0000000000277249
AUTHOR
Manuel Ventura-marco
Integrating retirement and permanent disability in NDC pension schemes
ABSTRACTIn this article, we develop a theoretical basis for integrating retirement and permanent disability using a generic nonfinancial defined contribution framework. The methodology we use relies on a multistate overlapping generations model that includes the so-called survivor dividend. Currently, this feature can only be found in the Swedish defined contribution (DC) scheme. The results achieved in the numerical example we present endorse the fact that the model works well. Special attention is given to the assumptions made about mortality rates for disabled people and disability incidence rates, which largely determine the contribution rate assigned to disability. The model could be o…
Integrating Retirement and Long-Term Care (LTC) Annuities Using a Notional Defined Contribution (NDC) Framework
This paper examines the possibility of embedding public long-term care (LTC) insurance within the retirement pension system, i.e. introducing life care annuities (LCAs) into a notional defined contribution (NDC) framework. To do this we develop a multistate overlapping generations model (MOLG) that includes the so-called survivor dividend and give special attention to the assumptions made about mortality rates for dependent persons and LTC incidence rates, which largely determine the contribution rate assigned to LTC. The proposed model could be of interest to policymakers because it could be implemented without too much difficulty, it would universalize LTC coverage with a "fixed" cost, an…
Converting Retirement Benefit into a Life Care Annuity with Graded Benefits: How Costly Would it Actually Be?
This paper deals with life care annuities, i.e. bundled products comprising a life annuity and long-term care insurance. It aims to assess the cost of converting retirement benefit into a life care annuity with graded benefits using a pre-existing public pay-as-you-go pension scheme. With this objective in mind, we present an actuarial method based on array calculus for valuing this type of life care annuity. The health dynamics of the annuitant rely on a reversible illness-death multistate framework. The paper contains a numerical example in which mortality and disability assumptions are based on data from the USA and Australia, although this should be viewed simply as an illustration. In …
An NDC approach to helping pensioners cope with the cost of long-term care
The aim of this paper is to analyse whether it would be possible to provide retirement and long-term care benefits using the same unfunded notional defined contribution scheme. We extend the multi-state overlapping generations model developed by Pla-Porcel et al. (2016) to include two new features: a long-term care benefit graded according to the annuitant's degree of disability and a minimum pension benefit for both contingencies. This brings the model closer to the reality of social insurance and enhances its political attractiveness. The paper contains a numerical example to show how the model functions and focuses especially on the mortality rates for dependent persons, the inception ra…
Automatic regrouping of strata in the goodness-of-fit chi-square test
Pearson’s chi-square test is widely employed in social and health sciences to analyze categorical data and contingency tables. For the test to be valid, the sample size must be large enough to provide a minimum number of expected elements per category. This paper develops functions for regrouping strata automatically no matter where they are located, thus enabling the goodness-of-fit test to be performed within an iterative procedure. The functions are written in Excel VBA (Visual Basic for Applications) and in Mathematica. The usefulness and performance of these functions is illustrated by means of a simulation study and the application to different datasets. Finally, the iterative use of …
Automatic regrouping of strata in the chi-square test
Pearson´s chi-square test is widely employed in social and health science to analyze categorical data and contingency tables and to assess sample representativeness. For the test to be valid the sample size must be big enough to provide a minimum number of expected elements per category. If the researcher chooses to regroup the strata in order to solve the failure on the minimum size requirement, the existence of automatic re-grouping procedures in statistical software would be very useful, especially when tests are applied sequentially. After comprehensively reviewing the software that can carry out this test, we find that, with a few exceptions, there is no automatic regrouping of the str…
Actuarial accounting for a notional defined contribution scheme combining retirement and longterm care benefits
This paper develops a social insurance accounting model for a notional defined contribution (NDC) scheme combining retirement and long-term care (LTC) contingencies. The procedure relies on standard double-entry bookkeeping and enables us to compile a “Swedish” type actuarial balance sheet (ABS) following a framework equivalent to an open group approach. This methodology is suitable for reporting the system’s solvency status and can show periodical changes in the system’s financial position by means of an income statement. The information underpinning the actuarial valuation is based on events and transactions that are verifiable at the valuation date, without considering expected future tr…
Social Insurance Accounting for a Notional Defined Contribution Scheme Combining Retirement and Long-Term Care Benefits
This paper develops a social insurance accounting model for a notional defined contribution (NDC) scheme combining retirement and long-term care (LTC) contingencies. The procedure relies on standard double-entry bookkeeping and enables us to compile a “Swedish” type actuarial balance sheet (ABS) following a framework equivalent to an open group approach. This methodology is suitable for reporting the system’s solvency status and can show periodical changes in the system’s financial position by means of an income statement. The information underpinning the actuarial valuation is based on events and transactions that are verifiable at the valuation date, without consid…
AN ACTUARIAL BALANCE SHEET MODEL FOR DEFINED BENEFIT PAY-AS-YOU-GO PENSION SYSTEMS WITH DISABILITY AND RETIREMENT CONTINGENCIES
AbstractIn this paper, we develop a theoretical basis for drawing up a “Swedish” type actuarial balance sheet for a defined benefit pay-as-you-go (DB PAYG) scheme with retirement and disability benefits. Our model enables us to obtain the system's expected average turnover duration, measure the scheme's solvency and explore the phenomenon identified as “pension reclassification”, a widespread practice that masks the system's real status unless further pension information becomes available. The model is clearly linked to actuarial practice in social security and gives partial support to the practical adaptation of Swedish methodology carried out by OSFI (2012) in applying the concept of the …
A “Swedish” actuarial balance for a notional defined contribution pension scheme with disability and minimum pension benefits
This article proposes a “Swedish” type actuarial balance sheet (ABS) for a notional defined contribution (NDC) scheme with disability and minimum pension benefits. The proposed ABS splits the pension system in two parts: the pure NDC part and the redistributive part, which includes the assets and liabilities originating from non-contributory rights. The article contains a numerical example that sheds light on the real applicability of our proposal. The model has practical implications that could be of interest to policy-makers, given that it integrates actuarial and social aspects of public pensions and discloses the real cost of redistribution through minimum pensions.
Solution to nonlinear MHDS arising from optimal growth problems
Abstract In this paper we propose a method for solving in closed form a general class of nonlinear modified Hamiltonian dynamic systems (MHDS). This method is used to analyze the intertemporal optimization problem from endogenous growth theory, especially the cases with two controls and one state variable. We use the exact solutions to study both uniqueness and indeterminacy of the optimal path when the dynamic system has not a well-defined isolated steady state. With this approach we avoid the linearization process, as well as the reduction of dimension technique usually applied when the dynamic system offers a continuum of steady states or no steady state at all.
How Do Unisex Life Care Annuities Embedded in a Pay-As-You-Go Retirement System Affect Gender Redistribution?
This paper deals with the idea of converting retirement benefit into a life care annuity with graded benefits using a pre-existing public pay-as-you-go pension scheme. Based on accurate biometric data from Australia and the US, the paper shows that using gender-neutral annuity factors to compute the initial benefit involves a large increase in ex-ante gender redistribution compared to a system without long-term coverage. In spite of the very different biometric data, the results are surprisingly similar for both countries. To disentangle the hidden redistribution, a methodology based on conversion (actuarial) factors is used. The value of the actuarial factor relies on a multistate framewor…
LIFE CARE ANNUITIES (LCA) EMBEDDED IN A NOTIONAL DEFINED CONTRIBUTION (NDC) FRAMEWORK
AbstractThis paper examines the possibility of embedding public long-term care (LTC) insurance within the retirement pension system, i.e. introducing life care annuities into a notional defined contribution framework. To do this, we develop a multistate overlapping generations model that includes the so-called survivor dividend and give special attention to the assumptions made about mortality rates for dependent persons and LTC incidence rates, which largely determine the contribution rate assigned to LTC. The proposed model could be of interest to policymakers because it could be implemented without too much difficulty, it would universalize LTC coverage with a “fixed” cost, and it would …
Does the Pension System’s Income Statement Really Matter? A Proposal for An NDC Scheme with Disability and Minimum Pension Benefits
This paper develops a full accounting model for monitoring the solvency of a notional defined contribution (NDC) pension scheme with disability and minimum pension benefits. Using the annual report of the Swedish pension system as a benchmark (TSPS, 2019), we extend the “Swedish” actuarial balance developed by Perez-Salamero et al. (2017) by adding an income statement which fully explains the reasons behind the changes in the system’s solvency by type of benefit. In line with the reference model, assets and liabilities are measured at present value at each reporting date, and changes in present value are reported in each period as income or expenses and are included on the income statement.…
Converting retirement benefit into a life care annuity with graded benefits
AbstractThis paper deals with life care annuities, i.e. bundled products comprising a life annuity and long-term care insurance. It aims to assess the cost of converting retirement benefit into a life care annuity with graded benefits using a pre-existing public pay-as-you-go pension scheme. With this objective in mind, we present an actuarial method based on array calculus for valuing this type of life care annuity. The health dynamics of the annuitant rely on a reversible illness-death multistate framework. The paper contains a numerical example in which mortality and disability assumptions are based on data from the USA and Australia, although this should be viewed simply as an illustrat…
From “Table 29” to the actuarial balance sheet: is it really that big a leap?
EU regulations since 2017 have required all Member States to disclose their accrued-to-date pension liabilities (ADL) using a standard actuarial cost method and some common assumptions. This applies to both Social Security (SS) schemes and unfunded defined benefit (DB) schemes covering civil servants. These pension liabilities have to be disclosed in a supplementary table referred to as Table 29. An actuarial balance sheet (ABS) can be defined as a financial statement that lists a pension system's obligations to contributors and pensioners at a particular date, together with the amounts of the assets (financial and in particular those from contributions) that underwrite those commitments. T…
An Actuarial Balance Model for DB PAYG Pension Systems with Disability and Retirement Contingencies
In this paper we develop a theoretical basis for drawing up a “Swedish” type actuarial balance sheet for a defined benefit pay-as-you-go (DB PAYG) scheme with retirement and disability benefits. Our model enables us to obtain the system's expected average turnover duration, measure the scheme's solvency and explore the phenomenon identified as “pension reclassification”, a widespread practice that masks the system's real status unless further pension information becomes available. The model is clearly linked to actuarial practice in social security and gives partial support to the practical adaptation of Swedish methodology carried out by OSFI (2012) in applying the concept of the contribut…
How do unisex life care annuities embedded in a pay-as-you-go retirement system affect gender redistribution?
This paper aims to assess gender redistribution when using unisex conversion factors to compute the initial benefit of life care annuities (LCAs) embedded in a pay-as-you-go (PAYG) pension system. We use a method based on actuarial factors to disentangle the hidden redistribution of LCAs with graded benefits. The value of the actuarial factor relies on a multistate framework in which transitions are modeled from the initial health state to the absorbing state. According to our calculations for Australia and the US, the amount of gender redistribution is by no means irrelevant. In spite of the very different biometric data, the results are surprisingly similar for both countries. Risk equali…
A Social Insurance Accounting for a Notional Defined Contribution Scheme Combining Retirement and Long-Term Care Benefits
This paper develops a social insurance accounting model for a notional defined contribution (NDC) scheme combining retirement and long-term care (LTC) contingencies. The procedure relies on standard double-entry bookkeeping and enables us to compile a “Swedish” type actuarial balance sheet (ABS) following a framework equivalent to an open group approach. This methodology is suitable for reporting the system’s solvency status and can show periodical changes in the system’s financial position by means of an income statement. The information underpinning the actuarial valuation is based on events and transactions that are verifiable at the valuation date, without considering expected future tr…
The Reduction of Dimension in the Study of Economic Growth Models
We examine the dimension reduction method and prove that it could be misleading if we try to get some insight into the dynamics of the original system from the dynamics of the transformed system alone. The reduced system seemingly may give rise to a continuum multiplicity of steady states when, actually, it does exist a unique and isolated steady state or even it does not exist a steady state at all. We show how the dynamics for the primary variables that is recovered from the solution to the reduced system may be refuted by solving the original one. In our opinion there is no alternative because nothing can be regarded as a close substitute for the study of the original system. Although th…
A "Swedish" actuarial balance sheet for a notional defined contribution pension scheme with disability and retirement benefits
This paper proposes a “Swedish” type actuarial balance sheet for a notional defined contribution scheme embedding disability insurance within the retirement pension system. The underlying framework supporting the actuarial balance relies on a multistate overlapping generations model that includes the so-called survivor dividend and a minimum pension benefit for both contingencies. The proposed ABS splits the system into two parts: the actuarial part (pure NDC) and the redistributive part, which includes the assets and liabilities originating from non-contributory rights. The paper also contains a numerical example that sheds light on the real applicability of our proposal and confirms that …
An Integrated Notional Defined Contribution (NDC) Model with Retirement and Permanent Disability
In this paper we develop a theoretical basis for integrating retirement and permanent disability using a generic NDC framework. The methodology used relies on a multistate overlapping generations model that includes the so-called survivor dividend. Currently this feature can only be found in the Swedish defined contribution (DC) scheme. The results achieved in the numerical example we present endorse the fact that the model works well. Special attention is given to the assumptions made about mortality rates for disabled people and disability incidence rates, which largely determine the contribution rate assigned to disability. The model could be of interest to policymakers because, after so…
Mortality and life expectancy trends in Spain by pension income level for male pensioners in the general regime retiring at the statutory age, 2005-2018
Abstract Background Research has generally found a significant inverse relationship in mortality risk across socioeconomic (SE) groups. This paper focuses on Spain, a country for which there continues to be very little evidence available concerning retirement pensioners. We draw on the Continuous Sample of Working Lives (CSWL) to investigate disparities in SE mortality among retired men aged 65 and above over the longest possible period covered by this data source: 2005–2018. We use the initial pension income (PI) level as our single indicator of the SE status of the retired population. Methods The mortality gradient by income is quantified in two ways: via an indicator referred to as “rela…