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Wykorzystanie łańcuchów Markowa do prognozowania zmian w strukturze polskich przedsiębiorstw

100%
Nehrebecka N.
Gospodarka Narodowa. The Polish Journal of Economics
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2011
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vol. 251
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issue 10
59-98
EN
The author proposes a method for predicting structural changes in Polish enterprises based on Markov chain theory. This method makes it possible to analyze the entry and exit of companies in specific business sectors, as well as to examine the migration of firms across sectors. Markov chains enable forecasts of the future composition of the corporate sector as well as computations of the average remaining lifetime and average age of companies in each category based on an appropriate fundamental matrix. This can serve as the basis for further conclusions concerning not only the economy as a whole, but also its individual components. The findings presented in the article testify to the stability of Polish companies in changing economic conditions. The level of migration across sectors is low and limited to several sectors and the expected company lifetime is relatively short. On average, the lifetime of Polish companies is less than half that of Belgian companies surveyed by the National Bank of Belgium, for example. Generally, Nehrebecka says, transport companies have the shortest lifetimes in Poland, followed by companies active in sectors such as construction, “other services” and trade. On the other hand, companies operating in agriculture, the hunting-and-forestry sector and industry tend to stay the longest on the market. The average maturity of a sector, measured with the so-called “closeness to extinction” index for all the companies, is 46%. Non-specialized exporters show the highest average age in the analyzed sectors. State-owned companies have significantly higher average age and remaining lifetime than private companies. The larger the company, the higher is its average age and average remaining lifetime. According to Nehrebecka, studies of the demographic evolution of businesses may be an additional point of reference for the evaluation of monetary policy transmission mechanisms and for shaping the institutional and legal environments in which businesses operate.
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Measurement of enterprise mobility among size classes, taking into account business demography

100%
Ferretti C.
Statistics in Transition new series
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2021
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vol. 22
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issue 1
55-73
EN
A extensive body of literature is devoted to the production of mobility measures based on transition matrices. The applications often involve panel data, and yet the impact of demographic events on enterprise mobility is not considered. The article aims provide a definition of enterprise mobility, in terms of the capability to create or liquidate jobs. Moreover, some existing mobility measures are modified so that they also take into account newborn and exiting firms. The proposed index has all the relevant basic properties which make it a rigorous descriptive statistics. The mobility of Italian capital-owned enterprises in the years 2010 2017 is analysed in the case study. What we propose may be an alternative tool for practitioners to measure the degree of mobility in the presence of demographic events. It may be considered an initial step in future research regarding its different applications (e.g. labour market flows or movements among income classes), also considering more complex theoretical backgrounds.
3

Some reasons why we should teach matrices to students of economics

75%
Rybicki W.
Didactics of Mathematics
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2012
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issue 9(13)
55-74
EN
The paper makes up the second part of the series of articles aimed at establishing the usefulness of matrices in the study of contemporary economic sciences. The series was initiated by the present author in his previous article of this subject (Rybicki, 2010). The items chosen to be presented here concern applications of (operating with) matrices in the field of welfare economics and to the description dynamics of economic systems. The first class of matrices we discuss serves as tools for indicating the inequalities of distributions of (finite) commodity bundles (and as devices to “equalize” these distributions). Other considered families of matrices consist of transition matrices of Markov chains. The presented statements are of an elementary character – they are intended to help students feel (and believe in) some uniformity of the content of lectures on mathematics and economics and (in a wider sense) operations research.
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