---
title: "Le Produit d'épargne retraite populaire (Perp) : caractéristiques des détenteurs et projection des niveaux de rentes"
title_en: "The Personal Retirement Savings Product (PERP): Characteristics of Holders and Projection of Annuity Levels"
authors:
  - name: "Alexis Direr"
    affiliation: "Laboratoire d'Économie d'Orléans (LEO); Paris School of Economics"
    email: "alexis.direr@univ-orleans.fr"
  - name: "Muriel Roger"
    affiliation: "Paris School of Economics; INRA"
    email: "muriel.roger@ens.fr"
date: "2010"
journal: "Économie & prévision"
issue: "194 (2010-3)"
pages: "79-92"
doi: "10.3406/ecop.2010.8050"
keywords: [household finance, retirement savings, PERP, Plan d'Épargne Retraite Populaire, Fillon Act, defined-contribution plan, annuitisation, replacement rate, simulated residuals method, bracket data, life-cycle savings, annuity puzzle]
language: [fr, en]
type: research-article
funding: "Agence Nationale de la Recherche (ANR)"
---

# Le Produit d'épargne retraite populaire (Perp) : caractéristiques des détenteurs et projection des niveaux de rentes

**Authors**
- Alexis Direr — Laboratoire d'Économie d'Orléans (LEO); Paris School of Economics — *alexis.direr@univ-orleans.fr*
- Muriel Roger — Paris School of Economics; INRA — *muriel.roger@ens.fr*

**Publication**: *Économie & prévision*, n°194, 2010-3, pp. 79–92. Article accepted 30 November 2009.

**DOI**: [10.3406/ecop.2010.8050](https://doi.org/10.3406/ecop.2010.8050)

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

**Keywords**: household finance, retirement savings, PERP, Fillon Act, defined-contribution plan, annuitisation, replacement rate, simulated residuals method, bracket data, life-cycle savings, annuity puzzle.

---

## Abstract

**Français (verbatim).** Un produit d'épargne retraite universel a été lancé en France en 2003, le Plan d'Épargne Retraite Populaire (Perp), dont l'objectif est de permettre aux ménages de compléter leur retraite future. À l'aide de données issues d'une large enquête réalisée par TNS-Sofres en 2007, dont un volet porte sur les ménages détenteurs d'un Perp, nous montrons que ce produit s'est diffusé dans l'ensemble des couches sociales et touche en proportion aussi bien les cadres et professions libérales que les ouvriers ou les employés. L'âge des détenteurs suit approximativement une courbe en U, avec une participation relativement plus importante des 25-34 ans et des 50-54 ans. Nous appliquons dans un second temps la méthode des résidus simulés pour obtenir des distributions de capital et de versements à partir des données en tranches fournies par l'enquête. Cela nous permet d'estimer le montant accumulé par les ménages de l'échantillon au moment de la liquidation de leur plan et d'évaluer ainsi quel supplément de ressources ces derniers sont susceptibles d'obtenir pendant la retraite en proportion du dernier revenu d'activité. Les résultats des simulations indiquent que la plupart des souscripteurs bénéficieront d'un revenu d'appoint inférieur à 1 % de leur dernier revenu d'activité.

**English (verbatim).** The French law called "Fillon Act", which came into effect on August 21, 2003, set up an individual savings contract called PERP (Plan d'Épargne Retraite Populaire) aimed at supplementing public pensions. It is a defined-contribution plan in which contributions are deductible from taxable income up to 10% of the holder's annual income. At retirement, benefits are paid in the form of annuities and taxed at a normal rate. We use a large dataset on saving behavior of 9,880 households in order to determine the profile by age, socio-economic status, income, wealth, and tax status of holders of at least one PERP. We show that this savings product has spread evenly across all socio-economic categories. The participation rate is highest for households headed by persons aged 25-34 or 50-54. We use simulated residuals and bracket information available in our dataset to simulate continuous distribution of PERP assets and contributions. We can thus project the future growth of assets in personal retirement plans until age 60 and estimate the annuities that households will obtain after retirement. We find that most households are likely to benefit from a very small annuity, equal to less than 1% of their last earnings before the conversion of their plans.

---

## 1. Motivation and contributions

The paper is the first individual-level evaluation of the PERP, the universal voluntary retirement savings product launched in France by the Fillon Act of August 2003. The PERP is open to all individuals regardless of employment status; contributions are deductible from taxable income up to 10% of professional earnings; the accumulated capital must be converted into a life annuity at retirement; and the resulting annuity is taxed as ordinary pension income. Aggregate statistics from the FFSA and DREES were available before this study (Burricand 2006; Augris 2007; Croguennec 2008), but no individual-level analysis of holder characteristics or projected annuity levels existed.

By 31 December 2007, the PERP covered 8.6% of salaried workers, with nearly 2 million plans, €3.4 billion in total assets, and a mean balance of €1,710 per plan — already more subscribers than the older Préfon (390,000 affiliates in 2008, civil servants) or Madelin (940,000 contributors in 2006, self-employed) contracts. New subscriptions slowed sharply after the launch (1.27 million in 2003–2004 → 130,000 in 2007).

The paper makes three main contributions.

1. **Socio-economic profile of PERP holders from individual survey data.** Using the 2007 TNS Sofres "Épargne et Stratégie Patrimoniale des Français" survey, the paper documents that PERP has diffused across all socio-economic categories — including manual workers and employees — rather than concentrating on high-marginal-rate households as the legislator's tax incentives had implicitly targeted (Woerth 2003). The age profile is U-shaped with peaks at 25–34 and 50–54.

2. **Recovery of continuous distributions from bracket data via simulated residuals.** Contributions and accumulated balances are observed only in brackets in the survey. The paper applies the simulated residuals method (Gouriéroux et al. 1987; Lollivier & Verger 1989; Arrondel 1996), assuming log-normal distributions, to estimate continuous distributions of contributions and balances. The simulated aggregates match FFSA totals closely (€1.02bn simulated vs €1.01bn observed contributions in 2006; €2.5bn vs €2.35bn assets at end-2006), validating the approach.

3. **Projection of replacement rates at retirement.** Using the simulated continuous distributions, the paper projects each household's accumulated capital at age 60 under explicit assumptions on contribution growth, real interest rate net of fees, and earnings growth, then converts the capital into an annuity using the legally mandated zero technical rate and TG05 mortality tables. The headline finding is that **about 44% of PERP-holding households will receive an annuity below 1% of their last labour earnings**, and roughly 30% below 0.5%.

---

## 2. Data and institutional setting

**Source.** "Épargne et Stratégie Patrimoniale des Français 2007", a postal survey conducted by TNS Sofres from March to May 2007. Sample: 20,000 households contacted, 60% response rate, 9,880 retained households after coherence checks. Data are reweighted by sex, age, and occupation of the household head to be representative of the French population (Insee Employment Survey, demographic balance, Insee 2005 projections).

**PERP sub-sample.** 326 households hold at least one PERP (raw), of whom 298 are used in the contribution and asset regressions.

**Institutional context (Fillon Act, 2003).** The PERP is a defined-contribution individual retirement savings contract open to anyone regardless of professional status. Contributions are deductible from taxable income up to 10% of net professional earnings; the accumulated capital must be converted into a life annuity at retirement (with a few legal exceptions: severe disability, end of unemployment benefits, judicial liquidation, first-residence purchase); annuity income is taxed at the standard pension rate. The first annuity is computed under a legally mandated zero technical rate using the TG05 mortality tables, which are sex-differentiated since 2007.

**Comparison to the Madelin product.** The Madelin contract (analysed in Direr & Yayi 2014, *Économie et Statistique* 472–473) is restricted to non-agricultural self-employed professionals and predates the PERP. Madelin holders are on average older and contribute larger amounts than PERP holders (Croguennec 2008).

### Holder characteristics (from Tables 1–2 in the paper)

Participation rate by household-head age (25–60 sub-population: **4.9%**):

| Age band | Participation rate |
|:---|:---:|
| 25–34 | 4.8% |
| 35–39 | 5.1% |
| 40–44 | 4.6% |
| 45–49 | 4.4% |
| 50–54 | **7.3%** |
| 55+ | 1.3% |

Participation rate by occupation of household head (25–65):

| Occupation | Participation rate |
|:---|:---:|
| Farmers | 2.7% |
| Shopkeepers, artisans, business owners | 4.9% |
| Senior managers, liberal professions | 5.8% |
| Intermediate professions | 5.1% |
| Employees | 5.1% |
| Manual workers | 5.0% |

Participation rate by net annual household income:

| Income band | Participation rate |
|:---|:---:|
| < €10,800 | 1.3% |
| €10,800–22,800 | 3.6% |
| €22,800–32,400 | 4.8% |
| €32,400–45,600 | 5.7% |
| ≥ €45,600 | 6.5% |

Participation rate by income tax bracket and financial wealth:

| Tax bracket | Rate | Financial wealth | Rate |
|:---|:---:|:---|:---:|
| Non-taxable | 3.2% | < €3,000 | 2.2% |
| < €300 | 4.5% | €3,000–9,000 | 3.1% |
| €300–1,500 | 4.9% | €9,000–37,500 | 4.9% |
| €1,500–3,000 | 4.8% | €37,500–107,500 | 6.8% |
| ≥ €3,000 | **8.2%** | ≥ €107,500 | **8.4%** |

**Distribution channel.** ~75% of PERP holders subscribed through a bank, ~19% through an insurance company. The product was massively distributed by retail banking networks, which the authors flag as a likely driver of the cross-class diffusion (banks did not screen clients by income or age).

### Bracketed contributions and balances (from Tables 3–4)

Monthly contribution distribution (25–65 holders):

| No contribution | €1–74 | €75–149 | €150–299 | ≥ €300 | NR |
|:---:|:---:|:---:|:---:|:---:|:---:|
| 17.4% | 43.7% | 17.5% | 6.9% | 3.7% | 10.8% |

Total balance distribution (25–65 holders):

| < €1,500 | €1,500–3,000 | €3,000–7,500 | €7,500–15,000 | €15,000–30,000 | ≥ €30,000 |
|:---:|:---:|:---:|:---:|:---:|:---:|
| 46.2% | 21.5% | 18.8% | 7.4% | 5.0% | 1.1% |

Roughly **60% of holders contribute less than €75 per month** and **two-thirds hold less than €3,000** in their PERP.

---

## 3. Methodology: simulated residuals and annuity projection

### 3.1 Recovering continuous contribution and asset distributions

Contributions $V_i$ and balances $M_i$ are observed only as the bracket each household falls into. Following Gouriéroux et al. (1987) and Lollivier & Verger (1989), the paper assumes log-normal distributions:

$$\log(V_i^*) = X_i \beta + \sigma_V \varepsilon_i$$
$$\log(M_i^*) = Z_i \gamma + \sigma_M \nu_i$$

with $\varepsilon_i, \nu_i \sim \mathcal{N}(0,1)$, treated as independent. Parameters are estimated by ordered polytomous Probit. Residuals $\tilde\varepsilon_i, \tilde\nu_i$ are then drawn by accept-reject conditional on the simulated values $\tilde V_i, \tilde M_i$ falling within the household's reported bracket. For households who did not declare a bracket, the first draw is kept. Each household's reported value is taken as the average over **1,000 draws**.

| Outcome | Estimation | N | Sample |
|:---|:---|:---:|:---|
| Log monthly contribution | Ordered Probit (log-normal) | 298 | PERP holders, 25–65 |
| Log total PERP balance | Ordered Probit (log-normal) | 298 | PERP holders, 25–65 |

**Selected coefficients (contribution equation, reference age 55–59).** Most age dummies below age 50 are negative and significant: −1.02 (under 30), −1.12 (35–39), −0.79 (40–44), −0.87 (45–49); coefficients become insignificant from age 50 onward. Income gradient is positive and monotone in monthly per-consumption-unit income (+0.83 to +1.15 across brackets). Subscribing through a bank (vs other channel) reduces contributions by **−0.52** (significant at 5%). Tax bracket and detailed occupation are not significant (except "tax info not reported," which is significantly higher and correlated with wealthier households).

**Selected coefficients (balance equation).** Age of head enters linearly with a positive coefficient (+0.06 per year, significant). Farmers hold significantly *less* than other categories (−4.34) despite having higher overall wealth. Annual household income is monotonically associated with higher balances (+0.56 to +1.34 across brackets).

### 3.2 Validation of the simulated distributions

| Aggregate | Simulated | Observed (FFSA, 2006) | Comment |
|:---|:---:|:---:|:---|
| Total contributions | €1.02 bn | €1.01 bn | Tight match |
| Total assets, end-2006 | €2.5 bn | €2.35 bn | Slight over-estimate; attributed to imputing €0–500 to households declaring zero balance but positive 2006 contributions |

Simulated mean monthly contribution: **€146** (median €32, range €15–~€1,700). Simulated mean balance: **€3,437** (median €840, range ~€20–~€20,000).

Mean contribution and balance by age band (after simulation):

| Age band | Mean annual contribution | Mean balance |
|:---:|:---:|:---:|
| 25–34 | €977 | €1,429 |
| 35–39 | €307 | €1,803 |
| 40–44 | €584 | €2,450 |
| 45–49 | €1,135 | €3,384 |
| 50–54 | €2,923 | €5,018 |
| 55+ | €1,590 | €6,630 |
| 25–65 | €1,325 | €3,285 |

Contributions trace a U-shape over 25–55 (high entry, dip when child-rearing/housing costs peak, rebound near retirement), then drop after 55. The authors caution that the cross-sectional shape may conflate age and cohort effects.

### 3.3 Capital projection and annuity calculation

Capital at age 60 is projected by capitalising current balance $W_i$ and simulated future contributions $S_{it}$ at real net return $r$:

$$\overline W_i = W_i (1+r)^{60-a_i} + \sum_{t=1}^{60-a_i} (1+r)^{60-a_i-t+1} S_{it}$$

Future contributions grow at the wage growth rate $g_Y$ plus age-based step adjustments calibrated from Table 7 (e.g. between 35–39 and 40–44, contributions jump by (584−307)/307 ≈ 90% at age 40 in addition to the 1.8% annual wage drift).

The first annuity at age 60 is given by the legal conversion formula with **technical rate $r^* = 0$** and the official **TG05 mortality tables** (sex-differentiated since 2007):

$$A_{i60} = \frac{\overline W_i}{\sum_{s=0}^{T} \frac{p_{60+s}}{(1+r^*)^s}}$$

The replacement rate at age 60 is $A_{i60}/\bar y_i$, where the last labour earnings $\bar y_i$ are extrapolated from the 2006 declared earnings using $\bar y_i = y_i (1+g_Y)^{60-a_i}$.

Because of the zero technical rate, the first annuity is mechanically low and grows over retirement as the unrecognised investment returns are redistributed to surviving annuitants; a **replacement rate at age 80** is also reported.

**Conversion rates (Table 3 in paper).** A woman born in 1941 converting €1,000 at 60 receives an annual annuity of €32 (no reversion option). Conversion rates decline by birth year — reflecting longer life expectancy projected in the official tables. The simulations average male and female tables since the survey does not report holder sex (Burricand 2006 reports an even gender split).

### 3.4 Calibration

| Parameter | Central value | Source / robustness |
|:---|:---:|:---|
| Real return net of fees, $r$ | 1.22% | Mendez et al. 2005: 2.12% real return on French sovereign bonds 1950–2003, minus 0.90pp fees (mean 2005 fees on 55 PERP contracts, *La vie financière*, May 2005) |
| Wage / earnings growth, $g_Y$ | 1.8% | Conseil d'orientation des retraites (2007) productivity projection |
| Robustness alt. 1 | $r = 2\%$ | Plausible upper bound given ~20% equity allocation (Marini 2006) |
| Robustness alt. 2 | $g_Y = 1.5\%$ | Less optimistic productivity scenario |

---

## 4. Results

### 4.1 Diffusion across all socio-economic categories

PERP holders are not concentrated in upper-income or high-tax households as the original tax-incentive design implicitly anticipated. Senior managers and liberal professions are over-represented (20.4% of holders vs 15.4% in the population), but manual workers are *also* over-represented (27.6% vs 24.4%) — a striking pattern given that they were not the legislator's primary target. Non-taxable households (who derive no contribution-phase tax benefit) and modest-income or modest-wealth households account for a non-trivial share of subscribers.

> **Authors' interpretation.** The cross-class diffusion is driven by the bank-distribution channel: ~75% of PERP contracts were subscribed through retail banks, which marketed the product without screening clients by income, age, or marginal tax rate. A secondary mechanism — the social-contribution exemption for non-taxable retirees that mechanically raises PERP returns for low-income households (Direr 2009) — is mentioned but flagged as little known by retail clients.

### 4.2 U-shaped age profile and low contribution levels

Participation peaks at 50–54 (7.3%) but is also relatively high at 25–34 (4.8%). The combination of (i) cross-class diffusion to lower-income workers and (ii) substantial participation among 25–34s drives the very low observed contribution levels: **60% contribute less than €75/month**, and **46% hold less than €1,500** in their plan.

### 4.3 Projected replacement rates (central scenario)

Central scenario: $r = 1.22\%$, $g_Y = 1.8\%$.

The age-60 replacement-rate distribution is tightly concentrated near zero, with a peak of households at **0.25%** of last earnings.

| Replacement rate threshold $x$ | Share of households < $x$, age 60 | Share < $x$, age 80 |
|:---:|:---:|:---:|
| 0.5% | **31.3%** | 28.2% |
| 1.0% | **43.7%** | 38.8% |
| 2.5% | 75.0% | 68.2% |
| 5.0% | 88.3% | 85.0% |

Replacement rates at age 80 are slightly higher than at 60 because the zero technical rate progressively releases unrecognised returns over retirement, but the gap is small. The paper notes that surviving high-annuity households may be over-represented at 80 due to the documented adverse-selection effect in annuity markets (Gaudemet 2001), which the simulation does not model.

### 4.4 Robustness

| Variant | < 0.5% at 60 | < 1.0% at 60 | < 0.5% at 80 | < 1.0% at 80 |
|:---|:---:|:---:|:---:|:---:|
| Central ($r$=1.22%, $g_Y$=1.8%) | 31.3% | 43.7% | 28.2% | 38.8% |
| $r$ = 2.0%, $g_Y$ = 1.8% | 30.6% | 42.4% | 25.1% | 34.8% |
| $r$ = 1.22%, $g_Y$ = 1.5% | 30.6% | 43.1% | 27.9% | 38.8% |

> **Authors' critical reading.** Plausible variations of the two central parameters change the conclusions only marginally. Two simplifications may bias the results in opposite directions. (i) Other annuity products (Madelin for the self-employed, Préfon for civil servants) are ignored, which under-states total annuity income. (ii) The simulation assumes no spousal reversion, which over-states the first annuity — a 100% reversion to a spouse would reduce a male holder's annuity by ~20%.

---

## 5. Conclusion

The first individual-level evaluation of the PERP, four years after its introduction, shows three things. First, the product has diffused remarkably evenly across socio-economic categories — bank distribution rather than tax incentives has been the binding driver of subscription. Second, the age profile is U-shaped, with strong participation at 25–34 and 50–54, and the combination of cross-class diffusion and young entrants drives observed contribution and balance levels far below those of comparable products such as Madelin. Third, projection of accumulated capital to age 60 under reasonable real-return and earnings-growth assumptions implies that **the majority of PERP holders will receive an annuity below 1% of their last labour earnings**, with about 30% below 0.5%.

The authors are explicit that this does *not* support the inference that French households save too little overall: the household saving rate has been stable around 15% since the early 1990s — among the highest in developed countries — and asset income represents 20–25% of retirees' total income (COR 2002). The result is more naturally read as evidence of household *distrust of products with mandatory annuitisation*, with savers preferring real estate and capital-preserving vehicles such as life insurance — a French manifestation of the international annuity puzzle (James & Song 2002; Mitchell et al. 1999; with the puzzle's robustness questioned by Lockwood 2010 once bequest motives are properly modelled).

### Limitations and research extensions

- Other complementary annuity products (Madelin, Préfon, occupational schemes) held by the same households are not observed, which under-states total expected annuity income.
- The simulation assumes no spousal reversion, which over-states each individual annuity (~20% over-statement under 100% reversion).
- The PERP age-profile and socio-economic profile cannot be extended to other voluntary regimes; Madelin holders are older and contribute more (Croguennec 2008).
- Adverse selection in the annuity market (Gaudemet 2001) is documented but not modelled in the simulation.
- Differential life expectancy across socio-economic categories is not modelled in the replacement-rate calculation; this disadvantages manual workers and, to a lesser extent, employees (Direr 2009).
- Cross-sectional age patterns may conflate age and cohort effects; the survey is not a panel.
- Data are bracketed; the simulated residuals method addresses this but the simulated distributions retain plateau artifacts due to the small number of brackets and explanatory variables.

---

## Acknowledgments

This work was conducted under funding from the Agence Nationale de la Recherche (ANR). The authors thank Véronique Noiville (TNS Sofres) for her assistance with the database.

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