How price-elastic is the demand for retirement saving?

Abstract

We exploit an administrative data set 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 in previous studies, annuity demand is measured by contributions to savings products that result in capital being 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 into 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 to saving accounts. We also document a very large anticipation effect created by the opportunity offered to early subscribers to benefit from older pricing.

Introduction

The rise in life expectancy in developed countries not only puts pressure on public pension systems and their financial equilibrium but also affects private retirement plans that guarantee a regular income until the death of the insured. Since longer lifespan raises the cost of guaranteed income payments in old age, insurers are concerned about preserving their solvency. They do so by updating the mortality tables they use to convert wealth into annuities, with the effect of lowering annuity payouts in proportion to capital at the date of conversion. To what extent this may discourage savers from purchasing annuities is an open issue.

In France, insurers use regulatory mortality tables in which survival probabilities have been revised upwards several times since the 1980s. The resulting decrease in annuity rates (the rates at which savings are converted into an annuity at retirement) may be illustrated by the experience of a hypothetical male saver born in 1952. His rate was reduced from 7% before 1985 to 5% in 2007 and further by 4.5% in 2013, representing an overall 35% decrease. The drop affects a particular generation and is entirely driven by successive upward revisions of longevity.

Longer life expectancy being an international phenomenon, the upward trend of annuity prices has been observed in other countries as well. Cannon and Tonks (2004) document a significant drop in conversion rates since the 80s in the U.K. Cannon and Tonks (2009) show that lower conversion rates recorded over the 1994–2007 period are largely explained by the strong revision of annuitants’ life expectancy. This trend is confirmed by Lowe (2014) who notes that to obtain a nominal income of GBP 10,000 in 1990 GBP 65,000 were needed but by 2013 over GBP 175,000 were needed. In Switzerland, insurance companies have significantly reduced the conversion rate in the unregulated segment of the annuity market for the same reasons (Bütler et al. 2013).

The long-term annuity price increase raises interesting questions about savers’ reactions and the future of longevity insurance. Does it mean a fall in demand for annuity with worrying long-term consequences for the adequacy of retirees’ income in a context of reduced state-provided public pensions (OECD 2011)? Or are savers willing to compensate rising prices by saving more so as to preserve their standard of living at retirement? Savers might also decide to stay away from annuity products altogether—meaning there is less insurance against longevity risk.

Answering these questions requires an estimate of the price elasticity of demand for annuity contracts. To do so, we investigate the effects of a major French revision of mortality tables in 2007, which affected savings contracts in which the payment of life annuities is deferred until retirement age. Our data cover the accumulation phase, not the distribution phase. However, since withdrawals are forbidden during the saving phase, and full annuitisation of savings is compulsory on retirement, the decisions to subscribe to a contract and how much to save into it are direct measures of demand for annuities. We exploit the fact that the reform produced asymmetric effects on men and women. Annuity rates for women who subscribed to a contract after 2007 were reduced by about 10% compared to those who already owned a contract before this date. The reform was approximately neutral to men insofar as they did not expect to opt for a joint and survivor annuity. We assume that single men did not expect to opt for reversion at retirement, and therefore we use this population as a control group.

We apply our identification strategy to a unique data set from a leading insurer that contains a rich set of administrative information on savings contracts targeted at self-employed workers over the 2003–2009 period. In addition to information on the number of monthly subscriptions and individual contributions, the data set records subscribers’ gender, birth date, family status, district of residence, proportion invested in risky financial assets, and the distribution channel. It is supplemented by data from the marketing department about income and wealth profiles.

We first study the reform’s anticipation effects on sales. Attracted by the benefits of previous mortality tables, women subscribed to six times more contracts in the last 6 months prior to the reform compared to normal. We also find a similar rush for men, and we discuss why they subscribed to more contracts despite being much less impacted than women. We then turn to the impact of the reform on subscriptions. Compared with sales to single men, contracts sold to women decreased by 16%, representing a price elasticity of − 1.5. By contrast, after we controlled for demand by single men, we found that the reform did not significantly alter contributions to savings accounts.

Our results may be analysed through the lens of economic theory. In a standard consumption-saving model with uncertain longevity, competitive markets and time-separable intertemporal utility functions, the longevity risk is fully insured by the purchase of annuities in the sense that consumption evolves smoothly over the life cycle (Yaari 1965). If longevity is revised upwards during the saving phase, life cycle sustainable consumption is reduced, leading to more savings. This result is empirically found by articles which study the relation between life expectancy and aggregate savings (Kinugasa and Mason 2007; Miles 1999; Deaton and Paxson 1997; Lee et al. 2001). Yet, there are several reasons why this relationship may not hold in real world annuity markets. First, as annuity prices are being adjusted stepwise on an irregular basis, they do not continuously track changes in savers’ average life expectations. Second, savers may misinterpret the increase in annuity prices. If they underestimate the longevity gains at the origin of the increase, they may wrongly conclude that annuities are not worth investing in. Lowe (2014) remarks that annuities have become unpopular in the U.K. after a large fall in conversion rates and that this disaffection is best explained by people not factoring in the improved benefit provided by annuities when longevity is increasing. In this regard, marked preferences by investors for cash out rather than annuities documented in the literature (Brown 2009; James and Song 2001; James and Vittas 1999 for international evidence) may well be amplified by the fall in conversion rates. Such a response may, however, be detrimental to investors, as cash is a poor protection against longevity risk. Davidoff et al. (2005) and many others find that annuity products are adequate to insure against the risk of outliving one’s resources in old age.

While theoretical and simulation studies on annuity demand are abundant, the empirical literature is still comparatively small. Several articles have analysed survey data in which a sample of the population is asked hypothetical questions about their willingness to annuitise their wealth (Hurd and Panis 2006; Cappelletti et al. 2013). Other articles study real choices between annuities and lump-sum payments by retiring employees (Warner and Pleeter 2001; Benartzi et al. 2011; Bütler and Teppa 2007). Only two articles investigate the relationship between demand and price in the annuity market. Chalmers and Reuter (2012) study the choice between life annuities and lump sums made by a large sample of retiring public employees. They find little evidence that retirees respond to variation in life annuity pricing, which suggests that cross-sectional variation in annuity pricing is not salient enough to be noticed by unsophisticated investors.

In contrast, Bütler et al. (2013) analyse the effects of a salient and sizeable decrease of conversion rates which apply to the unregulated segment of the annuity market. They find a 14 percentage point decrease in the proportion of individuals choosing to convert their savings into annuities at retirement. They observe a large anticipation effect in the form of a sharp increase in the number of annuitants in the months preceding the conversion rate reduction. We also study the consequences of a large and salient regulatory reform, but we focus on the demand for retirement saving during the accumulation phase rather than the choice at retirement between cash out and annuities. This is particularly relevant, given that many countries like the U.S., Germany or the U.K. have deferred annuity products. We confirm a significant price elasticity of annuity demand. We also find an anticipation effect of a size even greater than the one found in Bütler et al. presumably because opening a savings contract is easier than postponing one’s retirement date. Our results are also linked to the expanding literature on the behavioural factors that discourage savers from purchasing annuities. Some articles have shown that the demand is sensitive to how the choices are framed (e.g. Beshears et al. 2014), to the default choice (Bütler and Teppa 2007), or to the complexity of the annuity choice (Brown et al. 2017). We contribute to this literature by investigating a real case study in which many savers were wrong about the true effects of a reform impacting annuity rates and subscribed to a contract despite having no special interest in doing so.

This article is structured as follows. The next section describes the French pension system, examines the effects of the 2007 reform for savers and presents the database. Then, we investigate the pre-reform anticipation effects on demand, and we assess the effects of lower conversion rates on new subscriptions. Subsequently, we look at the impact on contributions to saving accounts. The final section concludes.

French background and the 2007 reform

French background

The French pension system is a three-pillar system with a first pay-as-you-go pillar covering most pension expenditures, and two funded pillars—one occupational, the other personal. In 2013 contributions to the second and third pillars represented 4.3% of first pillar contributions and 2.2% of total pension benefits during retirement (Laborde 2015). Annuities paid in proportion to last earned income remain low due to insufficient contributions (Direr and Roger 2011).

The main financial products sold in the third pillar are deferred annuities, which bundle a savings product and an annuity contract. Contrary to immediate annuities, which are exchanged against a lump sum of capital, savings are first accumulated during a person’s working life before being converted into an annuity at retirement. Contributions are tax-favoured during the accumulation phase, then annuity income is subject to the regular personal income tax during the distribution phase. In 2014, 7 million individuals held such products. Some products are specifically designed for civil servants (Préfon Retraite), others for wage-earners (Plan d’Épargne Retraite Populaire) or the self-employed (Madelin contracts). The self-employed invest more in retirement savings than wage earners due to their lower public pensions. Contributions by this occupational category added up to EUR 2.6 billion in 2014, with 1 million contracts in the accumulation phase and an average yearly contribution of EUR 2600 per contract.

The present study focuses on Madelin contracts. Created in 1994, they are a tax-deductible personal pension savings vehicle with a guaranteed deferred annuity. They start with an accumulation phase during which withdrawals are forbidden, except in exceptional cases (long-term unemployment, personal bankruptcy or permanent disability). Contributions are deductible from taxable benefit, and savings are allocated across a selection of mutual funds proposed by the insurer. Accumulated wealth is then fully converted into a lifelong nominal annuity at retirement age, with a requirement to annuitise by the age of 75. French self-employed workers are, on average, richer than the rest of the population. They are, however, more representative of the sub-population of annuity holders, as 50% of them hold a retirement savings contract compared to only 8% of wage earners.

Conversion rates of capital into annuities are regulated. The annuity is calculated so that the saver’s capital at retirement is equal to the expected actuarial sum of annuities weighted by survival probabilities at each age. The formula which relates the annuity rate to a mortality table and a discounting rate is presented in Appendix 1. At the time of subscription, insurers guarantee a mortality table and a minimum interest rate to savers. Mortality tables are enforced by government law. They are periodically updated with the latest revisions dating back to 1985, 1993, 2007 and 2013. Since the 2000s, the interest rate assumed by insurers to discount future flows (see Appendix 1) has varied between 0 and 2.5%, depending on the contracts. It is equal to 1.5% for the contracts in our data set.

In 2006, the government, led by a European directive, issued a decree forcing insurers to price annuities separately for men and women. In March 2011, the European Court of Justice unexpectedly ruled that it would, in future, be unlawful for European Union member states to use gender as a factor in the calculation of insurance premiums and benefits with effect two years later. This led to a new regulatory reform implemented in 2013. This article focuses on the consequences of the 2007 reform. The 2011 regulatory reversal is unlikely to bias our estimates since it came as a complete surprise for savers and even professionals in the market. The assumed interest rate may vary across contracts and periods but cannot be changed after subscription. It was the same for all contracts in our data, whatever the subscription year, so that the only exogenous change affecting the annuity rate around the 2007 period is the update of mortality tables.

The 2007 reform

In summer 2006, the government published new prospective mortality tables called TH05 differentiated by birth year and gender (TGH05 for men and TGF05 for women) to replace previous gender-neutral tables TPRV93 from 2007 onwards. The new tables only applied to contracts signed after this date. Plans that were subscribed to before 2007 retained the benefit of previous tables. Figure 1 shows annuity rates before and after the 2007 reform for female subscribers with respect to birth year.

Fig. 1

Female annuity rates by birth year in mortality tables TPRV93 and TGF05. Note The annuity rate is the annuity payout in proportion to accumulated wealth at the time of conversion. Table TPRV93 applied to female policy owners before 2007, and Table TGF05 after 2007. Calculation hypotheses Saving plan’s conversion at 65 y.o.; assumed interest rate of 1.5%; no reversion to the surviving spouse

Rates decrease with birth year for both tables since younger generations are expected to live longer than older ones.¹ Annuity contracts are much less attractive for women with the new tables TGF05 than with the older ones TPRV93. For example, cohorts born in 1950 benefited from a conversion rate of 5% before the reform but only 4.5% with the new tables, representing a 10% fall in annuity for a given amount of capital. The price rise has two causes: increasing longevity and the fact that annuity prices become solely based on female survivorship rates. Figure 2 shows the same graphic for men.

Fig. 2

Male annuity rates by birth year in mortality tables TPRV93 and TGH05. Note Table TPRV93 applied to men before 2007, TGH05 after 2007. Calculation hypotheses Conversion at 65 y.o.; assumed interest rate of 1.5%; no reversion to the surviving spouse

By contrast, the reform is more or less neutral to men. This comes from the coexistence of two opposite effects of similar magnitude. On the one hand, previous tables TPRV93 were used for both genders, whereas the new tables TGH05 are gender-specific and as a result more favourable to men since their statistical life expectancy is shorter. On the other hand, the new tables factor in improved longevity since the last time mortality was estimated, which reduces annuity rates.

The rates are valid for savers who will not opt for a joint and survivor annuity at retirement. The impact of the reform on joint-life annuities is less clear cut. Compared to single life annuities, women benefit from a lesser reduction, whereas men are negatively affected by the reform. We have data, provided by the same insurer, about who chose a joint survivor option at retirement (Table 1).

Table 1 Joint life annuity frequency by gender.

More than one in two men chose to opt for a survivor annuity either at 60% or 100% while the vast majority of women did not. Since the option is taken at retirement and we have data on the accumulation phase, we cannot sort out savers who expected to take the option from those who did not. This is only a real issue for men as few women take the option in Table 1. It is handled by assuming that men who declared they were single in our data (unmarried, divorced or widowed) at the time of subscription did not expect to choose a joint survivor option. Regarding our identification strategy of the reform’s effects, the saving choices of women will be investigated, and the group of single men will be our control group.

Data

We use data recording nationwide sales of Madelin contracts from a large insurance company between March 2002 and April 2009. It contains 7,853 subscriptions with information about savers and contracts: gender, date of birth, marital status, number of children, occupational category, residential district,² subscription date, contributions and contribution dates.

Contributions to Madelin contracts are allocated among several mutual funds preselected by the company, and a money market fund. Mutual funds, mostly composed of equities, are risky. The money market fund is composed of short-term debt and offers a risk-free rate of return. Our data indicates the share of wealth invested in risky mutual funds by policy owners at the end of each year.

We obtained an income index and a wealth index for customers in our data set from the marketing department. The higher the index, the higher the estimated customer’s income or wealth. From those indices we built two dummy variables, called high-income profile and high-wealth profile, which are equal to 1 if the policy owner’s index exceeds a conventional threshold; as a result, approximately 10% of customers are classified as high-income or high-wealth, respectively. The type of seller who distributed the contract is also recorded. It is either a general agent who sells all the company’s insurance products (home insurance, car insurance, etc.) or a specialised agent who focuses on financial planning (retirement, financial advice and insurance planning) targeting high-income customers. Both types of sellers are independent contractors who have an exclusive mandate with the insurer.

The implementation date for the new tables was set by government decree to 1 January 2007. However, some insurers delayed their application of new contracts by a few months for sales promotion. The insurer that provided us with the data switched to the new tables on 1 March 2007. Even for savers who subscribed before this date, previous tables were only guaranteed for plans converted into annuities before 31 December 2030. As most subscribers converted their plan before the age of 65, all savers born after 1965 are discarded from the data.

We observe all contributions made between January 2002 and February 2009 in plans still in the accumulation phase in 2009. Contribution frequency varies from one subscriber to another. Some contributed every month, others quarterly or annually. Contributions are annualised by aggregating those with a periodicity shorter than one year, starting from the first month of subscription.³

Table 2 shows summary statistics by subscription years.

Table 2 Summary statistics of the data set

Table 2 shows interesting raw results. Annual subscriptions reached a peak in 2006 just before the policy change. It represented 2.5 times the average number of sales recorded between 2003 and 2005 and 2.4 times the number observed in 2007. The share of women was stable at around 35% before the policy change then dropped to 28% two years after the reform, which may be attributable to the reform’s negative effects on new female subscribers. Contributions steadily increased between 2003 and 2007. We will show in the section ‘Reform’s effects on contributions’ that the trend was smooth around the reform date both for impacted and non-impacted populations.

The next two sections examine the extent to which the policy change affected subscriptions. The following section investigates the anticipation effects before the reform and the subsequent section studies the post-reform price effect.

Reform’s anticipation effects

Figure 3 documents how strong an anticipation effect was created by the reform. Subscriptions are merged by six-month periods and they separate women from single men. Contract sales are normalised to 100 for the first half of 2006, which was the last semester before the reform took effect. The vertical line indicates the date of the reform.

Fig. 3

Six-month subscriptions, index base 100: first half of 2006 (06S1). Note The first half of the year starts in March, so that the first half of 2007 starts the first month of implementation of the new tables. Hence, the period 02S1 aggregates subscriptions from March 2002 to August 2002, 02S2 from September 2002 to February 2003, etc. The number of subscriptions is normalised to 100 for the first half of 2006 (06S1). The vertical line indicates the implementation date of the new tables

The last 6 months of 2006 are characterised by a six-fold increase in female subscriptions and a seven-fold increase in male subscriptions compared to the first 6 months of the same year.⁴ Over this period, the insurer sold the equivalent of 3 years of the normal number of subscriptions. This represents a net demand rather than a sales displacement. The periods just before and after the peak did not appear to suffer from a trough of sales. Rather, it seems that the imminent implementation of the reform convinced new customers to take out a savings plan.

We conclude that the reform’s announcement opened a “sales period”, during which a product is temporarily sold at a discount. The same phenomenon is observed in other retail industries although its size is unusual. One explanation lies in the way insurance contracts are sold. Madelin contracts are distributed by insurance agents who sell multiple contracts to their customers (home insurance, car insurance, death insurance, etc.) and are in a long-term contracting relation with them. As a result, they have a full list of readily contactable customers. They also efficiently prospect their customer base as they know who is self-employed, and therefore eligible for the sales promotion, and who has not yet subscribed to a contract. Their easy access to a well-targeted list of potential purchasers who have already signed contracts with them in the past is a powerful marketing leverage that may explain a large part of the sales peak.

Outside the peak, sales remained approximately stable apart from a seasonal increase of about 50% in the second half of each year. The 2008 subscriptions seem not to have been affected by the concomitant financial crisis, presumably because savings can be invested in riskless assets with a minimal rate of return guaranteed by the insurer (see Appendix 1).⁵

The female peak can be simply explained by the reform. Indeed, we saw in the section ‘French background and the 2007 reform’ that women benefited from more favourable annuity rates by subscribing before March 2007. The male peak is more difficult to rationalise since the reform hardly affected them. Given that the increase in demand was mainly a net demand, it appears that a large number of male investors would not have subscribed if the reform had not taken place. It seems that men were confused by the actual effects of the reform and that the differential treatment according to gender was widely overlooked.

To further investigate the nature of the peak, we test two plausible scenarios, a demand-side effect and a supply-side effect. According to the first scenario, more informed women but less informed men should have disproportionately participated in the peak. We presume that the richest individuals, those with upper-class occupations or those who live in the wealthiest residential areas are better informed. Consistent with an offer effect, more informed sellers should be associated with more women and less men participating in the peak. Insurance agents specialised in financial planning have a priori better knowledge of regulatory constraints than general insurance agents. To test those scenarios, we estimate an OLS model over an 18 month period from March 2006 to August 2007. The explained variable PEAK is a binary variable equal to 1 if a saver subscribed during the six-month peak, and 0 if the subscription took place 6 months before or after that period. We regress separately for men and women on a series of explanatory variables listed in Table 3.

Table 3 Regression of subscribing during the peak vs before or after the peak for men and women separately (OLS model)

The demand-side story is not validated by the results. The richest or wealthiest, business managers and executives, or those from the wealthiest residential areas participated in the peak in the same proportion as other populations. One exception is female owners of mutual funds, who are presumably more knowledgeable about financial markets. Yet, contrary to intuition, male mutual funds owners also disproportionately subscribed during the peak.

Although it was not the one expected, an interpretation involving the supply side emerges from the results. Insurance agents specialised in financial planning did attract more female customers than general insurance agents during the peak but they also attracted more male savers. On the one hand, they were probably better aware of the imminence of the reform than general insurance agents and rightly alerted their female clientele in greater proportion. On the other hand, they seemed to disproportionately misreport the impact of the reform to men, either through ignorance of its gender-specific details or due to commercial incentives. The relative stability of the composition of savers by socio-demographic characteristics during the peak is consistent with the indiscriminate sales to the whole population.

Reform effects on new subscriptions

The analysis of the reform shows that the annuity rate for women who subscribed after the reform was reduced by about 10% compared to the rate for women who subscribed before it. We investigate whether the reform discouraged female savers from subscribing to a plan by comparing pre- and post-reform subscriptions of women after controlling for temporal effects by using single men subscriptions.

First, a methodological clarification is necessary. The sales peak presented in the previous section raises questions about the quality of the control group. We observed that single men massively subscribed right before the reform just as women did, which reveals some confusion about the reform’s differential impact on men and women. However, one may argue that while savers may have been easily mistaken about the reform’s consequences before it took effect, errors were unlikely after its implementation. The misinformation problem was critical before the reform since savers could not easily know in advance what their rate would have been if they had waited a few additional months. Because the effects of the reform are complex to understand, most of them relied on sellers’ information, which proved to be imperfect. On the contrary, once the reform was implemented, their annuity rate was known precisely. It is the rate guaranteed by the insurer at subscription and written in the contract’s general terms and conditions.

One might also fear that the sales peak dried up the market for several years, leading to a persistent depressed demand after the reform. However, a trough of sales after the peak cannot be detected in Fig. 3. Moreover, since the male peak was proportionately as important as the female one, this effect is also controlled by the evolution of the male demand. In other words, if a displacement effect biased down our estimate of the impact of the reform on sales to women, it also biased in a similar way sales to single men. From a methodological point of view, the fact that single men participated in the peak improves the ability of this group to control for confounding factors after the reform.

Figure 4 shows the evolution of the ratio of new subscriptions by women to new subscriptions by single men.

Fig. 4

Subscription ratio of women to single men, semi-annual frequency. Note The graphic plots the ratio of female subscriptions to single men’s subscriptions. Men in couples and subscribers whose family situation is not recorded are excluded (13% of male and female subscribers). Semester 02S1 aggregates subscriptions from March to August 2002, 02S2 from September 2002 to February 2003, etc. The vertical line indicates the implementation date of new tables

The ratio remained approximately flat from 2003 to 2006, then declined after the implementation date—indicated by a vertical bar—in accordance with a substantial effect of the reform on female demand. The impact is estimated by an OLS regression that controls for a large set of characteristics:

$$AFTER_{i} = \, f(\beta_{0} + \beta_{1} WOMEN_{i} + X_{i} \beta_{2} + \varepsilon_{i} )$$

where AFTER_i equals 1 if subscription i took place after the reform, from March 2007 to February 2009, and 0 before the reform, from March 2004 to February 2009. X_i is a vector of covariates described in the sub-section ‘Data’ and presented in Table 2. Our sample is restricted to women and single men. The variable of interest β₁ measures to what extent female subscriptions deviated from single men’s subscriptions after the reform. Table 4 shows the results for three models. In model (1) the dummy AFTER is regressed on WOMEN without any control variables. Model (2) adds a full set of covariates. One might worry that a six-fold increase in demand during a short period of time would bias our estimates. This is why the robustness of our results is checked in model (3) in which the six-month period of the peak has been removed.

Table 4 OLS regression of subscribing after vs before the reform date

In all three models and in accordance with the visual impression from Fig. 4, the WOMEN estimator is significantly negative at the 1% threshold. The marginal effect of WOMEN measures how much the female share varies due to the reform. It is equal to − 8.16% in model (1), − 10.02% in model (2) and − 13.15% in model (3). Taking the average share of women in the studied population after the reform as a reference, which was 62.3%, variation rates in female demand in models (2) and (3) are − 0.1/0.623 = − 16% and − 0.13/0.623 = − 20.9%, respectively. With a 10% increase in annuity price, price elasticities are − 16/10 = − 1.6, and − 20.9/10 = − 2.1, respectively. In both cases, the quantitative impact of the reform on annuity demand was quite significant.

Reform’s effects on contributions

Did the policy change also impact how much savers contributed to their plan? We exploit the asymmetric effects of the reform for women and single men to estimate the impact on contributions. We use a difference-in-difference approach with a treated group (women) and a control group (single men). However, we do not follow a cohort of subscribers before and after the reform since women who subscribed before the reform retained the benefit of the old tables afterwards. Instead, we compare the contributions of subscribers who opened a plan before and after the reform. This method allows us to control for time effects (contributions are compared with the same dates), but not for cohort effects. The latter are controlled by the inclusion in the regressions of demographic, geographic, socio-occupational variables and by income and wealth indices.

We may wonder to what extent anticipation effects documented in the section ‘Reform’s anticipation effects’ might bias the reform’s estimated impact on contributions. A bias could arise if unobserved variables are correlated with the propensity to contribute and the decision to subscribe before the reform. For example, if wealthier savers subscribed earlier due to better information, the reform’s impact on contributions could be biased down. In this regard, single men seem to adequately control for anticipation effects. This group experienced a subscription peak at the same time as women and of similar magnitude to women. This suggests that potential unobserved effects driving the anticipation effect affected women and single men in the same way. This impression is reinforced by the results of the section ‘Reform effects on new subscriptions’ which show that sales composition for both women and men was not significantly altered during the peak (see Table 3). Moreover, two major factors of the peak, subscribing through an agent specialised in financial planning, and investing in mutual shares, affected both genders in a similar way.

The validity of the difference-in-difference methodology is based on the parallel trend assumption according to which the contributions from the treated and control groups would have followed a common trend, had there been no reform. This assumption can be tested on years preceding the reform. If the 2007 reform is the unique event that differentially impacted the savings decisions of the two groups, a parallel trend in savings should be observed before 2007. Figure 5 plots average contributions for the first year of the contract by women and single men for every subscription year over the period 2002–2007.

Fig. 5

Average contributions for every first year of subscription. Note A year n goes from March n to February n + 1. Contributions in saving accounts are annualised to eliminate infra-annual fluctuations and differences in timing of contributions

The parallelism of contributions during years prior to the reform is graphically verified. Men’s contributions seem to control for women’s contributions in the absence of identified events differently affecting the two genders. Statistical tests reported in Appendix 2 confirm the parallel trend assumption. Figure 5 also shows that the difference remains approximately constant after the reform, suggesting that regulatory changes did not produce a significant impact on contributions. To test the absence of effect, we estimate contributions between March 2002 and February 2008 using the OLS model:

$$V_{i} = \beta_{0} + \beta_{1} AFTER_{i} + \beta_{2} WOMEN_{i} + \beta_{3} AFTER_{i} \times \, WOMEN_{i} + \beta_{4} D_{i} + \, X_{i} \beta_{5} + \varepsilon_{i}$$

(1)

where V_i denotes subscriber i’s log of annual contribution; AFTER_i equals 1 if subscription took place between March 2007 and February 2008, and 0 before; WOMEN_i is equal to 1 for female policyholders, and 0 for male ones; the cross-dummy variable AFTER_i × WOMEN_i equals 1 if the contribution is made by a woman after the reform, and 0 otherwise. Its coefficient measures the impact of the reform on contributions. The D_i are temporal dummies that cover annual periods from March to the following February over the period 2002–2006. X_i includes covariates described in the section ‘Data’.

Table 5 presents two sets of regression, one with control variables limited to temporal dummies, and another one with all control variables. In both models, women contribute significantly less than single men. The two groups contribute more after the reform than before, but the difference is not statistically different across groups. Hence, it is not possible to discern any controlled impact on female contributions.

Table 5 OLS regression of log of contribution 2002–2008

Other explanatory variables have the expected sign. In the full model, contributions increase with age. Upper occupational categories (business managers, executives and independent professions) contribute more than other occupations, and so do those with high income and great wealth. Customers who live in Paris or its wealthy suburbs and those who subscribe to a plan through an insurance agent specialised in financial planning contribute more as well. High proportions of wealth invested in risky mutual funds have no statistical impact on contributions.

Conclusion

Annuities are special savings products. They address the financial planning needs of people approaching retirement by protecting against the risk or outliving one’s assets. It is therefore of prime interest to study to what extent higher prices deter savers from purchasing life annuities. This study exploits the asymmetric effects on annuity prices of a French regulatory reform for the purpose of estimating the impact on the demand for retirement savings. Three margins of behavioural responses are distinguished: anticipation effects created by the brief opportunity of benefiting from old annuity rates, post-reform effects on subscriptions, and contributions.

A powerful increase in demand just before the reform is evidenced. Subscriptions were six times higher over a six-month period. A significant effect on subscriptions after the reform is also highlighted by comparing female subscriptions affected by the reform and subscriptions by single men who were not concerned by it insofar as they did not expect to take the joint survivor option. We find a large annuity price elasticity of − 1.6.

While the reform was anticipated by a large number of investors, contributions to savings accounts remained stable during the first year after the reform. Hence, the drop in annuity rate has not been offset by more saving, at least in the short-run. Savers are therefore likely to benefit from lower annuity income at retirement.

Overall, the reform had lasting positive effects on the number of subscriptions. Due to strong anticipation effects, the post-reform reduction in demand was more than offset by the initial strong increase in the 6 months preceding its implementation. Assuming that the demand is permanently 10% lower than what it would have been without the reform, post-reform effects would cancel out the initial peak sales only after 20 years of depressed demand.

The overall positive effect of the reform is largely based on excess demand by men, which represents two thirds of total demand. Yet, a close inspection of the reform reveals that men had no clear interest in subscribing before the reform. This puzzle reinforces the idea that annuity contracts are complex products that are poorly understood by investors (Brown 2009; Brown et al. 2011). Understanding the benefits of lifelong annuities involves knowledge about capital markets, mortality tables and the regulatory framework—knowledge that most savers lack. This study also highlights the ambiguous role of the supply side. Insurance agents specialised in financial planning were more likely than general insurance agents to persuade new customers before the regulatory reform, but they did not discriminate enough between men and women.

Appendices

Appendix 1: The annuity pricing formula in the French market

The way insurers determine annuity rates is regulated in the French market. At the time of conversion, the annuity is computed such that, given a mortality table and an assumed interest rate, the discounted expected sum of income received by annuitants is equal to accumulated wealth:

$$W = \sum\limits_{t = 0}^{T} {\frac{{P_{t} A}}{{(1 + r)^{t} }}}$$

where A is the annuity payout amount; W is capital at the time of conversion; P_t is the probability of being still alive in t periods; and r is the interest rate assumed by the insurer to discount future annuities. The resulting annuity rate is:

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

which decreases with survival rates p_t and increases with assumed interest rate r.

An important feature of the French regulatory framework is that the annuity rate is a minimal rate guaranteed at the time of subscription. It cannot be reduced over the course of the contract in case of financial underperformance (a realised rate below the assumed rate r) or if annuitants live longer than mortality tables anticipated. Insurers protect themselves against those downside risks by assuming from the start a low assumed interest rate and by using regulatory tables which are to some extent optimistic about savers’ longevity. Conversely, all financial gains coming from above expectation return or below expectation longevity must be redistributed to subscribers within a delay of 8 years through higher annuities. Insurers make a profit by charging fees similar to fees in mutual funds (front-end loads and investment management fees). They also levy mortality and expense fees during the distribution phase.

Appendix 2: Formal test of the parallel trend assumption

The parallel trend assumption is tested by a placebo strategy, which consists in replicating the difference-in-difference procedure in the section ‘Reform’s effect on contributions’, but shifted backward to a time when no known event had distinctly affected women’s and single men’s situation. Based on our data, starting in 2002 the econometric test presented in Eq. 1 can be replicated four times back in the past. Table 6 shows the regression results.

Table 6 Least ordinary square regressions of log of contribution for various sub-periods

Estimates of the variable of interest AFTER × WOMEN are not significant even at the 10% threshold for all sub-periods. The parallel trend assumption in the absence of differential treatment is therefore supported by our data.