countries. Therefore, 

EU countries ECM/T-ECM 
models 

Step II 
 

 

 

 

 

 

 

Production 
(Pt) 

Inflation (Int) 

Oil prices (Bt) 

ECM (linear error 

correction model) 

Long-run 
relationship 

Step I 
 

 

 

 

 

 

Causality 
test 

 

Step III 

L
in

e
a

r 
c
o

in
te

g
ra

ti
o

n
 

w
it
h

 s
y
m

m
e

tr
ic

 

a
d

ju
s
tm

e
n

t 

Two-step Enders-

Siklos approach to 

analyze threshold 

cointegration 

T-ECM (threshold 

error correction model 

with asymmetric 

adjustment) 

T
h

re
s
h

ld
 c

o
in

te
g

ra
ti
o

n
 

w
it
h

 T
A

R
 o

r 
M

-T
A

R
 

a
d

ju
s
tm

e
n

t 

Granger causali-

ty test 



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

68 

increases in oil prices will cause the increases in production (by the demand 

push) in oil exporting countries, however the oil importing countries will 

face the production decrease (Hamilton, 2011). 

 Both direct transmission mechanisms presents the direct and symmetric 

reaction of economic activity to changes in oil prices. However, some indi-

rect transmission channels amplify the effect of oil price shock and may lead 

to an asymmetric reaction of economic activity. 

 The sectoral reallocation associated with capital and labour reallocation 

from energy-intensive sectors to expanding sectors is a result of a positive 

oil price shock. In the case of oil-importing countries, sectoral reallocation 

will reinforce the recessionary effect of oil price increasing (Davis and 

Haltiwanger, 2001). However Hamilton (1988) presents that the lower eco-

nomic activity and higher unemployment rate are an outcome of the lack of 

sectoral reallocation. This disturbance is caused by workers who can be con-

fident about  the future improvement of their sector and decide not to relo-

cate even if they are offered a job in a different sector. However, both types 

off reallocation disturbances will lead to an asymmetric reaction of produc-

tion as a result of a positive or negative oil price shock. 

 Another explanation of an asymmetric reaction of economic activity to 

oil price shocks is connected with precautionary savings. For an oil import-

ing economy the rise of oil price can cause the future decrease in employ-

ment and real income, inducing an increase in precautionary savings, which 

in turn leads to the decrease in production (Edelstein and Kilian, 2009). 

 For oil importing economies the asymmetric reaction of monetary policy 

to oil price increases and decreases is still ambiguous. For instance, Ber-

nanke et al., (1997) pointed out the asymmetric reaction of the Federal Re-

serve to oil price shocks (authors show that the FED responds more aggres-

sively to oil price increases than oil price decreases). However, some other 

authors argue that the reaction of monetary policy to oil price shocks is in-

significant and doesn’t exist – see e.g. Hamilton and Herrera, (2004). 

 The evidence consistent with the model of asymmetric reaction of eco-

nomic activity to oil price shocks was provided by Herrera et al., (2015). 

Authors used data for 18 OECD countries and pointed out that the sectoral 

reallocation disturbances and the existence of a precautionary savings, when 

future employment level was uncertain, implied an asymmetric response of 

aggregate production. 



Asymmetries in the Relationship between EconomicActivity and Oil Prices… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

69 

2. Methods  

 To test the threshold cointegration among production, inflation and Brent 

oil prices in the selected EU countries the Enders-Granger approach and the 

Enders-Siklos approach is employed
1
. This technique is a residual based 

two-stage estimation and focuses on the residuals from the long-run equilib-

rium relationship. For this study, the long-run relationship can be expressed 

as:  

tttttt DTDUInBP   )()( *
4

*
3210 ,   (1) 

where tP , tIn  denote the industrial production index and consumer price 

index in selected economies respectively, 
tB stands for Brent crude oil pric-

es; all variables are in natural logarithms;   refers to the time break, i.e., the 

period at which the change in the parameters of the intercept and trend func-

tion occurs, )(* tDU  is the dummy variable for the break in intercept of 

production function where 1)(* tDU  if t  and  0 otherwise, )(* tDT  

is the variable for a change in the slope of the trend function where 

tDTt )(*   if t  and 0 otherwise, 43210 ,,,,   are parameters to 

be estimated and t  is the disturbance term that may be serially correlated. 

 Next, the analysis focuses on the estimation of 1  and 2  coefficients 

in the following regression: 




 
p

i

titittttt uII
1

1211 )1(    (2) 

where tu  is a white-noise disturbance, p  the number of lags, 1 , 2  and 

i  the coefficients, t  in equation (2) is extracted from long-run equation 

(1). tI  term is the Heaviside indicator function such that: 1tI  if , dt  

and 0 otherwise (for TAR model); or 1tI  if ,  dt  and 0 otherwise 

(for M-TAR model) where   is the threshold value. 

 The TAR model is designed to capture the potential asymmetric move-

ments in residuals t , while the M-TAR model is designed to capture the 

direction of the potential asymmetric movements (Fosten et. al, 2012). Nega-

tive deepness (i.e., 21   ) of the residuals implies that increases of t  

                                                 
1 see Geise and Piłatowska (2014), Piłatowska, Włodarczyk and Zawada (2014). 



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

70 

tend to persist, whereas decreases tend to revert quickly toward to equilibri-

um (Enders and Granger, 1998). 

The threshold value   can be set as zero or can be estimated according 

to the Chan’s search method
2
. The estimation of the threshold parameter is 

not obvious. When the threshold parameter is known (equal 0), the simply 

OLS can be used to estimate the slope parameter   ,  of equation (2). 

In the case of unknown threshold parameter the conditional LS must be used. 

To obtain an estimation minimizing the sum of squares or maximizing the 

log-likelihood, the OLS cannot be used, because as the objective function is 

highly erratic. A solution is obtained through concentration of the objective 

function. As the slope estimators given a threshold are the OLS one. The 

problem of using highly erratic function can be reduced by concentrating out 

the minimization problem through    and the corresponding sum of 

squares )(SSR . The objective function has the form: 

 


SSRminarg


 .  (3) 

Minimization of (3) is done through a grid search: the values of the vari-

able are sorted, a certain percentage of the first and last values is excluded to 

ensure a minimal number of observations in each regime, the SSR is esti-

mated for each selected value and the one that minimize the SSR is taken as 

the estimator (Stigler, 2010) 

 Before the threshold cointegration analysis is conducted, the Tsay linear-

ity test is used to verify the null hypothesis of linearity in threshold variable 

for different value of delay (d) – see more Tsay (1989). 

 Testing for threshold cointegration is performed in two steps. First, an 

Φ-test is employed to examine the null hypothesis of no cointegration  

( 0: 210  H ) against alternative of cointegration with either TAR or M-

TAR threshold adjustment. Second, the test F-test is used to verify the null 

hypothesis of symmetric adjustment ( 210 :  H ). Rejection of both hy-

pothesizes indicates the existence of threshold cointegration with an asym-

metric adjustment (Enders and Siklos, 2001). 

 The threshold error correction model (with two regimes) has the form: 

                                                 
2 see Chan (1993), Geise and Piłatowska (2014). 



Asymmetries in the Relationship between EconomicActivity and Oil Prices… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

71 

ttt

q

i

ti

q

i

itiit

q

i

it

tt

q

i

ti

q

i

itiit

q

i

itjt

BInP

BInPY





































}){1)((

}{)(

321

321

1

1

11

12

1

1
*

1

*

1

*
11

 (4) 

where  tttjt BInPY  ,, , 1t  represent the error correction terms, t  

is the threshold variable, which is a continuous and stationary transformation 

of the data and takes the form of dt  (when TAR adjustment mechanism is 

used) or dt  (when M-TAR adjustment mechanism is selected),   is 

the threshold parameter.  

 When the method proposed by Enders and Siklos (2001) cannot reject 

the hypothesis of symmetric cointegration the linear error correction model 

is estimated. The structure of model is determined by the following equation: 

t

q

i

ti

q

i

itiit

q

i

itjt BInPY   












321

1

1

11

11
 (5) 

where 1t is obtained from the estimated long-run equation (1) and t  is 

a white noise disturbance. 

3. Linear (ECM) and Threshold Error correction Models  
(T-ECM) of Production, Inflation and Oil Prices  
in the Selected EU Countries 

 In this section, the threshold cointegration analysis, threshold (T-ECM) 

and linear error correction models (ECM) for production, inflation and oil 

prices in Germany, France, the Netherlands, Denmark, Poland, Czech Re-

public and the European Union are discussed. To investigate the presence of 

asymmetries in the relationship between oil prices and economic activity the 

monthly data from January 1995 to April 2014 are used. In particular, indus-

trial production index at constant prices of 2010, consumer price index and 

Brent oil prices (each time series expressed in natural logarithms) were 

used
3
. The results of the ADF test revealed that all analyzed series were in-

tegrated of first order, I(1) – see Geise and Piłatowska (2014). Therefore, in 

further analysis the first differences of each series are used. 

 The structural break occurred due to the financial crisis peaked in 2008 

may change the nature of the long-run equation for production. Therefore we 

                                                 
3 Here, the identical sets of variables as in Geise and Piłatowska (2014) were used.  



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

72 

assume the long-term relationship with both one-time change in the intercept 

and change in the slope of the trend function (as in Perron, 1989). 

 To motivate the use of long-term relationship (with structural break in 

September 2008), we display the time series for production in analyzed 

economies in Figure 1 with the fitted values of the regression 

tttt DTtDUP   211
~~~~~

, estimated by the OLS, where 

0 tt DTDU  if 09:2008t  and 1tDU , tDTt   if 09:2008t . 

 As we can see in Figure 1 the production index for all analyzed econo-

mies has an upward trend. However when the financial crisis occurs (in 

2008–2009) the line slopes downward and the production index is falling. 

After 2009, production index returns to the pre-crisis path but at a slower 

pace than previously. Figure 1 reveals that the production response to the 

global financial crisis is higher in developed countries (i.e., Germany, 

France, Denmark, European Union) and lower in developing countries (i.e., 

Poland and Czech Republic).  

 
a) Logs in production in Germany 

 
b) Logs in production in France 

 
c) Logs in production in Denmark 

 
d) Logs in production in Netherlands 

4,1 
4,2 
4,3 
4,4 
4,5 
4,6 
4,7 
4,8 

L
o
g
 o

f 
p

ro
d

u
ct

io
n

 i
n

d
d

ex
 

Production (DE) Fitted 

4,4 

4,5 

4,6 

4,7 

4,8 

L
o
g
 o

f 
p

ro
d

u
ct

io
n

 i
n

d
ex

 

Production (FR) Fitted 

4,3 

4,4 

4,5 

4,6 

4,7 

4,8 

4,9 

lo
g
 o

f 
p

ro
d

u
ct

io
n

 i
n

d
ex

 

Production (DK) Fitted 

4,1 

4,2 

4,3 

4,4 

4,5 

4,6 

4,7 

L
o
g
 o

f 
p

ro
d

u
ct

io
n

 i
n

d
ex

 

Production (NL) Fitted 



Asymmetries in the Relationship between EconomicActivity and Oil Prices… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

73 

 
e) Logs in production in Poland 

 
f) Logs in production in Czech Rep. 

 
g) Logs in production in European Union 

Figure 1.  Logs in production and fitted trend line with break for selected EU coun-

tries 

 This findings reveal that the structural changes in production caused by 

the global financial crisis are more apparent in developed economies than in 

developing economies. The break point (set in September 2008) refers to the 

time of break, i.e., the period at which the change in the level of series (break 

in intercept) and lower growth rate (the change in the slope of a trend func-

tion) occur. In the case of Germany, France, Denmark and European Union 

the production response to the financial crisis is sudden and significant. For 

other economies (the Netherlands, Poland and Czech Republic) the change 

in production index is small but visible – see Figure 1. The estimated param-

eters 3  and 4  for all economies are statistically significant what is an 

argument for taking into account both a sharp change in the level of the se-

ries (break in intercept) and the change in the slope of a trend function – see 

Table 1. 
  

3,4 

3,9 

4,4 

4,9 

L
o
f 

o
f 

p
ro

d
u

ct
io

n
 i
n

d
ex

 

Production (PL) Fitted 

3,6 
3,8 

4 
4,2 
4,4 
4,6 
4,8 

5 

L
o
g
 o

f 
p

ro
d

u
ct

io
n

 i
n

d
ex

 

Production (CZ) Fitted 

4,3 

4,4 

4,5 

4,6 

4,7 

4,8 

L
o
g
 o

f 
p

ro
d

u
ct

io
n

 i
n

d
ex

 

Production (EU) Fitted 



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

74 

Table 1.  The ADF test for cointegration 

Country 
Estimated parameters of long-run equation with structural break ADF 

Const. Int Bt time DUt(λ) DTt(λ) Levels (C+t) 

DE –9.935 3.077 
[7.218] 

0.022 
[2.166] 

0.0017 
[14.58] 

–0.0992 
[–10.24] 

0.0008 
[3.778] 

–3.573 
(0.006) *** 

FR 0.498 0.911 
[3.334] 

–0.0302 
[–4.144] 

0.001 
[12.13] 

–0.16 
[–21.92] 

–0.0005 
[–3.18] 

–3.882 
(0.002) *** 

NL –0.262 0.979 
[4.452] 

0.038 
[5.746] 

0.001 
[12.83] 

–0.0329 
[–4.37] 

–0.001 
[–6.502] 

–4.673 
(<0.01) *** 

DK –2.735 1.614 
[4.425] 

–0.066 
[–6.811] 

0.0022 
[17.86] 

–0.220 
[–21.36] 

–0.0009 
[–4.425] 

–4.323 
(0.001) *** 

PL 2.33 0.256 
[2.103] 

0.044 
[2.761] 

0.005 
[15.95] 

0.163 
[3.24] 

–0.001 
[–4.892] 

–2.986 
(0.036) ** 

CZ –1.597 1.17 
[10.61] 

0.072 
[7.16] 

0.003 
[22.13] 

–0.114 
[–10.65] 

–0.002 
[–6.959] 

–4.051 
(0.001) *** 

EU 0.786 0.792 
[4.023] 

0.017 
[1.947] 

0.001 
[9.449] 

–0.043 
[–1.833] 

–0.0006 
[–4.353] 

–3.044 
(0.031) ** 

Note:  ***, ** and * denote significance at 1%, 5% and 10% level respectively; in parentheses the  
p-value are given, in brackets the t-statistics are given. 

 Before estimating the model, it is necessary to check whether the rela-

tionships between the variables are characterized by non-linearity. The Tsay 

method is employed to test for linearity of time series. In order to test for 

linearity of series, the optimal autoregression lag of model should be deter-

mined. For Germany and Poland the optimal lag p is equal to 1, for France 

and the EU the lag p is equal to 5. For Denmark, Netherlands and Czech 

Republic the optimal lag p is respectively equal to 3, 1 and 2. Table 2 sum-

marizes the result of linearity test. The F(p,d) statistic suggest that the time 

series for Germany, Denmark and Poland are nonlinear with d=1 (it appears 

that the threshold break with delay greater than 1 in the case of Germany is 

possible, however the threshold break with delay d=1 as the threshold varia-

ble showing the greatest effect). In the case of France and the EU the Tsay 

test rejects the linear hypothesis with delay d=5 with the greatest effect. For 

Netherlands the threshold delay is equal to 11 and for Czech Republic the 

Tsay test does not reject the null hypothesis of linear relationship  – see Ta-

ble 2. 

 When we allow the structural break in intercept and slope of trend func-

tion in long-run equation (1), the linear cointegration test reveals the long-

run relationship for all analyzed economies – see Table 1. However, the 

Engle-Granger approach assuming symmetric adjustment toward equilibri-

um is misspecified if the adjustment is asymmetric. Therefore, to test for 

cointegration with asymmetric adjustment, the threshold cointegration ap-

proach proposed by Enders and Sikols (2001) is used. 



Asymmetries in the Relationship between EconomicActivity and Oil Prices… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

75 

Table 2.  The Tsay (1989) linearity test 

Delay 
d 

Germany 
(DE) 

France 
(FR) 

Denmark 
(DK) 

Neder-
land (NL) 

Poland 
(PL) 

Czech 
Republic 

(CZ) 

European 
Union 
(EU) 

1 9.660 ** 4.176 ** 4.632 ** 0.634 6.960 ** 1.183 4.620 ** 
2 2.009 5.719 ** 0.765 1.126 2.787 2.446 5.011 ** 
3 5.394 ** 3.376 ** 0.064 0.682 1.095 0.902 3.240 ** 
4 2.598 0.969 1.021 0.568 0.527 0.946 1.788 
5 1.754 ** 6.294 ** 1.190 0.309 0.577 1.055 9.086 ** 
6 0.417 1.112 4.373 ** 0.277 1.185 0.796 1.138 
7 2.741 0.909 1.306 0.552 0.086 1.256 4.458 ** 
8 0.546 1.887 2.341 * 1.825 0.314 0.796 4.151 ** 
9 2.236 2.232 ** 0.211 0.917 0.049 0.306 2.532 
10 1.471 0.961 0.965 2.750 ** 0.020 1.831 0.900 
11 0.391 1.035 0.831 3.499 ** 0.895 0.687 0.931 
12 7.141 ** 0.334 0.902 1.664 0.503 0.144 0.411 

Note:  ** indicates the rejection of null hypothesis at the 5% significance level. 

 The asymmetric adjustment mechanism (TAR or M-TAR) is selected 

using the Akaike information criterion (AIC). Threshold cointegration test 

finds the evidence for threshold mechanism in the case of Germany, France, 

Poland and the European Union (both the null hypothesis of no cointegration 

( 0: 210  H ) and the null of symmetric adjustment ( 210 :  H ) are 

rejected). Here the M-TAR model with zero-value of threshold is used. For 

three other countries (Denmark, Netherlands and Czech Republic) the sym-

metric cointegration is found (only the null hypothesis of no cointegration is 

rejected but the null of symmetric adjustment is not rejected) – see Table A.1 

in appendix. 

 The selection of M-TAR model indicates that the direction in which 

production is moving (its momentum) is more important than whether devia-

tions from long-run equation are above or below the equilibrium (as in TAR 

model). 

 In the case of mentioned economies (Germany, France, Poland and the 

EU) the point estimates 1  and 2  have negative signs. It means that ad-

justment coefficients act to eliminate deviations from long-run relationship. 

For Germany, France and the EU deviations below the threshold adjust fast-

er toward the long-run equilibrium than the deviations above the threshold  

( 21   ). We can see that respectively 22.0%, 21.7% and 26.2% of the 

deviation from equilibrium is corrected in the next period when they are 

below the threshold, but only 0.8%, 7.3% and 5.9% when they are above the 

threshold. In the case of Poland the deviation above the threshold adjusts 

faster toward the long-term equilibrium (16.1% of deviation in the next peri-



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

76 

od is corrected) than deviations below the threshold (only 4.9% of deviation 

is corrected). 

 These results showed that the threshold cointegration occurs for devel-

oped countries (Germany, France and the EU). In the case of Poland the 

threshold cointegration also occurs, however it should be noted, that the 

value of adjustment coefficient in regime 1 is greater than regime 2 (since 

21   ). Results for Poland are inconsistent with the theory, where the 

greater value of coefficient 2  provides confirmation of the faster rever-

sion to the long-run equilibrium when the deviations from long-run equation 

are below the threshold value and the slowdown of economic activity (reces-

sion in business cycle) is mitigated by the interaction of fiscal and monetary 

policy. Some other mitigating factors of recession can be distinguished as 

follows: interaction between foreign trade and domestic economy or dynam-

ic expansion of the service-sector characterized by the greater resilience to 

temporary downturn in economic activity (Orłowska, Pangsy-Kania, 2003). 

 Given the findings of linearity test and threshold cointegration among oil 

prices, production and inflation, it is possible to estimate the threshold  

(T-ECM) and linear error correction models (ECM). The results of the 

threshold ECMs for German, France, Poland and the European Union econ-

omies are reported in Table 4. In this case, the M-TAR-ECM models for 

Germany, France, Poland and the European Union take the form of equa-

tion (5). 

 Parameters of an asymmetric adjustment of threshold models are pre-

sented in Table 3. The results for Denmark, Netherlands and Czech Republic 

are presented in Table 4. 

Table 3.  Adjustment coefficients (γ1 and γ2) of the estimated M-TAR-ECM (with 

=0) models for the selected EU countries 

Regime Variables Germany (DE) France (FR) European Union (EU) Poland (PL) 

High 
growth 

Pt –0.047 [–0.93] 0.052 [0.52] –0.002 [–0.02] –0.14 [–2.65] *** 

Int 0.013 [1.432] 0.045 [2.08] ** 0.005 [0.27] 0.011 [0.99] 

Bt –0.142 [–0.46] 0.788 [1.07] 0.234 [0.33] 0.269 [1.15] 

Low 
growth 

Pt –0.193 [–4.16] *** –0.106 [–2.46] ** –0.117 [–3.35]*** –0.03 [–0.54] 

Int 0.015 [1.75] * 0.003 [0.32] 0.014 [1.51] 0.016 [1.41] 

Bt 0.143 [0.494] –0.203 [–0.64] 0.333 [0.86] –0.312 [–1.30] 

Note:  ***, (**), (*) indicate significance at 1%, (5%) and (10%) level, t-statistics for 1 and 2 in brack-
ets, the Ljung-Box statistic for all estimated models show the lack of autocorrelation – the full results are 

available from the authors. 

 The M-TAR-ECM model allows for a different speed of adjustment to 

the long-run equilibrium depending on high- or low growth states of the 



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DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

77 

economy (i.e. production is above or below the long-run relationship respec-

tively). 

 The point estimates of 
1  and 

2  in the M-TAR-ECM models for 
tP  

have a negative sign but the coefficients of low growth regime (
2 ) are sig-

nificant in the case of Germany, France and the EU. In the case of Poland, 

the coefficient 
1  (in high growth regime) is significant – see Table 3. 

 The adjustment coefficients 
1  and 

2  in the model for 
tP  in Germany, 

France and the EU suggest that the speed of adjustment is more rapid for 

negative than for positive discrepancies (since ).21    In the case of 

German economy about 19.3% (for France10.6% and for the EU 11.7%) of 

the deviation from equilibrium is corrected in the next period when produc-

tion is falling, compared to about 4.7% (France – 5.2% and the EU – 0.2%) 

when production is rising
4
 – see Table 3. The greater value of coefficient 

2  

than 
1  provides confirmation that the business cycle is characterized by 

a shorter low growth phase. It means that the recession phase is mitigated 

(for example by effective interaction of fiscal and monetary policies – see 

Orłowska, Pangsy-Kania, 2003, p. 24) because the greater value of 
2 , the 

faster correction of deviations from long-run equilibrium is observed. In the 

case of Poland the results reported in Table 3 show that the production de-

viations above the threshold adjust faster toward the long-run equilibrium 

than the deviations below the threshold (since 21   ). We can see that 

only 3.0% of the production deviations from equilibrium are corrected in the 

next period when they are below the threshold, but 14.0% when they are 

above the threshold. 

 As can be seen in Table 3 the   coefficients in the threshold models for 

tIn  and 
tB  in Germany, France, Poland and the EU have a positive signs. 

That means the deviations to the long-run equation adjust to the ‘wrong’ 

direction (have positive signs) in either or both regimes, and additionally 

parameters 
1  and 

2  are not always significant. 

                                                 
4 In Geise and Piłatowska (2014), when the long-run equation (cointegration relationship) 

allows for a one-time change in the intercept of the trend function, the point estimates of 1 

and 2 in models for Pt in German’s economy suggest that the speed of adjustment is more 

rapid for positive than for negative discrepancies (since |1|>|2|). When the long-run specifi-

cation allows for the change in the intercept and the change in the slope of the trend function 

the M-TAR-ECM model for Pt in German’s economy reveals consistent dependencies 

(|1|<|2|). 



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

78 

 As can be seen in Table 4 (the results for linear ECM), only in the case 

of Denmark the deviation away from the long-run relationship is corrected 

not only by movements in production, but also by movements in inflation 

and oil prices. This can be seen by the negative signs and significance of the 

error correction coefficient 
1  in the ECMs for 

tP ,
tIn  and 

tB . For 

Netherlands and Czech Republic only in models for 
tP  a negative and sta-

tistically significant sign is observed. It means that the long-run equilibrium 

is restored only by the short-run movements in production. 

Table 4.  Adjustment coefficients of the estimated ECM models for the selected EU 

countries 

Variables Denmark (DK) Netherlands (NL) Czech Republic (CZ) 

Pt –0.272 [–3.63] *** –0.669 [–6.35] *** –0.174 [–2.82] *** 

Int –0.014 [–1.91] * 0.021 [2.88] *** 0.03 [2.98] *** 

Bt –0.467 [–2.13] ** 0.257 [0.88] 0.561 [3.04] *** 

Note: ***, (**), (*) indicate significance at 1%, (5%) and (10%) level, t-statistics for 1 and 2 in brackets, 

the Ljung-Box statistic for all estimated models show the lack of autocorrelation – the full results are 
available from the authors. 

 To summarize, the discussed results from threshold error correction 

model (M-TAR-ECM) confirmed the previous findings with regard to 

cointegration with asymmetric adjustment for deviations in production in the 

case of all analyzed economies (Germany, France, the EU and Poland). This 

can be seen by statistical significance of either adjustment coefficients which 

are properly signed. The Enders-Siklos procedure pointed out that the linear 

cointegration (symmetric adjustment) occurs for Netherlands, Denmark and 

Czech Republic. Also, the results of Engle-Granger test confirms these find-

ings. 

4. Granger Causality Test Based on Linear and Threshold Error 
Correction Model 

 In the previous section both the threshold error correction models  

(T-ECM) and linear error correction models (ECM) were estimated. Next, 

the Granger causality test is used to investigate the causal relationship 

among production, inflation and oil prices in the selected EU countries in the 

context of short- and long-run asymmetries.  
 The F-statistics for Granger causality is employed to examine whether 

all the coefficients of a given first differenced variable are jointly statistically 

different from zero (short-run causality) and whether the 
21,  coefficients 

of error correction term are significant (long-run causality). Moreover, the 



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DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

79 

jointly significance of the   coefficients and all the coefficients of a given 

explanatory variable is tested. The threshold error correction models allows 

us to distinguish between short- and long-run Granger causality in the con-

text of high growth and lower growth state of the economy. 

 Table 5 and 6 present the results of the Granger-causality test based on 

the T-ECM and ECM models for oil prices, inflation and production. 

 The results of Granger-causality test, based on the threshold ECM mod-

els for Germany, show that there is short-run unidirectional causal relation-

ship running from oil prices )( tB  to inflation )( tIn  in both economic activity 

regimes (in the case of France the unidirectional relationship is identified in 

high momentum period and for the EU economy causal relationship is found 

in low momentum period). Unidirectional causal relationship between oil 

prices and production exists for the EU in both regimes (for France the uni-

directional short-run causality running from oil prices to production is identi-

fied in the high momentum period). Bidirectional short-run causal relation-

ship between oil prices, production and inflation exists for Polish economy 

in high growth regime – see Table 5. The result of Granger-causality test for 

Poland should be treated with precaution because the impact of Polish econ-

omy on the world crude oil prices does not exist. However short-run asym-

metric reaction of inflation and production to oil price increases is highly 

probable. In the case of short-run causality the T-ECM models are able to 

identify the significance causal relationship from inflation to production for 

Germany in high momentum period (regime 1) – see Table 5. 

 The results of Granger-causality test, based on linear ECM models show 

that there is short-run unidirectional causal relationship running from oil 

prices to production and inflation in the case of Denmark (in the case of 

Czech Republic the unidirectional relation from tB  to tIn  is identified). For 

Netherlands the short-run causal relationship between explanatory variables 

is not confirmed – see Table 6.  

 In terms of long-run situation, a unidirectional strong causal relationship 

running from oil prices tB  to production tP  is found in the case of all ana-

lyzed economies. The asymmetric models show that the oil prices affect the 

production in a high growth regime (when the production is in upward path) 

in the case of Poland, and in low growth regime (when the production is 

decreasing) in the case of Germany, France and the EU. For Denmark, Neth-

erlands and Czech Republic the long-term linear relationship from oil prices 

to production (in the case of Denmark also to inflation) exists. This means 

that oil prices, among explanatory variables, contribute the most to the short-



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

80 

run adjustment to re-establish the long-run equilibrium in the case of all 

analyzed economies. 

Table 5.  Granger causality analysis based on threshold ECM models 

R
eg

im
e 

E
ffe

ct
s 

Causes 

Short-term 
Long-
term 

Both (short-term and long-term) 

Pt Int Bt ecmt-1 
(Pt, 

ecmt-1) 
(Int, 

ecmt-1) 
(Bt, 

ecmt-1) 

Germany (DE) 

I 

Pt – 4.823 ** 1.187 0.876 – 2.538 * 0.968 

Int 0.167 – 15.12 *** 2.05 1.025 – 9.055 *** 

Bt 0.238 0.374 – 0.21 0.301 0.364 – 

II 

Pt – 1.069 1.705 17.31 *** – 5.035 *** 6.603 *** 

Int 1.337 – 2.513 * 3.067 * 1.913 – 2.538 ** 

Bt 2.714 ** 0.52 – 0.244 2.152 * 0.454 – 

France (FR) 

I 

Pt – 0.179 5.344 ** 0.266 – 0.923 2.869 * 

Int 0.482 – 11.05 *** 4.313 ** 2.156 – 8.036 *** 

Bt 0.206 1.794 – 1.453 0.575 1.171 – 

II 

Pt – 0.823 1.215 6.036 ** – 1.41 1.94 ** 

Int 1.333 – 1.607 0.104 1.384 – 1.433 

Bt 1.144 1.21 – 0.415 1.039 1.1 – 

European Union (EU) 

I 

Pt – 0.924 2.966 * 0.982 – 0.472 1.543 

Int 0.015 – 12.08 *** 0.072 0.059 – 6.56 *** 

Bt 0.539 0.043 – 0.109 0.275 0.091 – 

II 

Pt – 0.468 2.533 * 11.23 *** – 3.054 ** 5.489 *** 

Int 1.513 – 0.22 2.27 1.816 – 0.704 

Bt 1.112 0.769 – 0.737 0.953 0.741 – 

Poland (PL) 

I 

Pt – 0.263 3.223 ** 7.018 *** – 1.8 4.081 *** 

Int 0.955 – 2.636 * 0.985 1.127 – 2.21 * 

Bt 2.686 ** 2.291 * – 1.34 2.564 ** 2.038 * – 

II 

Pt – 1.012 2.216 0.295 – 0.777 1.49 

Int 1.98 – 0.659 1.996 1.743 – 1.04 

Bt 0.044 3.119 ** – 1.693 0.625 2.395 * – 

Note:  ***, (**), (*) indicate significance at 1%, (5%) and (10%) level. 

 As can be seen, the Granger causality test shows the causal relationship 

from oil prices to production and/or inflation in both, short- and long-run 

terms. When we take into consideration the results of threshold cointegration 

under consideration, the Granger causality test based on the T-ECM models 

indicate the existence of causation in terms of high growth (expansion) and 



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DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

81 

low growth (recession) regime. The T-ECM models can detect more interest-

ing relations than the linear ECM models. They can identify the relations in 

terms of changes in a business cycle, showing the asymmetry not only in the 

case of different regimes but also in the case of different impact on analyzed 

economies. In this case the threshold models were able to identify the short-

run Granger causality in high regime (for Poland and France) and/or low 

regime (in the case of Germany and the EU). In the case of Denmark and 

Czech Republic the causal relationship between oil prices, production and 

inflation (however for Netherlands linear ECMs, the short-run Granger cau-

sality has been not found) exists.  

Table 6.  Granger causality analysis based on linear ECM models 

Effects 

Causes 

Short-term 
Long-
term 

Both (short-term and long-term) 

Pt Int Bt 
ecmt-1 

(Pt, 
ecmt-1) 

(Int, 
ecmt-1) 

(Bt, 
ecmt-1) 

Denmark (DK) 

Pt – 2.9262 * 1.8508 * 13.16 *** – 6.782 *** 4.2919 *** 

Int 2.1071 * – 2.3112 ** 3.6324 * 1.6863 – 2.4941 ** 

Bt 1.5822 0.6198 – 4.5344 ** 1.6961 2.1692 * – 

Netherlands (NL) 

Pt – 0.6688 0.2781 40.28 *** – 20.27 *** 21.857 *** 

Int 0.3858 – 1.197 8.262 *** 4.6314 ** – 2.0303 * 

Bt 0.4852 0.006 – 0.7693 1.3264 0.3855 – 

Czech Rep. (CZ) 

Pt – 0.0016 1.8884 * 7.957 *** – 4.0741 ** 2.866 ** 

Int 0.3049 – 1.3078 8.856 *** 4.6519 ** – 4.8005 *** 

Bt 1.0928 0.0942 – 9.216 *** 4.6292 ** 4.694 ** – 

Note: ***, (**), (*) indicate significance at 1%, (5%) and (10%) level. 

Conclusions 

 In this paper, we analyzed the results of Granger causality test among oil 

prices, production and inflation in the framework of the threshold (T-ECM) 

and linear (ECM) error correction models across the set of European Union 

countries which are very diverse with respect to the role of oil in their econ-

omy. Several important insights emerge from this analysis. 

 First, the threshold cointegration analysis carried out using the residuals 

obtained from the estimated long-run equation with a structural change in the 

intercept and a change in the slope of the trend function (structural break 

occur in September 2008 when the financial crisis peaked) allows to identify 



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

82 

the long-run relationship between production, inflation and oil prices for 

Germany, France, the EU and Poland. However, Polish economy reverts 

much faster toward its long-run equilibrium when the deviations are above 

the threshold value and tends to persist when the deviations are below the 

threshold. For Germany, France and the EU belonging to the developed 

countries the threshold cointegration has been found in high growth state of 

the economy. In the case of Denmark, Netherlands and Czech Republic the 

long-run relationship between production, inflation and oil prices is linear. In 

the case of Poland when the residuals were obtained from long-run equation 

with structural change in the intercept the Enders-Siklos procedure was not 

able to identify the long-run relationship between production, inflation and 

oil prices. Adding the change in the slope of the trend function in long-run 

equation cause the change in the residuals and then the Enders-Siklos ap-

proach was able to find the evidence for existing the long-term relationship 

between economic activity and prices of crude oil. 

 Second, both types of error correction models are capable to detect the 

significant relationship between oil prices, production and inflation in the 

analyzed European Union economies. The threshold models (T-ECM) out-

perform the linear ECM models because the former can reveal the asymmet-

ric connections among analyzed variables in terms of short-run and long-run 

relations, while the latter cannot. When the economy is in the high growth 

phase of business cycle (deviations form long-run equation are above the 

threshold – regime 1) the Granger causality test finds evidence of short-run 

relationship running from oil prices to inflation (for Germany, France and 

Poland) and production (for France, the EU and Poland). In the case, when 

the economy is in the low growth phase of business cycle (deviations form 

long-run equation are below the threshold value – regime 2) the short-run 

causality from oil prices to inflation (for Germany and the EU) and produc-

tion (for the EU) is identified. 

 Third, the Granger causality test finds the linear short-run causal rela-

tionship running from oil prices to production and inflation for Denmark and 

Czech Republic (with except for Netherlands). The long-run relationship 

running form oil prices to production was confirmed for all analyzed econo-

mies (for Denmark exists also the relation running form oil prices to infla-

tion). 

 In this study we focused on testing the causal relationship between eco-

nomic activity and oil prices using the ECMs with threshold cointegration 

and short-run asymmetries. In further studies we will concentrate on investi-

gating the relationship in the framework of multivariate threshold models 

(e.g. threshold VAR and Markov switching VAR models). 



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Asymetria zależności między aktywnością gospodarczą oraz cenami 
ropy naftowej w wybranych państwach Unii Europejskiej 

Z a r y s  t r e ś c i. W pracy zastosowano progowe (T-ECM) oraz liniowe modele korekty 

błędem (ECM) do badania krótkookresowej i długookresowej przyczynowości w sensie 

Grangera między produkcją, inflacją oraz cenami ropy naftowej w kontekście asymetrycz-

nych reakcji dla siedmiu gospodarek Unii Europejskiej (tj. Niemiec, Francji, Danii, Holandii, 

Polski, Czech oraz Unii Europejskiej jako całości). Relacje między aktywnością gospodarczą 

i cenami ropy naftowej analizowano przy założeniu występowania zmian strukturalnych 

w równaniach długookresowych, gdzie uwzględniano załamania strukturalne w wyrazie 

wolnym oraz w nachyleniu funkcji trendu. Progowe modele korekty błędem (T-ECM) wska-

zują na asymetryczną reakcję produkcji oraz inflacji na zmiany cen ropy naftowej w przypad-

ku Niemiec, Francji, Unii Europejskiej oraz Polski. Dla pozostałych gospodarek (tj. Danii, 

Holandii oraz Czech) reakcja aktywności gospodarczej na szoki naftowej jest symetryczna.  

S ł o w a  k l u c z o w e: krótkookresowa asymetria, kointegracja progowa, progowy model 

korekty błędem, przyczynowość w sensie Grangera, asymetryczny szok naftowy.  

  

http://dx.doi.org/10.1080/01621459.1989.10478760


Asymmetries in the Relationship between EconomicActivity and Oil Prices… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

85 

Appendix 

Table A.1. Results of TAR and M-TAR test for threshold cointegration in the long-

run equation with one structural break in production 

 Threshold cointegration test 

=0 0 

TAR M-TAR TAR M-TAR 

Germany (DE) 

 0 0 0.0152 –0.0131 

1 –0.105 [–1.889] * –0.008 [–0.137] –0.101 [–1.806] * –0.078 [–1.629] 

2 –0.133 [–2.173] ** –0.22 [–3.887] *** –0.138 [–2.261] ** –0.278 [–3.251] *** 

 3.681 7.93 ** 3.732 6.144 * 

F(1–2=0) 0.146 (0.70) 8.451 (0.004) *** 0.244 (0.62) 4.973 (0.03) ** 

Lag 5 5 5 5 
AIC –1190.5 –1198.6 –1190.6 –1195.2 

LB(12) 16.55 (0.17) 16.24 (0.18) 16.48 (0.17) 16.43 (0.17) 

France (FR) 

 0 0 0.0232 –0.0084 

1 –0.105 [–1.877] *  –0.073 [–1.221] –0.062 [–1.061] –0.108 [–2.183] ** 

2 –0.201 [–3.199] *** –0.217 [–3.697] *** –0.233 [–3.959] *** –0.256 [–3.276] *** 

 6.453 ** 7.33 ** 8.165 ** 7.159 ** 

F(1–2=0) 1.431 (0.233) 3.149 (0.077) * 4.693 (0.031) ** 2.824 (0.094) * 

Lag 2 2 2 2 
AIC –1297.01 –1298.74 –1297.26 –1298.42 

LB(12) 7.31 (0.2) 9.10 (0.11) 5.97 (0.31) 8.50 (0.13) 

Netherlands (NL) 

 0 0 0.0219 0.0126 

1 –0.422 [–4.244] *** –0.364 [–3.722] *** –0.456 [–4.136] *** –0.501 [–4.187] *** 

2 –0.378 [–3.859] *** –0.437 [–4.375] *** –0.368 [–4.041] *** –0.359 [–4.113] *** 

 12.858 *** 12.999 *** 13.084 *** 13.5 *** 

F(1–2=0) 0.144 (0.7) 0.397 (0.53) 0.55 (0.46) 1.298 (0.26) 

Lag 3 3 3 3 
AIC –1096.49 –1096.74 –1096.89 –1097.64 

LB(12) 12.2 (0.43) 11.71 (0.47) 12.60 (0.4) 12.55 (0.4) 

Denmark (DN) 

 0 0 –0.0214 –0.0188 

1 –0.444 [–4.42] *** –0.511 [–4.812] *** –0.458 [–4.622] *** –0.403 [–4.608] *** 

2 –0.461 [–5.09] *** –0.42 [–4.77] *** –0.45 [–4.899] *** –0.547 [–5.017] *** 

 17.692 *** 17.966 *** 17.682 *** 18.458 ** 

F(1–2=0) 0.023 (0.88) 0.631 (0.43) 0.005 (0.95) 1.482 (0.22) 

Lag 3 3 3 3 
AIC –973.8 –974.4 –973.7 –975.2 

LB(12) 12.25 (0.43) 12.77 (0.39) 12.17 (0.43) 12.17 (0.43) 

 

  



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 65–86 

86 

Table A.1. continued  

 Threshold cointegration test 

=0 0 

TAR M-TAR TAR M-TAR 

Poland (PL) 

 0 0 –0.009 0.0124 

1 –0.129 [–2.731] *** –0.161 [–3.321] *** –0.135 [–2.856] *** –0.18 [–2.634] *** 

2 –0.075 [–1.543] –0.049 [–1.028] –0.069 [–1.413] –0.079 [–2.022] ** 

 4.782 5.927 * 4.947 5.299  

F(1–2=0) 0.634 (0.43) 2.838 (0.09) * 0.952 (0.33) 1.675 (0.2) 

Lag 1 1 1 1 
AIC –1152.07 –1154.29 –1152.39 –1153.12 

LB(12) 6.22 (0.9) 6.18 (0.91) 6.23 (0.90) 6.4 (0.89) 

Czech Republic (CZ) 

 0 0 –0.014 –0.018 

1 –0.208 [–2.91] *** –0.263 [–3.54] *** –0.216 [–3.05] *** –0.231 [–3.94] *** 

2 –0.245 [–3.38] *** –0.194 [–2.79] *** –0.237 [–3.24] *** –0.206 [–1.95] *** 

 8.821 *** 8.975 *** 8.685 ** 8.644 ** 

F(1–2=0) 0.159 (0.69) 0.517 (0.47) 0.051 (0.82) 0.047 (0.83) 

Lag 2 2 2 2 
AIC –1040.1 –1040.5 –1040.0 –1039.99 

LB(12) 11.89 (0.45) 11.55 (0.48) 11.84 (0.46) 11.76 (0.46) 

European Union (EU) 

 0 0 –0.0134 0.0068 

1 –0.162 [–2.973] *** –0.059 [–1.046] –0.163 [–3.053] *** –0.041 [–0.481] 

2 –0.187 [–3.504] *** –0.262 [–4.992] *** –0.188 [–3.436] *** –0.201 [–4.575] *** 

 10.662 *** 12.979 *** 10.666 *** 10.648 *** 

F(1–2=0) 0.109 (0.74) 7.309 (0.01) *** 0.115 (0.73) 3.021 (0.08) * 

Lag 0 1 0 1 
AIC –1264.22 –1264.56 –1264.23 –1260.38 

LB(12) 13.62 (0.33) 16.49 (0.17) 13.55 [0.33] 14.63 [0.26] 

Note: ***, ** and * denote significance at 1%, 5% and 10% level respectively; in parentheses the  
t-statistics are given; in brackets the p-values are given. 

 


