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Treatment of sample under-representation and skewed heavy-tailed distributions in survey-based microsimulation: An analysis of redistribution effects in compulsory health care insurance in Switzerland
[Methoden zur Behandlung von Unterrepräsentation bei schiefen Verteilungen für die stichprobenbasierte Mikrosimulation: Eine Analyse zu den Umverteilungseffekten in der obligatorischen Krankenversicherung der Schweiz]


  • Tobias Schoch

    (University of Applied Sciences Northwestern Switzerland)

  • André Müller

    (Ecoplan AG – Research in Economics and Policy Consultancy)


The credibility of microsimulation modeling with the research community and policymakers depends on high-quality baseline surveys. Quality problems with the baseline survey tend to impair the quality of microsimulation built on top of the survey data. We address two potential issues that both relate to skewed and heavy-tailed distributions. First, we find that ultra-high-income households are under-represented in the baseline household survey. Moreover, the sample estimate of average income underestimates the known population average. Although the Deville–Särndal calibration method corrects the under-representation, it cannot achieve alignment of estimated average income in the right tail of the distribution with known population values without distorting the empirical income distribution. To overcome the problem, we introduce a Pareto tail model. With the help of the tail model, we can adjust the sample income distribution in the tail to meet the alignment targets. Our method can be a useful tool for microsimulation modelers working with survey income data. The second contribution refers to the treatment of an outlier-prone variable that has been added to the survey by record linkage (our empirical example is health care cost). The nature of the baseline survey is not affected by record linkage, that is, the baseline survey still covers only a small part of the population. Hence, the sampling weights are relatively large. An outlying observation together with a high sampling weight can heavily influence or even ruin an estimate of a population characteristic. Thus, we argue that it is beneficial—in terms of mean square error—to use robust estimation and alignment methods, because robust methods are less affected by the presence of outliers.

Suggested Citation

  • Tobias Schoch & André Müller, 2020. "Treatment of sample under-representation and skewed heavy-tailed distributions in survey-based microsimulation: An analysis of redistribution effects in compulsory health care insurance in Switzerland," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 14(3), pages 267-304, December.
  • Handle: RePEc:spr:astaws:v:14:y:2020:i:3:d:10.1007_s11943-020-00275-8
    DOI: 10.1007/s11943-020-00275-8

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    References listed on IDEAS

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    More about this item


    Simulation; Pareto distribution; Representative outliers; Nonresponse; Calibration; Imputation;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C54 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Quantitative Policy Modeling
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods
    • I13 - Health, Education, and Welfare - - Health - - - Health Insurance, Public and Private
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health


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