---
title: "Épargne retraite et redistribution"
title_en: "Retirement Savings and Redistribution"
authors:
  - name: "Alexis Direr"
    affiliation: "Université de Grenoble; Paris School of Economics; INRA"
    email: "alexis.direr@univ-orleans.fr"
date: "2008"
journal: "Économie et statistique"
issue: "417-418 (2008): Patrimoine — développements récents"
pages: "119-133"
section: "Revenus"
doi: "10.3406/estat.2008.7691"
keywords: [retirement savings, PERP, annuity, internal rate of return, redistribution, differential mortality, life expectancy, tax regime, EET vs TEE, life-cycle taxation, optimal capital taxation, gender, socio-occupational category, France]
language: [fr, en]
type: research-article
funding: "Agence Nationale de la Recherche (ANR)"
---

# Épargne retraite et redistribution

**Author**
- Alexis Direr — Université de Grenoble; Paris School of Economics; INRA — *alexis.direr@univ-orleans.fr* (LEA, 48 bd Jourdan, 75014 Paris)

**Publication**: *Économie et statistique*, n°417-418 (2008), thematic issue *Patrimoine — développements récents*, section "Revenus", pp. 119–133.

**DOI**: [10.3406/estat.2008.7691](https://doi.org/10.3406/estat.2008.7691)

**Funding**: Agence Nationale de la Recherche (ANR).

**Keywords**: retirement savings, PERP, annuity, internal rate of return, redistribution, differential mortality, tax regime, EET vs TEE, life-cycle taxation, optimal capital taxation, France.

> **Note on cross-citation.** This paper is the redistributive-analysis foundation cited as *Direr (2009)* in the body of the PERP holders paper (Direr & Roger, *Économie & prévision* 194, 2010 — see `Produit_Epargne_Retraite_Populaire_v.md`). Same paper; the 2009 citation reflects the issue's late distribution. The actual journal cover dates the issue 2008.

---

## Abstract

**Français (verbatim).** Le plan d'épargne retraite populaire (Perp), mis en place en 2003, occupe une place centrale dans le dispositif d'épargne retraite par capitalisation en France, avec plus de deux millions d'adhérents. Nous étudions son caractère redistributif en calculant le rendement d'un plan d'épargne pour des situations types qui varient en fonction de la catégorie sociale, du sexe et de la tranche d'imposition marginale. Le concept de rendement utilisé est le taux de rendement interne (TRI) qui égalise la somme espérée des versements à celle des souscriptions, en valeurs actualisées.

Les écarts de rendement sont plus marqués entre PCS qu'entre hommes et femmes. Pour les hommes, l'écart de rendement entre les cadres et professions intellectuelles supérieures et les ouvriers est de 0,9 point. Un tel écart équivaut à une différence d'environ 17 % d'annuités et d'économies fiscales perçues par ces deux groupes. L'écart est plus faible pour les femmes en raison d'inégalités d'espérance de vie de moindre ampleur.

Le régime fiscal du Perp, qui exonère les cotisations de l'impôt sur le revenu pendant la phase active puis ponctionne les rentes pendant la retraite, est à l'origine d'autres inégalités. Il introduit des écarts de rendement entre les tranches fiscales allant jusqu'à 3/4 de point. Les gains fiscaux n'évoluent pas linéairement avec le revenu mais fluctuent en fonction du passage ou non à une tranche fiscale plus favorable après la retraite. L'impact de la fiscalité est par conséquent difficile à caractériser en termes de régressivité ou de progressivité. Un régime fiscal alternatif consistant en une taxation partielle des versements aussi bien que des rentes assure une meilleure progressivité, mais grève en contrepartie le rendement, ce qui réduit l'attractivité de l'épargne retraite.

**English (verbatim).** With more than two million holders, the Plan d'Épargne Retraite Populaire (PERP), introduced in 2003, occupies a central position among French funded retirement savings instruments. We examine its redistributive power by calculating the return on a PERP for standard situations that vary according to socio-occupational category, sex, and marginal tax bracket. We use the concept of internal rate of return (IRR), i.e., the discount rate at which the present value of total expected returns will match the total cost of the investment. The return gaps are wider between socio-occupational categories than between sexes. Among men, managers and higher-level intellectual occupations display a 0.9-point gap in returns with blue-collar workers. That translates into a difference of about 17% in annuities and tax savings for the two groups. The gap is narrower for women because of the smaller inequality in life expectancy. Other inequalities are due to the PERP tax regime, which exempts contributions from income tax while holders are economically active, then taxes annuities during retirement. It introduces yield gaps of up to 0.75 points between tax brackets. Tax gains do not rise in a linear profile with income but fluctuate depending on whether or not holders move into a lower tax bracket on retirement. It is thus hard to characterize the impact of taxation as regressive or progressive. An alternative tax regime consisting in partial taxation of both contributions and annuities is more progressive but erodes the return — thereby reducing the attractiveness of saving for retirement.

> *The Persée version also reproduces the abstract in German and Spanish; not included here.*

---

## 1. Motivation and contributions

The PERP, introduced by the Fillon Act of 21 August 2003, is the universal voluntary retirement savings vehicle in France: contributions are deductible from taxable income up to 10% of net professional earnings; accumulated capital is mandatorily converted into a life annuity at retirement; the resulting annuity is taxed as ordinary pension income. By end-2007, around 2 million plans had been opened. Replacement-rate projections by the Conseil d'Orientation des Retraites (COR 2006) anticipate steep declines for higher-earning workers — from 64.1% to 56.7% for senior managers between 2003 and 2020 — making voluntary funded savings a politically central topic.

The redistributive properties of an instrument that locks subscribers in until death have not been studied at the individual level for France. The international literature on funded pensions has focused on average returns (e.g. Brown & Warshawsky 2001 for the US; Mendez et al. 2005 for France); only Brown (2003) examines redistribution in the US system, finding a 20% wealth-equivalent annuity gap for low-education African Americans. The closest French analogue is the work on differential mortality in *public* pension systems (Bommier et al. 2005 find that mortality differentials offset one-quarter to one-half of the redistributive mechanism; Walraet & Vincent 2003 find smaller anti-redistributive transfers).

The paper makes three main contributions.

1. **Quantification of redistribution within the PERP across socio-occupational category, sex, and marginal tax bracket.** Using the legal annuity conversion rules (zero technical rate, TGH05/TGF05 cohort mortality tables, sex-differentiated since 2007), the paper computes the post-tax internal rate of return (IRR) for stylised subscriber profiles. The headline finding is a **0.9-point IRR gap between male senior managers and male manual workers** — equivalent to roughly 17% in lifetime annuities-plus-tax-savings — with a smaller gap among women.

2. **Decomposition of the IRR gap into a mortality channel and a tax channel.** Holding tax treatment uniform across PCS, mortality differentials alone generate 70–95% of the observed IRR gap; holding mortality uniform, tax-regime differentials generate gaps of up to 0.72 points. The two channels are roughly comparable in magnitude.

3. **Comparison with alternative tax regimes.** The paper shows that the PERP regime (deduction at contribution, taxation at annuity) interacts with the progressive income-tax schedule to produce a *non-monotonic* relation between taxable income and net IRR — driven by which subscribers do or do not drop a tax bracket at retirement. A simulated *life insurance* regime (partial taxation at both ends) is more progressive but erodes returns. The paper's preferred alternative — integrating contributions in taxable income while granting a flat refundable tax credit — would smooth the income-IRR profile while preserving incentives.

---

## 2. Institutional setting and conversion mechanics

**Source of legal annuity rules.** *Arrêté du 1er août 2006* (Journal Officiel) homologating the TGH05 (men) and TGF05 (women) cohort mortality tables, constructed from observed 1994–2004 mortality of about two million annuity-product subscribers. The tables imply the over-survival typical of self-selected annuity buyers. The simulations use the 1950 birth cohort.

**Setup.** A subscriber of sex $i \in \{h, f\}$ contributes $S_t$ during active years $t = -L, \ldots, -1$, holds capital $W_0$ at retirement (date 0), and receives an annuity $A_t^i$ from $t = 0$ until death, with maximum survival horizon $T$. Accumulated capital:

$$W_0 = \sum_{t=-L}^{-1} (1+r-\tau)^{-t}(1-\delta) S_t$$

with $r$ the gross return, $\tau$ management fees on assets, and $\delta$ entry fees on contributions.

**Legal conversion at retirement.** Actuarial fairness with regulatory technical rate $r^*$:

$$W_0 = \sum_{t=0}^{T} \frac{p_t^i}{(1+r^*)^t} A_0^i$$

PERP regulation imposes $r^* = 0$, so:

$$\frac{A_0^i}{W_0} = \frac{1}{\sum_{t=0}^{T} p_t^i}$$

**First-annuity conversion rates (1950 cohort).** Men: 3.45%. Women: 3.07%. Women's lower rate reflects their higher life expectancy.

**Annuity growth.** Because $r^* = 0$ but the asset return $r$ is positive, the annuity grows over retirement as un-recognised investment returns are progressively redistributed. Under the assumption that the manager smooths annuity growth at a constant rate $g$ across the surviving cohort and that the cohort's actuarial value is exhausted at horizon $T$ (terminal constraint $V_T = 0$), the annuity grows at $g \approx 3.1\%$ per year for both sexes — implying the annuity *doubles by age 83*.

---

## 3. Model and calibration

### 3.1 The IRR concept

For category $j$ (sex × PCS × tax bracket), let $p_t^j$ be the survival probability, $\alpha^j$ the marginal income tax rate during active life, and $\beta^j$ the post-retirement tax rate on the annuity. The IRR $\rho^j$ solves:

$$\sum_{t=-L}^{-1} (1+\rho^j)^{-t} (1-\alpha^j) S_t = \sum_{t=0}^{T-1} (1+\rho^j)^{-t} p_t^j (1-\beta^j) A_t$$

with flows discounted to the annuitisation date. The expected present value (VA) measure, used as a secondary indicator, sums the discounted tax savings during active life and the discounted post-tax annuities.

The IRR captures both mortality (via $p_t^j$) and the full tax regime. As a sanity check: in the absence of fees, taxes, and mortality differentials, IRR = $r$. The choice of indicator follows Mitchell et al. (1999).

### 3.2 PCS-differentiated mortality tables

The official tables are sex- but not PCS-differentiated. The paper combines two sources to construct **PCS-differentiated cohort tables that preserve the overall TGH05/TGF05 life expectancies while reproducing the PCS gaps from the Insee Échantillon Démographique Permanent (EDP)** retrospective data (Robert-Bobée & Monteil 2005). For each age $t_0$, sex $s$, and PCS $x$, a new table $P(t_0, s, x)$ is calibrated to satisfy:

$$EV(P(t_0, s, x)) - EV(T(t_0, s)) = EV(Q(t_0, s, x)) - EV(Q(t_0, s))$$

where $T$ is the official table and $Q$ is the EDP-based PCS table. This corrects the EDP tables' two defects: retrospective bias (too low for upcoming cohorts) and absence of annuitant over-survival.

**Life expectancy at 60 (EDP, mid-1990s deaths):**

| PCS | Men | Women | F–M gap |
|:---|:---:|:---:|:---:|
| Senior managers / liberal professions (CPIS) | 23.5 | 26.5 | 3.0 |
| Employees | 20.0 | 25.7 | 5.7 |
| Manual workers | 18.5 | 24.5 | 6.0 |

### 3.3 Calibration

| Parameter | Value | Source |
|:---|:---:|:---|
| Annual contribution $S_t$ | €500 | Mean 2005 contribution (FFSA) |
| Subscription age | 40 | Median holder age 2004 (Burricand 2006) |
| Annuitisation age | 60 | Standard retirement age |
| Real gross return $r$ | 4% | Below post-war French equity mean (6.2%) and bond mean (4.6%); reflects 20% equity allocation and progressive de-risking before annuitisation |
| Entry fees $\delta$ | 4% | Mean of 55 PERP contracts, *La vie financière*, May 2005 |
| Management fees $\tau$ | 0.9% | Same source |
| Marginal tax rates | 0%, 5.5%, 14%, 30%, 40% | 2006 income tax schedule |
| CSG / CRDS on annuity | 6.6% / 0.5% (4.2% of CSG deductible) | 2006 rates |
| Cohort mortality | 1950 birth year | TGH05 / TGF05 with PCS adjustment |

---

## 4. Results

### 4.1 IRR by sex × PCS × tax bracket

Stylised subscriber profiles:
- **Senior managers (CPIS)**: marginal tax rate (TMI) drops 40% → 30% at retirement.
- **Employees, decreasing TMI**: 14% → 5%.
- **Employees, constant TMI**: 5% → 5%.
- **Manual workers**: 0% throughout (non-taxable).

| Profile | Men | Women (gap vs CPIS men) |
|:---|:---:|:---:|
| CPIS | 3.54% | 3.24% (−0.30) |
| Employees, TMI decreasing | 2.97% (−0.57) | 3.03% (−0.51) |
| Employees, TMI constant | 2.66% (−0.88) | 2.74% (−0.80) |
| Manual workers | 2.73% (−0.82) | 2.86% (−0.68) |

For men, the resulting first annuity is €464 (1950 cohort) and €413 for women (lower conversion rate). The annuity then grows at ~3.1%/year.

> **Authors' reading.** Manual workers earn a slightly higher IRR than the constant-TMI employees because the assumed non-taxability exempts them from CSG/CRDS on the annuity, an exemption which more than compensates for their shorter life expectancy. This exemption would equally benefit non-taxable employees (a category not separately profiled). Within the CPIS, women earn 0.30 less than men because their life-expectancy advantage is smaller than for other PCS, and is more than offset by the lower conversion rate they receive.

### 4.2 Expected present value (Table 3)

| Profile | Men | Women (gap vs CPIS men) |
|:---|:---:|:---:|
| CPIS | €8,219 | €7,799 (−5.1%) |
| Employees, TMI decreasing | €7,372 (−10.3%) | €7,468 (−9.1%) |
| Employees, TMI constant | €6,791 (−17.4%) | €6,886 (−16.2%) |
| Manual workers | €6,897 (−16.1%) | €7,111 (−13.5%) |

A 0.5-point IRR gap maps to roughly a 10% gap in lifetime expected returns plus tax savings.

### 4.3 Robustness

| Variant | Effect on IRR levels | Effect on IRR gaps |
|:---|:---|:---|
| $r$ = 6% instead of 4% | All IRRs +2pp | Unchanged (gaps invariant to $r$) |
| Contributions grow at 5%/year | < 0.05pp shifts | Unchanged |
| Heterogeneous contributions × PCS (CPIS €1,000 + 10%/year) | CPIS IRR: 3.60% (vs 3.54%) | Marginal |
| Differential retirement age (CPIS at 65, others at 60) | CPIS men: 3.52% (vs 3.54%) | Negligible |
| Management fees and positive technical rate | Negligible | Negligible |

**The IRR-level invariance to $r$ implies the cross-PCS *gaps* are pinned down by mortality and tax differentials, not by the gross return assumption.** The IRR-invariance to $S_t$ when contributions are constant is shown by combining equations (2)–(4) of Box 1.

### 4.4 Mortality channel

Holding tax treatment uniform (14% → 5% across all PCS):

| Profile | Men IRR (gap vs CPIS) | Women IRR (gap vs CPIS) |
|:---|:---:|:---:|
| CPIS | 3.40% (0) | 3.11% (−0.29) |
| Employees | 2.97% (−0.43) | 3.03% (−0.37) |
| Manual workers | 2.76% (−0.64) | 2.89% (−0.51) |

**Mortality differentials alone account for 70–95% of the total IRR gap by PCS.** The mortality channel is uniformly weaker for women.

### 4.5 Tax channel (uniform mortality)

Holding mortality at the population-average TGH05 (men's table), the IRR depends only on the pair $(\alpha, \beta)$:

| Marginal tax (active → retirement) | IRR |
|:---|:---:|
| **Constant** | |
| 0 → 0 | 3.07% |
| 5 → 5 | 2.79% |
| 14 → 14 | 2.78% |
| 30 → 30 | 2.76% |
| 40 → 40 | 2.74% |
| **Decreasing** | |
| 5 → 0 | 3.26% |
| 14 → 5 | 3.11% |
| 30 → 14 | **3.46%** |
| 40 → 30 | 3.25% |

For households who do *not* drop a tax bracket, IRR is essentially independent of the level of that bracket — a textbook result for EET retirement-savings regimes. The slight residual gradient comes from CSG/CRDS not being fully deductible. **The non-taxable household earns a notably higher IRR (3.07%) because of the social-contributions exemption** on its retirement income.

For households who *do* drop a bracket, the IRR jumps to as high as **3.46%** — for a 30 → 14 transition. This is the largest single source of tax-driven IRR heterogeneity (gap of 0.72 points within the tax channel alone).

### 4.6 No monotonic relation between taxable income and IRR

Assuming a uniform 30% drop in taxable income at retirement, the IRR-vs-income curve is non-monotonic (Figure I in the paper). A subscriber with €20,000 active-life taxable income remains in the 14% bracket throughout (IRR = 2.78%); one at €30,000 drops from 30% to 14% (IRR = 3.46%); but one with €120,000 income — staying in the top 40% bracket — earns a relatively low IRR (2.74%). The 2006 simplification of the income-tax schedule (from seven brackets to five) widened the bracket thresholds and *amplified* this fluctuation, since dropping a bracket at retirement now requires a larger drop in taxable income.

> **Authors' critical reading.** The widely-stated claim that the PERP's tax design "favours high-income households" (e.g. *Rapport sur la commercialisation des produits financiers*, 2005) is misleading: the high-marginal-rate household *only* gets a tax-IRR boost if it actually drops a bracket at retirement. Otherwise the tax channel is roughly neutral across brackets, and non-taxable households are disproportionately rewarded by the CSG/CRDS exemption.

### 4.7 Comparison with alternative regimes

**Pure entry taxation (TEE).** Under a hypothetical regime where contributions are integrated into taxable income but the annuity (apart from CSG/CRDS) is exempt, the IRR is **flat at 2.80%** across all income brackets — eliminating tax-driven IRR heterogeneity but offering a lower headline rate (Figure II).

**Life insurance regime (partial taxation at both ends).** With life insurance: contributions paid from after-tax income; 40% of the annuity (for liquidation between 60 and 69) taxable as ordinary income; 11% social contributions on the annuity (against ~7% for PERP). Under this regime:

| Profile | Men IRR (vs PERP) | Women IRR (vs PERP) |
|:---|:---:|:---:|
| CPIS | 2.50% (3.54%) | 2.25% (3.24%) |
| Employees, TMI decreasing | 2.42% (2.97%) | 2.51% (3.03%) |
| Employees, TMI constant | 2.42% (2.64%) | 2.51% (2.72%) |
| Manual workers | 2.72% (2.73%) | 2.86% (2.86%) |

The life-insurance regime is **more progressive** — IRR gaps across PCS shrink considerably and even reverse for manual workers, because the partial-taxation-at-both-ends design makes the progressivity of income tax bite harder against the higher-income, longer-lived households. But the average IRR is lower, which the author flags as a deterrent to annuity-product diffusion in a country already characterised by long-standing distrust of annuitisation (Gaudemet 2001).

---

## 5. Conclusion

The PERP's redistributive profile is dominated by mortality differentials, which account for the bulk of the cross-PCS IRR gap — about 0.9 IRR points between male senior managers and male manual workers, equivalent to roughly 17% in lifetime annuity-and-tax-saving terms. The tax channel adds a comparable but more idiosyncratic source of heterogeneity: the PERP's deduction-at-entry / taxation-at-exit design generates IRR gaps of up to 0.72 points, but driven not by income level *per se* — rather by whether the household drops an income-tax bracket at retirement. Households who do not drop a bracket earn essentially the same IRR regardless of bracket; households who drop from 30% to 14% earn the largest tax-IRR gain.

The interaction between the bracketed income tax and the PERP's tax timing produces a non-monotonic relation between taxable income and net IRR. The 2006 simplification of the income-tax schedule (seven to five brackets) *amplified* this effect by widening the thresholds. The popular narrative that the PERP is structurally tilted toward high-income households is therefore not strictly correct.

The paper identifies a more rationalised tax design that would smooth the income-IRR profile: integrate contributions into taxable income, then grant a flat *refundable* tax credit proportional to contributions (so that non-taxable households also benefit). To compensate the longevity-driven inequalities, a fraction of the annuity could be taxed in the manner of life insurance — with the trade-off that average IRR levels would fall, potentially deterring annuity product diffusion.

### Limitations and research extensions

- The IRR and expected-present-value criteria assume *risk-neutral* savers and therefore omit the longevity-insurance value of annuitisation. A welfare-based metric incorporating risk aversion would yield additional positive value to all annuity holders, with magnitude depending on the bequest motive (Lockwood, working paper at the time of writing).
- Stylised tax profiles assume marginal tax rates are constant during active life; in practice they may rise with earnings progression or with departure of dependent children.
- Adverse selection in the annuity market (Gaudemet 2001) is not modelled.
- A single 1950 birth cohort is simulated; younger cohorts face higher conversion-cost-per-euro under the projected mortality tables.
- The retirement age is assumed uniform; differential retirement timing across PCS is shown to have a small numerical effect but is not endogenously modelled.
- The paper does not endogenise the saving decision; it computes the IRR of a fixed contribution profile rather than a household optimum. The companion theoretical paper (Direr 2008, mimeo) and Brunner & Pech (2008) develop the optimal-tax dimension within a Mirrlees framework.

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## Acknowledgments

The author thanks the participants of the "Assurance et Allongement de la Vie" working group at Paris-Jourdan Sciences Économiques and the Insee Patrimoine survey exploitation group, Gabrielle Demange for her remarks, Muriel Roger for ongoing discussions, and the two anonymous referees. Funding from the Agence Nationale de la Recherche (ANR).

---

## Main references

Bommier, A., Magnac, T., Rapoport, B., & Roger, M. (2005). Droits à la retraite et mortalité différentielle. *Économie & Prévision* 168, 1–16.

Brown, J. R. (2003). Redistribution and insurance: mandatory annuitization with mortality heterogeneity. *Journal of Risk and Insurance* 70(1), 17–41.

Brown, J. R., & Warshawsky, M. J. (2001). Longevity-insured retirement distributions from pension plans: market and regulatory issues. NBER Working Paper 8064.

Brunner, J. K., & Pech, S. (2008). Optimum taxation of life annuities. *Social Choice and Welfare* 30, 285–303.

Burricand, C. (2006). L'épargne retraite en 2004. *Études et Résultats* 518.

Conseil d'orientation des retraites (2006). Retraites: perspectives 2020 et 2050.

Coronado, J. L., Fullerton, D., & Glass, T. (2000). The progressivity of social security. NBER Working Paper 7520.

Direr, A., & Roger, M. (2009). Le Produit d'Épargne Retraite Populaire (PERP): caractéristiques des détenteurs et projection des niveaux de rentes. PSE Working Paper 2009-5. *(Eventually published in Économie & prévision 194 (2010) — see `Produit_Epargne_Retraite_Populaire_v.md`.)*

Gaudemet, J.-P. (2001). Les dispositifs d'acquisition à titre facultatif d'annuités viagères en vue de la retraite : une diffusion limitée. *Économie et statistique* 348, 81–106.

Mendez, R., Ragot, L., & Marlier, G. (2005). Une évaluation des risques de la capitalisation en France. EUREQua Working Paper, Université Paris 1.

Mirrlees, J. A. (1971). An exploration in the theory of optimum income taxation. *Review of Economic Studies* 38, 175–208.

Mitchell, O. S., Poterba, J. M., Warshawsky, M. J., & Brown, J. R. (1999). New evidence on the money's worth of individual annuities. *American Economic Review* 89(5), 1299–1318.

Robert-Bobée, I., & Monteil, C. (2005). Quelles évolutions des différentiels sociaux de mortalité pour les femmes et les hommes? Insee Working Paper F0506.

Walraet, E., & Vincent, A. (2003). La redistribution intragénérationnelle dans le système de retraite des salariés du privé : une approche par microsimulation. *Économie et statistique* 366, 31–61.

Whitehouse, E. (1999). The tax treatment of funded pensions. World Bank Working Paper 9910.

*The full reference list appears in the published article.*