Working Papers

Abstract: Using rich Finnish population level registers, we examine the impact of fusing a flexible early retirement pathway with a more stringent pathway, without changing eligibility conditions, so- called ‘relabelling’, on individual application behaviour. Our findings show that among affected cohorts the likelihood of applying for (successfully claiming) disability-related early retirement declined by 1.8 (1.5) percentage points equivalent to a relative drop of approximately 37% (39%) following the reform. Individuals with below tertiary level education and stronger lifetime labour market attachment exhibit a stronger behavioural response to the reform. We find tentative evidence of programme substitution to early retirement pathways designed to keep individuals in the labour market albeit on a part time basis. Our findings suggest that social norms and lack of awareness associated with early retirement pathways can strongly influence application behaviour even when eligibility conditions remain unchanged, offering policymakers novel ways to extend working lives.

Keywords: Retirement, disability, pensions, Finland, regression discontinuity.

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2023Jun

Pooling Functional Disability and Mortality in Long-Term Care Insurance and Care Annuities: A Matrix Approach for Multi-State Pools

Doreen Kabuche, Michael Sherris, Andrés M. Villegas and Jonathan Ziveyi

Abstract: Mortality risk sharing pools such as pooled annuity funds and tontines provide an attractive and effective solution for managing longevity risk. They have been widely studied in the literature. However, such arrangements are not optimal for individuals in need of long-term care (LTC) insurance. Enhancing the design of pooled annuities and tontines factoring in LTC can aid in reducing the cost of LTC insurance. This paper presents a matrix-based approach for pooling mortality risk across heterogeneous individuals classified by functional disability states and chronic illness statuses. Based on multi-state models of functional disability and health statuses, we demonstrate how individuals with different health risks can share mortality risk in a pooled annuity design. A multi-state pool is formed by pooling annuitants vulnerable to longevity and LTC risks, determining the associated actuarially fair benefits based on individuals’ health states. We provide a general structure for setting up a pooled annuity product that can be applied even for complex multi-state models. An extensive analysis is also carried out to illustrate our approach with numerical examples using US Health and Retirement Study (HRS) data. From the numerical illustrations, there is an increasing trend in the expected annuity benefits with higher upsides for individuals in poor health than those in good health, especially when systematic trends and uncertainty are considered in pricing. Smaller pool sizes and higher mortality credits among ill and disabled individuals due to higher death probabilities are the two main factors for the increased benefits in dependency.

Keywords: long-term care insurance, pooled annuity, multi-state models, functional disability, health status.

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2023Jun

The Impact of Pension Reform on Employment, Retirement and Disability Insurance Claims

Erik Hernæs, Simen Markussen, John Piggott and Knut Røed

Abstract: We evaluate a comprehensive reform of Norwegian early retirement institutions in 2011 through the lens of a parsimonious random utility choice model. The reform radically changed work incentives and/or pension access-age for some (but not all) workers. We find that improved work incentives caused employment to rise considerably, at the expense of both early retirement and exits through disability insurance. Lower access-age to own pension funds caused a small increase in employment and a large drop in disability program participation. Properly designed pension reforms thus need to take the interplay between old age pension and disability insurance programs into account.

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2023May

Age-Dependent Multi-Cohort Affine Mortality Model with Cohort Correlation

Yuxin Zhou, Len Patrick Garces, Yang Shen, Michael Sherris and Jonathan Ziveyi

Abstract: Continuous-time affine mortality models are useful in the analysis of age-cohort mortality rates as they yield a closed-form expression for survival curves which are consistent with the dynamics of latent factors driving mortality and are well-suited for finance and insurance applications. We extend and improve these mortality models by introducing age dependence of mortality rates and correlation between cohorts. We propose and compare two classes of age-dependent mortality models, namely the age-dependent coefficient model and the age-dependent factor model. Specifically, we assess both Gaussian and CIR-type models for each category of age-dependent models. Both categories of age-dependent models involve age and calendar time, which in turn specifies the cohort. Thus, our models admit an analytical form for the instantaneous correlation between mortality rates of different cohorts. Moreover, we propose two improvements to the parameter estimation process. First, to improve the estimation of cohort correlations, we regularise the parameter estimation by adding a penalty term which penalises larger differences between empirical and estimated correlations. Second, we develop and assess a method to include incomplete cohorts into the Kalman filtering algorithm for parameter estimation. We calibrate the mortality models to data from multiple countries which include Australia, Denmark, UK, and USA to assess and compare in-sample fit and forecasting performance. By incorporating age dependence and using incomplete cohort mortality data, we improve the goodness of fit and produce more reasonable out-of-sample forecasts of survival probabilities. We also show that regularisation produces more realistic correlations between cohorts for varying age differences. Our results show that, under most circumstances, the correlation between cohorts decreases as the age difference increases.

Keywords: Mortality model, Age-dependent, Multi-cohort, Cohort correlation, Incomplete cohort, Affine, Regularisation

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2023Apr

An Augmented Variable Dirichlet Process Mixture Model for the Analysis of Dependent Lifetimes

Francesco Ungolo and Patrick J. Laub

Abstract: The analysis of insurance and annuity products issued on multiple lives requires the use of statistical models which account for lifetime dependence. This work presents a Dirichlet Process Mixture-based approach which allows to model dependent lifetimes within a group, such as married couples, accounting for individual as well as group-specific covariates. The model is analysed in a fully Bayesian setting, and illustrated to jointly model the lifetime of male-female couples in a portfolio of joint and last survivor annuities of a Canadian life insurer. The inferential approach allows to account for right censoring and left truncation, which are common features of data in survival analysis. The model shows improved in-sample and out-of-sample performance compared to traditional approaches assuming independent lifetimes, and offers additional insights into the determinants of the dependence between lifetimes and their impact on joint and last survivor annuity prices.

Keywords: Dependent lifetimes, Survival Analysis, Dirichlet Process, Bayesian analysis, Life insurance, MCMC, Mixture models

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2023Apr

A Dirichlet Process Mixture Regression Model for the Analysis of Competing Risk Events

Francesco Ungolo and Edwin R. van den Heuvel

Abstract: We develop a regression model for the analysis of competing risk events. The joint distribution of the time to these events is characterized by a random effect following a Dirichlet Process, explaining their variability. This entails an additional layer of flexibility of this joint model, whose inference is robust with respect to the misspecification of the distribution of the random effects. The model is analysed in a fully Bayesian setting, yielding a flexible Dirichlet Process Mixture model for the joint distribution of the time to events. An efficient MCMC sampler is developed for inference. The modelling approach is applied to the empirical analysis of the surrending risk in a US life insurance predictive performance of the surrending rates.

Keywords: Competing Risks, Survival Analysis, Dirichlet Processes, Bayesian analysis, Lapse risk, MCMC

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2023Mar

AffineMortality: An R package for estimation, analysis and projection of affine mortality models

Francesco Ungolo, Len Patrick Dominic M. Garces, Michael Sherris, and Yuxin Zhou

Abstract: This paper presents the AffineMortality R package which performs parameter estimation, goodness of fit analysis, simulation and projection of future mortality rates for a set of affine mortality models for use in pricing and reserving. The computational routines build on the univariate Kalman Filtering approach of Koopman & Durbin (2000) along other numerical methods to enhance the robustness of the results. This paper provides a discussion of how the package works in order to effectively estimate and project the models, and describes the available functions. Illustration of the package for mortality analysis of the US HMD dataset is provided.

Keywords: Longevity Risk, Kalman Filter, State-space models, Affine mortality

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2023Mar

Nonlinear Means-Tested Pensions: Welfare and Distributional Analyses

Daniel Wheadon, Gonzalo Castex, George Kudrna and Alan Woodland

Abstract: Several countries, including Australia, have a means-tested public age pension. Means testing the age pension can reduce the overall fiscal burden relative to a universal pension, but can also distort households’ incentives to work and save. Policymakers can influence the sizes of these distortions by adjusting the structure of the pension function (e.g., the withdrawal rate of the pension). In contrast with the standard piece-wise linear means test, we introduce a class of non-linear means tests that contain the standard linear test as a special case and allow for progressive or regressive tests in which the withdrawal rate respectively increases or decreases as means increase. To identify the socially optimal nonlinear income-tested pension function, we develop an overlapping generations model of a small open economy with heterogeneous agents with stochastic wage and mortality profiles. We find that the optimal nonlinear income test is strongly regressive with a low average withdrawal rate as income increases.

Keywords: Population aging, Sustainability, Social security, Means testing, Redis- tribution, Overlapping generations, Dynamic general equilibrium.

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2023Mar

The Economy-wide Effects of Mandating Private Retirement Incomes

George Kudrna

Abstract: This paper investigates the economy-wide effects of mandating private pensions. Drawing on Australia’s Superannuation Guarantee (SG) legislation, which mandates contributions to private retirement (superannuation) accounts, our objective is to quantify the long-term effects of the SG mandate on households’ economic decisions, welfare, and macroeconomic and fiscal indicators. We begin with the partial equilibrium (PE) life-cycle analysis that considers private (liquid) and superannuation (illiquid) assets, highlighting the interactions of the SG mandate with income taxation, public pensions, and bequest re- distribution. We then develop a general equilibrium (GE) model that includes overlapping generations of heterogenous households, labor income and survival risks, and both types of household assets. The model is calibrated using Australian data and incorporates a detailed representation of government policy, including mandatory superannuation. The simulation results indicate that higher SG rates lead to significantly greater household wealth, output and consumption per capita, and household welfare across the skill distribution in the long run. These positive effects are due to (combination of) increased tax subsidies, more binding means testing reducing public pensions, redistribution of increased accidental bequests and also GE effects on factor prices (with higher gross wage rates).

Keywords: Private Pension, Social Security, Income Taxation, Labor Supply, Life- Cycle, General Equilibrium

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