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Stochastic sensitivity analysis of concentration measures. (English) Zbl 1373.62568

Summary: The paper extends the traditional approach to measuring market concentration by embracing an element of stochasticity that should reflect the analyst’s uncertainty associated with the future development regarding concentration on the market. Whereas conventional practice relies on deterministic assessments of a market concentration measure with the use of current market shares, this says nothing about possible changes that may happen even in a near future. The paper proposes to model the analyst’s beliefs by dint of a suitable joint probability distribution for future market shares and demonstrates how this analytic framework may be employed for regulatory purposes. A total of four candidates for the joint probability distribution of market shares are considered – the Dirichlet distribution, the conditional normal distribution, the Gaussian copula with conditional beta marginals and the predictive distribution arising from the market share attraction model – and it is shown how their hyperparameters can be elicited so that a minimum burden is placed on the analyst. The proposed procedure for stochastic sensitivity analysis of concentration measures is demonstrated in a case study oriented on the Slovak banking sector.

MSC:

62P20 Applications of statistics to economics
91B82 Statistical methods; economic indices and measures
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