The Length of Working Life in Spain: Levels, Recent Trends, and the Impact of the Financial Crisis

While there has been considerable debate about extending the length of working life, relatively little is known about this issue. We use data from the Spanish Continuous Working Life Sample for 2004–2013 to calculate period working life tables, which in turn allows us to assess the impact of the financial crisis on working life expectancy in Spain. Before the recession hit, working life expectancy in Spain was around 38 years for males and 33 years for females. The recession had a tremendous impact on the Spanish labor market, but the effects differed considerably by gender and occupational category. Men working in skilled non-manual jobs were less affected, while men working in unskilled manual jobs lost close to 14 years of working life expectancy. Women were less affected than men. With working life expectancy decreasing, the average proportion of lifetime spent in unemployment and outside the labor market increased markedly, whereas the average number of years spent in retirement changed only a little. When we decompose losses in working life expectancy by age group, we find that economic fluctuations affect both older and younger workers. This result suggests that policies that focus on retirement ages only are incomplete. We also compare our findings to the results obtained by Sullivans method, which is based on prevalence rates rather than the incidence-based working life table approach. We find that the use of Sullivans approach does not accurately reflect the levels of and the trends in working life expectancy. Electronic supplementary material The online version of this article (10.1007/s10680-017-9458-9) contains supplementary material, which is available to authorized users.

The first four quantities on the right hand side can be estimated using the CWLS, while n t+1,dead t,a,g is taken from the HMD. Finally, the probability of staying inactive is calculated by using the fact that ∑ i p i j = 1.
In a second step, nonparametric estimates are used to adjust semiparametric estimates of transition probabilities starting in labor force state inactive by occupational category. Let p j,a,t,g,o be the probability of being in state inactive in age a at time t for gender g and occupational category o and moving to the state j (e.g. employed) in age a + 1 at time t + 1. Assume that this probability has been estimated using the semiparametric approach. Let P a,t,g (o) be the proportion of inactive individuals in age a at time t and of gender g and of occupational category o, which is estimated using the CWLS. The probability of moving to state j unconditional on occupational category is given by p j,a,t,g = ∑ o p j,a,t,g,o P a,t,g (o) Let p * j,a,t,g be the estimate of the unconditional probability obtained by applying the nonparametric approach outlined above. Semiparametric estimates p j,a,t,g,o are then multiplied by a correction factor a j,a,t,g which is calculated as a j,a,t,g = p * j,a,t,g p j,a,t,g .
Adjusted transition probabilities p A j,a,t,g,o are then calculated as p A j,a,t,g,o = p j,a,t,g,o a j,a,t,g c j,a,t,g,o , where c j,a,t,g,o = 1/ ∑ j a j,a,t,g p j,a,t,g,o is an additional scaling factor which guarantees that for each occupational category ∑ j p A j,a,t,g,o = 1 holds. Because of this additional scaling factor p * j,a,t,g = ∑ o p A j,a,t,g,o P a,t,g (o) will only hold approximately. Note that this approach based on indirect nonparametric estimates is not perfect. Our reasoning is that the CWLS should give a relatively complete picture of working trajectories of males as they typically have high labor force participation rates and most of them will either be employed, unemployed, disabled, or retired, implying that the semiparametric estimates of transition probabilities based on the CWLS should lead to reasonable results, i.e. results which are only slightly biased, if at all. If estimates of WLE derived completely nonparametrically coincide with those of the semiparametric approach and adjustment does not change the results of the semiparametric approach much, then the nonparametric estimates should not be totally off. If this is the case for males, completely nonparametric estimates of WLE for females can serve as a benchmark for unadjusted semiparametric estimates to assess whether selectivity of the social security population is strong and they can be used to assess whether the adjustment method outlined above leads to reasonable results.

A.2. Correcting for out migration
Another potential issue of the CWLS is that it is not possible to distinguish between moving from one of the "social security states" to inactivity and outmigration. For instance, assume that an individual is employed and is thus in contact with the social security system in 2004, and then moves abroad. Another individual is employed in 2004 and becomes inactive thereafter. In both cases, there are no entries in the social security data after 2004. Simply assuming that both individuals are inactive will lead to a potentially large overestimation of the probability of moving to inactivity, as the levels of outmigration were sizable for at least some of the years of our study period (Larramona, 2013;Izquierdo et al, 2015).
To deal with this issue, we first calculated out migration probabilities by age and gender using population counts obtained from the HMD and out-migration counts obtained from the Estadística de Variaciones and the Estadística de Migraciones (see below). Let m t,a,g denote these out-migration probabilities. Let p A i,a,t,g,o denote the adjusted probability of being in state i at time t and occupational category o and moving to the state inactive at t + 1 (adjusted using the method described in A.1). These adjusted probabilities will then be corrected via p A i,a,t,g,o − m t,a,g , yielding probabilities p M i,a,t,g,o . In a second step, transition probabilities are rescaled such that they sum to survival probabilities. These rescaled probabilities are then used for calculating WLE and so on.
While the data from the Estadística de Migraciones (EM) is considered to be better than the data from the Estadística de Variaciones (EVR) (Izquierdo et al, 2015), which has several potential issues and may give out migration counts which are too low (see Larramona, 2013), it is only available starting with 2008, while the EVR data is available for all years we study. Because of this, we use the age structure of out migration of 2008 obtained from the EM for the years 2004 to 2007. Out migration counts for 2004 to 2007 obtained from the EVR are assumed to be 10% too low and are multiplied by 1.1 to adjust for this issue. This value was obtained from a comparison of the EM and EVR for the years 2008 to 2012.
The approach to correct for migration assumes that out migration does only differ by age, gender, and year and does not differ by occupational category and current state. Unfortunately, we do not have access to data by occupational category. In theory one could use an approach similar as the one outlined above to correct for selectivity regarding inactivity. But while it seems reasonable and is in line with the literature to assume that transitions out of inactivity differ by highest occupational category ever obtained things are not so clear for out migration. While it is known that better educated have a higher probability of emigrating, this somewhat changed during the recession, as lesser educated have been hit more hard than others and economic factors have strong effects on migrating (Izquierdo et al, 2015). Moreover, the population of emigrants is highly selective with respects to other characteristics and consists to a large share of immigrants moving out of Spain (Larramona, 2013). As the CWLS does not contain any information on migration status we stick to the simple approach outlined above. A comparison of corrected and uncorrected results is given below. Figure A1 shows a comparison of estimates of WLE by gender and method. Results of the semiparametric method are presented with and without correction, where corrected results are adjusted for selectivity and out migration as outlined above. Survival probabilities are adjusted using the approach described by Dudel and Myrskylä (2016). Results of the nonparametric approach are also adjusted for out migration. In case of males most estimates are relatively close to each other, except for the year 2007 for which the absolute difference between the nonparametric and the unadjusted semiparametric estimates amounts to 1.9 years. For other years differences are smaller, e.g. 0.8 for 2012. Adjusted semiparametric estimates are mostly close to the nonparametric approach. Correcting for selectivity has an effect on estimates, but this effect is mostly small and differences are only in levels and not in trends. For females the differences between the nonparametric approach and the uncorrected semiparametric approach are larger and range between 2.3 years and 4.4 years. As can be seen in the figure trends are roughly equal but the levels differ considerably. Applying corrections the differences range between 0.0 and 0.6 years. Adjusting transition probabilities thus seems necessary. Figure A2 shows the effect of adjusting for out migration, showing results based on semiparametric estimates of transition probabilities both unadjusted and adjusted for out migration. For both males and females the effect of adjustment is relatively small for pre-crisis years and the biggest difference between adjusted and unadjusted results amounts to 0.5 years. During the crisis out migration increased considerably which leads to stronger effects of adjustment. For example, for males the difference between adjusted and unadjusted results in 2012 is roughly 1.5 years. Thus, the effect of adjusting for out migration is not as big as the effect of adjusting for sample selectivity, especially for pre-crisis years. As mentioned in the main text in section 3, we are able to assign the highest occupational category ever attained to roughly 91% of the individuals covered by the CWLS. While the occupational category itself changes over time, the highest occupational category ever attained is mostly stable after age 29. For example, between 2004 and 2005 this status is constant for roughly 90% of individuals. To assess whether missing information on occupational category affects our findings, we conducted sensitivity analyses in which all of the individuals with no information on occupational category were classified as skilled non-manual, skilled manual, unskilled non-manual, or unskilled manual. Otherwise, the analyses were carried out as described in the main paper.

A.3. Effects of adjustments
Exemplary results of the sensitivity analysis conducted to assess whether missing information on occupational category may bias our results are given in figures B1 and B2. The figures show our original findings for WLE by occupational category from the main text as well as results which were obtained by assuming that individuals with missing occupational category all belong to the category "skilled non-manual". Results of the sensitivity analyses where missing values were replaced with either " skilled manual", "unskilled non-manual", or "unskiled manual" are qualitatively similar.
In all cases levels and trends of WLE obtained from the sensitivity analysis are close to our original analysis. The only exception are skilled non-manual males, for whom the sensitivity analysis shows an increase in WLE from 2004 to 2007. Mean absolute deviations are 0.6 years (skilled non-manual), 0.6 years (skilled manual), 0.4 years (unskilled nonmanual), and 0.4 years (unskilled manual) for males. For females mean absolute deviations are all below 0.1 years and results of the analyses are close to identical.  Figure B2: Comparison of WLE estimates from the original and the sensitivity analysis for females.

C. Additional tables
The tables in this section present detailed findings of our analyses.
• Detailed results on life expectancy in all labor force states by gender and occupational category are given in tables C1 to C4. These results can be interpreted as those in table 2 of the main paper and the findings shown in figure 2 of the main paper are extracted from these tables.
• Tables C5 to C8 show detailed results for the composition of working life expectancy by age group discussed in section 4.4 of the main paper. Figure 3 and 4 in the main paper are based on these results.
• Additional results not presented in the main paper are given in tables C9 to C16, which decompose the life expectancy in inactivity and the life expectancy in unemployment by age group, similar to the findings discussed in section 4.4 of the main paper.