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.

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.