Historical and Projected Mortality for Mexico,Canada, and the United States

Abstract

This paper presents historical death rates for Canada, Mexico, and the U.S. by sex and broad age group. The time period for this historical analysis begins with 1900 (1930 for Mexico). These data provide a quite consistent basis from which experts can develop and contrast their expectations for future mortality trends. Official mortality projections developed by government agencies of each of the three countries provide a starting point for this discussion.

During this century, death rates declined fairly rapidly in all three countries. However, the rate of mortality improvement has varied considerably across time periods: distinct periods of rapid and slow improvement are evident in the data, but are not consistent across the countries and have not yet been explained.

The historical rates of improvement in mortality have also varied greatly by age and sex: younger age groups have shown the most rapid proportional improvement in mortality in all three countries, and mortality improvement during this century has generally been greater for females than for males. However, the data provide evidence that this difference in the rates of mortality improvement between men and women has recently slowed, and even reversed, in the U.S. and Canada. Historical experience and projections are provided in graphs, in which death rates are plotted on a logarithmic scale. This approach allows easy detection of the extent to which rates of improvement have been changing (death rates with constant rates of improvement would be plotted as straight lines).

The official projections supplied for comparison provide strikingly similar outlooks for future potential mortality improvement. In each case, the relatively average rapid rate of mortality improvement experienced so far this century is assumed to slow in the future. In addition, rates of improvement are projected to be much more similar for all three countries across age groups and between the sexes.     

Multi-population mortality forecasting using tensor decomposition

ABSTRACT

In this paper, we formulate the multi-population mortality forecasting problem based on 3-way (age, year, and country/gender) decompositions. By applying the canonical polyadic decomposition (CPD) and the different forms of the Tucker decomposition to multi-population mortality data (10 European countries and 2 genders), we find that the out-of-sample forecasting performance is significantly improved both for individual populations and the aggregate population compared with using the single-population mortality model based on rank-1 singular value decomposition (SVD), or the Lee–Carter model. The results also shed lights on the similarity and difference of mortality among different countries. Additionally, we compare the variance-explained method and the out-of-sample validation method for rank (hyper-parameter) selection. Results show that the out-of-sample validation method is preferred for forecasting purposes.     

Mortality Change and Forecasting

Abstract

Prospects of longer life are viewed as a positive change for individuals and as a substantial social achievement but have led to concern over their implications for public spending on old-age support. This paper makes a critical assessment of knowledge about mortality change. It is oriented toward the problem of forecasting the course of mortality change and the potential of existing work to contribute to the development of useful forecasts in Canada, Mexico, and the U.S.

We first examine broad patterns in the historical decline in death rates in the three countries, the effect of these on trends in life expectancy, and the epidemiological transition. Next we review theories of the age pattern and evolution of mortality, including graduations, evolutionary theory, reliability models, dynamic models, and relational models.

The analysis and forecasting of mortality change have been shaped largely by some key historical lessons, which we summarize next. We emphasize issues that have been or are likely to be significant in mortality analysis, especially the questions of the age pattern and time trend in mortality at old ages; we distinguish patterns and facts that are established from those that remain uncertain. Next, we consider mortality differentials in characteristics such as sex, marital status, education, and socioeconomic variables; we summarize their key features and also point to the substantial gaps in our understanding of their determinants.

Finally, we review methods of forecasting, including the scenario method used by the U.S. Social Security Administration and the time series method of Lee and Carter. We set out some important recommendations for forecasters: forecasting assumptions should be made more formal and explicit; there should be retrospective evaluations of forecast performance; and greater attention should be paid to the assessment and consequences of forecast uncertainty.     

Explaining Mortality Dynamics

Abstract

Using data for six OECD countries over the period 1950–2006, this paper studies the impact of macroeconomic fluctuations and cause of death trends on mortality dynamics in the Lee-Carter mortality forecasting model. The key results of this study are the following: (1) Periods can be identified in which the Lee-Carter mortality index k_t correlates significantly with macroeconomic fluctuations. (2) A few causes of death such as diseases of the circulatory system, influenza and pneumonia, and diabetes mellitus account for a large fraction of the variations in the Lee-Carter mortality index k_t . (3) Most cause-specific mortality rates show pronounced trends over the last few decades. These trends change the composition of deaths and alter how total mortality reacts to external factors such as macroeconomic fluctuations.     

A principal component model for forecasting age- and sex-specific survival probabilities in Western Europe

The assessment of future mortality is of high importance in many areas where the allocation of future resources has to be planned in time, especially in social security and private life insurance. This contribution represents an extension of the classic forecasting approaches of Bell–Monsell and Lee–Carter. Based on a forecast of the first two principal components, age- and sex-specific survival probabilities for 18 Western European countries are predicted simultaneously until the year 2070. In addition to the correlations in the mortality trends between the age groups and the genders, international trends in mortality are captured as well. A major improvement in the classic Lee–Carter models is the adequate quantification of the uncertainty associated with the whole system of variables by stochastic simulation of all remaining principal components with simple time series models. The model’s easy applicability to further analyses is illustrated by forecasting the median life span as well as the resulting Gender Gap for Germany, France, and Italy.     

Mortality of Smoking by Gender

Exposure to cigarette smoke has had and will continue to have a huge effect on mortality. Significant differences in smoking prevalence rates by gender have contributed to varying levels and rates of improvement in mortality over the last several decades and are expected to continue to influence mortality improvement differently over the next several decades. The combined effect of greater historical smoking prevalence rates by males and their corresponding earlier and larger reduction has in part been responsible for the recent improvement in mortality rates for males compared to that for females in the United States. Similar patterns are evident in almost all economically developed countries, although their timing and levels differ. The patterns in less-developed countries will likely follow similar patterns as concerns emerge about the effect of smoking on the mortality of their citizens. The objective of this article is to compare smoking prevalence and cessation by gender and the effect on smoking-attributable and, in turn, all-cause mortality. A summary of mortality attribution approaches used to enhance the evaluation of the effect of smoking and projections of mortality rates by gender is also provided.     

Approaches and Experiences in Projecting Mortality Patterns for the Oldest-Old

Abstract

In 1998 the United Nations Population Division extended the age format of its estimates and projections of population dynamics for all countries and areas of the world from 80 years and above to 100 years and above. The paper is based on experiences made during the implementation of relevant mortality projection methodologies and their application in two rounds of global population projections.

The paper first briefly addresses the need for the explicit inclusion of very old population segments into the regular UN estimates and projections. It is argued that since population aging is an important issue for both developed and developing countries, the need for more information regarding the elderly, and the oldest-old in particular, is significant.

The paper then documents the methods that have been evaluated and implemented, namely, the relational mortality standard proposed by Himes, Preston, and Condran, the Coale-Kisker extrapolation method for extending empirical age patterns of mortality to very high ages, and the Carter-Lee projection method for projecting model patterns of mortality to very high levels of life expectancy at birth. The methods are critically reviewed, and possible improvements to the methods are discussed.

The paper concludes with a discussion of different views regarding the future evolution of mortality at older ages, their regional variability, and the necessity to improve the coverage and quality of data collected in this area.     

Outlier analysis and mortality forecasting: The United Kingdom and Scandinavian countries

The Lee-Carter model and its variants have been extensively employed by actuaries, demographers, and many others to forecast age-specific mortality. In this study, we use mortality data from England and Wales, and four Scandinavian countries to perform time-series outlier analysis of the key component of the Lee-Carter model – the mortality index. We begin by employing a systematic outlier detection process to ascertain the timing, magnitude, and persistence of any outliers present in historical mortality trends. We then try to match the identified outliers with imperative events that could possibly justify the vacillations in human mortality levels. At the same time, we adjust the effect of the outliers for model re-estimation. A new iterative model re-estimation method is proposed to reduce the chance of erroneous model specification. The empirical results indicate that the outlier-adjusted model could achieve more efficient forecasts of variables such as death rates and life expectancies. Finally, we point out that the Lee-Carter forecasts are especially vulnerable to outliers near the forecast origin, and discuss the potential limitations of the application of the Lee-Carter model to mortality forecasting.     

A Cautionary Note on Natural Hedging of Longevity Risk

In this article, we examine the so-called natural hedging approach for life insurers to internally manage their longevity risk exposure by adjusting their insurance portfolio. In particular, unlike the existing literature, we also consider a nonparametric mortality forecasting model that avoids the assumption that all mortality rates are driven by the same factor(s).

Our primary finding is that higher order variations in mortality rates may considerably affect the performance of natural hedging. More precisely, although results based on a parametric single factor model—in line with the existing literature—imply that almost all longevity risk can be hedged, results are far less encouraging for the nonparametric mortality model. Our finding is supported by robustness tests based on alternative mortality models.     

Forecast of computer developments and applications 1968–2000

This study, based on the Delphi forecasting technique, is the result of two questionnaires circulated to the participants of FILE 68, an international seminar on file organisation held in Denmark in November, 1968.¹ Responses were received during a one-month period when questionnaires were mailed to and returned by participants. The method used for the study is described, and the results are reproduced graphically.     

The maximum entropy mortality model: forecasting mortality using statistical moments

ABSTRACT

The age-at-death distribution is a representation of the mortality experience in a population. Although it proves to be highly informative, it is often neglected when it comes to the practice of past or future mortality assessment. We propose an innovative method to mortality modeling and forecasting by making use of the location and shape measures of a density function, i.e. statistical moments. Time series methods for extrapolating a limited number of moments are used and then the reconstruction of the future age-at-death distribution is performed. The predictive power of the method seems to be net superior when compared to the results obtained using classical approaches to extrapolating age-specific-death rates, and the accuracy of the point forecast (MASE) is improved on average by 33% respective to the state-of-the-art, the Lee–Carter model. The method is tested using data from the Human Mortality Database and implemented in a publicly available R package.     

Measuring Basis Risk in Longevity Hedges

Abstract

In examining basis risk in index longevity hedges, it is important not to ignore the dependence between the population underlying the hedging instrument and the population being hedged. We consider four extensions to the Lee-Carter model that incorporate such dependence: Both populations are jointly driven by the same single time-varying index, the two populations are cointegrated, the populations depend on a common age factor, and there is an augmented common factor model in which a population-specific time-varying index is added to the common factor model with the property that it will tend toward a certain constant level over time. Using data from the female populations of Canada and the United States, we show the augmented common factor model is preferred in terms of both goodness-of-fit and ex post forecasting performance. This model is then used to quantify the basis risk in a longevity hedge of 65-year old Canadian females structured using a portfolio of q-forward contracts predicated on U.S. female population mortality. The hedge effectiveness is estimated at 56% on the basis of longevity value-at-risk and 81.61% on the basis of longevity risk reduction.     

A multi-dimensional Bühlmann credibility approach to modeling multi-population mortality rates

In this paper, we first propose a multi-dimensional Bühlmann credibility approach to forecasting mortality rates for multiple populations, and then compare forecasting performances among the proposed approach, the CBD model, the Lee-Carter model (LC), the joint-k (JoK-LC), the co-integrated (CoI-LC), and the augmented common factor (ACF-LC) Lee-Carter models for multiple populations. Mortality data from the Human Mortality Database are fitted to the underlying mortality models for both genders of three well-developed countries (the US, the UK, and Japan) and both genders of a developed country (France) and a developing country (Poland) with an age span 25–84 and a wide range of fitting year spans. Empirical illustrations show that the proposed multi-dimensional Bühlmann credibility approach contributes to more accurate forecast results, measured by AMAPE (average of mean absolute percentage errors over all fitting year spans), than the CBD, LC, JoK-LC, CoI-LC and ACF-LC models for three forecasting year spans 2004–2013 (10-year wide), 1994–2013 (20-year wide) and 1984–2013 (30-year wide).     

Improving the Forecast of Longevity by Combining Models

Mortality is a dynamic process whose future evolution over time poses important challenges for life insurance, pension funds, public policy, and fiscal planning. In this paper, we propose two contributions: (1) a new dynamic corrective methodology of the predictive accuracy of the existing mortality projection models, by modeling a measure of their fitting errors as a Cox-Ingersoll-Ross process and; (2) various out-of-sample validation methods. Besides the usual static method, we develop a dynamic one allowing us to catch the change in behavior of the underlying data. For our numerical application, we choose the Cairns-Blake-Dowd (or M5) model. Using the Italian and French females mortality data and implementing the backtesting procedure, we empirically test the ex-post forecasting performance of the CBD model both for itself (CBD) and corrected by the CIR process (mCBD). We focus on age 65, but we show results for a wide range of ages, also much younger, and for cohort data. On the basis of average measures of forecasting errors and information criteria, we show that the mCBD model is parsimonious and provides better results in terms of predictive accuracy than the CBD model itself.     

Investor Protection and Governance in the Valuation of Emerging Markets Investments

The combination of ineffective corporate governance at the company level and an uncertain legal and regulatory environment can significantly reduce the prices investors are willing to pay when investing in companies in emerging markets. The authors report the findings of their recent survey that asks investment professionals to compare the value of a hypothetical Australian company with that of its identical counterparts located in five emerging markets: Malaysia, Mexico, Saudi Arabia, South Africa, and Iran. The responding investors said they would value the emerging markets investments at discounts from the value of the Australian company that ranged from a low of 13.5% for its Malaysian counterpart to 51.2% for the Iranian company. Moreover, they indicated they would require costs of equity for these investments that were consistent with even larger valuation discounts. The investors' responses to the survey also suggest that corporate governance is especially important in countries with weaker investor protection. Well‐governed companies located in these countries enjoy significant value premiums that can partly offset the negative effect of the poor institutional environments, which suggests there may be a significant payoff for investors that succeed in improving the governance of the companies they invest in.     

Longevity and adjustment in pension annuities,with application to Finland

The aim of this paper is twofold. First, the improvement in adult mortality in Finland is studied. Lee-Carter (LC) Poisson log-bilinear model is used for mortality forecasting. Secondly, the paper studies how the pension annuities are adjusted to unexpected mortality pattern. A formula for funded plan is proposed. Application is made with Finnish mortality rates predicted using the LC model.     

The use of earnings and cash flows in investment decisions in the U.S. and Mexico: Experimental evidence

In this study, we investigate which of two accounting performance measures, earnings or cash flows, is used more in valuation decisions by non-professional investors in the United States and in Mexico. This issue is relevant for the Mexican Stock Market (Bolsa Mexicana de Valores) because the Bolsa's growth has stagnated compared with markets of other Latin American countries. Results of the study reveal that the majority of participants in the U.S. rely on earnings while the majority of participants in Mexico rely on cash flows. Results also suggest that the users’ predisposition can be dysfunctional to the extent that they do not consider using the other accounting measure, even when doing so made it easier to arrive at the correct valuation result (i.e. they did not choose to use the more persistent and therefore easier to forecast accounting measure). However, results are mixed for participants using earnings, since we document a higher chance of forecasting errors for participants in both countries when using earnings rather than cash flows in their calculations for the failure of these participants to adjust earnings for depreciation.This study extends the existing international literature by documenting a country-specific predisposition to use cash flows or earnings as a valuation tool by non-professional investors. Moreover, this study also shows that this predisposition can be dysfunctional, leading participants to make incorrect valuation decisions as a result of their failure to consider the differential persistence of the two accounting measures presented in the experiment.     

Cognitive representations of the future: Survey results

This paper reports the results of a web-based survey concerning how people think about the future. Five hundred and seventy-two people from 24 countries completed the survey. The results indicate that when the respondents hear the word ‘future’, they think about a point in time 15 years into the future, on average, with a median response of 10 years. Respondents think less about the future than the present. On the other hand, they tend to worry more about the future than the present. Respondents’ ability to imagine the future goes ‘dark’ around 15-20 years into the future. Most of the respondents are optimistic about the near term, but become more pessimistic about the longer term. Respondents believe that humankind is not acting very responsibly with respect to a whole host of environmental and social issues but is acting responsibly with respect to technology. Almost half of the respondents would not wish to have been born in the future. Most of the other respondents would have preferred to have been born 50-500 years into the future. Approximately 45% of the sample believes that humankind will become extinct. The data suggest that Christians are more optimistic and less worried about the future and do not believe that we will become extinct. Males worry less but also think more about the future. There is a strong correlation between thinking about the future, clearly imagining the future, and being optimistic about the future. It is concluded that individuals have diverse and rich conceptions about the future but that they think less about the future than futurists might hope. Individuals’ considerations of the future are highly influenced by their identities and worldviews. Future research should focus on better unraveling these relationships and on understanding their implications for futures-oriented policy making.     

A case study using forecasting as a decision-making aid

By experimenting with forecasting techniques, potential users can broaden their time horizons and improve their understanding of possible future outcomes. This paper describes the aims, structure and results of a seminar on Public Administration performed at the College of Europe in Bruges, Belgium, in September, 1969. The primary techniques used were the Delphi method and the Cross-impact matrix technique.