This paper develops a social insurance accounting model for a notional defined contribution (NDC) scheme combining retirement and long-term care (LTC) contingencies. The procedure relies on standard double-entry bookkeeping and enables us to compile a "Swedish" type actuarial balance sheet (ABS) following a framework equivalent to an open group approach. This methodology is suitable for reporting the system's solvency status and can show periodical changes in the system's financial position by means of an income statement. The information underpinning the actuarial valuation is based on events and transactions that are verifiable at the valuation date, without considering expected future trends. The paper also contains an illustrative example to make it easier for policymakers to understand the main advantages and difficulties of our proposal. The policy conclusions stress the need to properly report social insurance benefits to enhance transparency and sustainability and to improve decision-making because it is in the public interest to do so.

This article proposes a “Swedish” type actuarial balance sheet (ABS) for a notional defined contribution (NDC) scheme with disability and minimum pension benefits. The proposed ABS splits the pension system in two parts: the pure NDC part and the redistributive part, which includes the assets and liabilities originating from non‐contributory rights. The article contains a numerical example that sheds light on the real applicability of our proposal. The model has practical implications that could be of interest to policy‐makers, given that it integrates actuarial and social aspects of public pensions and discloses the real cost of redistribution through minimum pensions.

This paper studies the representativeness of the Continuous Sample of Working Lives (CSWL), a set of anonymized microdata containing information on individuals from Spanish Social Security records. We examine several CSWL waves (2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013) and show that it is not representative for the population with a pension income. We then develop a methodology to draw a large dataset from the CSWL that is much more representative of the retired population in terms of pension type, gender and age. This procedure also makes it possible for users to choose between goodness We gratefully acknowledge financial support from Ministerio de Economía y Competitividad (Spain) and from the Basque Government via projects ECO2015-65826-P and IT 793-13 respectively. We would also like to thank seminar participants at the Universities of the Basque Country, Barcelona, Valencia and Granada, and Chris Pellow and Peter Hall for their help with the English text. Comments and suggestions made by Prof. Guner and the anonymous referees were extremely helpful in improving the paper. Any errors are entirely due to the authors. of fit and subsample size. In order to illustrate the practical significance of our methodology, the paper also contains an application in which we generate a large subsample distribution from the 2010 CSWL. The results are striking: with a very small reduction in the size of the original CSWL, we significantly reduce errors in estimating pension expenditure for 2010, with a p value greater or equal to 0.999. Electronic supplementary material

The aim of this paper is to examine differences in life expectancy (LE) between selfemployed (SE) and paid employee (PE) workers when they become retirement pensioners, looking at levels of pension income using administrative data from Spanish social security records. We draw on the Continuous Sample of Working Lives (CSWL) to quantify changes in total life expectancy at ages 65 (LE65) and 75 (LE75) among retired men over the longest possible period covered by this data source: 2005-2018. These changes are broken down by pension regime and pension income level for three periods. Contrary to what has been observed in countries such as Italy, Finland and Japan, LE65 in Spain is slightly higher for the self-employed than for the paid employees when retirement pensioners. For 2005-2010, a gap in life expectancy of 0.23 years between SE and PE retirement pensioners is observed. This gap widens to 0.55 years for 2014-2018. A similar trend can be seen if pension income groups are considered. For 2005-2010, the gap in LE65 between pensioners in the lowest and the highest income groups is 1.20 years. This gap widens over time and reaches 1.51 years for 2014-2018. Although these differences are relatively small, they are statistically significant. According to our research the implications for policy on social security are evident: differences in life expectancy by socioeconomic status and pension regime should be taken into account for a variety of issues involving social security schemes, e.g. to establish the age of eligibility for retirement pensions and early access to benefits, to compute the annuity factors used to determine initial retirement benefits, and to value the liabilities taken on for retirement pensioners.

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.