METODY ILOŚCIOWE
W BADANIACH EKONOMICZNYCH
QUANTITATIVE METHODS IN ECONOMICS
Vol. XVIII, No. 3
Faculty of Applied Informatics and Mathematics
Department of Econometrics and StatisticsQUANTITATIVE METHODS IN ECONOMICS
METODY ILOŚCIOWE W BADANIACH EKONOMICZNYCH
Volume XVIII, No. 3
Warsaw 2017
EDITORIAL BOARD
Editor-in-Chief: Bolesław Borkowski Vice-Editor-in-Chief: Hanna Dudek Managing Editor: Grzegorz Koszela Theme Editors:
Econometrics: Bolesław Borkowski
Multidimensional Data Analysis: Wiesław Szczesny Mathematical Economy: Zbigniew Binderman Analysis of Labour Market: Joanna Landmessser Financial Engineering: Monika Krawiec Data Science: Michał Gostkowski Statistical Editor: Wojciech Zieliński
Technical Editors: Jolanta Kotlarska, Elżbieta Saganowska Language Editor: Agata Kropiwiec
Native Speaker: Yochanan Shachmurove Editorial Assistant: Luiza Ochnio
SCIENTIFIC BOARD
Adnene Ajimi (University of Sousse, Tunisia) Heni Boubaker (University of Sousse, Tunisia)
Vasily Dikussar (Doradnicyn Computing Centre of the Russian Academy of Sciences, Russia) Peter Friedrich (University of Tartu, Estonia)
Paolo Gajo (University of Florence, Italy)
Agnieszka Gehringer (University of Göttingen, Germany) Anna Maria Gil-Lafuente (University of Barcelona, Spain) Jaime Gil-Lafuente (University of Barcelona, Spain) Vasile Glavan (Moldova State University, Moldova) Francesca Greselin (The University of Milano-Bicocca, Italy) Ana Kapaj (Agriculture University of Tirana, Albania) Jirawan Kitchaicharoen (Chiang Mai University, Thailand) Yuriy Kondratenko (Black Sea State University, Ukraine)
Vassilis Kostoglou (Alexander Technological Educational Institute of Thessaloniki, Greece) Karol Kukuła (University of Agriculture in Krakow, Poland)
Kesra Nermend (University of Szczecin, Poland)
Nikolas N. Olenev (Doradnicyn Computing Centre of the Russian Academy of Sciences, Russia) Alexander N. Prokopenya (Brest State Technical University, Belarus)
Yochanan Shachmurove (The City College of The City University of New York, USA) Mirbulat B. Sikhov (al-Farabi Kazakh National University, Kazakhstan)
Marina Z. Solesvik (Nord University, Norway) Ewa Syczewska (Warsaw School of Economics, Poland) Achille Vernizzi (University of Milan, Italy)
Andrzej Wiatrak (University of Warsaw, Poland) Dorota Witkowska (University of Lodz, Poland)
ISSN 2082-792X e-ISSN 2543-8565
© Copyright by Department of Econometrics and Statistics WULS – SGGW (Katedra Ekonometrii i Statystyki SGGW)
Warsaw 2017, Volume XVIII, No.3 The original version is the paper version Journal homepage: qme.sggw.pl
Published by Warsaw University of Life Sciences Press
Volume XVIII, No. 3, 2017
CONTENTS 1
Elżbieta Badach, Lidia Luty, Monika Zioło, Jan Žukovskis – The Diversity
2
of European Union Countries According to Equipment
3
with Agricultural Tractors ... 399
4
Dariusz J. Błaszczuk, Joanna M. Landmesser – VAR Models for Economic
5
Policy Targets of OECD Countries in 1990-2016.
6
Assumptions and Estimation Results ... 408
7
Patrycja Chodnicka-Jaworska – Information Value of the Credit Rating
8
on the Credit Default Swaps Market ... 418
9
Sebastian Jarzębowski, Natalia Bezat – Costs as a Determinant of Choice
10
of Distribution Channel in a DIY Enterprise ... 429
11
Monika Jaworska, Renata B. Prokeinova – Ecological Awareness of Students
12
in the Light of Surveys ... 440
13
Monika Jaworska, Janina Szewczyk, Piotr Czekaj – Crime and the Standard
14
of Living in Poland ... 451
15
Marek Karwański, Urszula Grzybowska – Application of L-moments in
16
Homogeneity Examination for Groups of Production Companies
17
Distinguished by DEA ... 463
18
Katarzyna Ostasiewicz, Achille Vernizzi – Decomposition and Normalization
19
of Absolute Differences, when Positive and Negative Values Are
20
Considered: Applications to the Gini Coefficient ... 472
21
Aleksandra Staniszewska, Gema Fernandez-Avilez – Charity Banking:
22
Utopia or an Alternative to Greedy Finance? ... 492
23
Andrzej Wołoszyn, Romana Głowicka-Wołoszyn, Agnieszka Kozera – Application
24
of Generalized Distance Measure to the Construction
25
of a Synthetic Index of Subjective Sense of Financial Security
26
of Farmers’ Households ... 501
27
Monika Zioło, Lidia Luty, Elżbieta Badach, Astrida Miceikiene – Technical
28
Equipment of Farms in Małopolska and Lithuania
29
on the Basis of Survey Research ... 510
30
QUANTITATIVE METHODSIN ECONOMICS Received: 04.09.2017 Volume XVIII, No. 3, 2017, pp. 399 – 407 Accepted: 05.10.2017
DOI: 10.22630/MIBE.2017.18.3.37
THE DIVERSITY OF EUROPEAN UNION COUNTRIES 1
ACCORDING TO EQUIPMENT 2
WITH AGRICULTURAL TRACTORS 3
Elżbieta Badach 4
Lidia Luty (ORCID: 0000-0001-8250-8331) 5
Monika Zioło (ORCID: 0000-0003-0884-4083) 6
Faculty of Agriculture and Economics 7
University of Agriculture in Krakow, Poland 8
e-mail: mziolo@ar.krakow.pl 9
Jan Žukovskis 10
Faculty of Economics and Management 11
Aleksandras Stulginskis University, Lithuania 12
Abstract: The research of taxonomic structure of holdings owning
13
agricultural tractors in EU countries was conducted on the basis of statistical
14
information from EUROSTAT database, for 2013 year. The purpose of this
15
article was to present level of equipment of holdings in European Union
16
countries in agricultural tractors in the spatial aspect. The method of vector
17
elimination was used in the analysis. Apart from the analysis concerning
18
the fact of the possession of agricultural tractors according to areal groups
19
of arable land in the European countries, the groups of countries with similar
20
structure were distinguished. Percentage of holdings possessing tractors was
21
related with the number of holdings in each groups of areal groups of arable
22
land.
23
Keywords: agricultural tractors, European Union, additive structures
24
INTRODUCTION 25
Technical equipment of farms within the area of agricultural machines and 26
devices is one of the fundamental factors influencing effective agricultural 27
production. The level of this equipment in the countries of European Union (EU) 28
depends mainly on the agrarian structure of the region, crop structure and 29
productivity of farms. Technical equipment of agriculture of Middle-East countries 1
has been undergoing dynamic changes.
2
In spite of the fact that old machinery allows for performing basic 3
agricultural activities concerning farm, new sophisticated devices are much better 4
at stepping up farm productivity. Duczkowska-Małysz [1998] emphasizes that 5
modernized farms are capable of absorbing biological and technical progress, cost 6
reduction and meeting challenges of competence. In the EU policy there is a lot 7
of attention focused on tasks connected with bridging disproportions of agricultural 8
development in regional aspect.
9
In the countries of Western Europe (see Figure 1) in 2013 almost 100%
10
of farms were in the possession of agricultural tractor. Best equipped farms were 11
identified in Scandinavian countries and the countries of UE-12, in particular 12
Germany, Austria and Benelux countries, where more than 90% of farms were 13
equipped with agricultural tractor. One should also notice that the position 14
of Poland in the ranking arrangement of the EU countries in this aspect is relatively 15
high (66% of farms were in the possession of agricultural tractors). Moreover, 16
Poland position was better than those of Italy, Portugal and Spain. Another 17
observation is that agriculture in Romania and Bulgaria suffers from severe lack 18
of finances. The reason for this phenomenon seems to be a significant 19
fragmentation of farms.
20
Figure 1. Ranking arrangement of the EU countries with respect to the percentage of farms
21
equipped with agricultural tractors in 2013
22
0 20 40 60 80 100
Finland
Germany Sweden
Luxembourg Austria
Slovenia
Czech Republic
Denmark
Belgium
France
Netherlands United Kingdom Ireland
Croatia Poland Italy Portugal Slovakia Estonia Spain Latvia Lithuania
Greece Cyprus
Hungary Bulgaria
Malta Romania
23
Source: own elaboration on the basis of Eurostat data
24
The Diversity of European Union Countries … 401
In 2013 (see Table 1) in case of one fourth of the EU countries with the lowest level of 1
mechanization of agriculture the possession of agricultural tractors occurred in not more than 2
41.3% of farms. In turn, in case of half of the countries considered in the research the level of 3
mechanization was satisfactory, the index of farms in with agricultural tractors achieved at least 4
68%. Moreover, in farms of the area more than 20 hectares in the countries of the European 5
Union at least 86% of farms on average is equipped with agricultural tractors, while in the areal 6
group of farms up to 5 hectares the percentage is significantly lower and differentiated.
7
Table 1. Basic characteristics of the percentage of farms equipped with agricultural tractors
8
according to areal groups of arable land
9
Specification Areal groups [hectares]
Total
< =5 5-10 10-20 20-50 50-100 >=100
quartile 1 21.13 57.59 69.61 79.08 81.20* 83.15* 41.30 median 46.88 74.49 83.93 89.81 92.27* 90.91* 67.60 quartile 3 64.13 87.59 92.07 95.73 96.24* 95.60* 86.15 arithmetic mean 45.59 69.08 79.42 85.89 88.19* 87.58* 61.50 coefficient
of variation 55.89 30.08 19.82 13.66 11.79* 11.51* 45.77 Source: own elaboration; *estimated for 27 countries (apart from Malta)
10
The aim of the paper was to present the level of technical equipment 11
of farms in the EU countries with respect to agricultural tractors in spatial aspect.
12
The analysis of structure of farms being in the possession of agricultural tractors 13
was carried out, according to areal groups of arable land in the EU countries and 14
groups of countries with similar structure were distinguished.
15
MATERIAL AND METHOD 16
The analysis was conducted on the basis of data from the Polish Central Statistical 17
Office, concerning international statistics and EUROSTAT database. The data considered in 18
the research refer to the number of farms equipped with agricultural tractors according to areal 19
groups determined as follows: up to 5 hectares, 5-10 hectares, 10-20 hectares, 20-50 hectares, 20
50-100 hectares, more than 100 hectares in the European Union.
21
The structure under investigation according to the determined areal groups in 2013 in 22
the EU countries can be expressed in the form of the following matrix
a : ij23
nm n
n
m m
m j
n i ij
a a
a
a a
a
a a
a
a
...
....
...
....
....
....
...
....
....
...
...
2 1
2 22
21
1 12
11
,..., 2 , 1
,..., 2 ,
1 (1)
24
where aij describes the partition of number of farms equipped with agricultural 1
tractors from the areal group j in the total number of farms under investigation in 2
the country i, under the assumption that the following conditions are fulfilled:
3
1
0aij and 1
1
m
j aij , i =1, 2, …, n.
4
The measure of concentration degree of his phenomenon on the basis 5
of the information contained in the matrix
a can be obtained by the application ij6
of the following formula [Kukuła 1989]:
7
1
1
m
m W m
Ki m i (2)
8
where
12
1 2
m
j ij
i a
W is the specialization coefficient [Szyrmer 1975].
9
The measure Ki takes values from the interval [0, 1]. Low values of this 10
measure can be interpreted in terms of uniform distribution of the phenomenon 11
under investigation.
12
The basis for the division of countries into groups of objects that are similar 13
with respect to the structure under consideration is the symmetric matrix 14
) ,..., 1 ,
](
[dik ik n , elements of which represent measures of differentiation of structures 15
being investigated that are estimated for each pair of countries according to the 16
following formula [Kukuła 1989]:
17
2
1
m
j
kj ij
dik
18 (3)
Matrix [dik](i,k1,...,n) was transformed into binary matrix of similarities [pik](i,k1,...,n), 19
with elements pik defined as follows:
20
**
, 1
, 0
d d when
d d p when
ik ik
ik , (4)
21
where the threshold value was assumed to be at the following level:
22
) 1 ( 2
* 1
n n
d d
n
i k i ik
23 (5)
Matrix [pik](i,k1,...,n) is the starting point for grouping of voivodeships 24
according to the procedure of Victor elimination proposed by Chomątowski and 25
Sokołowski [1978].
26
The Diversity of European Union Countries … 403
RESEARCH RESULTS 1
High differentiation level expressed in the value of the coefficient 2
of variation (see Table 2) is observed in case of these elements of the structure that 3
refer to the farms of smallest area (up to 5 hectares) or large area (more than 20 4
hectares). Only in case of seven EU countries not more than 11% of agricultural 5
tractors were identified in farms of the area up to 5 hectares. Turn in half of these 6
countries at least 46% of the total number of tractors were in the possession 7
of these small farms.
8
Table 2. Basic characteristics of elements of the structure of farms equipped with
9
agricultural tractors according to areal groups of arable land
10
Specification Areal groups [hectares]
< =5 5-10 10-20 20-50 50-100 >=100
quartile 1 0.11 0.12 0.11 0.09 0.03* 0.03*
median 0.27 0.16 0.16 0.17 0.07* 0.08*
quartile 3 0.46 0.21 0.20 0.23 0.17* 0.15*
arithmetic mean 0.29 0.17 0.16 0.18 0.10* 0.10*
coefficient
of changeability 69.46 32.82 30.98 55.09 75.90* 83.64*
Source: own elaboration; *estimated for 27 countries (apart from Malta)
11
In the research of distribution uniformity of agricultural tractors in farms 12
with respect to their area the concentration coefficient described by the formula (2) 13
was applied. It is very useful due to its simple structure and easy interpretation. It is 14
based merely on frequencies of occurring some levels instead of their values.
15
Ranking arrangement of the EU countries with respect to the Ki value is presented 16
by Figure 2. The highest level of the concentration coefficient was observed in 17
Cyprus and Malta, in these countries there are most farms of the area up to 10 18
hectares and in fact there are no farms the area of which is more than 20 hectares, 19
therefore the majority of machines occurred in small farms. In case of eight 20
countries (Croatia, Portugal, Poland, Greece, Slovenia, Italy, Ireland and Romania) 21
the average level of concentration of the phenomenon was established. In general 22
in these countries most tractors were used in farms of the area up to 10 hectares.
23
This fact can be explained by significant fragmentation of agriculture in case of 24
countries classified in this group. The concentration coefficient in the other 25
eighteen countries presented in the research and slow, on the level of less than 0.2, 26
which show that the technical equipment of farms is uniform in all areal groups 27
under investigation.
28 29 30 31
1
Figure 2. Ranking arrangement of the EU countries with respect to the Ki value estimated
2
according to the formula (2)
3
0 0,2 0,4 0,6 0,8 Czech Republic
Estonia Sweden
France Germany
Denmark
Latvia
United Kingdom
Lithuania
Netherlands
Spain Luxembourg Belgium Austria Finland Hungary Slovakia Bulgaria Poland Ireland Italy Romania
Greece Slovenia
Portugal Croatia
CyprusMalta
4
Source: own investigation
5
The interesting issue concerning such disciplines as regional policy for 6
example, is the observation of objects with respect to the similarities that occur 7
among them. The problem of identifying groups of similar objects out of the 8
population under consideration can be solved with the help of vector elimination 9
method. The result of the application of the research methods discussed earlier is 10
the distinction of groups of objects of similar structure.
11
In 2013 assuming the thresh hold value for differentiation level to be 12
d*=0.345, basing on vector elimination method 4 groups of similar countries were 13
distinguished. Membership of particular objects in distinguished typological groups 14
is shown in Figure 3.
15 16 17 18 19 20 21 22
The Diversity of European Union Countries … 405
1
Figure 3. Groups of countries similar with respect to the structure of percentage of farms
2
with agricultural tractors in 2013
3
4
Source: own elaboration on the basis of the EUROSTAT database
5
Group I consists of Scandinavian countries and the EU-12 (Belgium, Czech 6
Republic, Denmark, Estonia, Finland, France, Germany, Luxemburg, The 7
Netherlands, Sweden, Great Britain), where the percentage of farms in the 8
possession of agricultural tractors in particular areal groups was the highest in case 9
of large farms, of the area more than 20 hectares.
10
In the countries of group II (Austria, Ireland, Latvia) the domination 11
of farms of the area 10-20 hectares and 20-50 hectares occurs. This is associated 12
with the highest percentage of farms with agricultural tractors.
13
The most numerous group III contains countries (Bulgaria, Croatia, Greece, 14
Hungary, Italy, Lithuania, Poland, Portugal, Romania, Slovakia, Slovenia, Spain) 15
with the agriculture of the highest level of fragmentation, where the percentage 16
of farms equipped with agricultural tractors according to areal groups of arable 17
land is the highest in the group of farms of the area up to 5 hectares.
18
Group IV consists of island countries (Malta, Cyprus), where small farms 19
of the area up to 5 hectares dominate and large farms of the area more than 20 20
hectares do not occur. Therefore the highest percentage of farms with agricultural 21
tractors is noticed in the lowest areal group up to 5 hectares.
22
The average profile of the percentage of farms with the agricultural tractors 23
in particular areal groups for the EU countries is moderated by the most numerous 24
groups – first and third group. The highest level of differentiation of average values 25
in groups of EU countries can be observed in case of farms of the area of less than 26
5 hectares. The average value for group IV (Malta and Cyprus) differs significantly 1
from the others indicating high level of average percentage of farms with 2
the tractors (76%) for the areal group of farms of he area less than 5 hectares.
3
In turn, in case of other areal groups one can observe some similarity of groups 4
of the countries considered.
5
Figure 4. Centres of gravity of distinguished groups of countries similar with respect
6
to the structure of farms in the possession of agricultural tractors in areal groups
7
0,0 0,2 0,4 0,6 0,8
< =5 5-10 10-20 20-50 50-100 >=100
area [ha]
group I group II group III group IV
8
Source: own elaboration
9
CONCLUSIONS 10
The problem of selection of objects of similar structure out of the global 11
population was solved with the help of the method of vector elimination. This 12
procedure can be applied in case of the division of set into subsets containing units 13
of similar structures. As a result of the application of this method four groups 14
of countries of s method four types of countries were distinguished according to the 15
similarity of the structure of farms being in the possession of agricultural tractors 16
in particular areal groups of arable land. Tools of statistical analysis of structures 17
turned out to be very helpful in the investigation that was carried out.
18
In case of farms of the area within 5-10 hectares, 10-20 hectares and 20-50 19
hectares one can observe a uniform distribution of the arithmetic mean and other 20
position measures within each group.
21
The concentration coefficient related to the eighteen countries under 22
investigation is rather low, less than 0.2, which proves uniform distribution of farm 23
equipment with agricultural tractors in all of the areal groups under investigation.
24
The percentage of farms with agricultural tractors is connected with the 25
character of areal structure of the particular country, therefore the highest 26
percentage of farms being in the possession of such machinery in case 27
The Diversity of European Union Countries … 407
of Scandinavian countries and the countries of Western Europe occurs in the areal 1
groups of 20-50 hectares, 50-100 hectares and more than 100 hectares.
2
The countries of Western Europe with the agriculture of high level 3
of fragmentation of farms (Italy, Portugal, Spain) and the EU members 4
the accession of which took place after 2004 display the highest percentage 5
of agricultural tractors for farms of the area up to 10 hectares. In countries such as 6
Austria, Ireland or Latvia the percentage of farms with agricultural tractors is 7
the highest in case of the areal groups of 10-20 hectares and 20-50 hectares. Island 8
countries – Malta and Cyprus, form a separate group. In this case the highest 9
percentage of farms in the possession of agricultural tractors occurs in small farms 10
up to 5 hectares.
11
REFERENCES 12
Chomątowski S., Sokołowski A. (1978) Taksonomia struktur. Przegląd Statystyczny, 2,
13
217-226.
14
Duczkowska-Małysz K. (1998) Rolnictwo-Wieś-Państwo. Wydawnictwo Naukowe PWN,
15
Warszawa, p. 38.
16
Kukuła K. (1989) Statystyczna analiza strukturalna i jej zastosowanie w sferze usług
17
produkcyjnych dla rolnictwa. Zeszyty Naukowe AE w Krakowie, Seria specjalna:
18
Monografie, 89, Kraków.
19
Szyrmer J. (1975) Stopień specjalizacji rolnictwa. Przegląd Geograficzny, 1, 117-135.
20
Mynarski S. (1992) Badanie przestrzenne rynku i konsumpcji. Przewodnik metodyczny.
21
Wydawnictwo Naukowe PWN, Warszawa, p. 93.
22
www.eurostat.eu [access 18.04.2017].
23
http://ec.europa.eu/eurostat/statistics-explained/index.php [access 19.04.2017].
24
Volume XVIII, No. 3, 2017, pp. 408 – 417 Accepted: 05.10.2017
DOI: 10.22630/MIBE.2017.18.3.38
VAR MODELS FOR ECONOMIC POLICY TARGETS 1
OF OECD COUNTRIES IN 1990-2016.
2
ASSUMPTIONS AND ESTIMATION RESULTS 3
Dariusz J. Błaszczuk 4
Faculty of Business and International Relations 5
Vistula University, Warsaw, Poland 6
e-mail: d.blaszczuk@vistula.edu.pl 7
Joanna M. Landmesser (ORCID: 0000-0001-7286-8536) 8
Faculty of Applied Informatics and Mathematics 9
Warsaw University of Life Sciences – SGGW, Poland 10
e-mail: joanna_landmesser@sggw.pl 11
Abstract: Paper presents estimation results of three-equational VAR models
12
separate for every of 34 OECD countries. The variables of every model are
13
economic policy targets: GDP growth rate, unemployment rate and inflation
14
rate. Quarterly data for period 1990 – 2016 were used. Special attention has
15
been given to analysis of cause-effects relationships and random fluctuations.
16
Keywords: economic policy targets, VAR models
17
INTRODUCTION 18
The aim of the paper is to present the objectives, methods and results of the 19
analysis using empirical vector autoregressive (VAR) models of the relationships 20
between the three, most often applied in practice, macroeconomic policy targets:
21
GDP growth rate and unemployment and inflation rates, separately for each OECD 22
country on quarterly data in the period: first quarter 1990 to first quarter 2016.
23
Economic theoreticians devoted special attention to dependencies between 24
every two of the above mentioned economic policy targets [Juselius 2006]. In these 25
respects the Okun’s curve (the relationship between the GDP growth rate and 26
unemployment rate) [Okun 1962], the Phillips curve (the relationship between 27
inflation and unemployment rates) [Phillips 1958], and aggregate supply curve [for 28
VAR Models for Economic Policy Targets … 409
instance, Błaszczuk 2015a] have been studied both theoretically as well as 1
empirically.
2
These three concepts Błaszczuk [2015b, 2015c] combined into one model.
3
Namely, the simultaneous relationships between every two targets were determined 4
and analysed, firstly. On these bases, the three-equational general equilibrium (B) 5
model has been constructed and solved yielding the long term equilibrium point.
6
The present analysis is a continuation of researches carried out by Błaszczuk 7
[2015b, 2016] since 2013. However, a different idea in relationships between 8
economic policy targets modelling is behind the VAR models. Essential novum 9
in the present analysis is study of dynamic dependencies between all three analysed 10
variables. Namely, formulating VAR model of an economic system one assumes 11
that "everything depends on everything". In other words, every of n variables is 12
explained as a function of n p lagged variables (where p is the number of delays) 13
and, possibly, of selected deterministic variables. Therefore, in the formulation 14
of the VAR model one a priori does not take into account either economic theory 15
assumptions or dependencies observed in practice. However, the latter 16
relationships influence the structure of the subsequent VAR model versions 17
at the stage of its (economic and/or statistical) verification if one does not stop on 18
the estimation of a "full" version, in which in every equation all n p variables are 19
present. Eventually one obtains dynamic cause-and-effect relationships between 20
every non-lagged variable and the all lagged ones. However, unlike in case 21
of dynamic structural models, one does not interpret the estimates of VAR model 22
parameters. Contrary, the response of every variable on the shock change of every 23
of the other variables is examined. In the following paragraphs of the paper we: 1) 24
show the basics of VAR modelling, 2) present and discuss results of our empirical 25
analysis, 3) characterise directions of further researches.
26
VAR MODELLING 27
In the seventies of the last century large structural models had been 28
constructed. They were criticised because [Sims 1980] that they forced to accept 29
a priori a number of assumptions about the nature of the analysed relationships for 30
which the compelling arguments were often lacking and because [Lucas 1976] they 31
were hardly applicable in practice. Sims has suggested substitution of the structural 32
models by vector autoregressive ones. Their concept is characterised by: (a) joint 33
modelling of all the analysed variables, (b) lack of division on the endogenous 34
variables and the exogenous ones, (c) no zero conditions, (d) rich dynamic 35
specification of the model, (e) good forecasting and simulation properties.
36
The principle of VAR modelling is to estimate the models on stationary data.
37
VAR model of the order p for n-dimensional vector of variables 38
T nt t t [Y1,...,Y ]
Y is given by the formula:
39
t p t p t
t t t p
i
i t i t
t A D AY ε A D AY A Y A Y ε
Y
0 1 1 2 2 ...1
0 , (1)
1
where n-dimensional random factor εt is subject to the following assumptions:
2
) , 0 (
~N
εt and Cov(εt,εs)0 for ts, and A0Dt is the deterministic part 3
of equation (for example, trend).
4
The VAR model equations may be estimated one by one using OLS or all 5
together using MLE. In the absence of theoretical justification on row of lags (p) 6
one can rely on the statistical properties of the model [Lütkepohl 2005, Juselius 7
2006]. Then the most common used are criteria: AIC, SIC, HQC. Another 8
possibility in this respect is the analysis of residuals. Random variables of every 9
equation should be characterised by lack of autocorrelation (to check this one can 10
use Box - Pierce statistic or Ljung - Box one). Hypothesis about the lack 11
of multidimensional autocorrelation of random variable can be tested with the help 12
of the Breusch - Godfrey test. An indication for the choice of the maximum delay 13
can also be the results of significance tests for the recent delays [Kusideł 2000, 14
Wójcik 2014]. One should also remember that in practice, in order to estimate 15
the model parameters properly, a large number of observations is required.
16
While verifying VAR model a special attention is paid to the analysis 17
of causality. In accordance with the definition, the variable Y2 is the cause of Y1 in 18
sense of Granger, if the current values of Y1, can be predicted with greater 19
precision, ceteris paribus, using past values of the Y2 than without their use 20
[Charemza & Deadman 1997]. The Granger test for causality is as follows. Let 21
p
i
t q
j
j t j i
t i
t Y Y
Y
1 0
, 2 ,
1
1 . (2)
22
Null hypothesis:H0:0 1q 0, so there are no one-way causal 23
dependencies between Y2 and Y1, i.e. Y2 is not the cause of Y1. Test statistics for 24
large samples converges to the 2(q)distribution.
25
Estimates of the VAR models parameters one does not interpret. Instead, one 26
interprets all of the estimated parameters simultaneously by calculating the impulse 27
response function (IRF). IRF reflects the dynamic (in k periods) response of the 28
endogenous variable Yi on the change of the j-th random variable (j):
29
jt k t
Yi
k j
i
, ) , , (
IRF . (3)
30
Analysis of the impulse response functions is a standard approach 31
in the VAR modelling to study the reaction of the economic systems to shocks.
32
VAR Models for Economic Policy Targets … 411
RESULTS OF INVESTIGATION 1
Sources of statistical data 2
In the analysis we used quarterly data on the GDP growth rates (rGDP), 3
unemployment rates (HUNR) and the inflation rates (CPI) in all (34) OECD 4
countries during the period 1990Q1 – 2016Q1 [http://stats.oecd.org/ (access 5
1.05.2016)].
6
Specification of the VAR models 7
In accordance with the purpose of the study, we decided to build comparable 8
vector autoregressive models for individual OECD countries based on their 9
historical data on rGDP, CPI and HUNR.
10
In our study we used nonstationary data because of the two circumstances.
11
First, we obtained stationary data for various differences for different variables for 12
different countries. Thus, comparing, computed on such data, relationships 13
between the analysed variables for different countries would not be very 14
meaningful, if reasonable at all. Secondly, we inputted deterministic variables 15
taking into account time (t and t2) and seasonality (Q1, Q2 and Q3) thus eliminating 16
to a large extent both non-stationarity and autocorrelation of random variables.
17
To determine the optimal order of lags we used, separately for every model, 18
the AIC, SIC and HQC information criteria. In the vast majority of cases lags were 19
rather small: 1 quarter: 10 countries; 2 quarters: 15 countries; 3 quarters:
20
4 countries; 4 quarters: 3 countries (see Table 1).
21
Table 1. VAR models types for OECD countries
22
VAR model type
Number of countries
państw
Countries
VAR (1) 10 Belgium, Chile, France, Hungary, Israel, Italy, Japan, Korea, New Zealand, Slovenia
VAR(2) 15
Canada, Czech Republic, Denmark, Finland, Germany, Greece, Iceland, Ireland, Luxembourg, Netherlands, Norway, Slovakia, Sweden, United Kingdom, USA VAR(3) 4 Australia, Mexico, Poland, Switzerland
VAR(4) 3 Estonia, Portugal, Spain
VAR(5) 1 Austria
VAR(8) 1 Turkey
Source: own calculations using the gretl package
23
The analysis of causality 24
In the majority of cases we identified one-way and/or two-way causalities.
25
Bidirectional dependencies occurred particularly frequently between 26
unemployment rate and the GDP growth rate. Just almost as often were one-way 27
dependencies: unemployment rate inflation rate, the GDP growth rate 1
unemployment rate, and a little less often: inflation rate the GDP growth rate 2
and the GDP growth rate inflation rate (see Table 2).
3
Table 2. One-way and/or two-way causalities in the 34 OECD countries VAR models
4
(the significance level 10%)
5
Causality between Number of countries CPI
rGDP
2
10 21
9
HUNR
rGDP
14
3 30
13
HUNR
CPI
6
15 25
4
Source: own calculations
6
We discovered the lack of causal dependencies for all three pairs of variables 7
only for Slovakia. There was causal dependence of for only one pair of variables:
8
(a) HUNR rGDP in case of: Slovenia, the Czech Republic, Ireland, (b) 9
HUNR CPI in case of Norway, (c) CPI rGDP in case of Luxembourg.
10
Table 3. The causal dependencies for all the three pairs of variables
11
Country Causal dependency type
CPI ? rGDP HUNR ? rGDP HUNR ? CPI
Poland
Japan
Austria
Belgium
France
Mexico
Turkey
Korea
Finland
Israel
Greece
Spain
United Kingdom
Iceland
Australia
Source: own calculations
12
VAR Models for Economic Policy Targets … 413
The causal relationships for two pairs of variables occurred for the larger 1
groups of countries: (a) HUNR and rGDP, HUNR and CPI in case of: Canada, the 2
Netherlands, Germany, Italy, Hungary, New Zealand, Sweden, (b) CPI and rGDP, 3
HUNR and rGDP in case of: Denmark, Chile, Estonia, USA, (c) CPI and rGDP, 4
HUNR and CPI in case of Portugal.
5
The causal dependencies for all three pairs of variables have been observed 6
in up to 15 countries. In Table 3, there are five groups of countries with similar 7
nature of causative dependencies between the analysed variables. In the first group 8
we discovered influence of the GDP growth rates on inflation rates, two-ways 9
relationships between HUNR and rGDP, and the impact of unemployment rates 10
on the inflation rates. In the second group, there is the influence of the GDP growth 11
rates on inflation rates and unemployment rates. Third group of countries is 12
characterized by the impact of price level changes on the GDP growth rates, GDP 13
growth rates on the unemployment rates and the unemployment rates on the 14
inflation rates. Only the last relationships are reversed in the fourth group 15
of countries when compared with the third one. The economies of the fifth group 16
tend to be in their reactions unlike the other countries concerned.
17
All the discovered causal dependencies are shown in Table 4. The names 18
of countries characterized by appropriate bi-directional causality are typed in bold.
19
Table 4. OECD countries by causal dependencies between analysed policy targets
20
→ rGDP CPI HUNR
r G D P
X
Austria, Belgium, Chile, Denmark, France, Japan, Luxembourg, Mexico, Poland, Portugal, Turkey
Austria, Belgium, Canada, Chile, Czech Rep., Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Israel, Italy, Japan, Korea, Mexico, Netherlands, New Zeeland, Poland, Slovenia, Sweden, Turkey, United Kingdom, United States
C P I
Australia, Estonia, Finland, Greece, Iceland, Israel, Korea, Poland, Portugal, Spain, United Kingdom, United States
X
Canada, Germany, Greece, Iceland, Italy, Japan, Mexico, Netherlands, Spain, United Kingdom
