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Analysis of business demography using markov chains : an application to Belgian data

Author

Listed:
  • François Coppens

    (National Bank of Belgium, Microeconomic Information Department)

  • Fabienne Verduyn

    () (National Bank of Belgium, Microeconomic Information Department)

Abstract

This paper applies the theory of finite Markov chains to analyse the demographic evolution of Belgian enterprises. While other methodologies concentrate on the entry and exit of firms, the Markov approach also analyses migrations between economic sectors. Besides helping to provide a fuller picture of the evolution of the population, Markov chains also enable forecasts of its future composition to be made, as well as the computation of average lifetimes of companies by branch of activity. The method is applied to Belgian data from the Crossroads Bank for Enterprises (CBE). To ensure compliance with Eurostat-OECD definitions, only 'active' enterprises, i.e. enterprises with a positive turnover and/or at least one employee, are considered. The forecasting method is applied to simulate the demographic evolution of the CBE population between 2000 and 2006. This simulation seems to match well the observed changes. Taking migrations into account yields better forecasts than if they are not considered. Moreover, several off-diagonal percentages in the transition matrix are sigificantly different from zero. A case study shows that these migrations are changes in main activity and not the consequence of corrections of wrongly classified firms. Next, the average remaining lifetime and the average age of enterprises in a particular branch of activity is computed and analysed. These lifetimes and ages differ considerably across branches. As expected the life-times of public services are longer than average. Shorter lifetimes combined with an increasing number of enterprises is an indication of renewal inside the branch. A low average age is a sign of relatively new branches. Comparing age to total expected lifetime yields an indicator of closeness to extinction. This might be an indicator of the maturity of the branch. The method is more generally applicable in the sense that it can be used to analyse other populations than those from the CBE and other partitions of the population

Suggested Citation

  • François Coppens & Fabienne Verduyn, 2009. "Analysis of business demography using markov chains : an application to Belgian data," Working Paper Research 170, National Bank of Belgium.
  • Handle: RePEc:nbb:reswpp:200907-03
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    File URL: https://www.nbb.be/doc/oc/repec/reswpp/wp170en.pdf
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    Citations

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    Cited by:

    1. Paweł Zając & Piotr Gurgul, 2012. "Forecasting of migration matrices in business demography," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 13(2), pages 387-404, June.
    2. Claude Mathys, 2017. "Economic importance of the Belgian ports: Flemish maritime ports, Liège port complex and the port of Brussels - Report 2015," Working Paper Research 321, National Bank of Belgium.
    3. George van Gastel, 2016. "Economic importance of the Belgian ports: Flemish maritime ports, Liège port complex and the port of Brussels - Report 2014," Working Paper Research 299, National Bank of Belgium.
    4. Frank Van Nieuwenhove, 2015. "Economic Importance Of The Belgian Ports : Flemish maritime ports, Liège port complex and the port of Brussels – Report 2013," Working Paper Research 283, National Bank of Belgium.
    5. Claude Mathys, 2017. "Economic importance of the Belgian ports: Flemish maritime ports, Liège port complex and the port of Brussels - Report 2015," Working Paper Research 321, National Bank of Belgium.

    More about this item

    Keywords

    Business demography; Markov chains; Transition matrix;

    JEL classification:

    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • M13 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - New Firms; Startups

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