Differences in Life Expectancy Between Self-Employed Workers and Paid Employees when Retirement Pensioners: Evidence from Spanish Social Security Records

Abstract

The aim of this paper is to examine differences in life expectancy (LE) between self-employed (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 age 65 (LE₆₅) among retired men over the longest possible period covered by this data source: 2005–2018. These changes are broken down by pension regime and initial pension income level for three periods. The literature presents mixed evidence, even for the same country–for Japan and Italy, for example–with some studies pointing to higher life expectancy for SE than for PE retirement pensioners while others argue the opposite. In Spain, LE₆₅ is slightly higher for the SE than for PE workers when retirement pensioners. For 2005–2010, a gap in life expectancy of 0.23 years between SE and PE retirement pensioners is observed. This 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 highest income groups is 1.20 years. This 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. These include establishing the age of eligibility for retirement pensions and early access to benefits, computing the annuity factors used to determine initial retirement benefits and valuing the liabilities taken on for retirement pensioners.

Appendix: an alternative approach to building confidence intervals

An alternative approach used to build life expectancy confidence intervals is based on Camarda (2012). To be specific, we modify the R routine (LifeTableFUN.R) provided by Camarda (2020) using the bootstrap method. In this process we use the function $rbinom(m\cdot {n}_{s}, Ntil,{ q}_{x})$) to generate life table deaths, Y, where m are the number of ages (65–101), ${n}_{s}$ the number of random samples, in this case 1000, $Ntil = round({ D}_{x}/{ q}_{x})$, where ${D}_{x}$ is the number of observed deaths at age x and ${q}_{x}$ the smoothed observed probabilities of death. Then we construct the simulated probabilities, ${Q}_{x} = Y/Ntil$, to be used to generate simulated life tables and, as a product of the ${n}_{s}$, simulated life expectancies at a given age, ${\mathrm{SLE}}_{\mathrm{X}(\mathrm{i})}, i=1,..., {n}_{s}$. Using the sample distribution of these ${n}_{s}$ replicates, we then construct the confidence interval for a given quantile.

Following Li (2015), we use the simulated life expectancies obtained from Camarda´s bootstrapping procedure to test whether a life table variable, in this case life expectancy at age 65 for one pension income group,${\mathrm{LE}}_{65}^{2}$, is bigger than the same variable for another pension income group, ${\mathrm{LE}}_{65}^{1}$ i.e. whether such a difference is statistically significant or whether it may appear purely by random chance.

We will denote by the use of ${\mathrm{SLE}}_{65(\mathrm{i})}^{1}$ and ${\mathrm{SLE}}_{65(\mathrm{i})}^{2},$ $i=1,..., {n}_{s}$ the simulated life expectancy for each group at age 65. Since the $i$ is chosen independently for ${\mathrm{SLE}}_{65(\mathrm{i})}^{1}$ and ${\mathrm{SLE}}_{65(\mathrm{i})}^{2},$ the sample distribution of z can be computed as:

$$z(i)=\frac{ {\mathrm{SLE}}_{65(\mathrm{i})}^{2}- {\mathrm{SLE}}_{65(\mathrm{i})}^{1} -{\sum }_{i=1 }^{{n}_{s}}({\mathrm{SLE}}_{65(\mathrm{i})}^{2}-{\mathrm{SLE}}_{65(\mathrm{i})}^{1})/{n}_{s}}{\sqrt{{\widehat{{\sigma }_{1}}}^{2}+ {\widehat{{\sigma }_{2}}}^{2}}}$$

(A1)

$i=1,...,{n}_{s}$ where ${\widehat{{\sigma }_{1}}}^{2}$ and ${\widehat{{\sigma }_{2}}}^{2}$ can be computed from the sample distributions as:

$${\widehat{{\sigma }_{m}}}^{2}=\frac{{\sum }_{i=1}^{{n}_{s}}{\left[{\mathrm{SLE}}_{65(\mathrm{i})}^{h} -{\sum }_{i=1 }^{{n}_{s}}{\mathrm{SLE}}_{65(\mathrm{i})}^{h} /{n}_{s}\right]}^{2}}{{n}_{s }-1}; m=\mathrm{1,2}$$

(A2)

Using the sample distribution of z, we can find the 95% confidence interval, namely $[{c}_{1},{c}_{2}]$, not exactly but approximately. The test statistic of the observed value $z$ is

$$z=\frac{{\mathrm{LE}}_{65}^{2} - {\mathrm{LE}}_{65}^{1}}{\sqrt{{\widehat{{\sigma }_{1}}}^{2}+ {\widehat{{\sigma }_{2}}}^{2}}}$$

(A3)

where ${\widehat{{\sigma }_{1}}}^{2}$ and ${\widehat{{\sigma }_{2}}}^{2}$ are the estimated variances of ${\mathrm{LE}}_{65}^{1}$ and ${\mathrm{LE}}_{65}^{2}$, which can be computed from the sample distributions as above.

If $z$ falls outside $[{c}_{1},{c}_{2}]$, then the null hypothesis leads to an observation that occurs with a probability smaller than 0.05, and hence it is rejected at the 0.05 level. Moreover, if the test is a one-tailed test to the right, then for a given significance level we can calculate the critical value ${Z}_{\alpha }$ using the sample distribution of z such that $Pr(z\le {Z}_{\alpha }) =1-\alpha$.

The main results of using this alternative methodology are shown in the following tables (Tables 9, 10, 11, 12, 13, 14, 15 and 16) and Figures (Figs. 6 and 7)

Table 9 Critical values right-tailed test for z score between pension regime groups

The robustness of the results is assured given that they are almost identical to what was seen in Sect. 3.

Table 10 Absolute differences in life expectancy between pension regime groups

Table 10 is equivalent to Table 4 shown in Sect. 3.

Table 11 Critical values right-tailed test for z score within pension regime groups between periods

Table 12 Absolute differences in life expectancy within pension regime groups by period

Table 12 is equivalent to Table 5 shown in Sect. 3

Table 13 Critical values right-tailed test for z score between initial PI groups by period

Table 14 Absolute differences in life expectancy between initial PI groups by period

Table 14 is equivalent to Table 6 shown in Sect. 3. Figure 6 illustrates the results shown in Table 14.  

Fig. 6

Histograms of the simulated LE₆₅ in P₁ for some PE and SE pension income groups

It shows the sample distributions of LE₆₅ in P₁ for some initial pension income groups of PE (Graph 1) and SE (Graph 2) beneficiaries_. The probability distributions of LE₆₅ are computed using 1000 simulations that capture the uncertainty in the survival process of these pension income groups.

Graph 1 shows that the DLE₆₅ for PE beneficiaries is statistically significant at 1%, given that the 95% confidence intervals are not overlapping. Graph 2 shows that the two distributions are quite different, but the 95% confidence intervals are partly overlapping, indicating that statistical significance is attained at the higher level.

For PE beneficiaries, the simulated LE₆₅ 95% confidence intervals are (18.90–19.92) and (20.27–21.21), respectively, for the Low and High pension income groups. The DLE₆₅ for the mean values is 1.37 years (20.74–19.37). For SE beneficiaries the simulated LE₆₅ 95% confidence intervals are (19.37–20.52) and (20.11–20.76), respectively, for the Low and Medium–Low pension income groups. The DLE₆₅ for the mean values is 0.46 years (19.98–20.43)

Table 15 Critical values right-tailed test for z score between PI groups by period

Table 16 Absolute differences in life expectancy between pension regime groups by equivalent pension income group and period

Table 16 is equivalent to Table 7 shown in Sect. 3.

Fig. 7

Histograms of the simulated LE₆₅ for equivalent low-income groups in P₁ and P₃

Figure 7 presents the histograms of the simulated LE₆₅ for equivalent Low groups in P₁ (Graph 1) and P₃ (Graph 2). These are a useful graphic tool to enable a better understanding of the results shown in Table 16.

Graph 1 shows that some of the 95% confidence intervals for LE₆₅ are overlapping, given that the values are (18.90–19.92) and (19.37–20.52), respectively, for PE and SE. This is why the level of statistical significance for DLE₆₅ is at 10% in the one-tailed test in P₁. Conversely, Graph 2 clearly shows that there is no overlap between the 95% confidence intervals for the simulated LE₆₅ for equivalent low-income groups in P₃. The simulated LE₆₅ 95% confidence intervals are (19.11–20.15) and (20.28–21.38), respectively, for PE and SE beneficiaries, and the DLE₆₅ for the mean values is 1.19 years (20.82–19.63). This is why the DLE₆₅ is statistically significant at 1% in the third period.