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Tuesday, July 19, 2022
Unisex Pricing of Annuities: Both Women, Men, and Providers Lose?
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Abstract
We are living in an increasingly long-lived world. In Spain, life expectancy exceeds 80 years, and most of today's young people will live to be 100 years old. Today, we know that longevity is synonymous with health; it is not about living longer than before, but living longer in a healthier way.
Professor Emeritus of Social Statistics at the University of Helsinki, Juha Alho, reflects on annuities from their origin in the late Middle Ages to the present day. Alho looks at and analyses the different factors that are directly related to annuities; life expectancy, mortality, age and gender, among others.
Articulo
Edmond Halley (1656-1742), a polymath, is primarily known as the astronomer who predicted the reappearance of the comet that we now know by his name. But, arguably, his demographic work is of
comparable value.
Based on the bills of mortality from Breslau, he was the first to produce a lifetable of actuarial value. In the late Middle Ages, annuities were sold at a flat price, independent of the buyer's age. This would be reasonable, if the hazard of death would not depend on age. Halley demostrated that the hazard generally increases with age, and computed the fair value for an annuity that pays one unit per year until death, under a discount rate. Setting the discount rate to zero, the result is that a fair price for a unit annuity purchased at age x equals the remaining life expectancy at x (plus
provider expenses and profit).
Just like age, gender is a determinant of longevity: women live longer than men. The female advantage has varied over the decades, and from country to country, but appears to have been universal.
During the 1900s, the difference in life expectancy at birth has been in Europe typically 3-8 years higher for women. Yet, a decade ago the European Union adopted Directive 2004/113/EC, which says
that annuities sold to women and men must have the same prices at every age x.
Actuarially minded observers noted immediately that this requirement runs counter to the basic principles that go back to Halley, if not earlier. I consider the EU policy from the point of view of an
individual and annuity provider, and argue that both men and women probably lose because of the directive. And so do the providers. Individual's Point of View Consider an individual at 65th birthday. If the person is a male, then using the lifetable (of Finland for 2019), we find his remaining life expectancy to be 18.55. If the person is a female, she is expected to live 22.02 more years. These are average values we expect in a large cohort of 65 olds.
More relevant for the individual is his/her own fate. If our person is a male, we find from the lifetable that chances are 9 out of 10 that his life will last between 3.5 and 31 years. If our person is a
female, the corresponding prediction interval is [6.0, 34]. In particular, there is a 5 % chance that the individual's remaining years exceed these intervals. This is a huge uncertainty for the
individual to prepare for!
I consider a situation in which the individual is covered by whatever statutory pension his/her country's legislation mandates. But, suppose our person has assets in the form of real estate, securities, or cash. Apart from bequest considerations, for a risk averse individual it would make sense to consider investing some of the assets into an annuity, to protect for the very real possibility that the person might live some 12 or more years, beyond the 20, or so, years expected. And possibly have a low level of consumption for many of these additional years.
Risk sharing among a cohort of annuitants is an envy-free contract: it is not known in what order deaths in the cohort occur, so no one has a reason complain about the fact that the annuity payments made by those who die early are used to cover the outlays to those who live longer.
Effect of Changing Mortality on Provider's Outlook
The idiosyncratic uncertainty the individual faces is relevant for the provider of annuities.
But, if the lifetimes of individuals are statistically independent, the laws of large numbers assure the provider that the relevant quantitity to consider is the expected remaining lifetime of the annuitants. Central limit theorems then enable the provider to assess the uncertainty remaining around the expectation.
The independence conditions are known not to hold generally, however. It was understood already in Halley's time that wars, famines, epidemics, crop failures etc. have caused shocks in mortality. (It seems that a reason for choosing data from Breslau was that such effects were not present in those data.) Being unpredictable, they can statistically be modeled by annual variance components that are shared by the population of a city, province, or a nation, each year.
The situation changed in the 1800s, when a secular decline in mortality began, in Europe. The producers of national mortality forecasts were typically aware of the decline, but through most of the 1900s, it was not believed to persist. Instead, mortality decline was assumed to slow down and stop by some chosen target day. During the past three decades, empirical estimates of the past forecasts have shown that massive errors in survivors have ensued from this assumption.
Nowadays, it is generally accepted by students of mortality that mortality declines may continue indefinitely.
The annual random shocks have reduced in size, but as evidenced by the current COVID pandemic, and more generally by the annual influenza epidemics, they continue to exist. The aggregate level uncertainty due to the annual shocks continues to be typically larger than the uncertainty resulting from the aggregation of idiosyncratic uncertainty.
The remaining question a potential provider of annuities faces is, how rapid the decline will be. In Halley's time there was no need to distinguish between period and cohort lifetables, but now adopting the cohort point of view is vital. It becomes necessary to rely on forecasts of future mortality trends. This is the dominant source of uncertainty for the potential provider of annuities.
Estimates of mortality decline are influenced by the data period chosen for analysis, as mortality is known to have had periods of slower and faster decline. A second choice that is of consequence is the measure of mortality that is chosen for analysis. It appears, that if age-specific mortality is extrapolated in log-scale, then mortality decline is underestimated, but if, e.g., Wang transformations (i.e., normal scores of survival probabilities) of are used, then faster decline is predicted. These choices are subject to error. Modeling error is an aspect of statistical analysis that is often ignored in time-series predictions.
Possibility of Adverse Selection Effects Remains
Above, I have written as if it were the case that the annuitants would come from a homogeneous population of individuals, who face the same (albeit, imperfectly known and random) mortality risks.
This is not accurate. In addition to age and gender, mortality is known to vary by economic status, country, and region of residence, for example.
Such factors can be measurable. If so, they can potentially be taken into account in the pricing of annuities. However, unlike gender, they are liable to vary over the life course.
Whenever the information about heterogeneity with respect to mortality is not available, or is not allowed by law, the provider of annuities is forced to make some assumption about the resulting selection effects. In the case of gender, the reasonable assumption is to price annuities based on a statistical model of mortality for women, and charge men the same rate, since it could be that only women, who are expected to live longer, would purchase annuities.
This is ostensibly discriminatory against men, especially since male and female mortalities have diverged during some decades, and converged during others. Analyzing genders as separate, but jointly, can produce forecasts that are more robust against modeling error than the independent consideration of either individually.
Similarly, since errors of male and female mortality forecasts are not perfectly correlated, losses in annuities sold to one gender are, to some extent, covered by gains from annuities sold to the other. Selling annuities at gender-specific prices would reduce selection effects markedly.
Tentative Conclusions
I believe it is correct to say that women's role in the labor market continues to be worse than that of men in many, if not all, European countries. Therefore, I also think that when a country's pension system includes a basic part guaranteed for everyone, and a mandatory earnings-related part, be it funded or pay-as-you-go, then one can fairly decide that those universal parts should not recognize gender in any way.
However, a well-functioning state should also offer its citizens other forms of risk sharing. In particular, informed citizens should have the option to purchase, at market price, supplementary coverage against risk of low income at old age, if they so choose.
I think that, despite its laudable aim of improving the lot of women in the labor market, the Directive 2004/113/EC uses the wrong tool. Privately purchased annuities can have high utility value as compared to other forms of consumption or saving, for both women and men. This is especially important now that the European populations age rapidly, and knowledge and interest in the quality of life in old age increases. This is one of the few tools European governments have at their disposal to encourage welfare gains from risk sharing that are both envy-free and effective, while still relying on market principles rather than being mandatory.
But, annuities should be priced using sound statistical principles, and taking advantage of advances in that field. Having a selection of different types of annuities available would benefit both genders. Giving up unisex-pricing requirement would remove an important source of uncertainty. The prices would be more accurate. The prices would also likely be lower, for both men and women, since the providers would have less need for overly conservative safety margins - and women would, under both unisex ja gender-specific pricing, be paying "women's prices" anyway. For the providers more marketable products and a larger market would be available. Women would win, men would win, and the providers would win. Banning the use of gender in annuity pricing is not only sub-optimal, it is medieval.
P.S. Transgender issues have deliberately been left out above. The details depend on national legislation.
Aplaudir
0 aplausos
THE AUTHOR ENCOURAGES US TO EXTEND THE DIALOGUE WITH THIS QUESTION
Con los precios unisex de las rentas vitalicias, ¿pierden tanto las mujeres como los hombres y los proveedores?
Respuestas de expertos
Juha Alho has argued against the EU directive on unisex pricing for annuities. This directive not only changes the pricing of annuities, it also applies to health insurances, life insurances and car insurances. For this reason, I want to take a somewhat broader perspective in my comment, although I completely support his negative view. Being an economist, I ask whether there could be an economic case for unisex pricing of insurance products? What could be the general economic guidelines or rational to apply? Based on these guidelines, how would we then asses the unisex pricing of various insurance products?
An economic price of an insurance product (or any other product) typically reflects the individual benefit (or in economic terms the utility) the buyer generates from consuming that product. In most cases, we are dealing with purely private benefits so that my own consumption has no impact on other people. If I only benefit from my own consumption, there is at least no clear intuitive reason, why the price should deviate from my individual benefit. Of course, this reasoning does not apply any more when my consumption or cost also affect other people in a positive or a negative way. In such cases, the (in an economic sense) appropriate price I pay also has to reflect such externalities.
For example, until 2008 the cost of child birth and motherhood were only borne by women in the German private health insurance. This practice ended in 2008 and I guess that hardly anybody would argue in favour of such gender-specific premiums. At least implicitly we have in mind that not only the mother, but also the father and at the end the whole society benefits from children. The reform reduced the premiums for women slightly but they still had to pay 15 to 20 percent higher premiums because of additional cost due to longer life spans. This practice ended in 2012 with the implementation of the EU directive. In my opinion, an equity argument could justify gender independent premiums in such mandatory health insurance contracts. But why does this not apply to annuity pricing? First, annuities are a typical private product where no externalities are involved.
Consequently, there is no justification for unisex pricing based on efficiency or allocative reasons. Second, there is in my opinion also no equity argument in favour of unisex pricing. Annuity products are typically not mandatory such as health insurance. If the insurance provider asks an average, gender independent price, the insurance premium rises for men and decreases for women. Consequently, fewer men will buy the product so that the price increases further until at the end only women buy the annuity at the previous gender-specific price. Consequently, women are not better off than before, but men are now excluded from the market. This is a clear deterioration in the sense of Pareto.
Of course, the same argumentation applies in the case of life insurances, but here women will be excluded from the market at the end. On the other hand, this argument does not apply in the case of car insurances. They are mandatory and the past driving behaviour can be taken into account when calculating individual premiums. I see no clear argument against unisex pricing.
I think that unisex pricing which is intended to prevent gender discrimination may induce in some situations more discrimination once the market reactions are taken into account.
Consequently, one has to be very careful to apply unisex pricing to insurance products. I do not completely dismiss it for all insurance products, but I see no economic case for unisex annuity pricing.
There is a great lack of knowledge of lifetime annuity insurance by a large part of the population, understood as a product that combines pension provision with an efficient means of saving or investment, as an alternative to the traditional offers of the banking sector, which prevents it from developing in Spain as it has in most European countries.
The excessive survival of people means that the savings made throughout their professional lives are insufficient to meet the needs of the last years of life, so we must ensure the payment of decent pensions throughout their lives, however long they may be.
To this end, it is necessary to start as soon as possible a social welfare system complementary to the social security system, and life annuity insurance is an excellent product for this purpose.
Life insurance companies operate through the grouping of risks and the law of large numbers, in such a way that, although it is not possible to know when the event is going to occur, it is possible to estimate the number of events in a certain period of time for a large number of insured persons through mortality tables.
Every welfare system must consider the coverage of the following contingencies:
1.- The sudden death of the person, leaving economic instability for their relatives.
2.- Excessive survival, so that the savings made throughout a person's professional life are insufficient to cover the needs of these final years.
3.- The occurrence of a violent, sudden and external accident or illness that diminishes or cancels the obtaining of current and future income.
The insurance company is in charge of the administration and control of all the contributions or premiums made by the different components of the group, as well as establishing the relationship between the money contributed by each of the components and the guaranteed sum insured that corresponds to them, depending on a series of variables, such as the valuation of the actuarial age, the financial profitability obtained on the funds of the money invested and the duration of the payment of the annuities.
In the case of pure annuity insurance, where there is no coverage in the event of death, the totality of the premiums paid is dedicated to savings and capitalised at the technical interest rate, giving rise to mathematical provisions.
The application of the mortality tables by sex in the contracting of lifetime annuity insurance, generates that the interest rate applied, taking into account the probability of death (higher in men than in women) is higher due to the probability of not paying the lifetime annuities if the beneficiaries of these annuities die, for this reason, the approach is not that women lose out compared to men, but that the annuity received is higher for men, due to the fact that their probability of death is higher than that of women and, therefore, it is foreseeable that these annuities will cease to be paid earlier in the case of men.
Unisex pricing leads to an increase in the probability of death for women and a similarity to that of men, so that the annuities received are equal for men and women.
Gender differentiation in annuity pricing is justified by the fact that gender is a determining factor in risk assessment based on relevant and accurate actuarial and statistical data.
Carlos A. Quero
Profesor del Postgrado en Previsión Social
Excluding sex in the pricing of individual life insurance, both survival and pure risk, does not make actuarial sense and must be understood as an application of the principle of equality of contributions, not of benefits, because if the premium is identical by sex, the benefits will be different. The logic of different rates used previously was that the same benefit was being insured, albeit with a different premium. We have therefore moved from a situation of "sex discrimination in the premium", where women and men paid for their own risk, to "sex discrimination in the benefit", where the unisex premium will depend on the male/female mix of the insurance provider. Nothing would prevent an "informed" consumer from arbitraging and taking out insurance products with a "favourable gender bias" and directing his or her savings to other financial products where it is unfavourable, especially in the current trend of not favouring some solutions over others within the third pillar. On the contrary, in company life insurance, in the second pillar, the pricing is by sex, so that we find that the same risk is priced differently, in an area, in the workplace, where the same criteria could be defended as in individual insurance.
It is not true that gender, like age, is the only variable that explains the premium. The world of Big Data may open the door to more precise, " near-individual " pricing, allowing insurers to reduce the current implicit risk by taking into account other factors (education, standard of living, income, medical factors, etc.). This argument, which is used to argue that the unification of rates by sex is consistent with principles of non-discrimination because rates can be adjusted for other factors, may clash with the consumers' point of view. For are consumers prepared to pay different premiums for risk factors of which they do not know the economic influence on the premium, and is there not a risk that future age discrimination, for example, will be prohibited by regulation?
The further risk pricing moves away from its empirical measurement, the greater the margin of safety that insurers may require, and thus the less attractive the price becomes for customers.
Jaime García Moral
Socio Director de Novaster
Almost 20 years ago, in 2003, I shared an article by the European Commissioner for Employment and Social Affairs, Anna Diamantopoulou, entitled "For insurance without sexual discrimination" with my students of the Actuarial Degree at the University of Barcelona. In which, the Commissioner explained how women are systematically discriminated against in survival insurance for the simple fact that they have a higher life expectancy than men and, consequently, defended the European Commission's draft directive aimed at achieving a equal treatment in the insurance industry.
From the interesting debate that took place in class, and having previously accused this professor and all the actuaries and future actuaries, as well as the (female) future actuaries present there, of being sexist (obviously in a humorous sense and only as a catalyst to promote discussion in class), several conclusions that I think are interesting and valid 20 years later. Which I dare to summarize below.
The mission of actuaries is to assess the risks that we face as a society, for which we base ourselves on the empirical data available to us and, based on a series of calculations and mathematical models, obtain the best possible estimate of its future evolution. This should allow us to face these future risks in the best possible way from an economic perspective. Our ultimate goal is to die of success, that is, reduce the risk factor to probability 1 (which would make us mere financiers).
In the biometric field, to predict future survival or mortality, we rely on tables that are prepared in accordance with accumulated historical experience. This experience tells us that women live longer, therefore, if we must calculate a life annuity for women and another for men based on the same accumulated capital, consequently the income will be less for women, given that the experience accumulated up to the date (and it always has been) in table form tells us that it will live longer. But, on the contrary, if what we are asked to calculate is life insurance, that is, the probability of death as of today, the premium that the man will have to pay will be higher, since the probability of his death is elderly.
If this empirical fact changes, the first interested in reflecting it in insurance prices will be the actuaries and the insurance market itself, since otherwise we will cease to be competitive and, above all, we will run the risk that our financial provisions will not cover the risk assumed.
In any case, we actuaries have always made our calculations and we will continue to do so, as it cannot be otherwise, based on the information available and if this information has any reduction or limitation for whatever reason, we will simply adapt . However, the less information we consider, the greater variability and risk in the future, so the safety margins applied should be higher. Otherwise, the insurer is in danger of going bankrupt and that all its clients are left without the protection for which they have paid.
Finally, in any healthy market and trade, the principle of free competition must exist and every customer must pay a fair price in relation to the goods and services that he requires. Also in the insurance market.
From a technical point of view, there is no problem in ignoring the gender variable, and we could even stop using other variables such as age, level of training, place of residence, etc. We will continue to produce insurance, and although we will undoubtedly obtain more egalitarians, the price will go up since precision is obviously lost.
Taking into account the above and in the specific case of ignoring the gender variable, a higher price is obtained globally for both men and women and, although it may seem otherwise, no one will win, not even the insurance companies, since with some products more expensive, surely the market will also suffer, in addition to the fact that it will promote situations of imbalance and anti-selection (a greater number of men will formalize life insurance, as their premium decreases, and a greater number of women will subscribe to savings insurance, as their benefit increases) and in At the extreme end, ignoring the empirical data, the insurance market will stop fulfilling its mission and we actuaries will die of failure given that there will only be a single equal premium without any relation to reality.
Luis María Sáez de Jáuregui
Vicepresidente Fundación AXA
The actuarial complexity of gender.
Gender equality is a fact and a legal, social and human right that sometimes clashes with economic reality.
A simple idea that, however, hides a much more complex reality. It has been demonstrated that, whatever the time, country, race or region of the world, women live longer and, as such, actuarial logic leads us to think that higher rates and greater mathematical provisions should be applied in life annuities, although for the last 15 years this has not been possible in a generalised manner in the calculation of the premium due to the application of Organic Law 3/2007, which transposed a European directive in this sense; specifically Council Directive 2004/113/EC of 13 December 2004 implementing the principle of equal treatment between men and women in the access to and supply of goods and services. Thus, Article 71 of the Organic Law, concerning actuarial factors, established in its first paragraph that it prohibited the conclusion of insurance or related financial services contracts in which, by considering sex as a factor in the calculation of premiums and benefits, differences in the premiums and benefits of insured persons are generated.
However, the Organic Law, like the Community Directive it transposed, opened a loophole to circumvent this natural right to equality and established an exception on the application in the calculation of the premium of actuarial tables that differentiate survival according to sex.
The Organic Law itself, in the second paragraph of its article 71.1, transposed the permissive text of the directive verbatim, where it was stated that cases could be established in which proportionate differences in premiums and benefits of persons considered individually are admitted, if sex constitutes a determining factor in the assessment of risk based on relevant and reliable actuarial and statistical data -something quite easy-. Consequently, the entire insurance industry in Europe continued to apply different tariffs according to gender.
This was the case until the judgment of the Court of Justice of the European Union (Grand Chamber) of 1 March 2011 in case C-236/09 (Association belge des Consommateurs Test-Achats ASBL) ruled that Article 5(2) of Council Directive 2004/113/EC of 13 December 2004 implementing the principle of equal treatment between men and women in the access to and supply of goods and services was declared invalid with effect from 21 December 2012.
From that moment on, the cat flap was tightly closed in pricing, totally to differentiate between the sexes, even though there was data verifying the higher life expectancy of women. This ruling repealed the "famous" second paragraph of article 71.1, which had until then left equality "in the doldrums" until 21 December 2012.
Now, of course, this legal prohibition is only for insurance contracts from financial services, i.e. individual insurance, because group insurance has its own legislation where, in the calculation of the premium, the differentiation of actuarial tables by sex is permitted. This is included in the current Law 20/2015, of 14 July, on the regulation, supervision and solvency of insurance and reinsurance companies, where in the third paragraph of article 94, relating to premium rates and technical bases, it is established, with regard to the principle of equal treatment between men and women, that insurance contracts linked to an employment relationship are exempt from this, in which differentiation in premiums and benefits is permitted when justified by actuarial factors. This is in accordance with Directive 2006/54/EC of the European Parliament and of the Council of 5 July 2006 on the implementation of the principle of equal opportunities and equal treatment of men and women in matters of employment and occupation.
Therefore, ladies and gentlemen, the actuarial legal gibberish is being served up, because at present, in the calculation of the premium, actuarial discrimination is permitted in the field of group insurance, i.e. in the field of employment, but actuarial discrimination is not permitted in the field of individual insurance, i.e. in the financial field. And, as if that were not enough, when calculating the mathematical provisions of the insurer, the use of the fact that women have a longer life expectancy is permitted in all cases.
The problem of gender discrimination due to women's longer life expectancy, a paradoxical situation, is not always solved by forcing - or recommending - the legislator to use unisex actuarial tables.
In the field of individual insurance, the mandatory use of a unisex table does solve gender discrimination, but it has its drawbacks, including the generalised increase in prices - assuming that the insurer is a rational economic agent - in order to maintain solvency ratios and the higher capital costs it entails. Therefore, the application of gender-differentiated tables improves the solvency of the system. At the same time, de facto, the application of unisex tables means that only insurance consumers finance this laudable social policy. Consequently, it is not society as a whole - applying criteria of equity and redistributive justice - that bears the cost of the gender equality policy, but only the consumers of the product. It can be said that, perhaps, the diffuse nature of this cost does not generate too much rejection, but, in any case, it exists and, therefore, it must be highlighted.
But in the field of employment, i.e. group insurance - including occupational pension schemes - using a unisex table does not solve gender discrimination, which is why the legislator allows differentiation by sex.
It is therefore necessary to provide for other measures to alleviate discrimination, especially in these products that fall within the scope of employment and whose contributions by employers - contributions - are wages. In this case, it is not discrimination based on the use of financial services, but wage discrimination, which is even more serious.
This is undoubtedly a complex issue on which there is no technical, political and social consensus. In 2006, the undersigned, together with Professor Dr. González Rabanal, published by the Institute of Fiscal Studies, carried out a study on the use of a unisex actuarial table and whether its use succeeded in avoiding discrimination between women and men. The conclusion was that with respect to individual insurance it does avoid discrimination - although it generates the problems mentioned above - but with respect to group insurance it does not. Alternatives in the field of employment, which are still in force, were analysed in order to fulfil the aim of non-discrimination, looking at what the economic cost would be and how it could be evaluated. Already then we fixed a solution through a subsidy to the employer, which can be instrumented as a deduction in his or her Corporate Tax quota, for the amount necessary to avoid discrimination and that this is calculated, for each fiscal year, as the difference in actuarial capitalisation that occurs between men and women.
Bibliography:
GONZÁLEZ RABANAL, Mª de la C. y SÁEZ DE JÁUREGUI SANZ. L. Mª (2006): La política comunitaria contra la discriminación de género: una propuesta de evaluación de su coste en los planes y fondos de pensiones de empleo. Su aplicación al caso español. INSTITUTO DE ESTUDIOS FISCALES. Madrid.
Directiva 2004/113/CE del Consejo, de 13 de diciembre de 2004, por la que se aplica el principio de igualdad de trato entre hombres y mujeres al acceso a bienes y servicios y su suministro.
Directiva 2006/54/CE del Parlamento Europeo y del Consejo, de 5 de julio de 2006, relativa a la aplicación del principio de igualdad de oportunidades e igualdad de trato entre hombres y mujeres en asuntos de empleo y ocupación.
Ley Orgánica 3/2007, de 22 de marzo, para la igualdad mujeres y hombres.
Ley 20/2015, de 14 de julio, de ordenación, supervisión y solvencia de las entidades aseguradoras y reaseguradoras.
SÁEZ DE JÁUREGUI SANZ, L. Mª (2007): "Las tablas actuariales de supervivencia y la igualdad efectiva de mujeres y hombres.". Indice: Revista de Estadística y Sociedad del INE, nº 23. Págs. 17-19.
SÁEZ DE JÁUREGUI SANZ, Mª Elena (2004): “La estrategia de discriminación de precios entre sexos en el sector asegurador: una cuestión de solvencia”. TESIS. Madrid. ICEA.
Sentencia del Tribunal de Justicia de la Unión Europea, de 1 de marzo de 2011.