The Effect of Marriage Tax Penalties and Subsidies on Marital Status

The United States personal income tax system treats married and unmarried couples differently, creating both penalties and subsidies for marriage. This paper examines the effect of these penalties and subsidies on the choice of marital status. Endogeneity between the marriage penalty a couple faces and its marital status is dealt with using a simulated instrument capturing variation in the tax code over time and between states. I find that a $1,000 change in the financial incentive for marriage has a 1.7 percentage point (1.9 per cent) effect on the probability of marriage. This effect is symmetric for subsidies and penalties and, whilst modest, is four times larger than previously estimated. Lower education groups and couples without children are the most responsive.     

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.     

“A Direct Approach to the Discounted Penalty Function”, Hansjörg Albrecher,Hans U. Gerber,and Hailiang Yang,Volume 14, No. 4, 2010

Abstract

Mortality improvements, especially of the elderly, have been a common phenomenon since the end of World War II. The longevity risk becomes a major concern in many countries because of underestimating the scale and speed of prolonged life. In this study we explore the increasing life expectancy by examining the basic properties of survival curves. Specifically, we check if there are signs of mortality compression (i.e., rectangularization of the survival curve) and evaluate what it means to designing annuity products. Based on the raw mortality rates, we propose an approach to verify if there is mortality compression. We then apply the proposed method to the mortality rates of Japan, Sweden, and the United States, using the Human Mortality Database. Unlike previous results using the graduated mortality rates, we found no obvious signs that mortality improvements are slowing down. This indicates that human longevity is likely to increase, and longevity risk should be seriously considered in pricing annuity products.     

Nuptiality,fertility, and reproductivity

Abstract

During the last few years quite a number of investigations – private as well as official– have been devoted to the study, by numerical methods, of the effect of a given mortality, and fertility (or nativity) on population growth. Considerable progress has also been made – above all by the researches of A. J. LOTKA – with the abstract mathematical treatment of this problem which leads to certain integral equations with interesting asymptotic properties. Until quite recently, however, no account has been taken of the effect of different marriage rates, or rates of nuptiality. For the sake of simplicity the fertility has, in fact, been assumed to have a certain value for each age-group of women as a whole, without any distinction whatever between married and unmarried women. This is of course only a first approach to the more general and more important problem of studying the combined effect of a given mortality, a given nuptiality, and a given fertility of married as well as of unmarried women.     

Minimum Death Rates and Maximum Life Expectancy: The Role of Concordant Ages

Only five populations have achieved maximum life expectancy (or best practice population) more than occasionally since 1900. The aim of this article is to understand how maximum life expectancy is achieved in the context of mortality transition. We explore this aim using the concepts of potential life expectancy, based on minimum rates at each age among all high longevity populations, and concordant ages. Concordant ages are defined as ages at which the minimum death rate occurs in the population with the maximum life expectancy. The results show the extent to which maximum life expectancy could increase through the realization of demonstrably achievable minimum rates. Concordant ages are concentrated at increasingly older ages over time, but they have produced more than half of the change in maximum life expectancy in almost all periods since 1900. This finding is attributed to their quantity and position whereby concordant ages are concentrated at the ages that have the greatest impact on mortality decline in a particular period. Based on mortality forecasts, we expect that concordant ages will continue to lead increases in female maximum life expectancy, but that they will play a weaker role in male maximum life expectancy.     

Estimation of future mortality rates and life expectancy in chronic medical conditions

Estimates of old-age mortality are necessary for the construction of life tables and computation of life expectancy, and are essential in the growing area of life insurance for the elderly. Two common assumptions are that either the excess death rate (EDR) or the relative risk (RR) stays constant with increasing age. It is known, however, that for most medical conditions the former underestimates the risk and the latter overestimates it. A third popular method is that of rating up: a subject is said to be "rated up k years" if his future mortality rates are assumed to be those of a person in the general population who is k years older. It is shown here that this method generally leads to gross overestimates of old-age mortality. We consider two less-commonly used models, log-linear declining relative risk (LDR) and constant proportional life expectancy (PLE), and compare them to the methods of constant EDR, constant RR and rating up. Although slightly more complicated to employ than the other methods, both LDR and PLE generally give better estimates of mortality and life expectancy. When mortality rates for chronic conditions are known within a certain age range, and estimates outside of the range are required, the LDR and PLE methods may be preferable to the more familiar methods of constant EDR, constant RR, or rating up.     

Systematic Mortality Improvement Trends and Mortality Heterogeneity: Insights from Individual-Level HRS Data

Providers of life annuities and pensions need to consider both systematic mortality improvement trends and mortality heterogeneity. Although how mortality improvement varies with age and gender at the population level is well studied, how trends vary with risk factors remains relatively unexplored. This article assesses how systematic mortality improvement trends vary with individual risk characteristics using individual-level longitudinal data from the U.S. Health and Retirement Study between 1994 and 2009. Initially a Lee-Carter model is used to assess mortality improvement trends by grouping individuals with similar risk characteristics of gender, education, and race. We then fit a longitudinal mortality model to individual-level data allowing for heterogeneity and time trends in individual-level risk factors. Our results show how survey data can provide valuable insights into both mortality heterogeneity and improvement trends more effectively than commonly used aggregate models. We show how mortality improvement differs across individuals with different risk factors. Significantly, at an individual level, mortality improvement trends have been driven by changes in health history such as high blood pressure, cancer, and heart problems rather than risk factors such as education, marital status, body mass index, and smoker status.     

How to prepare a life expectancy report for an attorney in a tort case

The purpose of this methodology article is to describe a suitable format for a legally acceptable report on the life expectancy of the principal in a tort case that is being advocated or defended by an attorney. Life insurance medical directors and underwriters are clearly skilled and experienced in mortality risk classification for life insurance. However, the judicial system is accustomed to measuring excess mortality only in terms of reduced life expectancy. The analyst preparing the report must convert the excess mortality into a figure for reduced life expectancy and compare this with the life expectancy of persons matched by age, sex and race in the latest Decennial US Life Tables. This process is different from the life insurance underwriting process. A life table projected to age 109 must be constructed as an essential part of the report, and the entire process must be presented clearly and convincingly. There are good reasons why the excess death rate (EDR) should be used as the index of excess mortality in constructing the life table, in preference to the mortality ratio (MR), which is used most of the time in life insurance risk classification. All of these considerations are discussed in this article, which is based on a sample of 40 cases handled by the author, a retired life insurance medical director.     

Auswirkungen von Enhanced Annuities auf den Bestand eines Versicherers

The value for money of a standard annuity is the higher, the longer the life expectancy of an insured, and therefore it is only acceptable for persons with an above average life expectancy. The discrepancy is intensified by tax regulations that favor lifelong annuity payments opposed to a lump sum. This discrimination of impaired insureds could be prevented if so-called enhanced annuities were offered, i.e. products where the annuity paid is the larger, the lower the person’s life expectancy. The article presents a quantitative comparison of the risk profile of insurance companies offering standard annuity contracts compared to enhanced annuities and an analysis of the impact of adverse selection on a standard insurer. By definition of individual mortality rates a heterogeneous insurance portfolio is specified. Besides we model the individual underwriting of enhanced annuities. A Monte Carlo Simulation provides results to compare the profit/loss situation of a portfolio of traditional annuity products and a portfolio of enhanced annuities with individual underwriting of different quality and to assess the impact of selection effects.     

Rethinking age-period-cohort mortality trend models

Longevity risk arising from uncertain mortality improvement is one of the major risks facing annuity providers and pension funds. In this article, we show how applying trend models from non-life claims reserving to age-period-cohort mortality trends provides new insight in estimating mortality improvement and quantifying its uncertainty. Age, period and cohort trends are modelled with distinct effects for each age, calendar year and birth year in a generalised linear models framework. The effects are distinct in the sense that they are not conjoined with age coefficients, borrowing from regression terminology, we denote them as main effects. Mortality models in this framework for age-period, age-cohort and age-period-cohort effects are assessed using national population mortality data from Norway and Australia to show the relative significance of cohort effects as compared to period effects. Results are compared with the traditional Lee–Carter model. The bilinear period effect in the Lee–Carter model is shown to resemble a main cohort effect in these trend models. However, the approach avoids the limitations of the Lee–Carter model when forecasting with the age-cohort trend model.     

The evolution of death rates and life expectancy in Denmark

From 1835 to date Denmark has experienced an increase in life expectancy at birth of about 40 years for both sexes. Over the course of the last 170 years, life expectancy at birth has increased from 40 to 80 years for women and from 36 to 76 years for men, and it continues to rise. Using a new methodology, we show that about half of the total historic increase can be attributed to the sharp decline in infant and young age death rates up to 1950. However, life expectancy gains from 1950 to date can be primarily attributed to improvements in the age-specific death rates for the age group from 50 to 80, although there is also a noticeable contribution from the further decline in infant mortality over this period. With age-specific death rates up to age 60 now at a very low absolute level, substantial future life expectancy improvements must necessarily arise from improvements in age-specific death rates for ages 60 and above. Using the developed methodology, we quantify the impact of further reductions in age-specific mortality. Despite being one of countries with the highest life expectancy at the beginning of the 20th century, and despite the spectacular historic increase in life expectancy since then, Denmark is, in fact, lagging behind compared to many other countries, notably the other Nordic countries. The main reason is an alarming excess mortality for cause-specific death rates related to ischaemic heart diseases and, in particular, a number of cancer diseases. Age-specific death rates continue to improve in most countries, and a likely scenario is that in the future Denmark will experience improvement rates at the international level or perhaps even higher as a result of a catch-up effect.     

Modeling cause-of-death mortality using hierarchical Archimedean copula

Studying changes in cause-specific (or competing risks) mortality rates may provide significant insights for the insurance business as well as the pension systems, as they provide more information than the aggregate mortality data. However, the forecasting of cause-specific mortality rates requires new tools to capture the dependence among the competing causes. This paper introduces a class of hierarchical Archimedean copula (HAC) models for cause-specific mortality data. The approach extends the standard Archimedean copula models by allowing for asymmetric dependence among competing risks, while preserving closed-form expressions for mortality forecasts. Moreover, the HAC model allows for a convenient analysis of the impact of hypothetical reduction, or elimination, of mortality of one or more causes on the life expectancy. Using US cohort mortality data, we analyze the historical mortality patterns of different causes of death, provide an explanation for the ‘failure’ of the War on Cancer, and evaluate the impact on life expectancy of hypothetical scenarios where cancer mortality is reduced or eliminated. We find that accounting for longevity improvement across cohorts can alter the results found in existing studies that are focused on one single cohort.     

Marriage and other risky assets: A portfolio approach

We study the joint impact of gender and marital status on financial investments by testing the hypothesis that marriage represents – in a portfolio framework – a sort of safe asset and that this attribute may change over time. We show that married individuals have a higher propensity to invest in risky assets than single ones, that this marital status gap is stronger for women and that, for women only, it evolves and declines at the end of the sample period. Next we explore a number of possible explanations of the observed gender differences by controlling for background factors that capture the evolution of family and society. We find that both the higher female marital status gap and its time variability vanish for those women who are employed. Our empirical investigation is based on a dataset drawn from the 1993–2006 Bank of Italy Survey of Household Income and Wealth.     

Temporal Evolution of Mortality Indicators

Abstract

In Spain, as in other developed countries, significant changes in mortality patterns have occurred during the 20th and 21st centuries. One reflection of these changes is life expectancy, which has improved in this period, although the robustness of this indicator prevents these changes from being of the same order as those for the probability of death. If, moreover, we bear in mind that life expectancy offers no information as to whether this improvement is the same for different age groups, it is important and necessary to turn to other mortality indicators whose past and future evolution in Spain we are going to study. These indicators are applied to Spanish mortality data for the period 1981–2008, for the age range 0–99. To study its future evolution, the mortality ratios have to be projected using an adequate methodology, namely, the Lee-Carter model. Confidence intervals for these predictions can be calculated using the methodology that Lee and Carter apply in their original article for expected lifetime confidence intervals, but they take into account only the error in the prediction of the mortality index obtained from the ARIMA model adjusted to its temporal series, excluding other sources of error such as that introduced by estimations of the other parameters in the model. That is why bootstrap procedures are preferred, permitting the combination of all sources of uncertainty.     

How long might the younger-old live: A predictive model

Life expectancy amongst older people in industrialised countries has been improving over an extended period and still continues to do so. This has ramifications for providers of services to this population, thus necessitating a level of forward planning. Predictive models of remaining life expectancy for older age groups can assist long-term planning processes. This paper presents an extrapolative approach to forecasting remaining life expectancy. Based on logistic modelling of historic mortality and survivorship for the “younger-old” male population of England and Wales over the period 1970-2005, a parsimonious two-parameter model is derived. This model provides a close correspondence to published period life table data. Trends in these parameters are then fitted and extrapolated to enable projections of life expectancy up to 40 years into the future. Alternative assumptions are used to determine a range of future life expectancy trajectories for a 65-year-old male. Occupational pension scheme provision is identified as an area of particular concern in the context of increasing longevity. As an illustration, the life expectancy trajectories are combined with differing discount rate assumptions to generate a number of alternative pension liability scenarios for the extrapolation period.     

Two-dimensional Hazard Estimation for Longevity Analysis

We investigate developments in Danish mortality based on data from 1974–1998 working in a two-dimensional model with chronological time and age as the two dimensions. The analyses are done with non-parametric kernel hazard estimation techniques. The only assumption is that the mortality surface is smooth. Cross-validation is applied for optimal bandwidth selection to ensure the proper amount of smoothing to help distinguishing between random and systematic variation in data. A bootstrap technique is used for construction of pointwise confidence bounds. We study the mortality profiles by slicing up the two-dimensional mortality surface. Furthermore we look at aggregated synthetic population metrics as ‘population life expectancy’ and ‘population survival probability’. For Danish women these metrics indicate decreasing mortality with respect to chronological time. The metrics can not directly be used for prediction purposes. However, we suggest that life insurance companies use the estimation technique and the cross-validation for bandwidth selection when analyzing their portfolio mortality. The non-parametric approach may give valuable information prior to developing more sophisticated prediction models for analysis of economic implications arising from mortality changes.     

Social security, life insurance and annuities for families

In this paper we ask whether an aspect of social security, namely its role as a provider of insurance against uncertain life spans, is welfare enhancing. To this end we use an OLG model where agents have a bequest motive and differ in sex and marital status and where families are formed and destroyed and their characteristics evolve (exogenously) according to U.S. demographic patterns of marriage, divorce, fertility and mortality. We compare the implications of social security under a variety of market structures that differ in the extent to which life insurance and annuities are available. We find that social security is a bad idea. In economies where the private sector provides annuities and life insurance, it is a bad idea for the standard reason that it distorts the intertemporal margin by lowering the capital stock. In the absence of such securities social security is still a very bad idea, only marginally less so compared with economies with annuities and life insurance. We also explore these issues in a world where people live longer and we find no differences in our answers. As a by-product of our analysis we find that the existence of life insurance opportunities for people is important in welfare terms while that of annuities is not.     

CEO marital status and corporate cash holdings

We examine the effect of CEO marital status on corporate cash holdings. Consistent with the classical agency framework, we find that firms with single CEOs hold more cash compared to otherwise similar firms with married CEOs and that the excess cash held by single CEOs is significantly discounted by shareholders. Our findings survive a battery of tests to ease endogeneity and selection bias, confirming that results are not simply reflecting innate heterogeneity in preferences. Overall, our findings indicate that a variable outside the common firm- and macro-level determinants, CEO marital status, can significantly influence corporate policies.     

A General Semi-Markov Model for Coupled Lifetimes

Joint-life annuities with a high last survivor benefit play an important role in the optimal annuity portfolio for a retired couple. The dependence between coupled lifetimes is crucial for valuing joint-life annuities. Existing bivariate modeling of coupled lifetimes is based on outdated data with limited observation periods and does not take into account mortality improvement. In this article, we propose a transparent and dynamic framework for modeling coupled lifetime dependence caused by both marital status and common mortality improvement factors. Dependence due to marital status is captured by a semi-Markov joint life model. Dependence due to common mortality improvement, which represents the correlation between mortality improvement patterns of coupled lives, is incorporated by a two-population mortality improvement model. The proposed model is applied to pricing the longevity risk in last survivor annuities sold in the United States and the United Kingdom.     

Structured settlement annuities, part 1: overview and the underwriting process

Structured settlement underwriting is the underwriting of medically impaired lives for the purchase of an annuity to fund the settlement. Other than risk assessment, structured settlement (SS) underwriting has little in common with traditional life insurance underwriting. Most noteworthy of these differences is the relative lack of actuarial data on which to base decisions about mortality and the necessity for prospective thinking about risk assessment. The purpose of this paper is to provide a foundation for understanding the structured settlement business and to contrast the underwriting of structured settlements with that of traditional life insurance. This is the first part of a two-part article on SS annuities. Part 2 deals with the mortality experience in SS annuitants and the life-table methodology used to calculate life expectancy for annuitants at increased mortality risk.