Health State Transitions and Longevity Effects on Retirees’ Optimal Annuitization

• Author: Linda L. Golden,Wei Zhu,Jing Ai,Patrick L. Brockett
• Published date: 01 April 2017
• Date: 01 April 2017
• DOI: http://doi.org/10.1111/jori.12168

©2016 The Authors Journal of Risk and Insurance published by Wiley Periodicals, Inc. on behalf

of American Risk and Insurance Association. Vol.84, No. S1, 319–343 (2017).

DOI: 10.1111/jori.12168

Health State Transitions and Longevity Effects on

Retirees’ Optimal Annuitization

Jing Ai

Patrick L. Brockett

Linda L. Golden

Wei Zhu

Abstract

The interplay between longevity risk and health state transitions for retirees’

optimal annuitization decisions is investigated. Using a life-cycle framework

incorporating wealth levels, bequest motives, and consumption floors cre-

ated by government subsidies, we examine how increased longevity in con-

junction with an individual’s health state transition process impacts annuity

purchase decisions. Health state transition matrices are estimated from the

Health and Retirement Survey (HRS) data. The effects of increased longevity

on annuitization decisions are considered when longevity is both accom-

panied by increased time spent in healthier states (morbidity compression)

or experienced by more time in unhealthy states (morbidity expansion).

We find that retirees’ annuity demand is affected by wealth, initial health

status, and expansion or compression of morbidity. Wealthier retirees have

higher annuity demand when health shocks are considered, and increased

longevity increases demand even more when retireesexpect an expansion or

This is an open access article under the terms of the Creative Commons Attribution-

NonCommercial-NoDerivs License, which permits use and distribution in any medium, pro-

vided the original work is properly cited, the use is non-commercial and no modifications or

adaptations are made.

Jing Ai is at the Shidler College of Business, University of Hawai’i at M¯

anoa, 2404 Maile Way

Honolulu, HI 96822. Ai can be contacted via e-mail: jing.ai@hawaii.edu. Patrick L. Brockett is

at the Department of Information, Risk, and Operations Management, University of Texas at

Austin, Austin, Texas 78712. Brockett can be contacted via e-mail: brockett@utexas.edu.Linda

L. Golden is at the Department of Marketing, University of Texasat Austin, Austin, Texas 78712.

Golden can be contacted via e-mail: utlindagolden@gmail.com. Wie Zhu is at the School of In-

surance and Economics, University of International Business and Economics, Beijing 100029,

PRC. Zhu can be contacted via e-mail: zhuwei@uibe.edu.cn. Wei Zhu acknowledges finan-

cial support from the research grant of National Science Foundation of China (NSFC) (Nos.

71201029, 71373044) and from the Fundamental Research Funds for the Central Universities in

UIBE (CXTD5-04).

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320 The Journal of Risk and Insurance

slight morbidity compression. Withhealth shocks and expectations of severe

morbidity compression considered, the opposite effect might occur.Thus, an

annuity can help retirees hedge health shock costs when slight compression

or expansion of morbidity occurs. For retirees with lower wealth, the con-

sumption floor provided by governmental subsidies will create a decreased

propensity to annuitize.

Introduction

Classic rational choice theory predicts that absent other motivations or constraints,

retirees optimally annuitize 100 percent of their wealth (Yaari, 1965; Davidoff, Brown,

and Diamond, 2005). This conflicts with the observation that relatively few retirees

annuitize a substantial portion of their wealth (the “annuity puzzle”). To explain this

puzzle, recent literature has identified factors affecting annuity demand, including

preannuitized wealth, such as social security and pension plans (Dushi and Webb,

2004), uncertain income (Scholz, Seshadri, and Khitatrakun, 2006), unfair annuity

pricing (Mitchell et al., 1999), bequest motives (Kopczuk and Lupton, 2007; Lock-

wood, 2012), minimum support from government subsidies (Ameriks et al., 2011;

Pashchenko, 2013), and illiquidity of assets (Pashchenko, 2013; Yogo, 2014).

A factor recently recognized as relevant in annuitization decisions is the pattern of

individual health state transitions and associated costs (Turra and Mitchell, 2008;

Davidoff, 2009; Ameriks et al., 2011; MacMinn and Weber, 2011; Pashchenko, 2013;

Yogo, 2014; Peijnenburg, Nijman, and Werker, 2015).1Another factor is anticipation

of increased longevity. How long a person anticipates living and in what health states

influence annuitization decisions.2

The longevity and annuity demand literature has yet to consider the interconnec-

tion between health state transitions (and associated health care costs) and increased

longevity (Cairns, Blake, and Dowd, 2008), and this article fills this gap.3While fo-

cusing on the interplay between longevity,annuitization, and health state transitions,

we also accommodate other factors (wealth level, bequest motives, and government

provided minimum support levels).

1Yogo’s (2014) experiment using a calibrated rational life-cycle model, wherein health expen-

diture and saving decisions respond endogenously to health shocks, finds retirees can obtain

welfare gain from private annuitization.

2Apart from rational choice based attempts to explain the annuity puzzle, there is a growing

literature on behavioral, psychological, and institutional considerations that enter into the

decision to annuitize wealth. Among these articles are Hu and Scott (2007), Brown et al. (2008),

and Benartzi, Previtero, and Thaler (2011).

3There is, however, a literatureconnecting demand for long-term care insurance and annuities

focusing on the natural hedge between long-term care insurance and annuity demand (see

Ameriks et al., 2011;Brown and Warshawsky,2013). These studies do not consider the interplay

between longevity and health shocks. Another strand of literature (e.g., see Majer et al., 2013;

Sherris and Zhou, 2014) models and calibrates the patterns of this interplay, but does not

investigate the impact of this interplay on optimal annuitization choices. The interested reader

is referred to Majer et al. (2013) and Sherris and Zhou (2014) for more details and references

on this topic.