C02 - Mathematical MethodsReturn

The paper deals with two related topics - a mathematical model of the Gini coefficient, and its application in the taxation theory. However, the mathematical part of the paper should not only be understood as a traditional methodological starting point, but it has also didactic character and correctly describes the properties of the Gini coefficient, pointing to misinterpretation deficiencies found in a number of contemporary works. In the application part of the paper, we study the fulfillment of redistribution function of the tax system in the Czech Republic by using the Musgrave-Thin index coefficient M. Our research implies that the global progressivity of the tax allowance system in the Czech Republic was moderately progressive throughout the analyzed period 2006-2016. The considerable change in the personal income tax structure made in 2008 did not essentially reflect the global tax progressivity. Key words: tax progressivity, Gini coefficient, Lorenz curve, redistribution

Researchers and analysts usually prefer to have long time series of gross domestic product as the most important indicator of the economy. However, gross national income presents indicator that covers not only what a country produce but it takes into account values produced by factors of productions owned by foreigners. From that point of view gross national income presents more interesting information than gross domestic product. This paper describes the recalculation of historical time series of gross domestic product in the Czech Republic into the standard of national accounts ESA 2010. It presents results for all three approaches to GDP, employment and gross national income. Although results of GDP and employment start in the year 1970, the lack of data allowed us prepared figures for gross national income from year 1984 onwards. Moreover, this paper shows some of the possibilities to the international comparison with European countries for the better description of the position of the Czech Republic in the European context.

Quarterly national accounts provide short-term macroeconomic information matched with those of the annual accounts. Their mission is to provide synthetic information as soon as possible after the end of the quarter. Due to the pressure, caused by Eurostat shortening deadlines on publishing this information, the task is more of creating a methodology to be used in the Czech Republic. Based on faster and more effi cient approaches, it should enable to perform and present estimates of aggregates of quarterly national accounts for the last quarter (and forecasts for the current quarter) at a satisfactory level of reliability. Basic considerations on the methods of quarterly estimation should therefore depend on indirect methods, ie., on mathematical and statistical models, that enable (given there is a system of short survey estimates) to accelerate and shorten publishing. The article off ers an original methodology of estimating quarterly national accounts values, based on time series analysis and presents the results on the data of national accounts of the Czech Republic.

The problem of population ageing and related questions of sustainability of the pension system in the Czech Republic represent serious and discussed topics. Pension and health care systems are significantly influenced by the changes in the population structure. There is a disproportion between paid retirement pensions and received pension contributions in the pension system. The problem lies in the proportion of economically active and inactive population and the possibility of our economy to ensure sufficient resources in the future. Pensioners will consume real goods and services and have the unquestionable right for satisfaction of all their needs. For the economy, it is not important if these needs are satisfied through public or private funds or if there is a system based on contributions or benefits. Our paper offers an economic view of ageing population from the perspective of the estimate of pension liabilities. The paper also shows that the influence of the choice of the system is not important in terms of the economy. Of course, it is important for each of individuals. The problem is connected with equity, solidarity and efficiency of the management of funds. Regardless of the system, liabilities to people in the retirement are equal. Although these estimates are based on various assumptions that may vary over time, the total value of pension entitlements represents key information for policy makers. Thus the estimated proportion of pension liabilities to GDP reflects the amount of output that will be needed to satisfy the needs of current and future retirees.

In 2014 notable changes in economy measuring have occurred. Primarily, it was caused by the implementation of a new ESA 2010 European standard of accounts subsequent to SNA 2008 an international Standards of accounts. Moreover, European statisticians executed other changes which met the requirements of Eurostat. These changes implemented the latest procedures in statistical models and used the most current data sources (e.g. Cenzus, 2011). The most notable changes represent the capitalization of research and development, the capitalization of government expenditures of military weapons and finally the capitalization of small material products. This paper describes all important details of the changes in economy measuring and shows the impact of the capitalization of new assets (research and development and military equipment) on productivity estimations in the Czech Republic.

The paper describes the development of household consumption expenditures from a longer perspective. Currently, there are available data for more than forty years and it means that lots of information about changes in structure and main tendencies can be studied. Since the emphasis is put on the comparable time series, it was necessary to prepare transformation of original data into national accounts. Historical figures on private consumption were published in line with the Material Product System that is not fully comparable with the System of National Accounts. Data on private consumption reflecting only material part of consumption had to be transformed into household consumption expenditures covering both expenditures for material and non-material products. The process of transformation of original data reflecting socialist statistical system is briefly described, as well as main differences. Key points of transformation are illustrated on selected years. Finally, original data are compared with reconstructed ones and differences are explained. The analysis provides useful information about main changes in consumption expenditures by CZ-COICOP. Finally, some often discussed issues like the relative increase of expenditures connected with housing, decrease of the share of foodstuff etc. can be proven now.

Herfindahl-Hirschman Index (HHI) that measure the concentration of the industry belongs to well-known special indices. The paper is devoted to the sensitivity of the HHI values, which allows simulations of changes in concentration of the relevant market in case of new entry into the market. Let assume model situation in which a new entity has entered the industry with a relevant market share while keeping the total production of the industry unchanged and the production of subjects operating on the market is proportionately reduced. Based on this assumption, it is possible to derive relations that allow to set the boundaries in which the characteristic of the sector remains the same (levels unconcentrated, moderately concentrated, concentrated on the base of methodology of European Commission). Derived relations of the HHI sensitivity can be successfully used as a tool in assessing the entry of a new subject in any industry. It may be difficult to use analysis based on the methodology of the European Commission in case of smaller economies with a smaller number of subjects. Therefore we proposed our approach of setting of the border ranges to characterize the concentration of the industry. Also, empirical analysis of the Slovak banking sector, in which currently operate 14 banks, was conducted on the basis of the methodology of the European Commission.

The ageing of population and its economical, social and political consequences is a topic very frequently discussed. This paper contains the analysis of consequences of the ageing of the Czech population during this century based on the population projection using the latest available data reflecting the results of the last census in 2011. Besides the usual simple (and of course very crude) measures of economic dependency in the population (e.g. various dependency ratios) the paper contains a computation of a more sophisticated measure - the ratio of social dependency - which takes into account not only the amount of personal consumption but also costs of education and health care.

The estimates of economic development in the countries of the socialist block were carried out in the framework of the so-called Material Product System (MPS). At that time the product was perceived more narrowly than today's gross domestic product (GDP). It included only the material goods and productive services (services that accompanying the circulation of goods). Non-productive services and services provided on non-market basis were not included in the estimates. The authors present their own methodology for data transformation based on MPS into (today's) System of National Accounts (SNA), on the basis of carrying out the reconstruction of the historical time series of the gross domestic product of the Czech Republic in the period between the years 1970 and 1989 in the current methodology. The results of this work will enable other users to perform analysis on significantly longer time series of gross domestic product, including the structure of its uses and resources. The authors primarily base the transformation of the original data on global product and national income (in the MPS methodology) contained in the balance of national income and symmetric input-output tables. Historical time series of GDP for the period has not been estimated for the Czech Republic yet.

Monthly and yearly inflation rates can be understood as rates of dynamics of the basic inflation indicator i.e. the consumer price index. These indicators modify the original inflation information. It is important to analyze the difference of the consumer price index, monthly and yearly inflation rates, from the viewpoint of their frequency content, time lag and deformations. The theory of linear filtration and its representation in the frequency domain is used. Under particular assumptions, in the time series of yearly inflation rate there can be spurious cycles and high-frequency motions. The time series of yearly inflation rate lags behind the time series of instantaneous inflation rate about six months in low frequencies and the time series of monthly inflation rate lags behind the time series of instantaneous inflation rate about half of the month in all frequencies.