Estimating Transition Probabilities Using Repeated Cross-sectional Data

28 Pages Posted: 24 Apr 2024

See all articles by Salvatory Kessy

Salvatory Kessy

UNSW Business School

Yang Shen

University of New South Wales (UNSW)

Michael Sherris

UNSW Business School

Jeromey Temple

The University of Melbourne - Melbourne School of Population and Global Health

Jonathan Ziveyi

University of New South Wales; ARC Centre of Excellence in Population Ageing Research and School of Risk & Actuarial Studies

Multiple version iconThere are 2 versions of this paper

Date Written: April 19, 2024

Abstract

Estimating transition probabilities using cross-sectional data is challenging due to the lack of state-to-state transitions over time for each observed individual. We propose a five-state Markov model (health, disabled, chronically ill, chronically ill and disabled, and dead) to calculate one-year transition probabilities using widely available general population mortality rates and annual prevalence rates derived from cross-sectional data. This results in an underdetermined system of transition probabilities which we solve by adding a set of mathematical relations between the unknown transition probabilities. We calculate annual prevalence rates and population mortality rates from five independent cross-sectional datasets from the Australian Survey of Disability, Ageing, and Carers (SDAC) and the Human Mortality Database, respectively. We use multinomial logistic regression to smooth the raw annual prevalence rates, accounting for age, gender, and time trends to remove noise. Finally, we graduate the estimated transition probabilities using the Whittaker-Henderson smoothing technique to remove the impact of data sampling fluctuations. The results show that the average occupancy probabilities across different states are highest between ages 65 − 74 and decline with advancing age for both genders. A healthy individual is more likely to transition to a chronic illness state than to become disabled. Conversely, a disabled individual is more likely to develop both chronic illness and disability than a chronically ill individual is to become disabled. A healthy individual is more likely to experience both chronic illness and disability than a disabled individual is to develop a chronic illness. Our proposed framework can enhance the development of longevity products in many countries because it relies on readily available population-level mortality and prevalence data to calculate transition probabilities.

Keywords: Disability, cross-sectional data, transition probabilities, prevalence rates, multiple-state model, long-term care, and longevity.

JEL Classification: C21

Suggested Citation

KESSY, Salvatory and Shen, Yang and Sherris, Michael and Temple, Jeromey and Ziveyi, Jonathan, Estimating Transition Probabilities Using Repeated Cross-sectional Data (April 19, 2024). UNSW Business School Research Paper Forthcoming, Available at SSRN: https://ssrn.com/abstract=4800795 or http://dx.doi.org/10.2139/ssrn.4800795

Salvatory KESSY (Contact Author)

UNSW Business School ( email )

UNSW Business School
High St
Sydney, NSW 2052
Australia

Yang Shen

University of New South Wales (UNSW) ( email )

Kensington
High St
Sydney, NSW 2052
Australia

Michael Sherris

UNSW Business School ( email )

Sydney, NSW 2052
Australia

Jeromey Temple

The University of Melbourne - Melbourne School of Population and Global Health ( email )

Australia

Jonathan Ziveyi

University of New South Wales; ARC Centre of Excellence in Population Ageing Research and School of Risk & Actuarial Studies ( email )

School of Risk and Actuarial Studies
UNSW Business School
Sydney, NSW 2000
Australia
+61 2 9065 8254 (Phone)
+61 2 9385 1883 (Fax)

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