Automatic Indexation of the Pension Age to Life Expectancy: When Policy Design Matters^{ †}
Abstract
:1. Introduction
2. Materials and Methods
2.1. Life Expectancy Measures
2.2. Retirement Age Policies in Selected Countries
2.2.1. The Netherlands
2.2.2. Denmark
2.2.3. Portugal
2.2.4. Slovakia
2.3. Forecasting Mortality
2.3.1. Bayesian Model Ensemble
2.3.2. Individual Stochastic Mortality Models
2.3.3. Data
3. Results
3.1. The Netherlands
3.2. Denmark
3.3. Portugal
3.4. Slovakia
4. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Stochastic Mortality Models: Technical Description
Appendix A.1. GAPC Stochastic Mortality Models
Appendix A.2. Weighted Hyndman–Ullah Method
Appendix A.3. CPSplines Model
Appendix A.4. Regularized SVD Model
Appendix B. Life Expectancy Gap and Implied Tax/Subsidies
Notes
1  For a detailed discussion of pensions taxation, see, e.g., Holzmann and Piggott (2018) and Bravo (2016). 
2  In private individual or employersponsored pension plans, diverse insurance and noninsurance longevity risksharing mechanisms (e.g., GroupSelf Annuitization schemes, longevitylinked life annuities, tontine annuities) have also been proposed and some successfully implemented (Piggott et al. 2005; Valdez et al. 2006; Stamos 2008; Milevsky and Salisbury 2015; Bravo and El Mekkaoui de Freitas 2018; Bravo 2019, 2020, 2021). 
3  Spain suspended the adjustment of pension benefits with the life expectancy sustainability factor in 2019 at least until 2023. 
4  The standard, normal or also full retirement age is defined here as the age at which individuals can first withdraw their full pension benefits, i.e., without actuarial decrements (reductions) or increments (bonus) for early (late) retirement. In most countries, standard pension ages are clearly defined in legislation. In many countries, different standards apply to different components of the overall retirementincome package. In addition, many countries have specific provisions allowing individuals to retire earlier than the standard age with full benefits given that certain contribution requirements are met. We note that some countries have opted not to have a “standard” retirement age, defining instead an age window at which pension benefits may first be drawn. 
5  In the last two decades, nearly all European countries have augmented the standard and early retirement ages (the only exception being Luxembourg), with particularly large increases legislated in some cases (e.g., Greece, Sweden, France and Finland). Some countries have limited or slowed down the increase in the retirement age following reforms adopted in the past (Italy, The Netherlands, and the Slovak Republic). 
6  For instance, in the United States, only those reaching age 65 are entitled to Medicare. Those who retire earlier receive less than full social security pension benefits and will have no employer and no Medicare health coverage during the years from retirement prior to age 65. This discourages workers from retiring at a younger age to avoid an extra pension decrement. 
7  Turkey has already announced it will phase out the sex difference for those entering the labour market in 2028. 
8  There are some notable exceptions to this pattern, namely, South Korea and Turkey, where the effective labour market exit age is considerably higher than the standard retirement age for both men and women. In recent years, we have seen some reform reversals in this area, with some countries (e.g., Italy and Portugal) easing earlyretirement conditions. For instance, in 2019, Italy suspended until 2026 the automatic indexation of both the statutory retirement age and the careerlength eligibility conditions for early retirement to life expectancy and expanded early retirement options by introducing the socalled “Quota 100” (which enables retirement at age 62 with 38 years of contributions until 2021 and allows combining work and pensions before the statutory retirement age, but subject to a labourincome ceiling) and the ”women’s option” which allows women to retire at age 58 with 35 years of contributions if they fully switch to the NDC benefit calculation. 
9  See, e.g., Lee and Carter (1992); Brouhns et al. (2002); Renshaw and Haberman (2003, 2006); Currie (2006); Cairns et al. (2006, 2009); Hyndman and Ullah (2007); Plat (2009); Blackburn and Sherris (2013); D’Amato et al. (2014); Villegas et al. (2017); Bravo and Ayuso (2020, 2021); Hunt and Blake (2021); Bravo and Nunes (2021) and references therein. 
10  The plan was to raise the eligibility age by one month per year between 2013–2015, three months per year between 2016–2018, and four months per year in 2019–2021, reaching the age of 67.2 by 2021 (European Commission 2019). 
11  Decreelaw 167D/2013 from December 31. 
12  The retirement age is kept at 65 years for beneficiaries legally prevented from working beyond that age (e.g., pilots, drivers of heavy vehicles). In addition, when the scheme participants reach the age of 65, the standard pensionable age is reduced by four months for each calendar year (with registered earnings) worked in excess of the contributions ceiling of 40 years, with a 60year threshold. There are specific early retirement provisions for those with very long contribution careers, in longterm involuntary unemployment or working in certain arduous jobs (e.g., miners). 
13  The SMAPE for model k and population g is defined by
$$SMAP{E}_{k},g:=\frac{1}{{n}_{x,t}}\sum _{x={x}_{min}}^{{x}_{max}}\sum _{t={t}_{min}}^{{t}_{max}}\frac{\left{\dot{\mu}}_{x,t,g}{\mu}_{x,t,g}\right}{0.5\times \left({\dot{\mu}}_{x,t,g}+{\mu}_{x,t,g}\right)},$$

14  For instance, model LC is nested within model RH, with ${\beta}_{x}^{(0)}=0$ for all x, and ${\gamma}_{tx}=0$ for all $c,$ being a special case of APC with ${\beta}_{x}^{(1)}=1$ for all x and no cohort effects. Model APC is a special case of RH with ${\beta}_{x}^{(1)}={\beta}_{x}^{(0)}=1$ for all x. The CBD model is a restricted version of M7 with ${\kappa}_{t}^{(3)}=0$ for all t and ${\gamma}_{tx}=0$ for all c. 
15 
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Model  Model Structure 

LC  ${\eta}_{x,t}={\alpha}_{x}+{\beta}_{x}^{(1)}{\kappa}_{t}^{(1)}$ 
APC  ${\eta}_{x,t}={\alpha}_{x}+{\kappa}_{t}^{(1)}+{\gamma}_{tx}$ 
RH  ${\eta}_{x,t}={\alpha}_{x}+{\beta}_{x}^{(1)}{\kappa}_{t}^{(1)}+{\beta}_{x}^{(0)}{\gamma}_{tx}$ 
CBD  ${\eta}_{x,t}={\kappa}_{t}^{(1)}+\left(x\overline{x}\right){\kappa}_{t}^{(2)}$ 
M7  ${\eta}_{x,t}={\kappa}_{t}^{(1)}+\left(x\overline{x}\right){\kappa}_{t}^{(2)}+\left({\left(x\overline{x}\right)}^{2}\sigma \right){\kappa}_{t}^{(3)}+{\gamma}_{tx}$ 
Plat  ${\eta}_{x,t}={\alpha}_{x}+{\kappa}_{t}^{(1)}+\left(x\overline{x}\right){\kappa}_{t}^{(2)}+{\left(\overline{x}x\right)}^{+}{\kappa}_{t}^{(3)}+{\gamma}_{tx}$ 
HUw  ${y}_{t}\left({x}_{i}\right)={f}_{t}\left({x}_{i}\right)+{\sigma}_{t}\left({x}_{i}\right){\u03f5}_{t,i}$ 
CPspl  $\eta =B\alpha $ 
RSVD  $m\left(x,t\right)={\sum}_{j=1}^{q}{d}_{j}{U}_{j}\left(t\right){V}_{j}\left(x\right)+\u03f5\left(x,t\right)$ 
Year  

Longevity Marker/Pension Age  2020  2025(a)  2030  2040  2050 
${e}_{65,g}^{P}(t)$  20.42  20.93  21.41  22.37  23.32 
${e}_{65,g}^{C}(t)$  21.82  22.35  22.87  23.87  24.81 
${e}_{65,g}^{Gap}(t)$  1.40  1.42  1.46  1.49  1.49 
${x}_{r}^{P}(t)$ (b)  66.33  67.25  68  69  70 
${x}_{r}^{C}(t)$ (c)  66.33  67.25  68.5  70.5  71.5 
${x}_{r}^{P}(t)$ (d)  66.33  67.67  68.15  69.11  70.06 
${x}_{r}^{C}(t)$ (e)  66.33  69.09  69.61  70.61  71.55 
${x}_{r}(t)[{e}_{{x}_{r},men}^{C}=18.26]$  67.20  67.81  68.37  69.39  70.31 
${x}_{r}(t)[{e}_{{x}_{r},women}^{C}=18.26]$  70.36  70.86  71.34  72.25  73.11 
Expected years in retirement  
 Men (b)  19.03  18.76  18.58  18.61  18.54 
 Women (b)  21.92  21.54  21.30  21.25  21.15 
 Men (c)  19.03  18.76  18.14  17.28  17.20 
 Women (c)  21.92  21.54  20.84  19.86  19.75 
Year  

Longevity Marker/Pension Age  2020  2030  2040  2050 
${e}_{60,g}^{P}(t)$  23.88  25.08  26.15  27.16 
${e}_{60,g}^{C}(t)$  25.87  27.01  28.04  29.01 
${e}_{60,g}^{Gap}(t)$  1.99  1.93  1.90  1.85 
${x}_{r}^{P}(t)$ (a)  67  68  70  71 
${x}_{r}^{C}(t)$ (b)  67  68  70  72 
${x}_{r}^{P}(t)$ (c)  67  68.70  70.00  71.12 
${x}_{r}^{C}(t)$ (d)  67  70.75  71.96  73.03 
${x}_{r}(t)[{e}_{{x}_{r},men}^{C}=14.5]$  71.64  72.88  73.96  74.92 
${x}_{r}(t)[{e}_{{x}_{r},women}^{C}=14.5]$  73.95  75.03  76.04  77.00 
Expected years in retirement  
 Men (a)  18.33  18.54  17.76  17.77 
 Women (a)  20.54  20.63  19.73  19.70 
 Men (b)  18.33  18.54  17.76  16.91 
 Women (b)  20.54  20.63  19.73  18.78 
Year  

Longevity Marker/Pension Age  2020  2030  2040  2050 
${e}_{65,g}^{P}(t)$  20.25  21.22  22.23  23.30 
${e}_{65,g}^{C}(t)$  21.59  22.75  23.96  25.04 
${e}_{65,g}^{Gap}(t)$  1.34  1.53  1.73  1.74 
${x}_{r}^{P}(t)$ (a)  66.42  67  67.67  68.42 
${x}_{r}^{C}(t)$ (b)  66.42  67.08  67.92  68.67 
Expected years in retirement  
 Men (a)  18.22  18.75  19.14  19.39 
 Women (a)  22.28  22.97  23.57  23.91 
 Men (b)  18.22  18.68  18.92  19.16 
 Women (b)  22.28  22.88  23.31  23.65 
Year  

Longevity Marker/Pension Age  2020  2030  2040  2050 
${e}_{65,g}^{P}(t)$  18.80  19.59  20.35  21.07 
${e}_{65,g}^{C}(t)$  19.83  20.65  21.40  22.09 
${e}_{65,g}^{Gap}(t)$  1.04  1.07  1.06  1.02 
${x}_{r}^{P}(t)$ (a)  62.67  63.53  64.30  65.04 
${x}_{r}^{C}(t)$ (b)  62.67  63.55  64.34  65.05 
${x}_{r}(t)$ 2019 Reform  62.67  64.00  64.00  64.00 
Expected years in retirement  
 Men (a)  17.90  18.15  18.40  18.59 
 Women (a)  21.91  21.99  22.08  22.15 
 Men (b)  17.90  18.14  18.37  18.57 
 Women (b)  21.91  21.97  22.05  22.13 
 Men: 2019 Reform  17.90  17.80  18.62  19.39 
 Women: 2019 Reform  21.91  21.55  22.36  23.12 
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Ayuso, M.; Bravo, J.M.; Holzmann, R.; Palmer, E. Automatic Indexation of the Pension Age to Life Expectancy: When Policy Design Matters. Risks 2021, 9, 96. https://doi.org/10.3390/risks9050096
Ayuso M, Bravo JM, Holzmann R, Palmer E. Automatic Indexation of the Pension Age to Life Expectancy: When Policy Design Matters. Risks. 2021; 9(5):96. https://doi.org/10.3390/risks9050096
Chicago/Turabian StyleAyuso, Mercedes, Jorge M. Bravo, Robert Holzmann, and Edward Palmer. 2021. "Automatic Indexation of the Pension Age to Life Expectancy: When Policy Design Matters" Risks 9, no. 5: 96. https://doi.org/10.3390/risks9050096