Multivariate Analysis of Pension Plan Mortality Data

Abstract

This paper uses the logistic regression model to examine private pension plan data for 1989–95 collected by the Retirement Plans Experience Committee of the Society of Actuaries. When only one explanatory variable, such as annuity class size, is used in modeling mortality rates, the model provides a reasonable fit to the data. Multiple explanatory variables give less satisfactory results.     

Social Transfers And Income Inequality In Old Age

Abstract

This paper examines variation in old-age income inequality between industrialized nations with modern welfare systems. The analysis of income inequality across countries with different retirement income systems provides a perspective on public pension policy choices and designs and their distributional implications. Because of the progressive nature of public pension programs, we hypothesize that there is an inverse relationship between the quality of public pension benefits and old-age income inequality—that is, countries with comprehensive, universal, and generous public pension systems will exhibit more equal distributions of income in old age.

Luxembourg Income Study data indeed show that cross-national variation in old-age income inequality is partly explained by differences in the percentage of seniors’ total income derived from public pension transfers. Sweden, for example, has the highest level of government transfers and the lowest level of old-age income inequality, while Israel and the United States have the lowest levels of dependency on government transfers and the highest levels of income inequality. A notable exception is Canada, where public transfers represent only a moderate portion of elderly income, yet old-age income inequality is relatively low. These findings suggest that quality of public pension benefits does indeed play a role in explaining differences in old-age income inequality between industrialized nations, yet these variations are also likely influenced by other factors.     

The Shift to Defined Contribution Pension Plans

Abstract

There has been a strong shift away from defined benefit (DB) pension plans toward defined contribution (DC) pension plans in the United States over the last 20 years. A variety of reasons for this shift have been proposed. In another paper in this issue, Krzysztof Ostaszewski presents a new hypothesis to explain the shift to DC plans in the United States. He argues that the decline in importance of DB plans is due to a shift in the way relative returns to macroeconomic factors of production, that is, capital and labor, are being rewarded in the national economy.

This paper attempts to test the Ostaszewski hypothesis using Canadian data. In Canada there has been only a slight decrease in DB plan coverage. It is shown that the Ostaszewski theory does not fit the Canadian experience well. Instead, it is argued that pension regulation and tax legislation play a crucial role in pension design and reform. It is also argued that the difference in pension regulation and taxation in Canada versus the United States has directly influenced plan sponsors in considering their pension objectives, costs, and risks. Differences in the proportion of the workforce that is unionized may also be important. The paper concludes that pension regulation and taxation are more important variables than are macroeconomic reward systems in the use of DB versus DC pension plans.     

The Earnings Implications of Pension Expense

Abstract

Recent challenges to the actuarial pension model and a movement to harmonize international accounting standards both suggest that the current Canadian standards for pension accounting, CICA 3461, may see substantial revision during upcoming years. To understand better the implications of these possible accounting changes, this paper presents the results of a stochastic analysis that quantifies how the volatility of pension expense for a sample of ten Canadian companies sponsoring defined benefit plans will be increased by the adoption of immediate recognition accounting. For certain companies this increase is significant and is shown to have a material earnings impact. The implications of this earnings volatility for the future of defined benefit pension plans are also explored.     

Deterministic Modeling of Defined-Contribution Pension Funds

Abstract

Formulas are derived to model the response of a money purchase, defined-contribution pension fund to the following types of investment shock: (1) an instantaneous fall in the value of the fund assets and (2) a permanent, uniform reduction in the rate of earned interest. An alternative defined-contribution fund, incorporating a variable defined-benefit scale, is then proposed, and its responses to the same investment shocks are compared with those of the money purchase fund. The comparison shows that the variable defined-benefit approach offers a useful alternative to the money purchase principle for defined-contribution pension funds.     

PAYG pension systems with capital mobility

This paper studies the design of an optimal pension scheme in an OLG and open economy model. The pension scheme provides a flat rate benefit and is based on the PAYG principle. It thus combines inter- and intra-generational redistribution. In this setting a number of symmetric economies are connected by an open and perfect capital market. When this number is very large, we have the small open economy case; when it is reduced to one, we have the case of autarky or perfect coordination. As the number of countries increases, there is more intragenerational redistribution, but less capital accumulation. JEL Code H55 · H87     

Contracting out of a state pension scheme

Abstract

The title of this paper is not common in actuarial literature, but the subject is one which has become familiar to every Briton in the last two years and which is essentially actuarial. The phrase "contracting out" has become English shorthand for an arrangement by which a private pension scheme may decide that it will not join a State pension scheme, usually because it already provides equal or better benefits. If the private scheme "contracts out" it will be excused the payment of contributions and will, of course, forgo the benefits.     

Relative Choice Models for Income Drawdown in a Defined Contribution Pension Scheme

Abstract

This paper extends a target-based model of income drawdown developed in Gerrard et al. (Insurance: Mathematics and Economics 35: 321–342 [2006]) (GHV) for the distribution phase of a defined contribution pension scheme. The optimal investment strategy of the pension fund and the optimal drawdown are found using linear-quadratic optimization, which minimizes the deviation of the fund and the drawdown from prescribed targets. The GHV model is modified by nondimensionalizing the loss function, so that there is a relative choice between outcomes.

Using this model, three classes of target are studied. Endogenous deterministic targets are suggested from the form of the optimal controls, while exogenous deterministic targets can be stated without knowledge of the optimization problem. The third class of stochastic targets is similar to recent annuity products, which incorporate investment risk. Each scheme represents a trade-off between investment risk and return, and this is illustrated by numerical simulation with reference to a canonical example. A particularly attractive form of income drawdown is given by an implied rate of return target. This yields a reasonable investment strategy and a robust consumption profile with age. In addition, it can be easily explained to pension scheme members.     

“On the Merger of Two Companies,” Hans Gerber and Elias S. W. Shiu,July 2006

Abstract

Bankruptcy risk falls to pension plan participants if a plan sponsor fails when a defined benefit (DB) pension plan is underfunded. This article examines the incidence of that risk and how it changes when public policy provides a guarantee fund. Although government-based guarantee funds are in a unique position to provide pension protection, primarily because of the extent to which the risk of sponsor default is systematic in nature, a looming question is the extent to which such guarantees are exposed to moral hazard. The article focuses on that question using data from four Canadian provinces, including one (Ontario) that operates a guarantee fund for pensions. The findings show that plan assets per DB-plan participant increase with the earnings of workers and decrease with higher unemployment, and that level of assets also is moderated by the influence of taxes, with higher plan assets observed when and where tax rates are higher. Plans in Ontario had on average $20,035 less in asset value per participant, and Ontario plans covered by the guarantee fund had an average of $16,497 less per participant than other Canadian DB plans not backed by a guarantee fund. A separate model finds the presence of a guarantee fund to be one of a very small number of variables significant in explaining variability in the plans’ funded ratios. These empirical results are consistent with the existence of moral hazard.     

New danish bases of calculation in life and pension insurance

Abstract

A committee consisting of actuaries representing private life offices, private pension offices, and Statsanstalten for Livsforsikring (The State Life Insurance Institution) transacting both life and pension business, have compiled a complete set of calculation bases, which have been adopted by all Danish life and pension offices with effect as from January 1, 1966.     

“Author’s Reply: Critique of Mexico’s New Social Security Act”, Octavio Maupomé-Carvantes,July, 1999

Abstract

This paper considers the pension plan as part of the capital structure of the sponsoring employer. This enables lessons from financial theory concerning capital structure to be used to answer the question, “What assets should a pension fund hold?” The standard Modigliani-Miller framework is expanded on to consider the implications of corporate tax. This leads to the conclusion that bond investment for pension plans has tangible advantages over holding risky assets (e.g., equities). The paper considers a case study of the pension plan of the Boots Company, a U.K. pharmacy retailer with a pension fund of around £2.3 billion ($3.5 billion), where these ideas were put into practice. Finally, the paper discusses the value released to shareholders and the extra security members of the pension fund have derived from putting theory into practice.     

Minimum Rate of Return Guarantees: The Danish Case

We analyze minimum rate of return guarantees for life-insurance (investment) contracts and pension plans with a smooth surplus distribution mechanism. We specifically model the smoothing mechanism used by most Danish life-insurance companies and pension funds. The annual distribution of bonus will be based on this smoothing mechanism after taking the minimum rate of return guarantee into account. In addition, based on the contribution method the customer will receive a final (non-negative) undistributed surplus when the contract matures. We consider two different methods that the company can use to collect payment for issuing these minimum rate of return guarantee contracts: the direct method where the company gets a fixed (percentage) fee of the customer's savings each year, e.g. 0.5% in Denmark, and the indirect method where the company gets a share of the distributed surplus. In both cases we analyze how to set the terms of the contract in order to have a fair contract between an individual customer and the company. Having analyzed the one-customer case, we turn to analyzing the case with two customers. We consider the consequences of pooling the undistributed surplus over two inhomogeneous customers. This implies setting up different mechanisms for distributing final bonus (undistributed surplus) between the customers.     

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.     

The new joint pension scheme established by collective agreement between the Norwegian employers' confederation and the Norwegian federation of trade unions

Abstract

Norway has a statutory old age pension scheme covering the whole population over 70 years of age. Since 1959, pensions are granted without a means test. As from 1 April 1962, the annual pension amounts are 3348 crowns for a single person and 5028 crowns for a married couple. For special groups, such as seamen, fishermen and forestry workers, additional pension schemes have been established by law. Many private companies, especially the larger firms, have established staff pension schemes on a voluntary basis, either in the form of actuarial pension funds, or through collective pension insurance. Many of these schemes cover only staff employees, not workers. In other cases both groups are covered, but with relatively higher benefits for staff than for workers.     

Human Survival at Older Ages and the Implications for Longevity Bond Pricing

Abstract

Governments are concerned about the future of pension plans, for which increasing longevity is judged to be an important risk to their future viability. We focus on human survival at age 65, the starting age point for many pension products. Using a simple model, we link basic measures of life expectancy to the shape of the human survival function and consider its various forms. The model is then used as the basis for investigating actual survival in England and Wales. We find that life expectancy is increasing at a faster rate than at any time in history, with no evidence of this trend slowing or any upper age limit. With interest growing in the use of longevity bonds as a way to transfer longevity risks from pension providers to the capital markets, we seek to understand how longevity drift affects pension liabilities based on mortality rates at the point of annuitization, versus what actually happens as a cohort ages. The main findings are that longevity bonds are an effective hedge against longevity risk; however, it is not only the oldest old that are driving risk, but also more 65-year-olds reaching less extreme ages such as 80. In addition, we find that the possibility of future inflation and interest rates could be as an important a risk to annuities as longevity itself.     

Financial literacy and voluntary savings for retirement: novel causal evidence

ABSTRACT

We utilise recent Household Finance and Consumption Survey microdata to report first causal effects of financial literacy on voluntary private pension schemes participation for a Central and Eastern European (CEE) country, namely Slovakia. Savings for retirement in the supplementary pension schemes are positively associated with financial literacy after controlling for a set of relevant socio-economic variables. One additional correctly answered financial literacy question leads to a 5.6 percentage points increase in the probability of having a voluntary pension savings plan in our ordinary least squares estimates. The causal impact of financial literacy increases to 19.5 percentage points when we address potential endogeneity problems by novel to the literature instrumental variables.     

Genetics,Alzheimer’s Disease,and Long-Term Care Insurance

Abstract

This paper applies a model of Alzheimer’s disease (AD) developed by Macdonald and Pritchard (2000) to the question of the potential for adverse selection in long-term care (LTC) insurance introduced by the existence of DNA tests for variants of the ApoE gene, the ε4 allele of which is known to predispose one to earlier onset of AD. It computes the expected present values (EPVs) of model LTC benefits with respect to AD for each of five ApoE genotypes, weighted average EPVs with and without adverse selection, and sample underwriting ratings. The paper concludes that adverse selection could increase costs significantly in a small LTC insurance market only if current population genetic risk is not much smaller than that observed in case-based studies, and if carriers of the ε4 allele are very much more likely to buy LTC insurance. Finally, the paper considers the cost of a combined retirement package, providing both pension and LTC insurance, and shows that it can reduce adverse selection.     

Annuity Choices in Chile: A Dynamic Approach

Abstract:

This study utilizes a variable derived from the Annuity Equivalent Wealth dynamic programming model developed by Brown (2001) and Mitchell et al. (1999). The model captures the benefits of having access to the annuity market. Using a unique data set of retirees from the Chilean labor market to analyze the empirical determinants of annuity choice, the study finds that sales agent contact, good health status, knowledge about the pension system, and greater education are associated with an increase in the probability of annuitization.     

The Public Role of Actuaries in Private Pensions in Canada

Abstract

Actuaries have played prominent public roles in the development of occupational pension plans and social security arrangements in Canada. These roles include advising governments and government-appointed committees about regulatory structures, establishing funding standards, actively participating in regulatory functions, and pioneering valuation work for pension plans covering public sector employees. The formation in 1965 of the Canadian Institute of Actuaries led to the accreditation of actuaries in pension and tax legislation and to the development of actuarial standards of practice for pension work.     

New Salary Functions for Pension Valuations

Abstract

This paper investigates salary functions as used in the valuation of pension plans. Pension actuaries as well as researchers in actuarial science may find many of the ideas in this article useful. The main conclusion of this paper is that salary functions, as derived from the parametric models, yield gains and losses that can be quite small and, in some cases, less variable than nonparametric methods. This paper starts by defining the salary function as an accumulation function based on inflation and merit. Next, we investigate traditional estimation methods in the context of this definition. We then present a parametric age-based model for the salary function and compare it with a parametric service-based model. Finally, we apply real pension plan data to derive age-and service-based salary functions and, through the use of two funding methods, investigate how these salary functions affect salary gains and losses.