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Working Papers

Loretti Dobrescu

Loretti I. Dobrescu and Akshay Shanker

Abstract: We introduce a fast upper envelope scan (FUES) method to solve and estimate dynamic programming problems with discrete and continuous choices. FUES builds on the standard endogenous grid method (EGM). EGM applied to problems with continuous and discrete choices, however, does not by itself generate the optimal solution, as the first order conditions used to retrieve the endogenous grid are necessary but not sufficient. FUES sequentially checks EGM candidate solution points and eliminates those not on the upper envelope of the value correspondence by only allowing discontinuities in the policy function at non-concave regions of the value correspondence. Unlike previous methods used to perform EGM in discrete-continuous dynamic models, FUES does not require the monotonicity of the policy functions. It is also computationally efficient, straightforward to implement, and for sufficiently large EGM grid sizes, guaranteed to recover the optimal solution.

Key Words: discrete and continuous choices, non-convex optimization, Euler equation, computational methods, dynamic programming

Ageing data

Tianyu Shen and Collin Payne

Abstract: A substantial body of prior research has explored patterns of disability-free and morbidity-free life expectancy (LE) among older populations. However, these distinct facets of later-life health are almost always studied in isolation, even though they are very likely to interact with each other. Using data from the US Health and Retirement Study (HRS) and a multistate life table approach, this paper explores the interactions between disability, morbidity, and mortality among four successive US birth cohorts, born from 1914-1923 to 1944-1953. These 10-year cohorts are compared in the periods 1998-2008 and 2008-2018. The LE and health expectancies (HEs) are calculated via demographic microsimulation, and are modelled separately by sex, educational attainment and race/ethnicity. We find little compression of disability but a substantial expansion of morbidity across cohorts in each of the three age ranges. Investigating interactions between morbidity and disability, we find that disability-free life expectancy (DFLE) among those living with chronic morbidities has increased, but that at the population level DFLE is largely unchanged across successive cohorts. Investigating patterns in population sub-groups, we find that less advantaged populations (low educated and non- white groups) live substantially fewer years free of disabilities or chronic morbidities. Broadly, these patterns suggest that the link between chronic morbidities and disability has weakened over time in the US population. However, at the population level, successive cohorts are spending fewer years of life free of both chronic morbidities and disability.

KeywordsMorbidity, Disability, Aging, Dynamic equilibrium, Health expectancy



Yafei Si, Hazel Bateman, Shu Chen, Katja Hanewal, Bingqin Li, Min Su and Zhongliang Zhou

Abstract: Overuse of health care is a potential factor in explaining the rapid increase in health care expenditure in many countries; however, it is difficult to measure overuse. This study employed the novel method of using unannounced standardised patients (SPs) to identify overuse, document its patterns and quantify its financial impact on patients in primary care in China. We trained 18 SPs to present consistent cases of two common chronic diseases and recorded 492 physician patient interactions in 63 public and private primary hospitals in a capital city in western China in 2017 and 2018. Overuse, defined as the provision of unnecessary medical tests and drugs, was identified by a panel of medical experts based on national clinical guidelines. We estimated linear regression models to investigate how hospital, physician and patient characteristics were associated with overuse and to quantify the financial impact of overuse after controlling for a series of fixed effects. We found overuse in 72.15% of the SP visits. The high prevalence of overuse was similar among public and private hospitals, low-competence and high-competence physicians, male and female physicians, junior and senior physicians and male and female patients, but it varied between patients presenting different diseases. Compared to the non-overuse group, overuse significantly increased the total cost by 117.8%, the test cost by 58.8% and the drug cost by 100.3%. The financial impact of overuse was consistent across the aforementioned hospital, physician and patient characteristics. We suggest that the overuse observed in this study is unlikely to be attributable to physician incompetence but rather to the financing framework for primary care in China. These findings illuminate the cost escalation of primary care in China, which is a form of medical inefficiency that should be urgently addressed.

Keywords: health care expenditure, overuse, primary care, standardised patient, China

Supplementary Material

Colleagues collaborating over data
Tianyu Shen, Collin Payne and Maria Jahromi 


Abstract: Many studies have compared individual measures of health expectancy across older populations by time-invariant variables. However, very few have included time-varying variables when calculating health expectancy. Since events in the life course are likely to be changing over time in related ways, it is valuable to incorporate time-varying socioeconomic factors. This paper proposes a Multiple Multistate Method (MMM) that situates the multistate model within the broader family of Vector Autoregression (VAR) models. When estimating multistate models with sample survey data, sparseness in the transition matrices often makes such models unfeasible should two or more time-varying variables be built into the state spaces. This approach allows for the estimation of more complex state spaces (including the modeling of time-varying covariates) by reducing less important interactions in the model. We then demonstrate the MMM in two empirical applications, showing the flexibility of the approach to explore health expectancies with complex state spaces.

Key words: Multistate model, discrete-time Markov processes, microsimulation, health expectancy, VAR model



Ricky Kanabar and Adriaan Kalwij


Abstract: We examine individuals’ retirement behaviour in response to changes in the State Pension eligibility age introduced in various Pension Acts in the UK. Our findings show that the annual probability of retirement reduced significantly in response to a one-year increase in State Pension eligibility age, by 16 pp and 13 pp for men and women respectively. They also show that women adjusted their expected retirement age downwards in response to an increase in their SP eligibility age. These findings suggest that whilst an increase in the State Pension eligibility age induces individuals to postpone actual retirement, it does not lead to individuals  revising their expected retirement age upwards, which could result in suboptimal retirement planning. The latter can be problematic for those who rely disproportionately on State Pension as their main source of income and, arguably, targeted communication campaigns are needed to improve retirement planning

Keywords: Retirement, Expectations, United Kingdom Household Longitudinal Study


Len Patrick Dominic M. Garces, Jovana Kolar, Michael Sherris, and Francesco Ungolo


Abstract: In this paper, we investigate the dynamics of age-cohort survival curves under the assumption that the instantaneous mortality intensity is driven by an affine jump-diffusion (AJD) process. Advantages of an AJD specification of mortality dynamics include the avail- ability of closed-form expressions for survival probabilities afforded by an affine mortality specification and the ease with which we can incorporate sudden positive and negative shocks in mortality dynamics, reflecting events such as wars, pandemics, and medical advancements. As we are interested in modelling the evolution of mortality rates, we propose a state-space approach to calibrate the parameters of the affine mortality process. This ensures consistent survival curves in the sense that forecasts of survival probabilities have the same parametric form as the fitted survival curves. As the resulting state-space model is non-Gaussian due to the presence of jumps, we apply and assess a particle filter-based Markov chain Monte Carlo approach to estimate the model parameters. We illustrate our methodology by fitting one- factor Cox-Ingersoll-Ross and Blackburn-Sherris mortality models with asymmetric double exponential jumps to historical age-cohort mortality data from USA. We find that these one-factor models with jumps have good in-sample fit, but their forecasting performance suggests the need for additional latent factors to improve the accuracy of forecasts.

Key words: Affine mortality models, affine jump-diffusion, age-cohort mortality rates, particle filter, particle Markov chain Monte Carlo


Tom Wilson and Jeromey Temple

Abstract: The recent release of preliminary rebased Estimated Resident Populations for 2021 by the Australian Bureau of Statistics (ABS) provides updated populations on which to base new population projections for Australia. New projections are necessary because of the disruption to demographic trends caused by Covid, rendering even quite recently produced projections out-of-date. This paper presents new population projections for Australia and the states and territories for the period 2021-2041. The paper describes the input data used, projection assumptions made, and an outline of the projection model. Key features of projected population ageing are presented, followed by brief projection profiles of Australia and the states and territories. Population projections data is available at the Centre of Excellence in Population Ageing Research (CEPAR) Population Ageing Futures Data Archive (https://cepar.edu.au/cepar-population-ageing-projections)

Key words: Population projections; population ageing; Australia; States and Territories

This work was supported by the Australian Research Council Centre of Excellence in Population Ageing Research (project number CE1101029).


Dr Miguel Olivo-Villabrille

Arezou Zaresani and Miguel Olivo-Villabrille

Abstract: Exploiting a quasi-natural experiment and using administrative data, we examine the effects of the return-to-work policies’ clawback regime in Disability Insurance (DI) programs on beneficiaries’ labor supply decisions, allowing them to collect reduced DI payments while working. We compare two return-to-work policies: one with a single rate clawback regime and another featuring a more generous clawback regime, where a reform further increased its generosity. The reform caused an increase in the mean labor supply: beneficiaries who already work, work more, and those who did not work started working. The effects are heterogeneous by beneficiaries’ characteristics, and the increase is driven mainly by top percentiles of earnings. Findings suggest an essential role for the clawback regime in return-to-work policies and targeted policies to increase the labor supply in DI programs.

Keywords: disability insurance; clawback rate; return-to-work policy, financial incentives; labor supply.



Results: Yafei Si, Katja Hanewald, Shu Chen, Bingqin Li, Hazel Bateman abd John R. Beard



Background: Maintaining and optimising intrinsic capacity (IC) across a person’s life course is a core component of the World Health Organization’s model of healthy ageing. However, the contribution of cumulative health inequalities over time to subtle changes in IC in late life is not well understood. 

Methods: We included 21,783 participants aged 45+ from the China Health and Retirement Longitudinal Study and calculated a validated prognostic value of IC. We included eleven early-life factors to investigate their direct influence on IC over thirty years later and cumulative influence through four current socioeconomic factors. We used multivariable linear regression and concentration index decomposition to investigate the contributions of each determinant to IC inequalities. Mediation analysis identified the direct and cumulative contribution of early-life factors. 

Results: Participants with an advantaged environment in childhood and a higher current socioeconomic position had a significantly higher IC score. This inequality was greatest for cognitive capacity and sensory capacity. Overall, early-life factors directly explained 13.92% (95% CI: 12.07% to 15.77%) of IC inequalities, while 28.57% (95% CI: 28.19% to 28.95%) of IC inequalities were explained through the cumulative effects of socioeconomic inequalities over a person’s life course. 

Conclusion: In China, unfavourable early-life factors appear to directly decrease late-life health status, particularly cognitive and sensory capacities rather than locomotor functioning, psychological capacity or homeostasis, and these effects are exacerbated by the cumulative socioeconomic inequalities over a person’s life course. Interventions in early life and subsequently across the life course may be effective in reducing these disparities. 

Keywords: intrinsic capacity, healthy ageing, life course inequality, cognition, China

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