APPLICATION OF MATHEMATICS AND STATISTICS IN ECONOMICS

2017

BOOK OF ABSTRACTS

SZKLARSKA PORĘBA, 30 AUGUST - 3 SEPTEMBER 2017

str_1.indd 1 2017-08-02 12:03:12

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SCIENTIFIC COMMITTEE

• Prof. dr hab. Walenty Ostasiewicz (Wrocław University of Economics, Po-land, chairman)

• Prof. dr hab. Joanna Dębicka (Wrocław University of Economics, Poland)• Prof. Ing. Richard Hindls, CSc., dr. h. c. (University of Economics in Pra-

gue, the Czech Republic)• Prof. Ing. Stanislava Hronová, CSc., dr. h. c. (University of Economics in

Prague, the Czech Republic)• Prof. RNDr. Rudolf Zimka, CSc. (Matej Bel University in Banská Bystrica,

Slovakia)• Doc. Ing. Emília Zimková, PhD. (Matej Bel University in Banská Bystrica,

Slovakia)• Mgr. Ing. Martin Boďa, PhD. (Matej Bel University in Banská Bystrica,

Slovakia)• Ing. Kristýna Vltavská, Ph.D. (University of Economics in Prague, the

Czech Republic)• Dr Beata Zmyślona (Wrocław University of Economics, Poland)

ORGANIZING COMMITTEE

• Dr Beata Zmyślona (chairman)• Dr hab. Edyta Mazurek (accommodation and budget manager)• Dr Albert Gardoń (secretary, technical proceedings editor)• Dr Cyprian Kozyra (webmaster)

SECTION OF THE CONFERENCE:

Papers are thematically related to applications of mathematics and statistics in economics and should fall in one of the following sections:• Macroeconomics, Public Economics and Methodological Issues of Econo-

mics• Social Economics, Economic Sustainability and Demographic Economics• Financial Markets, Risk Measurement and Insurance• Microeconomic Issues• Multidimensional Statistics in Economics

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LIST OF PARTICIPANTS

Milan BaštaMarek BiernackiDiana BílkováMartin BoďaJana CibulkováAdam ČablaMatej ČamajMagdalena DaszkiewiczJoanna DębickaMarek ĎuricaTomáš FialaJakub FischerSamue FlimmelJan FojtíkAlbert GardońKateřina GawthorpeStanisław HeilpernRichard HindlsRichard HorskýStanislava HronováSamuel HudecMiroslav HužvárMichaela JirkováMiloš KaňkaAlena KaščákováIgor KollárRadoslav KovářCyprian KozyraIvan KralikJana KramulováĽuboslava Kubišová

Katarína KyseľováPeter LacoJitka LanghamrováIvana MaláAgnieszka MarciniukLuboš MarekIwona MarkowiczPetr MazouchEdyta MazurekPetr MusilKatarzyna OstasiewiczWalenty OstasiewiczLucie PlzákováJiří ProcházkaAgnieszka Przybylska-MazurHana ŘezankováAnna Sączewska-PiotrowskaJaroslav SixtaVáclav SládekKarel ŠafrMartina ŠimkováOndřej ŠimpachJana ŠpirkováZdeněk ŠulcKristýna VltavskáProkop ZávodskýJan ZemanRudolf ZimkaEmília ZimkováPavel ZimmermannBeata Zmyślona

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WELCOMEby the Organizing Committee

It is a great pleasure for all of us from Wroclaw University of Economics to welcome all participants to the 20th AMSE Conference in Szklarska Poręba.

The beginning of the conference dates back to 1998. The 1rst conference was organized by Matej Bel University in Liptovský Trnovec in 3rd – 4th September, 1998. During the conference 23 papers were presented by scientists from many centres but mainly by the staff of Matej Bel University in Banská Bystrica in Slovakia and University of Economics in Prague in the Czech Republic. In 1999 a team from Wroclaw University of Economics joined the circle of participants and organizers. Since 2001, the conference has been organized periodically by the three centres mentioned.

The Matej Bel University has organized the following editions:3rd – 4th September 1998, Liptovský Trnovec2nd – 3rd September 1999, Liptovský Trnovec31st August – 1st September 2000, Poprad4th – 5th September 2003, Banská Bystrica29th August – 1st September 2007, Poprad25th – 29th August, 2010, Demänovská Dolina28th August – 1st September 2013, Gerlachov31st August – 4th September 2016, Banská Štiavnica

University of Economics in Prague has hosted the following conferences:13th – 14th September 2001, Zadov3rd – 4th September, 2004, České Budějovice31st August – 1st September 2006, Trutnov27th – 28th August 2009, Uherské Hradiště30th – 31st August 2012, Liberec 2nd – 6th September 2015, Jindřichův Hradec

Wrocław University of Economics has held the following meetings:4th – 7th September 2002, Kudowa Zdrój1st – 2nd September 2005, Wrocław27th – 29th August 2008, Wisła31st August – 3rd September 2011, Lądek Zdrój27th – 31st August 2014, Jerzmanowice

Since 2014, papers presented on AMSE have been included in the Conference Proceedings Citation Index of the Web of Science database.

In 2017, AMSE conference is taking place in Szklarska Poręba for the twentieth time. We hope that this Conference will be as fruitful and interesting as all the nineteen previous enjoyable meetings of friends from the three countries.

We wish you a nice stay in Szklarska Poręba.

Beata Zmyślona

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CONFERENCE PROGRAM

WEDNESDAY – 30.08.201717:00-18:30 Registration 18:30 Supper

THURSDAY – 31.08.20178:00-9:00 Breakfast9:00-9:20 CONFERENCE OPENING (ROOM A)

SESSION 1

ROOM A MACROECONOMIC ISSUESCHAIRMAN: RICHARD HINDLS

9:30-9:50 K. Kyseľová, R. Zimka

On Bautin Bifurcation in a Monetary Dynamic Model

9:50-10:10 L. Plzáková Evaluation of Public Finance in the Tourism Sector at the Municipal Budget Level

10:10-10:30 L. Marek, M. Vrabec, P. Berka

Are Wages in the Czech Republic and Poland equal?

10:30-10:50 M. Demetrian, R. Zimka, E. Zimková

On Liu´s Criterion in Asada’s Model of Monetary and Fiscal Policy

10:50- 11:10 A. Przybylska-Mazur Brake Public Debt Rule as An Instrument to Stabilize the Debt - Results for Poland

ROOM B FINANCIAL AND INSURANCE MARKET CHAIRMAN: STANISLAVA HRONOVÁ

9:30-9:50 M. Boďa,M. Kanderová

Selecting a Small Portfolio of Equities: One-stop Shopping Approach to Screening

9:50-10:10 B. Bieszk-Stolorz, I. Markowicz

The Assessment of the Situation of Listed Companies in Macrosectors in a Bear Market – Duration Analysis Models

10:10-10:30 S. Hudec Modelling the Force of Mortality Using Local Polynomial Method in R

10:30-10:50 J. Špirková, P. Laco, P. Kráľ, J. Štrangfeldová

Determination of the Optimal Premium for the Economically Active and Inactive Population in Health Insurance in Slovakia

11:10-11:40 Coffee break

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THURSDAY – 31.08.2017

SESSION 2

ROOM A TIME SERIES ANALYSIS METHODS CHAIRMAN: RUDOLF ZIMKA

11:40-12:00 M. Kaňka Segmented Regression Based on the Principle of Cut-off Polynomials with Solved Economic Example

12:00-12:20 S. Flimmel, M. Čamaj, I. Malá, J. Procházka

Comparison of Robust Methods for ARMA Order Estimation

12:20-12:40 J. Procházka, S.Flimmel, M. Čamaj, M. Bašta

Modelling the Number of Road Accidents

12:40-13:00 R. Horský Non-stationary Stochastic Sequences as Solutions to Ill-posed Problems

13:00-13:20 A. Gardoń Relative Jump Size Distribution for the Net Freight Process in Container Shipping

ROOM B INSURANCE MARKET CHAIRMAN: EMÍLIA ZIMKOVÁ

11:40-12:00 J. Špirková, I. Kollár, G. Szűcs, M.Spišiaková

Valuation of Second Pillar Pension Products in Slovakia

12:00-12:20 A. Marciniuk Marriage Reverse Annuity Contract and Reverse Mortgage – Application of a Generalized Model of Reversionary Annuity

12:20-12:40 M.Gerthofer, V. Sládek, P. Zimmermann

Estimation of Incurred but not yet Reported Claims Based on Poisson Distributed Reporting Delay

12:40-13:00 J. Dębicka, S. Heilpern

Investor’s Expected Profit from Viatical Settlements

13:00-13:20 J.Fojtík, J. Procházka, P. Zimmermann

Alternative Approach for Fast Estimation of Life Insurance Liabilities

13:30-14:30 Lunch

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SESSION 3ROOM A DEMOGRAPHY AND LABOUR MARKET ISSUES

CHAIRMAN: JAKUB FISCHER15:00-15:20 T. Fiala,

J.LanghamrováPension Age which Would Guarantee Stabilization of the Old Age Dependency Ratio

15:20-15:40 O. Šimpach Normality and Principal Component Approach Towards Fertility Time Series in Poland and Czechia

15:40-16:00 A. Kaščáková, V. Mendelová, G.Nedelová

Weighting Methods in Construction of Active Ageing Indicator

16:00-16:20 M. Šimková, L. Marek

Age Structure of Labour Force and Its Impact on Wages and Product

16:20-16:40 A. Čabla Right Tail of the Unemployment Duration in the Czech Republic

ROOM B SOCIAL ECONOMICS ISSUES CHAIRMAN: KRISTÝNA VLTAVSKÁ

15:00-15:20 H. Řezanková, Z. Křečková

Selected Gender Gap Indicators – Comparison of EU Countries

15:20-15:40 E. Mazurek, M. Daszkiewicz

The Perception of Wroclaw as a Liveable City

15:40-16:00 M. Biernacki Comparison of Selected National Healthcare Systems’ Efficiency

16:00-16:20 B. Zmyślona Cost-Sharing Model for Medical Services Incurred by the Public Payer. Estimation of Treatment Cost

16:20-16:40 C. Kozyra Implicit Equivalence Scales Deducted from the Personal Income Tax System in Poland, Slovakia and Czechia

16:40-17:10 Coffee breakROOM A SPECIAL SESSION

CHAIRMAN: WALENTY OSTASIEWICZ17:15-17:45 THE 20th AMSE CONFERENCE19:30 Banquet

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FRIDAY – 01.09.2017

8:00-9:00 Breakfast SESSION 4

ROOM A REGIONAL ANALYSIS CHAIRMAN: STANISŁAW HEILPERN

9:00-9:20 D. Bílková Clusters of the Czech Regions and 31 Chosen European Countries According to the Wage Level, Wage Models and Gender Gap by the Czech Regions

9:20-9:40 K. Gawthorpe, K. Šafr

Regional & Multi-Sector Input-Output Model for the Czech Republic

9:40-10:00 K. Šafr, J. Sixta Estimates of Regional Economic Structures

10:00-10:20 K. Gawthorpe Potential of Local Currencies in the Czech Republic: DSGE model

10:20-10:40 P. Musil, J. Kramulová, J. Zeman, V. Vrabec

Possible Extension of Regional Statistics – Households’ Wealth – Methods and Preliminary Results

ROOM B EDUCATION ISSUES AND SOCIAL WELFARE CHAIRMAN: BEATA ZMYŚLONA

9:00-9:20 M. Jirková, P. Musil Analysis of Economies of Scale in Czech Households Based on Different Approaches

9:20-9:40 M.Grausová, M. Hužvár, Z. Rigová

Efficiency Assessment of Slovakian Universities

9:40-10:00 L. Švábová, M. Ďurica Application of Logistic Regression in Counterfactual Impact Evaluation of Graduate Practice Measure in Slovakia

10:00-10:20 A. Sączewska- -Piotrowska, D. Piotrowski

Lifestyle Characteristics of Poor and Rich People in Poland

10:20-10:40 I. Malá The Use of L-Moments in Modelling of Deprivation of the Population Aged over 50 in the Czech Republic

10:40-11:10 Coffee break

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SESSION 5

ROOM A APPLICATION OF STATISTICAL METHODS IN ECONOMICS CHAIRMAN: MARTIN BOĎA

11:10-11:30 Z. Sulc, J. Cibulková, J. Procházka, M. Matějka

Comparison of Economic and Non-economic Datasets with Categorical Variables in Hierarchical Clustering

11:30-11:50 K. Ostasiewicz Comparing Some Properties of „Leftist” and „Rightist” Measures of Inequality

11:50-12:10 P. Laco, M. Kallová Factors Influencing Corporate Websites’ Value

SESSION 6

ROOM A HISTORY OF STATISTICS CHAIRMAN: JOANNA DĘBICKA

12:10-12:30 P. Závodský, O. Šimpach

Karl Czoernig and the State Statistics of the Habsburg Monarchy

12:30-12:50 W. Ostasiewicz Remarks on the History of Statistics

12:50-13:10 CONFERENCE CLOSING

13:30-14:30 Lunch

15:00 Trip to Szklarka River Waterfall

19:00 Supper – barbecue

SATURDAY – 02.09.2017

8:00-9:00 Breakfest

9:15 Trip

19:00 Supper

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Marek BiernackiWrocław University of Economics, Faculty of Management and Computer Science,

Department of Mathematics and Cybernetics, Wrocław, Poland email: marek.biernacki@ue.wroc.pl

COMPARISON OF SELECTED NATIONAL HEALTHCARE SYSTEMS’ EFFICIENCY

The efficiency of selected national healthcare systems in the European Union was analyzed with Eurostat 2004 and 2013 data, in particular considering countries which made a transition after 1990. The analysis of efficiency was performed using DEA – a nonparametric method implemented in MaxDEA 6.3.mdb software. Estonia, Hungary and Slovakia improved their efficiency of medical treatment, Poland and the Czech Republic deteriorated, while effectiveness of medical treatment measured by HLY improved in the Czech Republic and deteriorated in Poland in the period under study. Among the transition economies after 1990, Poland’s healthcare system was most efficient as a result of healthy population and relatively low financial inputs to healthcare. It is worth emphasizing that when life expectancy is below the trend line, then people in those countries live longer, whereas if infant mortality is also below the trend line, it shows that obstetrical care in those countries is excellent.

Keywords: health care system, efficiency, DEA

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Beata Bieszk-Stolorz, Iwona MarkowiczUniversity of Szczecin, Faculty of Economics and Management,

Department of Econometrics and Statistics, Mickiewicza Street 64, 71-101 Szczecin, Poland

emails: beatus@wneiz.pl, iwona.markowicz@wneiz.pl

THE ASSESSMENT OF THE SITUATION OF LISTED COMPANIES IN MACROSECTORS

IN A BEAR MARKET – DURATION ANALYSIS MODELS

The aim of the article is the use methods of duration analysis to assess the fluctuations in the prices of shares of companies listed on the Stock Exchange in Warsaw during the bear market in 2011 and over the next two years. The specific objectives of this study are as follows: the assessment of risk and intensity of the drop in stock prices in individual macrosectors in 2011, the assessment of the odds and intensity of recovery by the end of 2013, the similarity analysis of the duration function for stock market macrosectors in the times of bear market and of recovery, comparison of the situation in the stock market macrosectors in the observed period of the bear market and during the financial crisis of 2008--2009. The analysis is conducted by means of the logit model, Kaplan-Meier estimator, Cox regression model. The hypotheses have been set that the 2011 downturn strongly affected the financials macrosector, the price fluctuations in the macrosectors during the analysed bear market and crisis were similar. The study is based on the data of 378 companies (listed in the whole period under analysis) that are grouped in 3 macrosectors: industry, finance, services.

Keywords: Warsaw Stock Exchange, listed companies’ shares, bears market, macrosectors, duration analysis

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Diana BílkováUniversity of Economics, Prague, Faculty of Informatics and Statistics

W. Churchill Sq. 1938/4, 130 67 Prague 3, Czech Republic email: bilkova@vse.cz

CLUSTERS OF THE CZECH REGIONS AND 31 CHOSEN EUROPEAN COUNTRIES

ACCORDING TO THE WAGE LEVEL, WAGE MODELS AND GENDER WAGE GAP

BY THE CZECH REGIONS

The main aim of this paper is the creation of the clusters of the Czech regions that are close as possible by the wage level in these regions and clusters of 31 chosen European countries according to the same criterion. The Czech regions were clustered into three or five clusters, while the European countries were clustered into three, five or seven clusters. The number of clusters has been selected based on the number of clustered objects and due to the clarity of the results obtained. Using the methods of cluster analysis, the clusters with similar wage level were created. Methods of the furthest neighbour and Euclidean distance metric were used. For the Czech regions, the model wage distribution was constructed to enable the comparison of wage development during recent seven years. Three-parametric lognormal curves present the basis of the theoretical wage distribution. The special attention was paid to the situation of wage level within European countries and its comparison with the wage level in the Czech Republic. The researched variable is the gross monthly (nominal) wage. Database comes from the official website of the Czech Statistical Office.

Keywords: clusters of the Czech regions by wage level, clusters of 31 chosen European countries by wage level, wage models in the Czech regions, gender wage gap by the Czech regions, prediction of gender wage gap by the Czech regions

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Martin Boďa, Mária KanderováMatej Bel University in Banská Bystrica, Faculty of Economics, Department of Quantitative Methods and Information Systems,

Tajovského 10, 975 90 Banská Bystrica, Slovakia emails: martin.boda@umb.sk, maria.kanderova@umb.sk

SELECTING A SMALL PORTFOLIO OF EQUITIES: ONE-STOP SHOPPING

APPROACH TO SCREENING

Investing into equities requires that a pre-selection of candidate equities be made, which is frequently accomplished by means of a screening criterion such as market capitalization, a fundamental indicator of past performance. The paper considers four screening criteria – market capitalization, two multiples (the P/B and P/E ratios) and historical yield – and investigates how the pre-selection choice based on any of these criteria and orientation towards small/low or big/high poles of equity styles affects the performance of a small portfolio comprising 50 equities at most. The goal of the investigation undertaken in the paper is to assess usefulness of these distant poles of equity styles and evaluate their performance against trending patterns of the market. The method is experimental and in order to assure robustness of results it employs 5 consecutive four-year datasets from 2009 to 2016 and three conceptually different methods of portfolio selection, setting the S&P 500 Index as benchmark. The results indicate that superiority of equity styles and selection methods is contingent on market cycle: in bull markets with steady growth, equity styles with small/low polarity seem more dependable, but when market price patterns change between bull and bear markets, big/high poles seem guarantee better performance.

Keywords: equity style, asset pre-selection, market capitalization, multiple, historical yield, performance.

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Adam ČablaUniversity of Economics in Prague, Faculty of Informatics and Statistics,

Department of Statistics and Probability, W. Churchill Square 1938/4, Prague 3, Czech Republic

email: adam.cabla@vse.cz

RIGHT TAIL OF THE UNEMPLOYMENT DURATION IN THE CZECH REPUBLIC

The aim of the paper is to compare three different approaches to modelling the distribution with supposed heavy tail using data about unemployment duration in the Czech republic – two models of spliced distributions and model with dynamic weights. All three aproaches are based on the Pickands-Balkema-de Haan theorem and incorporate the parametric distribution of the body of the probability distribution and generalized Pareto distribution used for the modelling of the right tail. The data come from the Labour Force Survey from three distinct periods – before the last economic crisis, during it and during the recovery from the crisis. The paper shows the differences between the right tails of the three periods and discussion of the used methods.

Keywords: unemployment duration, Labour Force Survey, right tail, Extreme Value Theory, spliced models, Dynamic Weight Mixture Model

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Magdalena DaszkiewiczWroclaw University of Economics, Faculty of Economic Science

Department of Marketing Research, Komandorska Street 118/120, 53-345 Wroclaw, Poland

email: magdalena.daszkiewicz@ue.wroc.pl

Edyta MazurekWroclaw University of Economics, Faculty of Management,

Computer Science and Finance, Department of Statistics, Komandorska Street 118/120, 53-345 Wroclaw, Poland

email: edyta.mazurek@ue.wroc.pl

THE PERCEPTION OF WROCLAW AS A LIVEABLE CITY

Contemporary cities face the increasing global competition and the necessity to take actions for retaining and attracting residents, tourists, business and investments and highly qualified human capital. Retaining and attracting talented young people may be at the heart of growing a high prosperity of cities. As we know young people are the most likely demographic group to move. The primary challenge for cities is to create places that young talents not only visit, but also treat as attractive places to study, work and live. Therefore, it is important to conduct studies to identify factors affecting city liveability perception and people’s decisions regarding the choice of a city as a place to live, study and work.

The main aim of the paper is to determine the perception of Wroclaw’s attractiveness as a city to live and identify the impact of selected factors affecting city liveability perception. The logit model is used for the assessment of the effects of explanatory factors on the chance that Wroclaw is perceived as a good place to live. The analysis is made basing on real data from the survey on the attractiveness of Wroclaw through the eyes of international students. We focused on evaluating the overall perception of the liveability of the city, in relation to perception of Wroclaw’s liveability for different groups of residents. We also tested if perception of Wroclaw as a liveable city depends significantly on the national wealth of home country of international students. We discuss the findings and provide some managerial implications regarding city development and implications for future research.

Keywords: city attractiveness, city liveability, perceived liveability, logit model, categorical data

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Michal DemetrianComenius University, Faculty of Mathematics, Physics and Informatics,

Mlynská dolina F1, Bratislava, Slovakia email: michal.demetrian@ fmph.uniba.sk

Rudolf ZimkaMatej Bel University in Banská Bystrica, Faculty of Economics, Department of Quantitative Methods and Information Systems,

Tajovského 10, Banská Bystrica, Slovakia email: rudolf.zimka@umb.sk

Emília ZimkováMatej Bel University in Banská Bystrica, Faculty of Economics,

Department of Finance and Accounting, Tajovského 10, Banská Bystrica, Slovakia

email: emilia.zimkova@umb.sk

ON LIU´S CRITERION IN ASADA´S MODEL OF MONETARY AND FISCAL POLICY

It is known that a simple Hopf bifurcation in a dynamic model can arise if the Jacobian matrix of the model has a pair of purely imaginary eigenvalues and others have negative real parts. Liu´s criterion gives conditions under which the eigenvalues have required properties. In this paper, a six-dimensional dynamic model of Asada (2014), describing the development of the firms´ private debt, the output, the expected rate of inflation, the rate of interest, the government expenditures, and the government bond is introduced. There are found conditions on the parameters of the model under which Liu´s criterion is satisfied. A numerical example illustrates the reached result.

Keywords: macroeconomic dynamic model, equilibrium, Jacobian matrix, Liu´s conditions

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Joanna Dębicka, Stanisław HeilpernWroclaw University of Economics, Faculty of Management, Information Systems and Finance, Department of Statistics,

ul. Komandorska 118/120, 53-345 Wrocław, Poland emails: joanna.debicka@ue.wroc.pl, stanislaw.heilpern@ue.wroc.pl

INVESTOR’S EXPECTED PROFIT FROM VIATICAL SETTLEMENTS

For an insured person who needs money because of suffering from a terminal illness that requires costly diagnosis and treatment, the easiest way of receiving money from life insurance is to withdraw from the contract of insurance. Then the insurer is obliged to pay the surrender value of policy. It appears that there is another possibility for the insured to receive prior financial gratification from life insurance. The insured can sell his policy on the secondary market of life insurance (the viatical market). In such a situation he obtains an amount that is greater than the surrender value (and less than the death benefit). Then the viatical company takes a fee for the insurance premiums, and in case of death of the insured gets the death benefits. Such agreements to resell the rights to death benefits are offered to people who have become terminally ill (viatical settlement). The aim of the paper is to study the influence of the moment of falling ill (compared to the age and sex of the insured and duration of insurance) on the expected profit of the viatical company. For this purpose, we apply the methodology used by insurance companies in the valuation of the contract.

Keywords: viatical market, life insurance, multistate model

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Tomáš Fiala, Jitka LanghamrováUniversity of Economics, Prague, Faculty of Informatics and Statistics

nám. W. Churchilla 4, 130 67 Praha 3, Czech Republic emails: fiala@vse.cz, langhamj@vse.cz

PENSION AGE WHICH WOULD GUARANTEE STABILIZATION OF THE OLD AGE

DEPENDENCY RATIO

According to the current legislation the statutory retirement age in the Czech Republic should permanently increase with constant increment 2 months for each subsequent generation. This fact is very often criticized by both politicians and experts. A proposal of halting the rise in retirement age in 2030 at the threshold 65 years is discussed in the Parliament this year.

The main reason for increasing the retirement age in the Czech Republic since 1995 was to eliminate the consequences of population ageing for increasing financial burden of the pension system. Because of this permanent increase the proportion of population size in retirement age and population size in productive age (old age dependency ratio) would be not so rapidly growing after 2040 when numerous generations born in the 70th will retire.

The paper presents computations of the old-age dependency ratio in the Czech Republic for various variants of development of fertility, mortality, migration and retirement age in the case of the Czech Republic and for each variant also the retirement age threshold (changing in time) which would guarantee stabilization of the old-age dependency at its present time value.

Keywords: old-age-dependency ratio, retirement age, population projection, the Czech Re-public

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Samuel Flimmel, Matej Čamaj, Ivana Malá, Jiří ProcházkaUniversity of Economics, Prague, Faculty of Informatics and Statistics,

Department of Statistics and Probability, W. Churchill Sq. 1938/4, Prague, Czech Republic emails: samuel.flimmel@vse.cz, matej.camaj@vse.cz, malai@vse.cz, xproj16@vse.cz

COMPARISON OF ROBUST METHODS FOR ARMA ORDER ESTIMATION

In financial markets, we are facing big data problems. Loads of information are stored almost every second, but usually standard methods have problems to process them all. With growing number of observations, the probability of outlier presence also rises. That is the reason of increase in importance to work with sufficiently robust methods. As it is known, standard methods are not able to work correctly with outliers and consequently standard estimates are usually biased. ARMA processes are frequently used in financial mathematics and one of the important steps is to estimate the order of a given process. Usually it is the second step in Box-Jenkins method after solving stationarity and seasonality. In this paper we present robust methods for ARMA order estimating and we compare them using a simulation study. For the simulation study we are using the R statistical software.

Keywords: robust methods, ARMA process, ARMA order estimation

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Jan Fojtík, Jiří Procházka, Pavel Zimmermann, Simona Mackova, Markéta Švehláková

University of Economics, Prague, Faculty of informatics and statistics, Department of statistics and probability calculus,

W. Churchill Sq. 4, Prague 3, Czech Republic emails: xfojj00@vse.cz, xproj16@vse.cz, zimmerp@vse.cz, xsvem35@vse.cz,

simona.mackova@vse.cz

ALTERNATIVE APPROACH FOR FAST ESTIMATION

OF LIFE INSURANCE LIABILITIES

Estimation of future liabilities is one of the essential actuarial tasks. With the huge client portfolios nowadays, not only the accuracy of liability estimates is of great importance but also the time within which the results are calculated. Especially in the case of estimates of life insurance liability, the computing time can be very high, because the estimation is based on a projection of future cash flow of each contract separately. Therefore, methods to reduce computation time while as do not significantly decrease accuracy are welcomed by many actuaries. Cluster analysis can be applied for this purpose. Basic idea is to split contracts into clusters and represent all contracts within the cluster by a specific contract, so called model point. Projection is only calculated for these model points and weights are assigned to reflect the number of contracts of the cluster. The main contribution of this paper consists in the analysis of clustering variables in the case of approximate life insurance liability model.

Keywords: Life insurance, estimation of BEL, cluster analysis

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Albert GardońWrocław University of Economics, Institute of Applied Mathematics, Chair of Statistics,

Komandorska 118/120, PL-53-345 Wrocław, Poland email: Albert.Gardon@ue.wroc.pl

RELATIVE JUMP SIZE DISTRIBUTION FOR THE NET FREIGHT PROCESS

IN CONTAINER SHIPPING

As it was checked out in our previous investigations a weekly average net freight in container shipping may be modeled by means of the jump-diffusive process with homogeneous Poissonian jumps. So far, the relative jump size was generated from the empirical distribution which is asymmetrical and does not seem to be one of typical distributions. Generally, upward jumps appear more often, whereas relative drops are more concentrated around their mean.

In this paper we try to fit to the jump data a mixture of two distributions, taking into account negative and positive jumps separately. We use the jump-diffusive model to the evaluation of the net premium of the European Call options for the net freight. The knowledge of the theoretical jump-size distribution may lead to the analytical formula for the option premium which will make the calculations faster and more exact.

Keywords: liner shipping, net freight call options, jump-diffusion, relative jump-size distri-bution

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Kateřina GawthorpeUniversity of Economics Prague, Faculty of Business Administration,

Department of Microeconomics, W. Churchill 4 Sq., Prague 3, Czech Republic email: xzimk04@gmail.com

POTENTIAL OF LOCAL CURRENCIES IN THE CZECH REPUBLIC: DSGE MODEL

The Czech Republic is an economy with one of the most municipalities per squared kilometer in Europe. The localization factor of individual municipalities causes their different reaction to exogenous shocks. The subsequent varying transmission of shocks into prices questions the convenience of the dominant position of the Czech currency for all regions. Instead, community currencies respect regional heterogeneity as well as endorse social values national currency is weak of targeting. Individuals, companies but also municipalities in other countries seem to realize these benefits of community currencies. Over four-thousands of community currencies operate worldwide. Spain belongs among one of the most recent member of such local-currency movement. High unemployment rate in Spain has motivated local activists to launch several time-banking schemes. These schemes multiplied into more than four hundred. Greece copied such effort to provide unemployed and impoverished individuals with additional means of exchange along with independence on scarce euro currency. Local currencies could help Czech Republic to respect regional discrepancies and allow local communities to be more flexible to transmission shocks and varying economic conditions. This study analyzes the benefits of such potential scenario with local currencies in the Czech Economy. The applied method represents an enhancement of the DSGE model as designed by the Ministry of Finance in the Czech Republic for local-currency variables. All set of monetary policy and fiscal policy shocks along with a shock into the local currency will allow to determine the potential importance of community currencies for the Czech Economy.

Keywords: Local currencies, Alternative currencies, DSGE model, Czech Republic

26

Kateřina GawthorpeUniversity of Economics Prague, Faculty of Business Administration,

Department of Microeconomics, W. Churchill 4 Sq., Prague 3, Czech Republic email: xzimk04@gmail.com

Karel ŠafrUniversity of Economics Prague, Faculty of Informatics and Statistics,

Department of Economic Statistics, W. Churchill 4 Sq., Prague 3, Czech Republic email: karelsafr@gmail.com

REGIONAL & MULTI-SECTOR INPUT-OUTPUT MODEL FOR THE CZECH REPUBLIC

Central authorities as well as many other institutions around the world base their economic predictions on simulations of Dynamic Stochastic General Equilibrium models. The Czech central institutions utilize so-called New Keynesian type of DSGE model. Variant of the Czech Ministry of Finance model Hubert will serve as a benchmark model in this study. As well as the original model, the composition of the model will incorporate New Keynesian characteristics such as price or wage stickiness. Furthermore, the model is extended for features which allow a detailed disaggregation of the initial model into eight regions and eight sectors. The generous dataset from the Czech Statistical Office offers aggregate data as well as regional input-output tables. These data allow precise estimation of individual parameters. The applied method can be of use to other analysts or central authorities questioning the varying impact of policies on regional but also sectoral-level.

Keywords: DSGE, regional model, multi-sector model, input-output.

27

Michal Gerthofer, Václav Sládek, Pavel ZimmermannUniversity of Economics Prague, Faculty of Informatics and Statistics,

Department of Statistics and Probability, Winston Churchill Sq. 4, Prague 3, Czech Republic

emails: germ00@vse.cz; xslav20@vse.cz; zimmerp@vse.cz

ESTIMATION OF INCURRED BUT NOT YET REPORTED CLAIMS BASED ON POISSON

DISTRIBUTED REPORTING DELAY

A claim frequency model, which estimates number of claims that incurred but are not reported (IBNR), is a key component of an insurer’s future liability prediction. Several possible modelling approaches were developed in the past. Chain ladder method is a particularly popular distribution free method, which models development of the cumulative liability through weighted averages of the past development factors. The assumption of this model is that developments of the cumulative claims for each occurrence year are independent. If a trend is identified in occurrence years, predictions are biased. A modification of this method can be applied to relax this assumption. For example, development factors, can be extrapolated to the future by a trend function. Other approaches may be based e.g. on variety of regression specifications. In this contribution, a new approach is presented, which is based on the assumption that number of discrete years until the claim is registered has Poisson distribution. The mean of this distribution is estimated by maximum likelihood method, taking in to account that observations are truncated. An empirical study is presented and our approach is compared with the traditional Chain ladder method as well as the above-mentioned modification.

Keywords: frequency model, Chain ladder, modified Chain ladder, Poisson distribution

28

Mária Grausová, Miroslav Hužvár, Zuzana RigováMatej Bel University, Banská Bystrica, Faculty of Economics, Department of Quantitative Methods and Information Systems,

Tajovského 10, 975 90 Banská Bystrica, Slovakia emails: maria.grausova@umb.sk, miroslav.huzvar@umb.sk, zuzana.rigova@umb.sk

EFFICIENCY ASSESSMENT OF SLOVAKIAN UNIVERSITIES

The paper studies the performance of public higher education institutions in Slovakia. Data envelopment analysis is applied to assess the efficiency of selected universities in their two core mission areas: providing education and doing research and development. We focus on how the size and the structure of the academic staff and the capital resources influence the educational and research outputs. Data from public sources for years 2014–2015 is used in the analysis. Efficiency scores and projections calculated by designed DEA models serve to benchmark assessed universities and provide recommendations for improvement of their performance.

Keywords: data envelopment analysis, efficiency, public higher education institutions

29

Richard HorskýUniversity of Economics in Prague, Faculty of Statistics and Informatics,

Department of Mathematics Ekonomická 957, 148 00 Praha 4, Czech Republic

email: rhorsky@vse.c

NON-STATIONARY STOCHASTIC SEQUENCES AS SOLUTIONS TO ILL-POSED PROBLEMS

The mathematical formulation of any problem in applied sciences leads usually to an operator equation. In linear models the operator is a matrix or a difference, differential or an integral operator. If we try to solve such an operator equation we often meet different difficulties. The solution need not exist or it is not unique or it is unstable. All these bad properties of a mathematical model reflect the complexity of the real problem we are to solve. Such difficult problems are called ill-posed problems. It is not surprising that we also meet these problems in time series analysis. In this area the ill-posedness is demonstrated by the non-stationarity of a stochastic process. In economics it is well-known that the time series of logaritms of GDP or the price of overall market portfolio are almost certainly non-stationary. The typical example of the non stationary process is the random walk.

Keywords: ill-posed problem, regularization, non-stationary sequence, differencing, lag operator, least square solution, random walk, GDP, market portfolio

30

Samuel HudecMatej Bel University, Faculty of Natural Sciences, Department of Mathematics,

Tajovského 40, Banská Bystrica, Slovakia email: samuel.hudec@umb.sk

MODELLING THE FORCE OF MORTALITY USING LOCAL POLYNOMIAL METHOD IN R

This paper discusses the use of non-parametric regression approach as a new view of modelling the force of mortality which is an important and fundamental concept in modelling the future lifetime. The local polynomial method uses robustness ideas from the linear regression combined with the local fitting ideas from the kernel methods. Our topic is to compare this approach with Gompertz Makeham’s law based method. Differences are presented throught the amounts of selected product of supplementary pension saving constitutes the third pillar of the pension system in Slovakia. All of the computations for this paper was undertaken in statistical software R.

Keywords: force of mortality, local polynomial method, Makeham’s law, non-parametric regression

31

Michaela Jirková, Petr MusilUniversity of Economics Prague, Faculty of Informatics and Statistics,

Department of Economic Statistics, W. Churchill Sq. 4, 130 67 Prague 3, Czech Republic Czech Statistical Office, Prague, Na padesátém 81, 100 82 Prague 10, Czech Republic

e-mails: michaela.brazdilova@vse.cz, petr.musil@vse.cz

ANALYSIS OF ECONOMIES OF SCALE IN CZECH HOUSEHOLDS BASED

ON DIFFERENT APPROACHES

The economic situation of households could be evaluated using different approaches. Nevertheless, all methods have to deal with the same fact: economies of scale. The household structure meaning the size and other demographic and economic characteristics of household members should be always taken into account. Economies of scale are represented by the equivalence scale of consumption units. The current international consumption unit scale may not be appropriate as economies of scales might differ among countries. Therefore, the national scale should be estimated. Economies of scale of Czech households and subsequently consumption unit scales are analysed from more perspectives in the paper.

An alternative approach to consumption unit scales applied in other countries is based on household expenditures. We have estimated the consumption unit scale within our previous research. Another method that uses utility function is applied in this paper and compared to the previous one. This utility function of households is indirectly measured using subjective data of financial satisfaction. The analysis is based on data from EU_SILC. Consumption units are estimated applying regression. At first the estimation of economies of scale based on expenditures and utility function are provided. Subsequently, the results of estimated consumption unit’s scale are compared also with international scales. Finally, all approaches are compared and the impact on indicators of income or consumption is assessed.

Keywords: economies of scale, consumption units, equivalence scale, household expendi-tures, utility function

32

Miloš KaňkaUniversity of Economics, Faculty of Informatics and Statistics

Department of Mathematics, Ekonomická 957, Prague 4, 148 00 email: kanka@vse.cz

SEGMENTED REGRESSION BASED ON THE PRINCIPLE OF CUT-OFF POLYNOMIALS

WITH A SOLVED ECONOMIC EXAMPLE

This article deals with segmented regression that is based on the so called cut-off polynomials of the first, or second, respectively third order. Most of the attention is given to the inference of the system of the normal equations gained by minimisation of the criterion of the least squares method. Certain attention is also given to the calculation of the unknowns of such a system with one of the Gauss methods. Parametric equations of the output regressive curve in the given model and the determination indexes of the observed variables are inferred. Those indexes also enable to assess the “quality” of each model. The author of this article also wrote a program for the three types of segmented regression. This program helps solve the aforementioned phases in much faster and simpler way.

Keywords: Cut-off polynomials, system of normal equations, indexes of determination of observed values.

33

Alena Kaščáková, Viera Mendelová, Gabriela NedelováMatej Bel University in Banská Bystrica, Faculty of Economics, Department of Quantitative Methods and Information Systems,

Tajovského 10, 975 90 Banská Bystrica, Slovakia emails: alena.kascakova@umb.sk, viera.mendelova@umb.sk, gabriela.nedelova@umb.sk

WEIGHTING METHODS IN CONSTRUCTION OF ACTIVE AGEING INDICATOR

A newly developed tool to measure and promote the potential of the older population in EU countries is the Active Ageing Index (AAI). The index measures the active ageing performance across twenty indicators in four distinct domains with respect to employment, healthy, independent and autonomous living, and to make other unpaid family, social and cultural contributions to the society in a given country. For the construction of aggregation indices in years 2010, 2012 and 2014 one easy aggregation method based on the recommendation of the Expert group was used. The aim of this contribution is to show the differences in active ageing performance of European countries based on AAI when different methods for weights determination and different multi-criteria methods for ranking countries are used. The results of using the different weighting methods for aggregation of indicators and domains are compared and the recommendation for ranking countries is given.

Keywords: Active Ageing Index, weighting methods, population of EU countries

34

Cyprian KozyraWrocław University of Economics, Faculty of Management, Information Systems and Finance, Department of Statistics,

ul. Komandorska 118-120, 53-345 Wrocław, Poland email: cyprian.kozyra@ue.wroc.pl

IMPLICIT EQUIVALENCE SCALES DEDUCTED FROM PERSONAL INCOME TAX SYSTEM

IN POLAND, SLOVAKIA AND CZECHIA

The paper presents analysis of Personal Income Tax system in Poland, Slovakia and Czech Republic in terms of implicit equivalence scale. Equivalence scales are used in economic analysis to equalize living level in different size households. Child tax credit is a popular way of tax allowance in many countries. Amount of child tax credit and other forms of rules supporting families in tax system could be used to calculate implicit equivalence scale, deducted from PIT system assuming that living cost of taxpayer children are deducted from payable tax. Although equivalence scales used in official statistics, e.g. OECD equivalence scales, are relative, the absolute implicit equivalence scale is more adequate to child tax credit. Additional analysis could be made by inclusion of child benefits independent of tax system in different countries. Results for Poland, Slovakia and Czechia are compared.

Keywords: implicit equivalence scale, child tax credit, personal income tax, taxes and bene-fits system, absolute and relative scales.

35

Katarína Kysel’ováTechnical University in Zvolen, Faculty of Wood Sciences and Technology,

Department of Mathematics and Descriptive Geometry, T. G. Masaryka 24, Zvolen, Slovakia email: katarina.kyselova@tuzvo.sk

Rudolf ZimkaMatej Bel University, Faculty of Economics,

Department of Quantitative Methods and Information Systems, Tajovského 10, Banská Bystrica, Slovakia

email: rudolf.zimka@umb.sk

ON BAUTIN BIFURCATION IN A MONETARY DYNAMIC MODEL

In the paper a two-dimensional dynamic model of Asada (2011) describing the development of nominal rate of interest and expected rate of inflation is investigated. There are found conditions under which Bautin bifurcation (generalized Hopf bifurcation) arises. This kind of bifurcation enables the existence of so called corridor stability, when around the stable equilibrium two cycles emerge, the inner one which is unstable and the outer one which is stable. Numerical simulations of the model illustrating the achieved results are presented.

Keywords: dynamic model, equilibrium, stability, limit cycles

36

Peter Laco, Martina KallováMatej Bel University, Faculty of Economics,

Department of Quantitative Methods and Information Systems, Tajovského 10, Banská Bystrica, Slovakia

emails: peter.laco@umb.sk, matakallova@gmail.com

FACTORS INFLUENCING CORPORATE WEBSITES’ VALUE

The importance of corporate websites is indisputable. Websites allows companies to spread the information about contacts, products or services at relatively fair costs. The structure of these costs of the website creation, development and maintenance is described in our paper. The main aim of the paper is to present results of survey conducted out to describe factors that influence the value of corporate websites. This survey was realized by questionnaires for both users and companies. User point of view and corporate evaluation of website value was investigated to compare and summarize the results. The results of the survey may help companies to estimate the value of their websites and compare it with the real costs.

Keywords: internet, website, website value, website costs, survey.

37

Ivana MaláUniversity of Economics, Prague, Faculty of Informatics and Statistics,

Department of Statistics and Probability, W. Churchill Sq. 1938/4, Prague, Czech Republic

THE USE OF L-MOMENTS IN THE MODELLING OF DEPRIVATION FOR THE POPULATION AGED OVER 50 IN THE CZECH REPUBLIC

In the Survey of Health, Ageing and Retirement in Europe (SHARE) the European population aged over 50 is of interest; SHARE provides a multidisciplinary approach that delivers the comprehensive picture of the ageing process in Europe. In the fifth wave of the survey (carried out in 2013) two composite indicators of deprivation are evaluated. The answers to the selected questions (11 items for the material deprivation index and 15 items for the social deprivation index) from the survey are weighted into two composite indices with values transformed to the interval from 0 to 1. In the contribution, the empirical distributions of these indices in the Czech Republic are analysed and dependence on gender and size of household is treated. A mixture of two normal distributions for social inclusion index and a mixture of one discrete and two normal distributions for the index of material deprivation are fitted into the data. The models identify two homogenous subpopulations for social deprivation index and for positive values of material deprivation. 40 percent of respondents without any material deprivation were found in our data in comparison with less than 1 percent for the social deprivation index. Maximum likelihood estimates are compared to estimates obtained by the moment method based on robust moments.

Keywords: deprivation, SHARE data, finite mixture of distributions, L-moments

38

Agnieszka MarciniukWroclaw University of Economics, Faculty of Management, Information Systems and Finance, Department of Statistics,

ul. Komandorska 118/120, 53-345 Wrocław, Poland email: agnieszka.marciniuk@ue.wroc.pl

MARRIAGE REVERSE ANNUITY CONTRACT AND REVERSE MORTGAGE – APPLICATION

OF A GENERALIZED MODEL OF REVERSIONARY ANNUITY

The purpose of the paper is applying the generalized model of reversionary annuity to determine the benefit of marriage reverse annuity contracts and reverse mortgages. First of all, benefits depend on the age of spouses, their future lifetime and the real value of their properties which, in turn, determines the place where they live. In addition, the frequency of payments affects the amount of benefit. Therefore, the periodic benefits are determined for some regions of Poland on the basis of real Polish data from 2015, which mostly comes from The Central Statistical Office of Poland. Calculations of annuities are based on the fixed interest rate and the interest rate function depending on time t for Polish real data. The results are later compared.

Keywords: reverse annuity contract, reverse mortgage, reversionary annuity

39

Lubos Marek, Michal VrabecUniversity of Economics, Prague, Faculty of Informatics and Statistics

Department of Statistics and Probability W. Churchill Sq. 4, Prague, Czech Republic

emails: marek@vse.cz, vrabec@vse.cz

Petr Berka University of Economics, Prague, Faculty of Informatics and Statistics

Department of Information and Knowledge Engineering W. Churchill Sq. 4, Prague, Czech Republic

email: berka@vse.cz

ARE WAGES IN THE CZECH REPUBLIC AND POLAND EQUAL?

One of the most watched characteristics used in economics and statistics is the wage. Every employee is interested in its value. It is interesting to compare one’s own wages with those of others, or with the effects of other economic changes. Is my real wage rising or falling? Can I buy more this year than last year? Comparison with other countries is also interesting. For these reasons, we will try in this article to compare wages and their development during the most recent few years in the Czech Republic and Poland. Because each country has a different currency and inflation rate, we will have to convert the wages to the same currency (EUR) for the same periods, and adjust our data to eliminate the inflation. We will also be interested in the time evolution. We have reviewed this evolution with respect to the basic characteristics (growth rate and the average absolute increment) and we have also compared the trends. The classical decomposition of time series has been used to model these trends. Our output is formulated in the form of tables and charts created in MS Excel. The data sources are taken from the publications by the statistical offices of both countries and Eurostat.

Keywords: wage, real wage, inflation, trend, statistical characteristic

40

Petr Musil, Jana Kramulova, Jan Zeman, Vaclav VrabecUniversity of Economics in Prague, Faculty of Informatics and Statistics,

Department of Economic Statistics, W. Churchill Sq. 4, Praha 3, Czech Republic emails: petr.musil@vse.cz, jana.kramulova@vse.cz, jan.zeman@vse.cz, xvrav00@vse.cz

POSSIBLE EXTENTION OF REGIONAL STATISTICS – HOUSEHOLDS’ WEALTH – METHODS AND PRELIMINARY RESULTS

Economic situation of households can be assessed from many perspectives, such as income, consumption or wealth. Indicators describing income, consumption and wealth are so far available for countries only, although step by step more and more attention is paid also to the regional level. Yet official regional statistics is usually limited to several main indicators due to demanding character of indicators’ estimation.

We have done academic research and extended the range of available indicators, e.g. regional consumption expenditures in Czech regions. Our subsequent research has been focusing on regional wealth of households whose estimation is more complicated. There are very few possible data sources therefore several models have to be applied. The aim of the paper is to estimate regional wealth of households in 14 Czech NUTS 3 regions. Our results are compared to other indicators published in regional accounts. Also, the analysis of incompatibility of indicators is carried out. Regional differences in wealth may vary from differences in income or expenditure as the nature of indicators is dissimilar. On one hand, wealth expresses status on the particular date resulting from the previous accumulation as well as from households’ preferences (e.g. living in own or rented dwelling). On the other hand, income and expenditure describe transactions occurring during the given period regardless previous transactions. The results may lead to slightly different assessment of regional well-being of households.

Keywords: regions, national accounts, households, wealth

41

Katarzyna OstasiewiczWrocław University of Economics, Department of Statistics

Komandorska 118/120, Wrocław, Poland email: katarzyna.ostasiewicz@ue.wroc.pl

COMPARING SOME PROPERTIES OF LEFTIST AND RIGHTIST MEASURES OF INEQUALITY

Most of commonly used measures of inequality belongs to the so-called rightist measures which are defined by scale-invariance. However, there exist also so-called leftist measures, defined by translation invariance. According to surveys of subjective feelings of people, some feel that after multiplying each value of the distribution by the same constant value the inequality remains constant, while the other group feel that the inequality does not change after adding the same value to each value of the distribution. This ambiguity led to proposing by some authors measures of inequality that have properties of both rightist and leftist measures, that is, are invariant over rescaling and over translation. In this paper we examine the potential differences between iso-inequality contour plots for these two groups of measures, confronting with the properties of measure belonging mutually to both of the groups.

Keywords: rightist inequality measure, leftist inequality measure, iso-inequality contour, inequality measurement

42

Lucie PlzákováThe Institute of Hospitality Management in Prague, Travel and Tourism Department,

Svídnická 506, Prague, Czech Republic email: plzakova@vsh.cz

EVALUATION OF PUBLIC FINANCE IN THE TOURISM SECTOR AT

THE MUNICIPAL BUDGET LEVEL

The Assessment of public finance in the context of their allocation function is usually defined by criteria called. 3E: economy, efficiency and effectiveness. This approach is used for analyses of public finance at the municipal level from the point of view of revenues from local taxes in direct connection with tourism and expenditures invested into tourism sector on the other hand.

There is a total of 6,252 municipalities in the Czech Republic (2015). 903 municipalities (14.4 %) applied a local spa or recreational stay fee and 1,387 municipalities (22.2 %) applied local accommodation capacity fee in 2015. Municipalities gained 6.8 bn. CZK from both local fees during the reporting period 2000 – 2015. Prague, the capital city, holds a dominant position as far as the volume of financial means drawn through these fees is concerned. Investments into tourism development is much lower on the local level.

The article aims to evaluate utilization of public finances in the tourism sector on local budget levels in the Czech Republic. A time series analysis, Pearson correlation coefficient, index analysis and comparison were used to achieve the goal. The primary and secondary data were subjected to the analysis.

Keywords: 3E, local fees, tourism, municipalities, public finance

43

Jiří Procházka, Samuel Flimmel, Matĕj Čamaj, Milan Bašta University of Economics, Prague, Faculty of Informatics and Statistics,

Department of Statistics and Probability, W. Churchilla Sq.4, Prague, Czech Republic emails: xproj16@vse.cz, samuel.flimmel@vse.cz, matej.camaj@vse.cz,

milan.basta@vse.cz

MODELING THE NUMBER OF ROAD ACCIDENTS

Modelling the number of daily road accidents can be beneficial not only for insurance companies but also for other institutions such as the national road administration, national insurers’ bureau etc. Accurate predictions of the number of road accidents could be beneficial in terms of efficient liquidation planning, improving the reserving processes, streamlining the capital allocation and road maintaining. Consequently, it is relevant to build a viable model for predicting the number of daily road accidents. One of the most important parts of the model is the model of daily seasonality. Since this seasonality exhibits a long seasonal period, approaches based on basis expansion can be used for its modelling. We also investigate the multiple seasonality pattern and specific time events which could potentially affect the number of accidents. Furthermore, the impact of different external variables, such as the average daily temperature, rainfall and other factors influencing human driving skills, will also be investigated.

Keywords: road accidents, long seasonality modeling, multiple seasonality

44

Agnieszka Przybylska-MazurUniversity of Economics in Katowice, Faculty of Economics,

Department of Statistical and Mathematical Methods in Economics, ul. 1 Maja 50, 40-287 Katowice, Poland

email: agnieszka.przybylska-mazur@ue.katowice.pl

THE BRAKE PUBLIC DEBT RULE AS AN INSTRUMENT TO STABILIZE THE DEBT – RESULTS FOR POLAND

The public debt brake rule is the numerical fiscal rule applied the first time in Switzerland. In this paper we use the expenditure rule that is the core of the brake public debt rule for analyses the general government deficit and the government debt in Poland. When we use the brake public debt rule we assume that government spending does not result from a predetermined path, but they are linked to the level of revenue and variable economic situation. Unlike the original version of the brake public rule, in the paper we include the total expenditure and the total revenues being the sum of tax and non-tax revenues assumed in the Budget Laws. The potential GDP was determined on the basis of the HP filter. In addition my contribution to the topic is to investigate whether the implementation of the public debt brake rule in Poland will stabilize the general government deficit and the government debt over the business cycle and will reduce the ratio of debt to GDP.

Keywords: brake public debt rule, expenditure rule, balanced budget, business cycle

45

Hana ŘezankováUniversity of Economics, Prague, Faculty of Informatics and Statistics,

Department of Statistics and Probability W. Churchill Sq. 4, Prague 3, Czech Republic

email: hana.rezankova@vse.cz

Zuzana KřečkováUniversity of Economics, Prague, Faculty of International Relations,

Department of Retailing and Commercial Communications W. Churchill Sq. 4, Prague 3, Czech Republic

email: zuzana.kreckova@vse.cz

SELECTED GENDER GAP INDICATORS – COMPARISON OF V4 COUNTRIES

WITHIN EU CONTEXT

The paper examines similarities and distinctions of EU countries based on the Global Gender Gap Index and its four subindexes (Economic Participation and Opportunity, Educational Attainment, Health and Survival, Political Empowerment) reported in 2016. Multivariate statistical methods (cluster analysis and discriminant analysis) are applied for this purpose. Influence of individual subindexes on results of statistical analyses is discussed. The groups of countries are identified and models for country classification are proposed and compared. Changes in index values, as well as, relationships between selected gender and economic indicators (Global Competitiveness Index and GDP per capita) are investigated for period 2006 to 2016. Special attention is paid to the Visegrad Group countries within EU context.

Keywords: gender gap indicators, multivariate statistical methods, EU countries

46

Anna Sączewska-PiotrowskaUniversity of Economics in Katowice, Faculty of Economics,

Department of Labour Market Research and Forecasting, 1 Maja St. 50, Katowice, Poland

email: anna.saczewska-piotrowska@ue.katowice.pl

Damian PiotrowskiMedical University of Silesia,

School of Medicine with the Division of Dentistry in Zabrze, Department of Infectious Diseases and Hepatology, Aleja Legionów 49, Bytom, Poland

email: dpiotrowski@sum.edu.pl

LIFESTYLE CHARACTERISTICS OF POOR AND RICH PEOPLE IN POLAND

The health of individuals and communities depends on various factors. Medical condition is mostly related to unhealthy characteristics such as smoking, heavy alcohol consumption, obesity and lack of physical activity. These characteristics may occur singly or they can accumulate which can contribute to serious diseases at very young age. The lifestyle vary depending on socio-economic characteristics of people, e.g. age, sex, education, place of residence, income, kind of job. The aim of this paper was to compare lifestyle characteristics of poor and rich people. The attention was paid on certain unhealthy characteristics: alcohol consumption, smoking, overweight and obesity, and physical activity. There were compared shares of smoking, drinking too much alcohol, overweight and obese, and physically inactive among poor, middle class and rich people. The shares of leading a healthy lifestyle (no unhealthy characteristics) were also compared. The logistic regression models were estimated to determine the impact of economic situation to lifestyle behaviour (controlling for other variables: sex, age, education and place of residence). Using the odds-ratios there was evaluated the relationship between cigarette smoking and other unhealthy characteristics.

Keywords: lifestyle, poverty, richness, health

47

Zdenek Sulc, Jana Cibulkova, Jiri Prochazka, Martin Matejka

University of Economics, Prague, Faculty of Informatics and Statistics, Department of Statistics and Probability, W. Churchill Sq. 4, Czech Republic

emails: zdenek.sulc@vse.cz, cibj00@vse.cz, jiri.prochazka@vse.cz, martin.matejka@vse.cz

COMPARISON OF ECONOMIC AND NON-ECONOMIC DATASETS WITH CATEGORICAL VARIABLES IN HIERARCHICAL CLUSTERING

he economic datasets have their specifics; they usually describe human behavior or activity, which are difficult to measure. Thus, in comparison to non-economic datasets, they are less consistent. The paper analyzes differences between categorical economic and non-economic data sets in hierarchical clustering (HCA). To achieve this goal, two analyses based on 25 real world datasets are carried out. In the first one, groups of economic and non-economic data sets are compared from the point of view of their internal characteristics based on HCA results; in the second one, homogenous groups of datasets are recognized and they are further examined by internal characteristics and graphical outputs. For each group of datasets, the most appropriate similarity measures are identified. The results show substantial differences between economic and non-economic datasets, primarily in terms of the within-cluster variability decrease. We were also successful in classification of the examined datasets into easily interpretable groups, for which suitable similarity measures were identified.

Keywords: economic datasets, categorical data, hierarchical clustering, similarity measures

48

Lucia SvabovaUniversity of Zilina, The Faculty of Operation and Economics of Transport

and Communications, Department of Economics, Univerzitna 8215/1, 010 26 Zilina, Slovakia

email: lucia.svabova@fpedas.uniza.sk

Marek DuricaUniversity of Zilina, The Faculty of Operation and Economics of Transport

and Communications, Department of Quantitative Methods and Economic Informatics, Univerzitna 8215/1, 010 26 Zilina email: marek.durica@fpedas.uniza.sk

APPLICATION OF LOGISTIC REGRESSION IN COUNTERFACTUAL IMPACT EVALUATION

OF GRADUATE PRACTICE MEASURE IN SLOVAKIA

In the paper we discuss the results of Counterfactual impact evaluation of Graduate practice that is one of Active labour market policy (ALMP) interventions in Slovakia for unemployed jobseekers. Counterfactual impact evaluation is usually made using various multivariate statistical methods; one of the most used methods is Propensity score matching. Propensity score for every individual jobseeker means the probability of taking a part of an ALMP intervention and can be obtained using logistic regression model. Counterfactual evaluation is based on comparison of placeability and sustainability of treated and non-treated jobseekers on open labour market and is very important for valuation of impact of intervention not only on individual jobseekers and their employability but also for valuation of whole intervention and its economic impact.

Keywords: logistic regression, propensity score matching, counterfactual impact evalu-ation, active labour market policy, intervention

49

Karel Šafr, Jaroslav SixtaUniversity of Economics in Prague, Department of Economic Statistics

W. Churchill Sq. 4, Prague 3, Czech Republic Emails: karel.safr@vse.cz, sixta@vse.cz

METHODS FOR THE ESTIMATES OF REGIONAL ECONOMIC STRUCTURES

The paper brings an overview of statistical methods used for estimation of regional economic structures. The methods are presented using the case of the Czech Republic and Czech regional Input-Output tables for 2013. Several models used and derived for these purposes are presented within the paper, and their results are subjected to sensitivity analysis with the aid of the CGE model. Regional economic structures are necessary for advanced economic analyses aimed at the regional level, and since they are not published by official statistical agencies, they must be based on academic research. The core of regional structures is derived from both national and regional Input-Output tables and, therefore, they provide a good basis for the use of Input-Output analysis. From the statistical point of view, computational process results in a big square matrix depicting the flows of products allowing the use of dynamic Input-Output models. There can be found several methods for obtaining the flows between the regions and we briely focus on gravity method, optimalization of distance, physical flows and distance betweem the centroids. The results presented within the paper should be useful for economists dealing with regional economic models.

Keywords: Regional Input-Output, interregional flows, computable general equilibrium

50

Martina ŠimkováUniversity of Economics, Prague, Faculty of Informatics and Statistics,

Department of Demography, W. Churchill Sq. 4, Prague, Czech Republic email: martina.simkova@vse.cz

Luboš MarekUniversity of Economics, Prague, Faculty of Informatics and Statistics,

Department of Statistics and Probability, W. Churchill Sq. 4, Prague, Czech Republic, email: marek@vse.cz

AGE STRUCTURE OF LABOUR FORCE AND ITS IMPACT ON WAGES AND PRODUCT

Ageing of population is connected with significant changes in many areas of human life. It influences both social environment and economy, not only in the Czech Republic. Potential impact of the changes of labour force in developed countries is a subject of ongoing research in scientific community. Among all aspects, at least changes of labour productivity may appear because of changes of age structure of labour force. The issue of dependency of labour productivity on age has not been deeply discussed in the Czech Republic up to now. It is also affected by difficult availability of appropriate data. Our contribution provides the guidance how to combine different types of data. Our dataset is based on the combination of data from business statistics, statistical survey on wages and national accounts. The paper estimates the effects of age structure of labour force on level of wages and value added. It also identifies these effects both on level of total economy and particular industries for the Czech Republic between 2005 and 2015. Our findings provide additional information about population ageing to be discussed by policy makers.

Keywords: ageing of population, average wage, gross value added, labour force

51

Ondřej ŠimpachUniversity of Economics Prague, Faculty of Informatics and Statistics

W. Churchill Sq. 4, 130 67 Prague 3, Czech Republic email: ondrej.simpach@vse.cz

NORMALITY AND PRINCIPAL COMPONENT APPROACH TOWARDS FERTILITY TIME

SERIES IN POLAND AND CZECHIA

The aim of this paper is to analyse changes of trends in time series of age-specific fertility rates (functional data, where fertility rate is a function of women’s age) in Poland and Czechia. Data from Eurostat database are available from 1990 to 2014 for both countries. During this period, the behaviour of the population has changed in terms of family planning. The birth of the first child is being continuously postponed to later ages. Also, the fertility rates are lower. However, the situation between Poland and Czechia differs. Therefore, we compare the development.

First, it is searched whether and when the distribution of age-specific fertility rates was normal. Series of Jarque-Bera tests of normality is applied on individual time series of age-specific fertility rates. The analysis revealed that the fertility was normally distributed in the age groups 15–49+ in both countries during the whole period. It has not been skewed to the right (to higher ages) yet. Second, the medians of fertility rates were analysed using principal components method implemented in “demography” and “rainbow” packages of the RStudio software. The changes in median fertility curves were examined based on two 10-years long time intervals: 1990–1999 and 2005–2014. We found that they were significantly shifted to the right.

These results are important for subsequent analyses because for working with demographic data about fertility it is important to consider the most recent data, which are not significantly skewed and influenced by a range of factors. Estimated parameters of fertility distribution can be also used for predictions.

Keywords: normality, principal components method, fertility rates, Poland, Czechia

52

Jana Špirková, Peter Laco, Pavol Kráľ Matej Bel University, Faculty of Economics,

Department of Quantitative Methods and Information Systems, Tajovského 10, Banská Bystrica, Slovakia

emails: jana.spirkova@umb.sk, peter.laco@umb.sk, pavol.kral@umb.sk

Jana ŠtrangfeldováMatej Bel University, Faculty of Economics,

Department of Public Economics and Regional Development, Tajovského 10, Banská Bystrica, Slovakia

email: jana.strangfeldova@umb.sk

DETERMINATION OF THE OPTIMAL PREMIUM FOR THE ECONOMICALLY ACTIVE

AND INACTIVE POPULATION IN HEALTH INSURANCE IN SLOVAKIA

Health insurance in the Slovak Republic is the main source of the health system funding. It consists of contributions from employees, employers, self-employed, by the voluntary insured person and the state from the state budget for economically inactive population. These contributions are set by the assessment bases and corresponding percentage rates. For employees and employers, the assessment basis corresponds to employee’s gross salary, for self-employed this basis is determined by the income, for the voluntarily insured person and for state insured persons the basis of assessment is defined by the average gross salary in the national economy. Due to cumulated debt in the health system of Slovak Republic, which may continue to arise as a result of lack of financial resources and continually rising expenses, there is a need for persistent reevaluation of these resources. The increase of the health insurance payments is undesirable for economically active population. For this reason, our aim is to determine the optimal percentage rate, so the optimal state conscription from the state budget for the state insured (economically inactive) and also for economically active population.

Keywords: hea1th care, insurance, premium rate, gross salary

53

Jana Špirková, Igor KollárMatej Bel University, Faculty of Economics, Department of Quantitative Methods

and Information Systems, Tajovského 10, 975 90 Banská Bystrica, Slovakia email: jana.spirkova@umb.sk, igor.kollar@umb.sk

Gábor SzűcsComenius University, Faculty of Mathematics, Physics and Informatics,

Department of Applied Mathematics and Statistics, Mlynská dolina, 842 48 Bratislava, Slovakia

email: Gabor.Szucs@fmph.uniba.sk

Mária SpišiakováMatej Bel University, Faculty of Economics,

Department of Language Communication in Business, Tajovského 10, 975 90 Banská Bystrica, Slovakia

email: maria.spisiakova@umb.sk

VALUATION OF SECOND PILLAR PENSION PRODUCTS IN SLOVAKIA

This paper presents selected products of the payout phase of the second pillar pension scheme in the Slovak Republic which are stated by Act 43/2004 Coll. on the Old-Age Pension Saving Scheme and on amendments to some acts. By means of stochastic modeling of the force of mortality, it models and analyses the amounts of pension annuities in the selected designed products of the second pillar pension saving according to the requirements of the Council Directive 2004/113/EC, which sets the rules on gender-neutral pricing in insurance, and of the Council Directive 2009/138/EC, which, among other things, sets also the rules relating to the technical provisions, Solvency Capital Requirement, Minimum Capital Requirement and investment rules.

Keywords: annuity, product, force of mortality, technical interest rate, gender

54

Prokop Závodský, Ondřej ŠimpachUniversity of Economics Prague, Faculty of Informatics and Statistics

W. Churchill Sq. 4, 130 67 Prague 3, Czech Republic emails: prokop.zavodsky@vse.cz; ondrej.simpach@vse.cz

KARL CZOERNIG AND THE STATE STATISTICS OF THE HABSBURG MONARCHY

The beginnings of the first specialized body for managing state statistics of the Austrian Empire, in the form of a small statistical office, go back to 1829. Later, in 1840, this office developed into an independent Directorate of administrative statistics. The radical quantitative development and significant modernization of work of the Directorate happened mainly thanks to Karl Czoernig (1804–1889), who led the Austrian national statistics in the years 1841–1865. The transition from a mechanical summarization of less credible data inconsistently collected by auxiliary officers to a professional statistical processing and later to scientific analysis of the results started already in 1840s thanks to the “father of Austrian official statistics”. Czoernig put huge importance on the necessary qualification of his staff and, he was in charge of the series of lectures on statistics for employees of various central offices of the monarchy.

Management of the Austrian state statistics joined the starting international cooperation in the field. The third International Statistical Congress was held in year 1857 in Vienna. Following the model of Quételet of Brussels the Central Statistical Commission was founded in Austria in 1863 as the authority managing the Directorate of administrative statistics. Czoernig became the first president of this commission. He was born in Černousy (Tschernhausen) in North Bohemia (near Szklarska Poręba), he studied law in Prague and Vienna. He was conferment for merits in year 1852 as Freiherr von Czernhausen. From his extensive scientific activities and publications, we focus primarily on several notable early works related to Bohemia.

Keywords: Karl Czoernig, history of statistics, Austrian state statistics

55

Beata ZmyślonaWrocław University of Economics, Department of Statistics

ul. Komandorska 118/120, 53-345 Wrocław email: beata.zmyslona@ue.wroc.pl

COST-SHARING MODEL FOR MEDICAL SERVICES INCURRED BY THE PUBLIC PAYER.

ESTIMATION OF TREATMENT COST

Expenditures on health care incurred by the public payer are very significant and will grow in all countries due to aging of societies and the development of costly modern medical technologies. Public health care system is permanently underfunded, and the deficit on the medical service market will continue to intensify. Introduction of cost-sharing models to health care system seems to be a necessity. Two kinds of cost-sharing models can be considered, the models based on co-payment and models based on private health insurance. The paper concerns the proposition of the cost-sharing model in case of non-refunded procedures used in oncology treatment incurred by the public payer. Calculation of cost-sharing rate is estimated on the basis of data set concerning the histories of treatment in case of lung cancer for inhabitants of Lower Silesia.

Keywords: cost-sharing model, unit cost of treatment, co-payment rate, general linear model

NOTATKI

NOTATKI

TypesettingMałgorzata Myszkowska

Cover design:Beata Dębska

© Copyright by Wrocław University of EconomicsWrocław 2017

ISBN 978-83-7695-664-0

Printing: TOTEM