Improving the Representativeness of a Simple Random Sample: An Optimization Model and Its Application to the Continuous Sample of Working Lives

Abstract

This paper proposes an optimization model for selecting a larger 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 size of the subsample taken from a stratified random sample with proportional allocation and restricting it to a p-value large enough to achieve a good fit to the population of interest using Pearson’s chi-square goodness-of-fit test. The paper also applies the model to the Continuous Sample of Working Lives (CSWL), which is a set of anonymized microdata containing information on individuals from Spanish Social Security records and the results prove that it is possible to obtain a larger subsample from the CSWL that (far) better represents the pensioner population for each of the waves analyzed.

Mortality and life expectancy trends in Spain by pension income level for male pensioners in the general regime retiring at the statutory age, 2005–2018

“…4% of the reference population. It contains administrative data on the working lives which provide the basis for the sample taken from Spanish Social Security records and comprises anonymized microdata with detailed information on individuals [ 47 , 48 ].…”

“…We have found an inverse relationship between PI levels and mortality for a selected group of male retirement pensioners (first research question). Given that we selected a representative sample from the total population of male retirement pensioners [ 47 , 48 ], it can be said that the weight within the Spanish public pension system of the beneficiaries analyzed in this study is by no means negligible: the amount of pension expenditure for this group represented 81.27% of the total expenditure on retirement pensions for men in 2018.…”

From ‘Table 29’ to the Actuarial Balance Sheet: Is It Really That Big a Leap?

“…The CSWL contains administrative data on working lives that form the basis of this sample taken from Spanish social security records and comprises anonymized microdata with detailed information on individuals. It provides a unique data set with very rich information about employment histories and personal characteristics Núñez-Antón, et al 2020). Along with the use of dynamic mortality tables, the main assumptions are a nominal discount rate of 5% and 4% for 2015 and 2018 respectively, an inflation rate of 2% for both years, and pensions in payment indexed at 0.25% throughout the projected period.…”