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Silesian University in Opava School of Business Administration in Karviná Czech Society of Operational Research Czech Econometric Society Proceedings of 30th International Conference Mathematical Methods in Economics edited by Jaroslav Ramík and Daniel Stavárek Karviná, Czech Republic 11 – 13 September 2012 Editors: Jaroslav Ramík Daniel Stavárek Publisher: Silesian University in Opava, School of Business Administration in Karviná Year of publishing: 2012 Number of pages: 1050, Part I. (pp. 1–523), Part II. (pp. 524–1050) © Copyright: Authors of papers ISBN 978-80-7248-779-0 Suggested citation: AUTHOR, A. Title of the paper. In: RAMÍK, J. and STAVÁREK, D. (eds.) Proceedings of 30th International Conference Mathematical Methods in Economics. Karviná: Silesian University, School of Business Administration, 2012, pp. xxx-xxx. ISBN 978-80-7248-779-0. All published papers have been reviewed by two referees before publishing. The proceedings have not been amended or proofread and editors are not responsible for the language used in papers. i Programme Committee of the Conference: Chair: Prof. Dr. Jaroslav Ramík Silesian University, School of Business Administration, Karviná, Czech Republic Members: Prof. Dr. Petr Fiala University of Economics Prague, Faculty of Informatics and Statistics, Czech Republic Assoc. Prof. Dr. Jana Hančlová VŠB – Technical University Ostrava, Faculty of Economics, Czech Republic Prof. Dr. Josef Jablonský University of Economics Prague, Faculty of Informatics and Statistics, Czech Republic Assoc. Prof. Dr. Ladislav Lukáš University of West Bohemia Pilsen, Faculty of Economics, Czech Republic Prof. Dr. Jan Pelikán University of Economics Prague, Faculty of Informatics and Statistics, Czech Republic Dr. Karel Sladký Czech Academy of Sciences, Institute of Information Theory and Automation, Czech Republic Assoc. Prof. Dr. Daniel Stavárek Silesian University, School of Business Administration, Karviná, Czech Republic Assoc. Prof. Dr. Tomáš Šubrt Czech University of Life Sciences Prague, Faculty of Business and Economics, Czech Republic Prof. Dr. Karel Zimmermann Charles University, Faculty of Mathematics and Physics, Czech Republic ii Organizing Committee of the Conference: Chair: Assoc. Prof. Dr. Daniel Stavárek Silesian University, School of Business Administration, Karviná, Czech Republic Members: Mr. Tomáš Heryán Silesian University, School of Business Administration, Karviná, Czech Republic Ms. Zuzana Kiszová Silesian University, School of Business Administration, Karviná, Czech Republic Dr. Jiří Mazurek Silesian University, School of Business Administration, Karviná, Czech Republic Dr. Elena Mielcová Silesian University, School of Business Administration, Karviná, Czech Republic Dr. Radomír Perzina Silesian University, School of Business Administration, Karviná, Czech Republic Dr. Ramila Stoklasová Silesian University, School of Business Administration, Karviná, Czech Republic Dr. Irena Szarowská Silesian University, School of Business Administration, Karviná, Czech Republic Dr. Zuzana Szkorupová Silesian University, School of Business Administration, Karviná, Czech Republic Dr. Pavla Vodová Silesian University, School of Business Administration, Karviná, Czech Republic Conference website: http://mme2012.opf.slu.cz Organizer’s website: http://www.slu.cz/opf/cz/ iii List of Referees: prof. RNDr. Jaroslav Ramík, CSc. Ing. Pavla Vodová, Ph.D. doc. Ing. Daniel Stavárek, Ph.D. Ing. Irena Szarowská, Ph.D. prof. Ing. RNDr. Petr Fiala, CSc. Ing. Zuzana Szkorupová, Ph.D. prof. Ing. Josef Jablonský, CSc. Ing. Petr Seďa, Ph.D. prof. Ing. Miloslav Vošvrda, CSc. Ing. Jan Nevima, Ph.D. prof. Ing. Evžen Kočenda, Ph.D. Ing. Michal Tvrdoň, Ph.D. doc. Ing. Tomáš Šubrt, Ph.D. Ing. Tomáš Tichý, Ph.D. doc. Mgr. Ing. Martin Dlouhý, Dr. MSc. Ing. Jiří Valecký, Ph.D. doc. RNDr. Helena Brožová, CSc. doc. Ing. Danuše Nerudová, Ph.D. doc. Ing. Jana Hančlová, CSc. Ing. Karel Sladký, CSc. doc. RNDr. Jana Talašová, CSc. Ing. Michal Kvasnička, Ph.D. doc. RNDr. Ing. Ladislav Lukáš, CSc. prof. RNDr. Jan Černý, DrSc. prof. RNDr. Milan Vlach, DrSc. Ing. Michal Černý, Ph.D. prof. RNDr. Karel Zimmermann, DrSc. Ing. Lenka Flusserová, Ph.D. prof. RNDr. Jan Pelikán, CSc. doc. RNDr. Jarmila Radová, Ph.D. prof. RNDr. Jaroslav Janáček, PhD. Ing. Jan Zouhar, Ph.D. prof. RNDr. Jitka Dupačová, DrSc. Ing. Jan Fabry, Ph.D. prof. Ing. Václava Pánková, CSc. Ing. Petr Rozmahel, Ph.D. prof. Ing. Roman Hušek, CSc. Ing. Ladislava Grochová, Ph.D. prof. Ing. Jan Kodera, CSc. doc. Ing. Svatopluk Kapounek, Ph.D. prof. RNDr. Ing. František Turnovec, CSc. Ing. Miroslav Čulík, Ph.D. prof. RNDr. Jan Hanousek, CSc. Ing. Rajmund Mirdala, PhD. prof. Ing. Dr. Zdeněk Zmeškal Mgr. Šárka Čemerková, Ph.D. prof. RNDr. Ján Plávka, PhD. doc. Ing. Osvald Vašíček, CSc. doc. RNDr. Petr Lachout, CSc. Ing. Radomír Perzina, Ph.D. Mgr. Jiří Mazurek, Ph.D. Ing. Filip Tošenovský, Ph.D. Mgr. Radmila Stoklasová, Ph.D. Ing. Elena Mielcová, Ph.D. iv CONTENTS Part I. Preface ............................................................................................... 1 Asset pricing in DSGE models - comparison of different approximation methods ……………………………………............. 2 Tomáš Adam Jaromír Baxa Rule-of-thumb households in the Czech Republic ........................... 8 David Bartl Application of cooperative game solution concepts to a collusive oligopoly game ……………………………………... 14 Jan Bartoška Tomáš Šubrt Use of the three-point PERT estimate in Critical Chain method ….. 20 Jitka Bartošová Vladislav Bína Sensitivity of monetary poverty measures on the setting of parameters concerning equalization of household size ……………. 25 Jiří Benesch Hana Mihalčinová Radim Valenčík Resolved and unresolved problems in theory of redistribution systems …………………………………………………………….. 31 Adam Borovička The investment decision making under uncertainty ………………. 37 Josef Botlík Milena Botlíková Criteria for evaluating the significance of transport infrastructure in precedence analysis ………………………………………………... 43 Milena Botlíková Josef Botlík The usage of precedence in analysis of impact of the economic crisis for accommodation services ………………………………… 49 Milena Botlíková Šárka Čemerková Analysis of factors influencing toll amount collected on the Czech roads ………………………………………………………………. 55 Martin Branda Underwriting risk control in non-life insurance via generalized linear models and stochastic programming ....................................... 61 Helena Brožová AHP analysis of teacher’s managerial competencies ……………... 67 Richard Cimler Eva Kautzká Kamila Olševičová Martin Gavalec Agent-based model for comparison of aircraft boarding methods ... 73 Martin Cupal Oleg Deev Dagmar Linnertová Network structures of the European stock markets ……………….. 79 Jan Acedański v Jan Čapek Comparison of recursive parameter estimation and non-linear filtration ……………………………………………………………. 85 Anna Černá Jan Černý Note on optimal paths for non-motorized transport on the network ………................................................................................. 91 Michal Černý A note on the choice of a sample of firms for reliable estimation of sector returns to scale ……………………………………………… 95 Ondřej Čížek Identifiability issue in macroeconomic modelling …………........... 101 Oleg Deev Veronika Kajurová Daniel Stavárek Stock market speculative bubbles: the case of Visegrad countries …………………………………………........................... 107 Martin Dlouhý Efficiency and resource allocation within a hierarchical organization ………………………………………………………... 112 Michal Dorda Dušan Teichmann About a modification of Er/Es/1/m queueing system subject to breakdowns ………………………………………………………. 117 Jitka Dupačová Output analysis and stress testing for mean-variance efficient portfolios …………………………………………………............... 123 Efficient score test for change detection in vector autoregressive models ……………………………………………………………. 129 Peter Ďurka Silvia Pastoreková ARIMA vs. ARIMAX – which approach is better to analyze and forecast macroeconomic time series? …………………………….. 136 Jan Fábry Maria Kobzareva Multiple messenger problem ………………………….…………… 141 Eleonora Fendeková Michal Fendek Microeconomic analysis of cartel equilibrium optimization model .……………........................................................................... 148 Petr Fiala Modeling of competition in revenue management …………….….. 154 Jan Fiedor Jiří Mazurek Optimizing permutation methods for the ordinal ranking problem ............................................................................................. 160 Martin Flégl Helena Brožová Publication efficiency at DSI FEM CULS – an application of the Data Envelopment Analysis ……………………………….………. 166 Tomáš Formánek Roman Hušek Monetary policy effects: comparing macroeconomic impulse responses for the Visegrad Group countries …………….………… 172 Zdeněk Franěk Miloš Masařík Quality optimization of slab casting with use of software monitoring tool and statistical methods ……………………….…... 178 Richard Frensch Jan Hanousek Evžen Kočenda Incomplete specialization and offshoring across Europe …………. 184 Marek Dvořák vi Ludvík Friebel Jana Friebelová Quantitative evaluation of life quality of Czech districts ……….… 190 Lýdia Gábrišová Jaroslav Janáček Polygon regular location problem …………….…………………… 196 Zuzana Gallová A causal relationship between foreign direct investment, economic growth and export for Central and Eastern Europe ……………….. 201 Simulation-assisted Horvitz-Thompson statistic and isotonic regression ………………………….………………………………. 207 Martin Gavalec Zuzana Němcová Matrix period in max-drast fuzzy algebra ……………….………… 213 Roman Gavuliak Relevance of the material deprivation indicator, evidence based on Slovak EU-SILC microdata ……………………………………….. 219 Nicolae Ghiba Diana Sadoveanu Anamaria Avadanei Real exchange rate behavior in 4 CEE countries using different unit root tests under PPP paradigm ………………………………... 225 Agata Gluzicka Donata KopańskaBródka Review of selected experiments related to the Allais paradox ……. 231 Ladislava Grochová Petr Rozmahel Business cycle correlation of the CEEC and the Euro area: some methodological controversy ……………………...………………... 237 David Hampel Jan Vavřina Jitka Janová Predicting bankruptcy of companies based on the production function parameters ………………….…………….......................... 243 Jana Hančlová Milan Šimek Jiří Horák Factors influencing the long-term unemployment level and development in the European Union ……………………….……… 249 Jan Hanousek František Kopřiva Do broker/analyst conflicts matter? Detecting evidence from internet trading platforms ……………..………………………….... 255 Jelena Hartsenko Ako Sauga Does financial support from the EU structural funds has impact on the firms’ performance: evidence from Estonia …………………... 260 Simona Hašková Pavel Kolář Determination of mutually acceptable price of used manufacturing equipment ……………….................................................................. 266 Radek Hendrych Different approaches to dynamic conditional correlation modelling: the case of European currencies ………………….…… 272 Tomáš Heryán The credit market model with three parameters ……….………...... 278 Milan Hladík An interval linear programming contractor ……………….………. 284 Robert Hlavatý Interpretation of dual model for piecewise linear programming problem ……………………………………………………………. 290 Wojciech Gamrot vii Miroslav Hloušek DSGE model with collateral constraint: estimation on Czech data …………………………………………………………….…... 296 Jiří Hofman Ladislav Lukáš Quantitative measuring of operational complexity of suppliercustomer system with control thresholds …………….…… 302 Milan Horniaček Collusive general equilibrium between aggregated industries ……. 308 Michal Houda Convexity in stochastic programming model with indicators of ecological stability ………………………………………................ 314 Tomáš Houška Jaroslav Bil Definition of relevant market in beer industry: application of LA-AIDS model ……………………............................................... 320 Jiří Hřebíček Mathematical modeling of economic phenomena with Maple ……. 326 Radek Hřebík Jana Sekničková ARIMA model selection in Matlab ……………………………….. 332 Viktor Chrobok Miroslav Rada Discontinuous optimization of harvesting natural resources …….... 338 Silvie Chudárková Tomáš Verner Relationship between human capital and economic growth: The case of Austria ………………………………………………..…… 344 Zuzana Chvátalová Jiří Hřebíček Modelling of economic phenomena and dependences for corporate sustainable performance ……………………………….………….. 350 Vladislav Chýna Martina Kuncová Jana Sekničková Estimation of weights in multi-criteria decision-making optimization models ……………………….………………………. 355 Kristýna Ivanková Financial stability indicator predictability by support vector machines ………………………………………………….……….. 361 Josef Jablonský Data envelopment analysis models with network structure ………. 367 Marta Janáčková Alžbeta Szendreyová Territory decomposition parameters of distribution tasks ……….... 373 Jitka Janová Jan Vavřina David Hampel DEA as a tool for bankruptcy assessment: the agribusiness case study …………………………………………………….…………. 379 Filip Ježek Mathematical methods in comparative economics ……….……….. 384 Jana Juriová Influence of cyclical development of the most significant foreigntrade partners on small open economy (VAR approach) ………….. 390 Empirical estimates in economic and financial problems via heavy tails .................................................................................................... 396 Usage of analytic hierarchy process for evaluating of regional competitiveness in case of the Czech Republic ………….………... 402 Vlasta Kaňková Zuzana Kiszová Jan Nevima viii Miroslav Kľúčik VAR model with current-optimal leading indicators …………….... 408 Evžen Kočenda Mathilde Maurel Gunther Schnabl Short-term and long-term growth effects of exchange rate adjustment …………………………………………......................... 414 Jan Kodera Jarmila Radová Tran Van Quang A modification of Kaldor-Kalecki model and its analysis ………... 420 Michal Koháni Exact approach to the tariff zones design problem in public transport ………………………………….………………………... 426 Using technical analysis indicators in the terms of currency hedging ……………………………….……………………………. 432 Implementation of blending problem algorithm into information system ………………………………………..…............................. 438 Robustness and bootstrap approaches to SSD portfolio efficiency testing …………..........................………………………………….. 443 Miloš Kopa Petr Lachout Characterization of uniformly quasi-concave functions ……….….. 449 Václav Kozmík Multistage risk-averse asset allocation with transaction costs …….. 455 Ondřej Krčál An agent-based model of price flexing by chain-store retailers ....... 461 Igor Krejčí Roman Kvasnička Application of aging chain model on demographical data of the Czech Republic ……………………………………......................... 467 Igor Krejčí Jaroslav Švasta The impact of alternative approaches to the measurement of fixed capital ................................................................................................ 473 Michal Krempl Allocation of trains to platforms optimization ……………….……. 478 Aleš Kresta Backtesting of market risk estimation assuming various copula functions …………………………………………………….……... 484 Non-stationary volatility with highly anti-persistent increments: An alternative paradigm in volatility modeling? ……………………… 490 Ladislav Krištoufek Miloslav Vošvrda Measuring capital market efficiency with tools of statistical physics ……………………………………....................................... 496 Jiří Krtek Comparing neural networks with other predictive models in artificial stock market ………………………………………….….. 502 Petr Kučera Multiple-criteria assessment of edges in vehicle routing problems .. 508 Zuzana Kučerová The role of foreign trade in the process of financial integration: The case of European Union countries ……………………………. 512 Markets, social networks, and endogenous preferences ……….….. 518 Roman Kolář Pavel Kolman Miloš Kopa Ladislav Krištoufek Michal Kvasnička ix Part II. Bohdan Linda Jana Kubanová Bootstrap application of the Bornhuetter-Ferguson method ………. 524 Ladislav Lukáš Contribution to financial distress and default modeling and new 2-D aggregated model – SME case studies …………………….….. 530 Tomáš Machálek Kamila Olševičová Richard Cimler Modelling population dynamics for archaeological simulations ….. 536 Dušan Marček Alexandra Kotillová Michal Ulbricht Managerial D-M: Measuring of risk scenes and tools of their reducing …………………………………….……………………… 540 Adrianna MastalerzKodzis Application of fundamental analysis methods to compare efficiency of complex portfolios consisting of values listed on stock exchange ………………………..…………………………… 546 Jiří Mazurek The ordinal consensus ranking problem with uncertain rankings … 552 Jiří Mazurek Zuzana Kiszová Modeling dependence and feedback in ANP with fuzzy cognitive maps …………………………….…………………………………. 558 Jan Melechovský Evolutionary local search algorithm to solve the multicompartment vehicle routing problem with time windows ……….. 564 Optimal allocation of government debt for the Czech Republic: Managing vulnerability of debt service charges to macroeconomic shocks ……………………………………………………………… 569 Lukáš Melecký Michaela Staníčková National efficiency evaluation of Visegrad countries in comparison with Austria and Germany by selected DEA models ……………... 575 Elena Mielcová Shapley value of simple cooperative games with fuzzy coalitions applied on the real voting data ………………………………..…… 581 Resource allocation among academic departments as a coalition game ……………………………………………………………….. 587 Štěpán Mikula Risk of abrupt changes in the property rights protection ……….…. 593 Monika Molnárová Helena Myšková Ján Plavka Efficient algorithm for checking periodicity of interval circulant fuzzy matrices ……………………………………........................... 599 Monika Molnárová Helena Myšková Ján Plavka Periodicity of interval matrices in fuzzy algebra ……….…………. 605 Tomáš Motl Using nonstationary time series for estimating small open economy model with financial frictions ……………………………….…….. 611 Aleš Melecký Martin Melecký Hana Mihalčinová x Petr Mynařík Martina Kuncová Multi-criteria evaluation of alternatives applied to the mobile phone tariffs in comparison with Monte-Carlo simulation results ……………………………………………………………… 617 An algorithm for testing T5 solvability of max-plus interval systems ……………….……………………………………………. 622 A simulation study on an approximate confidence region of parameters of a quadratic calibration function …………..………… 628 Labour market frictions in a small open economy model of the Czech Republic ………………………………………………...….. 634 Pavla Nikolovová The impact of FDI on the host economy ……………….…………. 640 Martina Novotná Modelling corporate bond rating with the use of market – based indicators ........................................................................................... 646 The relationship between monetary and financial stability: Evidence from Central and Eastern European countries ……….…. 652 Vladěna Obrová Construction and application of scoring models ............................... 658 Stanislav Palúch A new (?) k-shortest path algorithm ………………….…………… 664 Václava Pánková Permanent income and consumption ……………..……………….. 670 Monika Papież Sławomir Śmiech Causality in mean and variance between returns of crude oil and metal prices, agricultural prices and financial market prices ……… 675 Jan Pelikán Skip pickup and delivery problem with vehicles circulation ……… 681 Jan Pelikán Jiří Henzler Double system parts optimization: statistic and dynamic model ….. 686 Pavlína Pellešová Selected econometric methods of optimization of economic policy ……………………………………………………………… 692 Radomir Perzina Jaroslav Ramik DAME – Microsoft excel add-in for solving multicriteria decision problems with scenarios …………………………………………… 697 Štefan Peško Michal Turek Richard Turek Max-plus algebra at road transportation ……………….………….. 703 Jakub Petrásek Effects of heavy tails on optimal investment and consumption …... 709 Klára Plecitá Luboš Střelec Behavioral equilibrium exchange rate in Greece and Ireland ……... 715 Jiří Polanský Jaromír Tonner Osvald Vašíček The macro-financial linkages modelling for the Czech economy ………….………………………………………………... 721 Helena Myšková Kateřina Myšková Daniel Němec Anca-Elena Nucu xi Ondřej Popelka Jiří Hřebíček Michael Štencl Michal Hodinka Oldřich Trenz Comparison of different non-statistical classification methods …… 727 Alena Pozdílková Richard Cimler Usage of the extermal algebra in solving the travelling salesman problem ……………………………………………………............. 733 Pavel Pražák Elimination of regional economic disparities as optimal control problem ............................................................................................. 739 Peter Princ Sára Bisová Adam Borovička Forecasting financial time series …………………………….…….. 745 Jaroslav Ramík Measuring transitivity of fuzzy pairwise comparison matrix ……... 751 Jaroslav Ramík Milan Vlach Fuzzy linear programming duality ……………….………………... 757 Svetlana Ridala Ants Aasma Consumption in the Baltic states: Myopia or liquidity constraints? ……………………………………...………………… 763 Michal Rusek Possibilities of control congested intersections controlled by traffic lights ……………………………………………………………….. 769 Jan Rydval Quantification of framing effect using ANP ……………….……… 774 Iveta Řepková Measuring the efficiency in the Czech banking industry: Data Envelopment Analysis and Malmquist index ………………...…… 781 Impact of the global financial crisis on stock market volatility: evidence from Central European stock market ……………………. 787 Veronika Skocdopolova Construction of time schedules using integer goal programming … 793 Karel Sladký Risk-sensitive and average optimality in Markov Decision Processes ……………………..………............................................ 799 Lenka Slámová Lev B. Klebanov Modeling financial returns by discrete stable distributions ……..… 805 Martin Slanicay A proposal of flexible trend specification in DSGE models ………. 811 Ivan Soukal Martina Hedvicakova Classification of the electronic retail core banking market consumers ……………….……………............................................ 817 Jana Soukopová Jiří Kalina Mathematical model of economics of municipal waste management ……………………….................................................. 823 Rostislav Staněk Price competition with capacity constraint and imperfect information …………………….………........................................... 830 Petr Seďa xii Radmila Stoklasová Model of the unemployment rate in the Czech Republic …………. 836 Tereza Suchánková Radka Bezděkovská Crop production function - study ……………….……………......... 842 Milan Svoboda Ladislav Lukáš Application of Markov chain analysis to trend prediction of stock indices …………………...………………........................................ 848 Irena Szarowská Voracity effect and Wagner’s law in the PIIGS ………….……….. 854 Petr Šenk Stanislav Biler Estimation of value of travel time savings using Conditional Logit model ………………………............................................................ 860 Jana Šimáková Bilateral J-Curve between Slovakia and its major trading partners ………………………………………………..…………… 864 Faster convergence for estimates of parameters of GompertzMakeham function using available methods in solver MS Excel 2010 ………………………………………………………………... 870 Irena Šindelářová Exchange rate prediction: a wavelet-neural approach …………..… 875 Václav Školuda Possibilities of computable general equilibrium techniques for analysis of the impact of selected government policies using the CGE of the Czech Republic ………………………………………. 879 Roman Šperka Marek Spišák Tobin tax introduction and risk analysis in the Java simulation ….. 885 Dean Teneng NIG-Levy process in asset price modeling: case of Estonian companies ……………………………………….………………… 891 Some findings about risk estimation and backtesting at the world FX rate market .................................................................................. 897 The use of the genetic algorithm for the upper bound calculation of the vehicle assignment problem …………………………………… 903 Hana Tomášková Martin Gavalec Hankel max-min matrices and their applications ............................. 909 Filip Tošenovský Comparison of two different approaches to stock portfolio analysis …………………………………………………….………. 915 Filip Tošenovský Elena Mielcová Multivariate time-series model of GDPs of the Czech Republic and its major economic partners ……………………………………….. 921 Tran Van Quang Jarmila Radová Managing monetary policy with fuzzy control …………….……… 926 František Turnovec Two-dimensional voting bodies: the case of European Parliament ………………………………………………….……… 932 Regional unemployment disparities and their dynamics: evidence from the Czech Republic ………………………………………….. 938 Ondřej Šimpach Tomáš Tichý Ľubomír Toman Michal Tvrdoň Tomáš Verner xiii Stanislav Tvrz Jaromír Tonner Osvald Vašíček Financial accelerator mechanism in a small open economy: DSGE model of the Czech economy ………………………….…………... 944 Klára Václavinková Milena Botlíková Miroslava Kostková Analysis of the impact of selected variables on the availability of accommodation facilities ………………………………………….. 950 Jiří Valecký Fractional polynomials analysis of relation between insured accident and selected risk factors ……………………………….…. 956 Pavla Vodová Determinants of commercial banks’ liquidity in Poland ………..… 962 Petr Volf On problem of optimization under incomplete information …….… 968 Barbora Volná Models of unexpected fluctuations of aggregate income or real interest rate ........................................................................................ 974 Alicja WolnyDominiak Modeling of claim counts using data mining procedures R CRAN …………………………………….................................... 980 Alicja WolnyDominiak Agnieszka OrnatAcedańska Grażyna Trzpiot Insurance portfolios rate making: quantile regression approach ...... 986 Alicja Wolny Dominiak Katarzyna Zeug-Żebro Spatial statistics in the analysis of county budget incomes in Poland with the R CRAN …………………………………………. 992 Joanna Wyrobek Zbigniew Stanczyk Marek Zachara Synchronization of business cycles between Poland, the euro zone and the new member states of the European Union …………….… 998 Marek Zachara Dariusz Pałka Ewa MajchrzykZachara Agent based simulation of the selected energy commodity market ……………………………………………………….…….. 1004 František Zapletal Radek Němec The usage of linear programming to constructing the ecologiceconomical model for the industrial company profit optimization ………………………………………………….……. 1010 Constructing business cycle regime switching model for Czech economy …………………………………………………………… 1016 Application of methodology Value at Risk for market risk with normal mixture distribution …………………………….…………. 1021 Modelling the sequential real options under uncertainty and vagueness (fuzzy-stochastic approach) ……………………….…… 1027 Jana Závacká Kateřina Zelinková Zdeněk Zmeškal xiv Jan Zouhar Irena Havlová Are fast food chains really that efficient? A case study on crew optimization ……………………….................................................. 1033 Libor Žídek Daniel Němec Impact of the real exchange rate on Czech trade ……………….…. 1039 Miroslav Žižka Cluster analysis of the Liberec region municipalities ……….…….. 1045 xv 30th International Conference Mathematical Methods in Economics Two-dimensional voting bodies: The case of European Parliament František Turnovec1 Abstract. By a two-dimensional voting body we mean the following: the body is elected in several regional voting districts by proportional system based on multi-party competition of national political parties. Then the members of the body exercise dual responsibility: responsibility following from the party membership and responsibility following from regional affiliation. In this paper we formulate the following problem: Taking as decisional units national chapters of European political parties, is there a difference between a priori voting power of national groups in the case of “national” coordination of voting and in the case of “partisan” coordination of voting? By coordination of voting we mean two step process: in the first step there is an internal voting in the groups of units (national or partisan), in the second step there is a voting coordination of aggregated groups (European political parties or national representations). In the both cases the voting has an ideological dimension (elementary unit is a national party group), difference is only in dimension of aggregation. Power indices methodology is used to evaluate voting power of national party groups, European political parties and national representations in the cases of partisan and national coordination of voting behaviour. Keywords: European Parliament, European political parties, ideological coordination, national coordination, Shapley-Shubik power index, two-dimensional voting bodies, voting power of national party groups JEL Classification: D71, C71 AMS Classification: 91F10 1 Introduction By a two-dimensional voting body we mean the following: the body is elected in several regional voting districts by proportional system based on multi-party competition of national political parties. Then the members of the body exercise dual responsibility: responsibility following from the party membership and responsibility following from regional affiliation. There exist more examples of two-dimensional voting bodies (committees). Practically all national parliaments have in some sense two-dimensionality features, especially upper houses in bi-cameral systems. Their individual members represent citizens of the region they were elected in and on the other hand they are affiliated to some political party. One of the voting bodies clearly exhibiting two-dimensional face is the European Parliament. Increasing number of studies are focusing attention to constitutional analysis of European Union institutions and distribution of intra-institutional and inter-institutional influence in the European Union decision making. Most of the studies are related to distribution of voting power in the EU Council of Ministers as reflecting the influence of member states (or, more precisely, member states governments). Significantly less attention is paid to the analysis of European Parliament. It is usually studied in one-dimensional (partisan) framework, taking as a basic decision making unit European political party. In this paper we extend Nurmi [5] and Mercik, Turnovec, and Mazurkiewicz [4] analysis and formulate the following problem: Taking as decisional units national chapters of European political parties, is there a difference between a priori voting power of national groups in the case of “national” coordination of voting and in the case of “partisan” coordination of voting? By coordination of voting we mean two step process: in the first step there is an internal voting in the groups of units (national or partisan), in the second step there is a voting coordination of aggregated groups (European political parties or national representations). In the both cases the voting has an ideological dimension (elementary unit is a national party group), difference is only in dimension 1 Charles University in Prague, Faculty of Social Sciences, Institute of Economic Studies, Opletalova 26, 110 00 Praha 1, Czech Republic, [email protected]. - 932 - 30th International Conference Mathematical Methods in Economics of aggregation. Power indices methodology (Shapley and Shubik [6]) is used to evaluate voting power of national party groups, European political parties and national representations in the cases of partisan and national coordination of voting behaviour. EP is institutionally structured on ideological principle, the individual members (national party groups) work in factions of the European political parties. Hix, Nouri and Roland [1] demonstrated, using empirical data about voting acts in EP of the fifth term, that while ideological dimension in EP voting prevails (in almost 80% of cases EP members voted according European party affiliation), there were still more than 20% of voting driven by national dimension (voting by national affiliation). Consequently, to measure the influence in the EP, basic decision making unit is a national party groups and it makes sense to measure not only voting power of European political parties and/or voting power of national representations, but also the voting power of national party groups, both in ideologically driven voting and nationally driven voting. European political parties cohesion is lower than cohesion of their national chapters. 2 Two-level committee model of power decomposition Let N = {1, 2, …, n} be a set of agents, [γ, ω], be a committee with quota γ and weights ωi, i ∈ N, and π = (π1, π2, …, πn) be the vector of Shaply-Shubik power indices of agents of the committee. Then πi is a probability that agent i ∈ N will be in a pivotal situation. Each agent i can be understood as a group Gi with cardinality ωi (individual members of the committee belonging to i). Clearly card (Gi ) = ωi , ∑ card (Gi ) =τ . Let Gij ∈ Gi be a subgroup j of the group Gi and ωij = card i∈N (Gij), number of members belonging to Gij. Assume that each group (agent) i is partitioned into m(i) subgroups Gij. Then we can consider the following two step procedure of decision making: first each agent Gi looks for joint position in a subcommittee [γi; ωi1, ωi2, …, ωim(i)], where γi is the quota for voting in subcommittee i (e.g. the simple majority). There is a vote inside the group first (micro-game) and then the group is voting jointly in the committee on the basis of results of internal voting (macro-game). If p(Gi) = (pi1, pi2, …, pim(i)) is the power distribution in subcommittee Gi where pij be and internal power of subgroup Gij in micro-game, then the voting power πij of the subgroup Gij in macro-game is πij = πipij expressing the probability of the subgroup Gij being pivotal in the committee decision making. Using SS-power concepts it is easy to prove that m(i ) ∑π ij = πi j =1 so we obtained decomposition of the power of agent i among the subgroups Gij. 3 Modeling distribution of power in European Parliament To evaluate distribution of power of national party groups in European Parliament as basic decision making units we use the model of two-level committees from section 2. To reflect the double dimensionality in voting we use two dimensions of committee structure: the European party factions decomposed into national groups, and the national representations decomposed into the party groups. Basic unit remains the same in both cases: national party group. Then we obtain two schemes of decision making coordination: first based on European party factions and national party groups, second based on national representations and national party groups. First (ideological) dimension leads to committee model A with European parties as agents voting together, [γ, p1, p2, …, pn], the second (national) dimension leads to committee model B with national representations as agents voting together, [γ, n1, n2, …, nm], where γ is the quota (the same for both models), pi is the weight (number of seats) of European party i, nk is the weight (number of seats) of member state k (n is the number of European parties, m is the number of member states). Committee A generates n subcommittees Aj such that [γj, p1j, p2j, …, pmj], where pkj denotes number of members of party group j from country k, γj being a specific quota for subcommittee Aj. Each of these subcommittees consists of at most m national subgroups of the European political party j, where in each subcommittee the members of each party from the same member state k are voting together. We shall refer to the corresponding two-level model as the hierarchically structured committee {A/Aj}. Committee B generates m subcommittees Bk such that [δk, pk1, pk2, …, pkn], where pki denotes number of members of party group j from country k, δk being a specific quota for subcommittee Bk. Each of these subcommittees consists of at most n party subgroups of the - 933 - 30th International Conference Mathematical Methods in Economics national representation k, where in each subcommittee the members of from the same party j are voting together. We shall refer to the corresponding two-level model as the hierarchically structured committee {B/Bk}. Let us denote by αj voting power of the European party j in the committee A (voting by ideological dimension), probability that party j will be pivotal in ideologically coordinated voting, βk voting power of the nation k in the committee B (voting by national dimension), probability that nation k will be pivotal in nationally coordinated voting, αkj voting power of the national segment k of party j in subcommittee Aj, probability that national segment k of party j will be pivotal in internal party voting, βkj voting power of the national segment k of party j in subcommittee Bk, probability that party segment j of representation of country k will be pivotal in internal national voting, πkj voting power of the national segment k of party j in the committee {A/Aj}, probability that national segment k of party j will be pivotal in the grand committee voting based on ideological coordination, ϕkj voting power of the national segment k of party j in the committee {B/Bk}, probability that party segment j of national representation k will be pivotal in the grand committee voting based on national coordination. Using standard algorithms we can find SS-power indices αj in committee A and αkj in committees Aj (probabilities of being pivotal in corresponding committees) and then calculate π kj = α kjα j as conditional probability of two independent random events – pivotal position of j in grand committee A and pivotal position of k in subcommittee Aj. From probabilistic interpretation and properties of SS-power indices it follows m m k =1 k =1 that ∑ π kj = α j ∑ α kj = α j . The sum of voting powers of national groups of European political party j in ideological voting is equal to the voting power of the European political party. The total power is decomposed among the national units of the party. In a more intuitive way: the national group k of political party j is in a pivotal position in compound committee {A/Aj} if and only if it is in pivotal position in subcommittee Aj and the party j is in a pivotal position in committee A. Less trivial is the following result: The country k is in a pivotal position in ideological coordination of voting if some party group from k is in pivotal position. Pivotal positions of national party groups of the same country in ideologically voting are mutually exclusive random events, hence the probability that some party group from n n j =1 j =1 state k is in a pivotal position is ∑ π kj = ∑ α j α kj = θ k (sum of power indices of all party groups from member state k). Then θk can be interpreted as a measure of country k influence in ideologically coordinated m m n n m n j =1 k =1 j =1 voting. From properties of SS-power it follows that ∑ θ k = ∑ ∑ α jα kj = ∑ α j ∑ α kj = ∑ α j = 1 . k =1 k =1 j =1 There is no other direct way how to evaluate θk. In the same way we can find βk in committee B and βkj in committees Bk and then calculate ϕ kj = β kj β k as conditional probability of two independent random events - pivotal position of k in grand committee B and pivotal position of j in subcommittee Bk). Measure of party j influence in nationally coordinated voting is m m k =1 k =1 ∑ ϕ kj = ∑ β k β kj = ϑ j (sum of power indices of party group j from all member states). - 934 - 30th International Conference Mathematical Methods in Economics 4 Illustrative example To illustrate methodology introduced above we use a simple hypothetical example.2 Let us consider a parliament consisting of representatives of three regions A, B, and C decomposed into three super-regional parties L, M, R (altogether 9 regional party chapters of 3 super-regional parties). Distribution of seats is provided in Table 1. Entries in last row provide total number of seats of each party in the parliament, entries in the last column total number of seats of each region in the parliament, and entries in the main body of the table provide number of seats of each regional party chapter. Regions A B C Total L 7 15 3 25 parties (seats) M 10 15 22 47 R 3 0 25 28 total 20 30 50 100 Table 1 Distribution of seats Let us start with evaluation of distribution of power of super-regional parties in the parliament under assumption that regional chapters of each party are voting together. To do that we have to calculate power indices in the committee [51; 25, 47, 28].Total influence of super-regional parties in ideologically coordinated voting measured by Shapley-Shubik power indices (assuming simple majority quota): (1/3, 1/3, 1/3). Total influence of regional representations in regionally coordinated voting measured by Shapley-Shubik power indices (assuming simple majority quota) we have to calculate power indices in the committee [51; 20, 30, 50], voting power (1/6, 1/6, 2/3). Influence of regional party chapters in ideologically coordinated voting: Party group L: committee [13; 7, 15, 3]; voting power of regional party chapters of party L: (0, 1, 0). Total voting power of L in the parliament ideological voting equal to 1/3 is decomposed among the regional party chapters: (0, 1/3, 0). Party group M: committee [24; 10, 15, 22]; voting power of regional party chapters of party M: (1/3, 1/3, 1/3). Total voting power of M in the parliament ideological voting 1/3 is decomposed among the regional party chapters: (1/9, 1/9, 1/9) Party group R: committee [15; 3, 0, 25]; voting power of regional party chapters of party R: (0, 0, 1). Total voting power of R in the parliament ideological voting 1/3 is decomposed among the regional party chapters (0, 0, 1/3). Evaluation of voting power of regional party chapters in ideologically coordinated voting is provided in Table 2. Entries in last row provide total voting power of each party in the parliament, entries in the last column total voting power of each region in the parliament in the case of ideologically coordinated voting, and entries in the main body of the table provide voting power of each regional party chapter. Regions A B C Total parties (voting power) L M 0 1/9 3/9 1/9 0 1/9 3/9 3/9 R 0 0 3/9 3/9 Total 1/9 4/9 4/9 1 Table 2 Decomposition of power in ideologically coordinated voting 2 European Parliament elected in 2009 has 8 party groups, and decomposition might consist of 216 national party chapters; it is difficult to handle such a structure on limited space of conference proceedings. The results of empirical analysis for the European Parliament elected in 2009 will be provided during the presentation. Results for European Parliament elected in 2004 see in Turnovec [7]. - 935 - 30th International Conference Mathematical Methods in Economics Now let us calculate influence of regional party chapters in regionally coordinated voting, when all regional party chapters from the same region are voting together. Region A: committee [11; 7, 10, 3]. Voting power of regional party chapters L, M, R in region A: (1/6, 4/6, 1/6). Total power of region A in the parliament regionally coordinated voting 1/6 is decomposed among the regional party chapters: (1/36, 4/36, 1/36) Region B: committee [16; 15, 15, 0]. Voting power of regional party chapters L, M, R in region B: (1/2, 1/2, 0). Total power of region B in the parliament regionally coordinated voting 1/6 is decomposed among the regional party chapters: (3/36, 3/36, 0). Region C: committee [26; 3, 22, 25]. Voting power of regional party chapters in region C: (1/6, 2/60, 3/6). Voting power of region C in the parliament regionally coordinated voting 4/6 is decomposed among the regional party chapters: (4/36, 8/36, 12/36) Evaluation of voting power of regional party chapters in regionally coordinated voting is provided in Table 3. Entries in last column provide total voting power of each region in the parliament in the case of regionally coordinated voting, entries in the last row total voting power of each party in the parliament in the case of regionally coordinated voting, and entries in the main body of the table provide voting power of each regional party chapter. regions L 1/36 3/36 4/36 8/36 A B C total parties (voting power) M 4/36 3/36 8/36 15/36 R 1/36 0 12/36 13/36 Total 6/36 6/36 24/36 1 Table 3 Decomposition of power in regionally coordinated voting Let us assume that (based on empirical evidence) in average 3/4 of voting acts are ideologically coordinated and 1/4 of voting acts are regionally coordinated. Then, from the following matrix equation 0 3 12 4 36 0 4 36 4 36 4 36 1 0 36 1 3 0 + 4 36 12 4 36 36 4 36 3 36 8 36 1 1 16 1 36 144 144 144 39 15 0 = 0 144 144 20 48 12 4 36 144 144 144 we obtain the mathematical expectation of voting power of regional party chapters, super-regional parties and regional representations under assumption that ideologically coordinated voting takes place with probability ¾ and regionally coordinated voting with probability 1/4 (see Table 4).3 Regions A B C Total parties (voting power) L M 1/144 16/144 39/144 15/144 4/144 20/144 44/144 51/144 R 1/144 0 48/144 49/144 Total 18/144 54/144 72/144 1 Table 4 Mathematical expectation of voting power 3 As was mentioned above, for the European Parliament these probabilities are estimated as 0.8 for ideologically coordinated voting and 0.2 for regionally coordinated voting, see Hix, Noury and Roland [1]. - 936 - 30th International Conference Mathematical Methods in Economics 5 Concluding remarks We tried to show that it is possible to evaluate not only the influence of European political parties as entities in ideologically driven voting and of national representations as entities in nationally driven voting, as it is usually done in analytical papers (Holler and Kellermann [2], Hosli [3], Nurmi [5]) but also the influence of national chapters of European political parties both in ideological and national voting and national influence in ideological voting, as well as the European political parties influence in national voting. It was demonstrated that different dimensions of voting (ideological, national) lead to different levels of influence of the same national party group, European political party and national representation. The findings of our model analysis open the problem of strategic considerations, such as coalition formation, that can go across the existing structure, e.g. coalition of a country representation with some European political party, or preferring national coordination of different party groups of the same country to ideological coordination (this problem was opened with respect to Poland in Mercik, Turnovec, and Mazurkiewicz [4]). There is a broad area for extensions of presented model. Acknowledgements This research was supported by the Grant Agency of the Czech Republic, project No. 402/09/1066 “Political economy of voting behavior, rational voters’ theory and models of strategic voting”.. References [1] Hix, S., Noury, A. G., and Roland, G.: Democratic Politics in the European Parliament. Cambridge University Press, Cambridge, 2006. [2] Holler, M., and Kellermann, J.: Power in the European Parliament: What Will Change? Quantity and Quality, 11 (1977), 189-192. [3] Hosli, M..O.: Voting strength in the European Parliament: the influence of national and of partisan actors. European Journal of Political Research 31 (1977), 351-366. [4] Mercik, J. W., Turnovec, F., and Mazurkiewicz, M.: Does voting over national dimension provide more national influence in the European Parliament than voting over ideological dimension. In: Integration, Trade, Innovation and Finance: From Continental to Local Perspectives, (Owsinski, J. W., ed.), Polish Operational and Systems Research Society, Warszawa, 2004, 173-186. [5] Nurmi, H.: The representation of voters’ groups in the European Parliament, a Penrose-Banzhaf index analysis. Electoral Studies, 16 (1977), 317-327. [6] Shapley, L. S., and Shubik, M. A Method for evaluation the distribution of power in a committee system. American Political Science Review 48 (1954), 787-792. [7] Turnovec, F.: Duality of power in the European Parliament. IES Working Paper Series, 6/2008. - 937 -
