---
title: "How Price Elastic is the Demand for Retirement Saving?"
authors:
  - name: "Alexis Direr"
    affiliation: "Université d'Orléans, CNRS, LEO, UMR 7322, and Paris School of Economics"
  - name: "Rim Ennajar-Sayadi"
    affiliation: "AXA France"
date: "2018-08-27"
doi: "10.1057/s41288-018-0112-5"
journal: "The Geneva Papers on Risk and Insurance — Issues and Practice"
volume: "44"
issue: "1"
pages: "102–122"
year_published: 2019
publisher: "Palgrave Macmillan (Springer Nature)"
keywords: [retirement savings, mortality, insurance]
jel_codes: [D8, E21]
language: en
type: research-article
---

# How Price Elastic is the Demand for Retirement Saving?

**Authors**
- Alexis Direr — Université d'Orléans, CNRS, LEO, UMR 7322, and Paris School of Economics — *alexis.direr@univ-orleans.fr* (corresponding author)
- Rim Ennajar-Sayadi — AXA France

**DOI**: [10.1057/s41288-018-0112-5](https://doi.org/10.1057/s41288-018-0112-5)

**Published in**: *The Geneva Papers on Risk and Insurance — Issues and Practice*, vol. 44, no. 1, pp. 102–122, 2019. Palgrave Macmillan / Springer Nature. (The published version uses the title "How price-elastic is the demand for retirement saving?".)

**Keywords**: retirement savings, mortality, insurance.
**JEL codes**: D8, E21.
**Research framework**: Laboratoire d'Économie d'Orléans (LEO, UMR 7322 CNRS) and Paris School of Economics. Data and assistance provided by a major French insurance company (data confidentiality preserved in the paper).

---

## Abstract

We exploit an administrative dataset of a big insurance company to assess the effects on annuity demand of a French regulatory reform which impacted actuarial return to deferred life annuity products. Unlike previous studies, annuity demand is measured by contributions in saving products which capital is converted into annuities at retirement. Our identification methodology is based on the fact that while female savers' annuity rate (conversion rate of capital into annuities) fell by 10%, male savers who did not expect to take the survivor option at retirement, were not affected by the reform. Assuming that single men fall in this category, and using this population as a control group, we find a decrease in demand by women of −16% which corresponds to a price elasticity of subscriptions of −1.5. The reform did not significantly alter contributions in saving accounts. We also document a very large anticipation effect created by the opportunity offered to early subscribers to benefit from older pricing.

---

## 1. Motivation and contributions

Rising life expectancy forces insurers to update mortality tables, which mechanically lowers conversion rates from accumulated capital into lifelong annuities. The literature documents this trend internationally — e.g. Cannon & Tonks (2004, 2009) for the UK, Bütler, Staubli & Zito (2013) for Switzerland — but the empirical literature on **the price elasticity of annuity demand** is thin. Two existing papers offer contrasting answers: Chalmers & Reuter (2012) find little evidence that retirees respond to cross-sectional variation in annuity prices in a US public-employee sample; Bütler, Staubli & Zito (2013) find a 14 percentage point drop in annuitisation rates in response to a salient Swiss conversion rate reform.

The paper makes the following contributions.

1. **Demand for annuities measured during the accumulation phase.** Previous empirical work focused on the choice between cash-out and annuity at retirement. This paper instead studies a deferred annuity product (the French *Madelin* contract) in which withdrawals are forbidden and full annuitisation is compulsory at retirement, so that subscription decisions and contribution flows during the accumulation phase are direct measures of annuity demand. This setting is relevant for many countries (US, Germany, UK) with deferred annuity products.

2. **A natural experiment with a clean treatment-control structure.** The 2007 reform (TPRV93 → TGF05/TGH05 mortality tables) cut the female annuity rate by about **10%** while leaving male annuity rates approximately unchanged for savers who did not expect to opt for a joint-survivor annuity. **Single men** are used as the control group; **women** as the treated group. The asymmetry is driven by the combination of two offsetting effects on men (gender-specific tables now favouring men, but improved longevity) that nearly cancel out.

3. **Evidence of a large anticipation effect.** Subscriptions in the six months preceding the reform implementation were six to seven times normal-time levels — a sales surge larger than the one documented by Bütler, Staubli & Zito (2013), plausibly because subscribing a savings contract is administratively easier than postponing retirement.

4. **A behavioural anomaly on the male side.** Single men, who had no clear interest in subscribing before the reform, participated in the peak almost as strongly as women. The paper traces this to the supply side: insurance agents specialised in financial planning marketed the reform indiscriminately across genders, suggesting either ignorance or commercial incentives at the agent level.

5. **No contribution response.** While subscriptions fell, contributions per contract showed no statistically detectable response to the reform. Lower annuity rates were not offset by higher saving — savers therefore bear the full longevity-pricing pass-through into annuity income at retirement.

---

## 2. Institutional setting and data

### 2.1 The French pension system and Madelin contracts

The French pension system has three pillars: a dominant pay-as-you-go first pillar and two funded pillars (occupational and personal). Together, the funded pillars represented **2.2%** of total pension benefits during retirement in 2013 (Laborde, 2015).

The paper studies **Madelin contracts**, created in 1994, a tax-deductible personal pension savings vehicle for the self-employed with a **guaranteed deferred annuity**. Key features:

- Withdrawals during accumulation are forbidden (with narrow exceptions: long-term unemployment, personal bankruptcy, permanent disability).
- Contributions are deductible from taxable benefit; savings are allocated across a menu of mutual funds and a money-market fund.
- **Full annuitisation is compulsory** at retirement, with a deadline at age 75.
- Self-employed are over-represented among annuity holders: 50% hold a retirement saving contract vs. 8% of wage earners.
- 2014 industry size: 7 million holders across all products; for self-employed Madelin, 1 million contracts in accumulation, average yearly contribution €2,600, total contributions €2.6bn.

### 2.2 Annuity pricing formula

At conversion, the annuity payout $A$ is set to satisfy the actuarial fair-value condition

$$ W = \sum_{t=0}^{T} \frac{p_t A}{(1+r)^t} $$

with $W$ capital at conversion, $p_t$ the survival probability $t$ periods ahead, and $r$ the assumed interest rate. The annuity rate is therefore

$$ \frac{A}{W} = \left(\sum_{t=0}^{T} \frac{p_t}{(1+r)^t}\right)^{-1} $$

decreasing in survival probabilities $p_t$, increasing in $r$. The annuity rate is a **floor guaranteed at subscription** — it cannot be revised downward over the life of the contract. Insurers protect themselves by assuming low $r$ and somewhat optimistic mortality at issuance; eight-year ex-post redistribution rules apply when realised returns or longevity outperform assumptions.

In the paper's data, $r = 1.5\%$ for all contracts regardless of subscription year, so the only exogenous source of variation in the annuity rate around 2007 is the mortality table update.

### 2.3 The 2007 reform

In summer 2006 the government published new prospective gender-differentiated mortality tables (**TGH05** for men, **TGF05** for women) replacing the gender-neutral **TPRV93** for contracts signed from 2007 onwards. Plans subscribed before the reform retained the benefit of the previous tables.

For a representative cohort (born 1950, conversion at 65, $r = 1.5\%$, no reversion):

| Group | Pre-reform rate (TPRV93) | Post-reform rate | Change |
|:---|:---:|:---:|:---:|
| Women | ~5.0% | ~4.5% | **−10%** |
| Men | ~5.0% | ~5.0% | ≈ 0% |

For men, two opposing effects nearly cancel: the new tables are gender-specific (favouring men whose life expectancy is shorter than the unisex average) and incorporate longevity gains (lowering rates). For women, both effects work in the same direction (specifically female mortality is now applied, *and* longevity gains are factored in).

The **rates are valid only if the saver does not opt for a joint-and-survivor annuity** at retirement. Insurer's internal data on actual retirement choices (Table 1 in the paper):

| Reversion option | Men | Women |
|:---|:---:|:---:|
| No reversion | 46.6% | 92.5% |
| 60% reversion | 16.2% | 5.3% |
| 100% reversion | 37.2% | 2.2% |

Since the option is taken at retirement and the data covers the accumulation phase, the paper proxies men who do *not* expect to take the option by **single men** (unmarried, divorced, or widowed at subscription). Identification then compares female demand to single-male demand.

The implementation date was set by decree to 1 January 2007 but the focal insurer in the data delayed application to **1 March 2007** for sales-promotion reasons. All savers born after 1965 are dropped because previous tables are guaranteed only for plans converted before 31 December 2030 (and most subscribers convert before age 65).

### 2.4 The dataset

Nationwide sales of Madelin contracts from one large French insurer, **March 2002 – April 2009**, **7,853 subscriptions**. Variables include: sex, birth date, marital status, number of children, occupational category, *département* of residence, subscription date, contributions and contribution dates, share invested in risky mutual funds at year-end, distribution channel (general agent vs. specialised financial-planning agent), and marketing-department income/wealth indices (high-income and high-wealth dummies marking the top ~10%).

**Summary statistics by year (Table 2 in the paper).**

| | 2003–5 | 2006 | 2007 | 2008 |
|:---|:---:|:---:|:---:|:---:|
| Number of subscriptions | 3,023 | 2,536 | 1,054 | 1,240 |
| Women share | 0.341 | 0.358 | 0.283 | 0.285 |
| Avg. annual contribution (€) | 6,067 | 7,718 | 9,213 | — |
| Share of couples | 0.585 | 0.569 | 0.533 | 0.527 |
| Mean age | 48.3 | 49.5 | 50.4 | 51.0 |
| Share independent professions | 0.713 | 0.733 | 0.581 | 0.561 |
| Share business managers / executives | 0.075 | 0.068 | 0.114 | 0.125 |
| Share invested >50% in mutual funds | 0.334 | 0.420 | 0.391 | 0.203 |
| Share via specialised agents | 0.601 | 0.788 | 0.626 | 0.640 |

Two raw stylised facts already visible: subscriptions peaked in **2006** (the year before the reform), and the female share **drops from 35.8% in 2006 to 28.3% in 2007**, consistent with a differential treatment effect.

---

## 3. Methodology

The paper relies on three empirical strategies, mapped to three results sections.

| Section | Question | Sample | Specification |
|---|---|---|---|
| 3 | Anticipation: who subscribed during the peak? | Men and women separately, March 2006 – August 2007 | OLS, dependent variable = `PEAK` dummy (=1 if subscribed Sept 2006 – Feb 2007) |
| 4 | Post-reform subscription effect | Women + single men, March 2004 – February 2009 | OLS, dependent = `AFTER` dummy; coefficient on `WOMEN` measures the differential post-reform shift |
| 5 | Effect on contributions | Women + single men, March 2002 – February 2008 | Difference-in-differences; key coefficient on `AFTER × WOMEN` |
| App. 2 | Placebo / parallel-trends test | Same DiD specification, reform date shifted backward | Tests `AFTER × WOMEN ≈ 0` in pre-reform periods |

The control group of single men addresses two concerns simultaneously: (i) general time trends in the annuity market, and (ii) anticipation effects, since the male peak was proportionally as large as the female peak — supporting a parallel evolution of unobservables across the two groups.

The DiD parallel-trend assumption is supported visually (Fig. 5 in the paper) and formally by the four placebo regressions in Appendix 2 (Table 6), where the placebo `AFTER × WOMEN` coefficient is statistically insignificant in every sub-period.

---

## 4. Results

### 4.1 Anticipation effects (Section 3, Table 3)

**Magnitude.** Over September 2006 – February 2007 (the six months immediately before the implementation), women subscribed **6×** more contracts than the previous semester (778 vs. 131); single men subscribed **7×** more (512 vs. 73). The peak represents net new demand, not displacement: there is no detectable trough either before or after.

**Composition of the peak (Table 3).** OLS regressions of a `PEAK` dummy on a full set of socio-demographic and channel covariates yield two consistent findings.

- **Demand-side hypothesis rejected.** Higher-income, higher-wealth, business-manager/executive savers, or those living in Paris's wealthier districts, did **not** participate disproportionately in the peak. The few significant coefficients (e.g. women with children, share invested in mutual funds) do not consistently follow an "informed insider" pattern — male mutual-fund holders also disproportionately subscribed.
- **Supply-side mechanism dominates.** Subscriptions through **insurance agents specialised in financial planning** were strongly over-represented in the peak: marginal effect of **+18.75% for women** (p < 1e−6) and **+16.14% for men** (p < 3e−9). Specialised agents appear to have alerted their full client base to the reform regardless of gender, suggesting either incomplete knowledge of the gender-specific incidence or commercial incentives that overrode informational accuracy.

> **Authors' reading.** The male peak is the puzzling part: men had no clear gain from subscribing before the reform. The fact that they participated almost as strongly as women supports the broader "annuities are complex" literature (Brown 2009; Brown et al. 2017) and shows that even at the moment of a salient reform, the differential incidence was widely missed.

### 4.2 Post-reform subscription effect (Section 4, Table 4)

The dummy `AFTER` (=1 if subscription took place March 2007 – February 2009, =0 March 2004 – February 2007) is regressed on `WOMEN` plus controls, on the joint sample of women and single men.

| | Model (1) — bivariate | Model (2) — full controls | Model (3) — controls, **peak excluded** |
|:---|:---:|:---:|:---:|
| WOMEN coefficient | **−0.0816 ***** | **−0.0915 ***** | **−0.1202 ***** |
| Marginal effect (% point shift) | −8.16 pp | −10.02 pp | −13.15 pp |
| **% change in female demand** (÷ 0.623, post-reform female share) | — | **−16%** | **−20.9%** |
| **Implied price elasticity** (÷ 10% rate cut) | — | **−1.6** | **−2.1** |
| N | 3,835 | 3,835 | 2,545 |
| R² | 0.007 | 0.096 | 0.098 |

The headline number is a **price elasticity of subscriptions of approximately −1.5 to −2.1**, with the abstract reporting **−1.5** as the primary estimate (corresponding to model 2 rounded). Excluding the peak (model 3) widens the gap, which the paper interprets as evidence that the bias from anticipation cuts in the opposite direction (treating peak subscribers as post-reform subscribers attenuates the estimate, since the peak crowd had revealed-preference reasons to subscribe pre-reform).

### 4.3 Effect on contributions (Section 5, Table 5)

DiD specification:

$$ V_i = \beta_0 + \beta_1 \mathit{AFTER}_i + \beta_2 \mathit{WOMEN}_i + \beta_3 \mathit{AFTER}_i \times \mathit{WOMEN}_i + \beta_4 D_i + X_i \beta_5 + \varepsilon_i $$

where $V_i$ is log of annualised first-year contribution. The coefficient of interest is $\beta_3$ on `AFTER × WOMEN`.

| Specification | Model (1) — temporal dummies only | Model (2) — full controls |
|:---|:---:|:---:|
| AFTER × WOMEN | −0.0802 (s.e. 0.0941) | **−0.0567 (s.e. 0.0913)** |
| AFTER (level) | 0.3519*** | 0.1846** |
| WOMEN (level) | −0.1344*** | −0.1114** |
| N | 4,214 | 4,214 |
| R² | 0.015 | 0.082 |

**The reform did not significantly affect contributions.** Women contribute ~11 log-points less than single men on average (regardless of period), and both groups contributed more after 2007 than before, but the differential `AFTER × WOMEN` effect is statistically indistinguishable from zero.

Other coefficients in the full model behave as theory predicts: contributions rise with age and over the life cycle, are higher for independent professions and business managers, for high-income and high-wealth savers, and for residents of Paris and its richest suburbs (Yvelines, Hauts-de-Seine). Holding mutual funds has no significant effect on contributions.

### 4.4 Placebo / parallel trends (Appendix 2, Table 6)

The DiD is replicated four times with the reform date artificially shifted backward (2003-, 2004-, 2005-, 2006-cutoffs). The placebo `AFTER × WOMEN` coefficient is insignificant at the 10% level in every sub-period, supporting the parallel-trend assumption.

---

## 5. Conclusion

The paper exploits the gender-asymmetric incidence of the 2007 French mortality-table reform on Madelin deferred-annuity contracts to estimate three margins of demand response.

1. **Anticipation.** A six-month sales surge of approximately **6× normal volume** for women and **7× for men**, driven primarily by specialised insurance agents marketing the reform indiscriminately across genders.
2. **Post-reform subscriptions.** A 10% cut in the female annuity rate produced a **−16%** drop in female new subscriptions relative to single men, implying a **price elasticity of roughly −1.5** (and up to −2.1 if the peak window is excluded).
3. **Contributions.** No statistically detectable response. Savers do not compensate for lower annuity rates by saving more during accumulation, so the full pass-through of longevity-pricing reaches annuity income at retirement.

**Net effect.** Strong anticipation more than offset the post-reform demand drop in the short run. Under a constant −10% post-reform demand depression, it would take roughly **20 years** for cumulated lost subscriptions to absorb the initial six-month surge. Two-thirds of total demand came from men, for whom the reform had essentially no fundamental impact — a striking illustration that complex insurance products (Brown 2009; Brown et al. 2012, 2017) are widely misunderstood by both demand- and supply-side participants.

### Limitations and research extensions

The authors flag the following caveats and open questions, in line with their own framing:

- **Cohort effects vs. time effects.** The DiD compares contributions of *different* cohorts (because pre-2007 subscribers retain old tables forever), so cohort heterogeneity is controlled only through observables, not through following one cohort through the reform.
- **Assignment of single men to "no reversion" expected behaviour** is an assumption; the data show 46.6% of all men forgo reversion at retirement, but the share among savers who were single at subscription is unobserved.
- **Single insurer.** Generalising to the broader French Madelin market requires assuming the focal insurer's clientele is representative.
- **2011 European ruling on gender pricing** introduces a second regulatory shock from 2013 onwards, outside the sample window.

---

## Acknowledgments

The authors thank the insurance company for providing the data and its staff for advice; Ekedi Mpongo-Dika and Claire Lebarz for excellent research assistance; Michael Visser, Carine Milcent, and seminar participants at Paris School of Economics, the AFSE Annual Conference, the European Group of Risk and Insurance Economists Conference, and the World Congress of the Econometric Society for useful comments. The views expressed in the article are the authors' own and do not necessarily reflect those of their institutions.

---

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*The full reference list appears in the PDF.*