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