Projeções dos níveis e padrões da mortalidade no Brasil e grandes regiões 1950-2010-2110 pelo método coerente Lee-Carter estendido e outros: a tábua BR-Geracional e o risco de longevidade nas instituições previdenciárias do país

Abstract

BACKGROUND The twentieth century recorded significant improvements in mortality rates. Rapid population aging in recent years has been a global phenomenon that has profound implications not only for societies but also for governments. In many developed countries, concerns are focused on the health care of older individuals and on the sustainability of the Pension Systems, leading to the emergence of the term coined as Longevity Risk. In this context, mortality projections are fundamental tools for estimation of the survival expectancy of men and women over the years in the future. In the last decades, methods of mortality projection have undergone substantial improvements, whose watershed was the seminal work developed by Lee-Carter. As other developing countries in the world, Brazil does not have long time series of mortality curves, which makes it difficult to apply the modern methods of stochastic projection. OBJECTIVES The present work has three main objectives: 1) to construct a long time series of mortality curves from 1950, based on the IBGE tables of 1980, 1991, 2000 and 2010, for Brazil and its five Major Regions; 2) to present a methodological and results discussion using different methods of mortality projection for the Brazilian context, within a projection horizon of 100 years until 2110; and 3) from the projected tables, to construct a generation life table for Brazil, to be used to measure the impact of the longevity risk in its various Pension System segments. METHODS For the construction of the time series of mortality curves, the level given by life expectancy at birth (e0) was inverse projected to 1950, 1960 and 1970, based on a logistic regression with IBGE´s 1980, 1991, 2000 and 2010 abridged life tables, and the age schedule (pattern) of 1980 has been adjusted to the estimated level in these three first points. These seven abbreviated tables were transformed into complete ones, and then extrapolated from the open interval 80+ to 100+, by the Kannisto model. In the sequence, a log-linear interpolation of the mortality rates (Mx´s) was performed from these seven base points, resulting in a mortality surface for the period 1950-2010. With this constructed mortality surface, nine different stochastic mortality projection methodologies were tested, within the approach proposed by Lee-Carter (seven independent methods and two coherent methods). Once defined the most adequate method for Brazil, the table named BR-Generation was constructed based on the projected mortality, introducing the perspective of future cohort survival, whose impact of the longevity risk in Pension System segments was measured by the ratio between actuarial annuities calculated with the generation life table and those of a specific segment, by it´s benchmark period life table. RESULTS With regard to Mortality Projections, after several methodological exercises conducted for Brazil, from the mortality surfaces of 1950-2010, the technique of projection in two stages was adopted. In the 1st stage the e0´s were estimated by the Coherent Method of Hyndman (Product-Ratio) and in the 2nd stage the Mx's were estimated by the Coherent Method of Li, Lee & Gerland (Extended Lee-Carter), resulting in equivalent e0's of the 1st stage. As these methods present XV consistent results in one dimension only, gender coherence was chosen. After the final adjustments were made, e0 in Brazil in 2110 was estimated at 88.26 years for men and 90.94 years for women, with 95% confidence intervals. Mortality projections for the Major Regions were also consistent in the long run, except for the Midwest Region, due to the limitation concerning one-dimension of the coherent methods. With respect to the impact of the longevity risk calculated from the BR-Generation table constructed, it was observed that: 1) it´s inversely proportional to the age of the individual, 2) it´s greater for men than for women, 3) it´s directly proportional to the age of retirement and 4) it´s inversely proportional to the interest rate. From an arbitrary scale created, it was defined that the RPPS's would be very exposed, the EFPC's and the FUNPRESP would be exposed, and the EAPC's would be little or not exposed to longevity risk, but just in the case of adoption of mortality tables based on the survival of the Brazilian insurance market. The actuarial simulation carried out in the final part of the study based on fictitious information of more than 15,000 insured lifes among working age individuals, retirees and pensioners, pointed out to a longevity risk of 13.88%. CONCLUSION In spite of all limitations existing in the country, both for the construction of long time series of Mx´s that gave origin to the historical surface constructed and for the application of different methods of stochastic mortality projection tested here, the results of the projections in two stages have been satisfactory for Brazil and almost all it´s Great Regions, having been non-divergent and feasible, for men and women, even over the long horizon of 100 years of projection adopted. Despite the good results obtained, it is fundamental that a new methodology be created, to provide coherent results in several dimensions. In the delicate scenario of impending Pension System reform, like the Brazilian one, the results obtained here from the BR-Generation life table demonstrate that the impact of Longevity Risk, although differentiated according to the specific Pension System segment, must be considered in the new legal framework that will emerge in a very near future and must not be neglected. CONTRIBUTION It is understood that the main contributions of the work carried out here were: 1) the long time series of 61 years of Mx´s built for Brazil and it´s Major Regions in the period 1950-2010, information that gave rise to the mortality surfaces created, until then absent due to lack of information on deaths by age before 1974; 2) to show that it is possible to use, even in a developing country like Brazil, methods of mortality projection inside the framework proposed by Lee-Carter, that have numerous advantages when compared with the traditional methods of targeting used by the official statistics agency in the country, the IBGE, among them, the possibility of obtaining confidence intervals for projected mortality and less dependence on expert opinion, which has different degrees of subjectivity; and 3) the BR-Generation life table constructed from mortality projections, which may even be used by the Brazilian Social Security market in their actuarial reports as a reference, and which resulted in the estimation of the impact of longevity risk on these entities, by specific segment.