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Improving the representativeness of a simple random sample: an optimization model and its application to the Continuous Sample of Working Lives

Author

Listed:
  • Vicente Nuñez-Antón

    (Department of Applied Economics III (Econometrics and Statistics), Faculty of Economics and Business, University of the Basque Country UPV/EHU, Bilbao. (Spain).)

  • Juan Manuel Pérez-Salamero González

    (Department of Financial Economics and Actuarial Science, Faculty of Economics, University of Valencia, Valencia. (Spain).)

  • Marta Regúlez-Castillo

    (Department of Applied Economics III (Econometrics and Statistics), Faculty of Economics and Business, University of the Basque Country UPV/EHU, Bilbao. (Spain).)

  • Carlos Vidal-Meliá

    (Department of Financial Economics and Actuarial Science, Faculty of Economics, University of Valencia, Valencia (Spain) and research affiliation with the Instituto Complutense de Análisis Económico (ICAE), Complutense University of Madrid (Spain) and the Centre of Excellence in Population Ageing Research (CEPAR), UNSW (Australia).)

Abstract
This paper develops an optimization model for selecting a large subsample that improves the representativeness of a simple random sample previously obtained from a population larger than the population of interest. The problem formulation involves convex mixed-integer nonlinear programming (convex MINLP) and is therefore NP-hard. However, the solution is found by maximizing the “constant of proportionality” – in other words, maximizing the size of the subsample taken from a stratified random sample with proportional allocation – and restricting it to a p-value high enough to achieve a good fit to the population of interest using Pearson’s chi-square goodness-of-fit test. The beauty of the model is that it gives the user the freedom to choose between a larger subsample with a poorer fit and a smaller subsample with a better fit. The paper also applies the model to a real case: The Continuous Sample of Working Lives (CSWL), which is a set of anonymized microdata containing information on individuals from Spanish Social Security records. Several waves (2005-2017) are first examined without using the model and the conclusion is that they are not representative of the target population, which in this case is people receiving a pension income. The model is then applied and the results prove that it is possible to obtain a large dataset from the CSWL that (far) better represents the pensioner population for each of the waves analysed.

Suggested Citation

  • Vicente Nuñez-Antón & Juan Manuel Pérez-Salamero González & Marta Regúlez-Castillo & Carlos Vidal-Meliá, 2019. "Improving the representativeness of a simple random sample: an optimization model and its application to the Continuous Sample of Working Lives," Documentos de Trabajo del ICAE 2019-20, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    • Handle: RePEc:ucm:doicae:1920
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    File URL: https://eprints.ucm.es/id/eprint/55423/1/1920.pdf
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    Cited by:

    1. Anne M. Garvey & Juan Manuel Pérez-Salamero González & Manuel Ventura-Marco & Carlos Vidal-Meliá, 2021. "From “Table 29” to the actuarial balance sheet: is it really that big a leap?," Documentos de Trabajo del ICAE 2021-05, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

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    More about this item

    Keywords

    Optimization; Subsampling; Chi-square test; P-value; Continuous Sample of Working Lives.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • H55 - Public Economics - - National Government Expenditures and Related Policies - - - Social Security and Public Pensions
    • J26 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Retirement; Retirement Policies

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