---
title: "Modéliser la distribution des richesses en France"
authors:
  - name: "Alexis Direr"
    affiliation: "École Normale Supérieure et CEPREMAP URA 928"
  - name: "Thomas Weitzenblum"
    affiliation: "EURIsCO, Université Paris Dauphine et CEPREMAP"
date: "2005-06"
keywords: [wealth distribution, bequests, saving, life-cycle model, France, socioprofessional categories, inheritance taxation, differentiated returns]
jel_codes: [D31, J62, D91]
language: [en, fr]
type: working-paper
---

# Modelling French Wealth Distribution

**Authors**
- Alexis Direr — École Normale Supérieure & CEPREMAP URA 928 — *direr@ens.fr*
- Thomas Weitzenblum — EURIsCO, Université Paris Dauphine & CEPREMAP — *thomas.weitzenblum@dauphine.fr*

**Keywords**: wealth distribution, bequests, saving, life-cycle model, France.
**JEL codes**: D31, J62, D91.

---

## Abstract

**English.** A life-cycle consumption model is developed and calibrated using French data. We focus on several assumptions regarding the saving decision which allow the model to display wealth statistics close to the empirical French distribution of wealth. To do so, seven income classes are included, which differ by their permanent income, their life expectancy, their likelihood to benefit from an intergenerational gift and by their employment transition in the labor market. We show that differences in saving return across income groups and the existence of a voluntary motive of bequest are two major ingredients which significantly improve the ability of the model to reproduce the French distribution of wealth.

**Français.** Nous développons un modèle théorique détaillé de cycle de vie que nous calibrons sur données françaises et nous testons sa capacité à reproduire la distribution des richesses observée en France. Nous incluons pour cela six catégories socioprofessionnelles qui diffèrent par leur revenu, leur espérance de vie, leur probabilité de bénéficier d'un héritage et leurs transitions emploi-chômage. Nous montrons que l'introduction de rendements de l'épargne différenciés et d'un motif de legs volontaire permettent d'améliorer sensiblement la capacité du modèle à rendre compte de la répartition des richesses en France. Nous étudions dans un second temps différentes variantes du modèle permettant d'évaluer certaines sources d'accroissement ou de réduction des inégalités de richesse comme les droits de succession.

---

## 1. Motivation and contributions

In France, as in all industrialised countries, wealth is highly unequally distributed. The empirical Gini coefficient on wealth lies in the [60%, 70%] interval (Kessler & Wolff 1991; INSEE Synthèses 1996), well above the income Gini of 30%–40% (Hourriez & Roux 2001). The paper asks: among the many theoretically possible drivers of wealth concentration, which ones matter quantitatively in the French case?

| Quantile | France (data) | United States (Diaz-Gimenez et al. 2002) |
|:---|:---:|:---:|
| Gini | 60–70% | 78% |
| Top 50% | 92–95% | 95–98% |
| Top 20% | 70–75% | 82% |
| Top 10% | 45–50% | 70% |
| Top 5% | 35–40% | 58% |
| Top 1% | 15–25% | 35% |

The paper contributes to the literature on calibrated life-cycle wealth-distribution models — previously focused on the United States (Huggett 1996; Quadrini & Ríos-Rull 1997; Gokhale et al. 2000; Quadrini 2000) and Sweden (Domeij & Klein 2002; De Nardi 2003) — through several specific channels.

1. **A life-cycle structural model calibrated on French socioprofessional categories.** Heterogeneity is organised around six PCS (Professions et Catégories Socioprofessionnelles) defined by the INSEE rather than around continuous income or wage processes as in the US/Swedish literature. Each PCS differs in (i) earned and replacement income, (ii) age-earnings profile, (iii) employment-unemployment transitions, (iv) saving return, and (v) life expectancy. Intergenerational transmission of these traits follows a Markov mobility matrix.

2. **Differentiated saving returns across income classes.** Building on observed portfolio composition by PCS (Arrondel 1996), the model assigns to each PCS a return computed from the empirical mix of low-yield administered savings (Livret A, CODEVI), housing, financial assets and equities. Quarterly real returns range from **0.691% (unskilled workers) to 1.506% (business owners)**. Quadrini & Ríos-Rull (1997) and Dynan, Skinner & Zeldes (2000) had suggested this channel without integrating it in a calibrated model.

3. **Positive correlation between income and life expectancy.** Mortality tables are PCS-specific and reproduce the well-documented gradient: at age 35, an unskilled worker household expects 18.3 years of retirement against 25.9 years for senior executives and liberal professions.

4. **Voluntary bequests as a luxury good.** The bequest motive follows De Nardi (2003): the donor evaluates the consumption gain transmitted to the heir but only imperfectly (impure altruism). This specification gives bequests luxury-good characteristics — consistent with Menchik & David (1983) — and reproduces the strong concentration of transmissions among high-income households.

5. **Quantitative evaluation of inheritance taxation.** The paper is, to the authors' knowledge, the first to quantify in a calibrated model how French inheritance taxation reshapes the wealth distribution.

---

## 2. The model

### 2.1 Demographic and life-cycle structure

Overlapping-generations economy with six PCS:

1. Artisans, commerçants
2. Chefs d'entreprise
3. Cadres et professions libérales
4. Professions intermédiaires
5. Employés et ouvriers qualifiés
6. Ouvriers non qualifiés

Households enter active life at age 20 (period $i = 0$), retire at age 60 ($i_R = 160$ quarters), and die at most at age 100 ($i_{\max} = 320$ quarters). The intergenerational gap is $i_p = 120$ quarters (30 years). Households are assumed to be two-adult couples within the same PCS. Mortality is zero before age 50, then exponential. The household mortality rate $m_i^j$ is the probability that no member of the couple is still alive.

PCS is fixed at birth and conserved over the life-cycle. Intergenerational transitions follow a Markov chain with transition matrix $(ms_{j'j})$. There is no intra-generational mobility — agents do not switch PCS during working life — but income evolves over the career according to the 1996 Enquête Fiscale.

During working life, households occupy one of six employment states $l \in \{1,\dots,6\}$ depending on the joint employment status of the two spouses (bi-active, bi-unemployed, bi-inactive, active+unemployed, active+inactive, unemployed+inactive). Transitions between these states follow age- and PCS-specific Markov processes. Unemployment benefits use a flat replacement ratio of 60%; pensions use PCS-specific replacement ratios $\eta_2^j$ between 50% and 80%.

### 2.2 Asset returns

Each PCS faces its own quarterly real return $r^j$ on saving, computed as the weighted average of returns on different asset classes (current accounts, Livret A, plan d'épargne logement, life insurance, equities, housing, professional assets) using empirical PCS-level portfolio composition from Arrondel (1996).

| PCS | Quarterly return on total wealth |
|:---|:---:|
| Chefs d'entreprise | 1.506% |
| Artisans, commerçants | 1.261% |
| Cadres supérieurs et professions libérales | 1.000% |
| Cadres moyens | 0.851% |
| Professions intermédiaires | 0.779% |
| Employés et ouvriers qualifiés | 0.746% |
| Ouvriers non qualifiés | 0.691% |

### 2.3 Household problem

The household maximises expected discounted utility with constant relative risk aversion $\gamma = 1.5$:

$$u(c) = \frac{c^{1-\gamma}}{1-\gamma}.$$

Consumption is normalised by the Oxford household-size scale $1.7 + 0.5 \cdot x_n$ where $x_n$ is the number of children. The state vector is $z = (a, j, i, l, j')$ where $a$ is wealth, $j$ is own PCS, $i$ is age, $l$ is employment status and $j'$ is the parent's PCS (used to form inheritance expectations). A strict liquidity constraint $a' \geq 0$ is imposed.

Households whose ascendant is still alive forecast an expected inheritance $\hat{h}(j', i + i_p)$ equal to the average wealth (net of inheritance tax) of agents of PCS $j'$ at age $i + i_p$.

### 2.4 Bequest motive

Following De Nardi (2003), the indirect utility from leaving wealth $a$ is:

$$v(a, i, j) = \phi_1 \cdot \left( \bar{c}_i^j + \frac{a - t(a)}{\phi_2} \right)^{1-\gamma}$$

where $\bar{c}_i^j$ is the expected consumption of the descendant when the donor has PCS $j$ and age $i$, $t(a)$ is the inheritance tax, and $\phi_2$ is set slightly below $i_p$ at $\phi_2 = 100$ quarters. The functional form is approximately equivalent to a standard bequest utility with a luxury-good threshold: poor agents bind against the non-negativity of wealth and leave nothing accidentally; richer agents whose expected consumption exceeds the descendant's actively choose to bequeath.

### 2.5 Inheritance taxation

The model implements the French inheritance tax schedule (Code général des impôts, articles 775–791): zero up to €46,000 per child, then progressive marginal rates from 5% to 40%. Following the French system, the tax is applied to each child's share assuming two children per household. The (smoothed, piecewise-continuous) schedule is:

| Bequest per child (€k) | Marginal rate |
|:---|:---:|
| 0 – 46 | 0% |
| 46 – 53.6 | 5% |
| 53.6 – 57.4 | 10% |
| 57.4 – 61 | 15% |
| 61 – 566 | 20% |
| 566 – 896 | 30% |
| 896 – 1,746 | 35% |
| > 1,746 | 40% |

Tax revenue, plus bequests with no surviving heir, are redistributed lump-sum as a per-capita transfer $f$.

---

## 3. Calibration

To minimise discretion, only **two parameters are calibrated**: the discount factor $\beta$ and the altruism intensity $\phi_1$. All other parameters (mortality, mobility matrix, employment transitions, age-earnings profiles, replacement ratios, asset returns) are fixed empirically from French sources.

**Calibration targets:**
- Aggregate wealth-to-quarterly-output ratio $A/Q = 13$ (i.e. $A/Y = 3.25$ annual). Aggregate household wealth in 1997 is €4,077 bn, against a quarterly GDP of €313 bn (Insee Première 595).
- Aggregate bequest-to-wealth ratio $B/A \approx 1.25\%$ annual. Bequests include inheritances (€18.6 bn), official donations (€16.9 bn) and downward financial transfers (€15 bn) for 1994 (Barry et al. 1996; Marini 2002), giving $B = €50.5$ bn ($B/Q = 4.44\%$).

**Calibrated values:**
- $\beta = 0.9982$ quarterly (0.993 annual)
- $\phi_1 = -170$, equivalent to $\nu = 0.926$ in a luxury-bequest interpretation

### Replacement ratios and life expectancy by PCS

| PCS | Replacement ratio $\eta_2^j$ | Life expectancy at 35 (years) | % deceased before 65 (individual) |
|:---|:---:|:---:|:---:|
| Artisans, commerçants | 70% | 41.0 | 19.0% |
| Chefs d'entreprise | 50% | 43.5 | 12.5% |
| Cadres et professions libérales | 56% | 44.5 | 13.0% |
| Professions intermédiaires | 70% | 42.0 | 17.0% |
| Employés et ouvriers qualifiés | 78% | 40.0 / 38.5 | 23% / 24.5% |
| Ouvriers non qualifiés | 80% | 37.0 | 29.0% |

The replacement ratio is **decreasing in income** because of the floor on minimum pensions, which is itself a force pushing high earners to save more.

### Numerical method

The state space combines discrete variables (age, PCS, parent's PCS, employment state) with continuous wealth, discretised on a non-uniform grid (denser at low wealth). Decision rules are computed by backward induction using the Euler equation; inheritance expectations are solved by fixed-point iteration between the saving rules and the cross-sectional wealth distribution.

---

## 4. Results

### 4.1 Life-cycle wealth profiles (reference model)

All PCS exhibit a hump-shaped life-cycle wealth profile, accumulating until retirement and decumulating thereafter. Profiles are not homothetic in permanent income: the three highest-income PCS retain significantly positive wealth at the oldest ages, while employees and unskilled workers run wealth down to zero by age 100.

Mean lifetime wealth by PCS:
- **Chefs d'entreprise: ~€970,000** at peak (vs. €790,000 in INSEE Synthèse n°28 — the model overshoots by ~20%).
- Artisans-commerçants and cadres/prof. libérales: peak around €270,000–€300,000 near age 60.
- Professions intermédiaires: peak around €130,000.
- Employés/ouvriers qualifiés: peak around €60,000.
- Ouvriers non qualifiés: peak around €40,000.

### 4.2 Wealth concentration: reference model

| (in %) | Gini | Top 50% | Top 20% | Top 10% | Top 5% | Top 1% |
|:---|:---:|:---:|:---:|:---:|:---:|:---:|
| Data | 60–70 | 92–95 | 70–75 | 45–50 | 35–40 | 15–25 |
| Reference model | **67.2** | **92.9** | **69.8** | **50.6** | **34.9** | **16.1** |

The model reproduces the empirical wealth distribution well across all reported quantiles. The simulated Gini lies inside the empirical interval; the share of the top 1% (16.1%) sits at the lower end of the [15%, 25%] empirical range; intermediate quantiles (top 5%, 10%, 20%, 50%) fall inside narrower, more reliably measured empirical brackets.

### 4.3 Bequest distribution

The model partially reproduces the concentration of bequests but **overstates concentration at the top** and understates the share of households leaving any bequest (60% in the model vs. 67% in 2000 data).

| (in %) | Top 80% | Top 60% | Top 40% | Top 20% | Top 10% |
|:---|:---:|:---:|:---:|:---:|:---:|
| Data 1994 (DGI) | 97.6 | 90.6 | 79.0 | 59.8 | 43.9 |
| Data 2000 (DGI) | 97.8 | 91.6 | 80.6 | 61.9 | 46.3 |
| Model | 99.0 | 95.5 | 87.5 | 70.0 | 54.5 |

The authors note two sources of incomparability: French statistics record individual successions (so a married couple generates two transmissions while the model records one), and life-insurance contracts (up to €152,500 per beneficiary) escape the inheritance statistics.

### 4.4 Stationarity correction

The PCS distribution implied by long-run iteration of the social mobility matrix differs from the observed distribution: it understates both very rich (chefs d'entreprise: 0.7% vs. 1.0% observed) and very poor (ouvriers non qualifiés: 5.8% vs. 8.6%) categories. After uniformly rebalancing rows and then columns of the mobility matrix to match observed marginals, the wealth distribution is barely affected:

| (in %) | Gini | Top 50% | Top 20% | Top 10% | Top 5% | Top 1% |
|:---|:---:|:---:|:---:|:---:|:---:|:---:|
| Reference model | 67.2 | 92.9 | 69.8 | 50.6 | 34.9 | 16.1 |
| Corrected mobility | 67.6 | 92.7 | 70.2 | 52.0 | 36.5 | 17.1 |

Corrected statistics also lie inside the empirical target intervals.

---

## 5. Counterfactual experiments

### 5.1 No voluntary bequest motive ($\phi_1 = 0$)

Setting altruism to zero leaves only accidental bequests. Recalibrating $\beta$ alone to match $A/Y = 3.25$ gives $\beta = 1.0006$ quarterly. The bequest-to-wealth ratio falls to $B/A = 0.5\%$ annual — **2.5 times below** the empirical target — confirming that voluntary bequests are essential to reproduce the observed transmission volume.

| (in %) | Gini | Top 50% | Top 20% | Top 10% | Top 5% | Top 1% |
|:---|:---:|:---:|:---:|:---:|:---:|:---:|
| Reference model | 67.2 | 92.9 | 69.8 | 50.6 | 34.9 | 16.1 |
| No bequest motive | **59.4** | 89.7 | 61.2 | 41.7 | 26.6 | **8.9** |

The Gini drops by 7.8 points; the top 1% share falls by **7.2 points**. The mechanism: high-PCS households anticipate that their descendants will, on average, regress toward the mean of PCS earnings; conditional on a luxury-good bequest specification, this triggers active transmission only above a consumption threshold reached by the rich.

### 5.2 Equal saving returns across PCS

Replacing the PCS-specific returns by a single rate of 0.8% per quarter (intermediate between low-yield administered products and equities) yields $\beta = 0.9984$, $\phi_1 = -211$ ($\nu = 1.15$).

| (in %) | Gini | Top 50% | Top 20% | Top 10% | Top 5% | Top 1% |
|:---|:---:|:---:|:---:|:---:|:---:|:---:|
| Reference model | 67.2 | 92.9 | 69.8 | 50.6 | 34.9 | 16.1 |
| No bequest motive (recall) | 59.4 | 89.7 | 61.2 | 41.7 | 26.6 | 8.9 |
| Equal returns | **59.7** | 90.2 | 61.4 | 41.4 | 26.4 | **8.9** |

Differentiated returns and voluntary bequests turn out to be **roughly equally important** — neither can be assigned a dominant role in generating wealth concentration in this calibration.

### 5.3 Abolition of inheritance taxation

| (in %) | Gini | Top 50% | Top 20% | Top 10% | Top 5% | Top 1% |
|:---|:---:|:---:|:---:|:---:|:---:|:---:|
| Reference model | 67.2 | 92.9 | 69.8 | 50.6 | 34.9 | 16.1 |
| No inheritance tax | **70.4** | 94.0 | 73.5 | 54.6 | **38.8** | **18.7** |

Removing inheritance taxation raises the Gini by 3.2 points. The top 20% gains 3.7 percentage points, virtually all of which is captured by the top 5% (+3.9 pp). Inheritance taxation has **first-order distributional effects** in the French context.

> **Authors' comparative reading.** Equalising saving returns across savings products would reduce the top 5% share by roughly **8 percentage points**, about twice the redistributive impact of progressive inheritance taxation (~4 pp). The financial heterogeneity of household portfolios is therefore at least as policy-relevant as inheritance taxation in shaping French wealth concentration.

---

## 6. Conclusion

The paper builds a life-cycle model with heterogeneous agents, calibrated on French socioprofessional categories, that closely reproduces the observed wealth distribution in France (Gini, top 1%–50% shares). Wealth concentration emerges from the interaction of several mechanisms that reduce saving incentives at the bottom and raise them at the top:

- A pension replacement ratio decreasing with income, due to the minimum pension floor.
- Higher life expectancy at higher PCS, which lengthens the retirement horizon for the rich.
- Differentiated saving returns favouring richer portfolios.
- Voluntary bequests concentrated among high-PCS households via the luxury-good bequest specification.
- Imperfect intergenerational mobility, leading high-income parents to expect descendants with lower permanent income and to actively transmit wealth.

Counterfactuals show that **voluntary bequests** and **differentiated returns** each account for roughly half of the explanatory power for top wealth shares, while **inheritance taxation** has first-order but more modest effects than equalising saving returns would.

### Limitations and research extensions

The authors flag several limitations. PCS-based heterogeneity, while convenient for the French statistical system, fails to resolve the very top of the income distribution where the largest fortunes form. The model abstracts from preference heterogeneity and from cohort-specific accumulation contexts (e.g. baby-boom wage trajectories differ from later generations'). Marriage regime heterogeneity (community vs. separation of property), more frequent among rich couples, is not modelled. Suggested extensions include: studying the impact of personal income taxation on wealth distribution, and combining PCS data with high-income surveys to better capture the upper tail.

---

## Acknowledgments

The authors thank Thomas Piketty and Mireille Chiroleu-Assouline for comments, as well as participants in the GIDE and EUREQua seminars at the University of Paris 1, the EPEE seminar at the University of Évry, the Journée Jourdan, and the 16th Congress of the European Economic Association in Lausanne (August 2001). They also thank Olivier Guillemin (INSEE, "Revenus des ménages" section) for facilitating access to the Enquêtes fiscales data. A more developed version of the paper appears in chapter 3 of T. Weitzenblum's PhD thesis (2001).

---

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*The full reference list appears in the PDF.*