A common thread linking the design of guarantee and nonescalating payments of public annuities

• Published date: 01 September 2023
• Author: Sau‐Him Paul Lau,Qilin Zhang
• Date: 01 September 2023
• DOI: http://doi.org/10.1111/jori.12419

Received: 21 August 2021

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Revised: 8 November 2022

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Accepted: 11 January 2023

DOI: 10.1111/jori.12419

ORIGINAL ARTICLE

A common thread linking the design

of guarantee and nonescalating payments

of public annuities

Sau‐Him Paul Lau

1

|Qilin Zhang

2

1

Faculty of Business and Economics,

University of Hong Kong, Hong Kong,

China

2

School of Accounting and Finance,

Hong Kong Polytechnic University,

Hong Kong, China

Correspondence

Sau‐Him Paul Lau, Faculty of Business

and Economics, University of Hong

Kong, Pokfulam Road, Hong Kong,

China.

Email: laushp@hku.hk

Funding information

Research Grants Council, University

Grants Committee, Hong Kong,

Grant/Award Number: 17503219

Abstract

Motivated by recent experiences in economies adopting

the defined‐contribution pension system, we study

public annuities in the presence of survival probability

heterogeneity. It is found that the difference of

annuitization‐weighted and unweighted averages of

survival probabilities is a useful measure of the severity

of adverse selection. We then examine public annuities

with a guarantee feature which bundles annuity

income and bequeathable wealth components. We

show that when the heterogeneity in survival probabil-

ity is limited, the magnitude of guarantee proportion is

irrelevant. On the other hand, an increase in the

guarantee proportion mitigates adverse selection when

the extent of heterogeneity is sufficiently large, because

the share of annuity purchase by retirees with lower

(resp., higher) survival probabilities is increased (resp.,

decreased). We also obtain a similar set of results for

public annuities with nonescalating payments. The

results have useful implications regarding the design of

public annuities.

J Risk Insur. 2023;90:703–742. wileyonlinelibrary.com/journal/JORI

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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, provided the original work is properly cited, the use is non‐commercial and no modifications or

adaptations are made.

© 2023 The Authors. Journal of Risk and Insurance published by Wiley Periodicals LLC on behalf of American Risk and Insurance

Association.

KEYWORDS

asymmetric information, guarantee element, nonescalating

payments, public annuity, severity of adverse selection

JEL CLASSIFICATION

H55, G52, D15

1|INTRODUCTION

According to the World Bank, life expectancy at birth worldwide increased from 62.8 yearsin

1980to72.6 yearsin2018. Amongthosewhoare65 yearsold,35%ofwomenintheUSAare

expected to survive to 90 years old; the corresponding figures are 34% in the UK, 46% in France,

and 52% in Japan. These increases in life expectancy bring benefits to most individuals, but they

also cause problems, especially if individuals do not respond appropriately. One of these

potential problems is that individuals may outlive their resources and face financial difficulties

during old age.

In principle, people may insure against longevity risk (the risk of having inadequate

financial resources when living longer than anticipated) by purchasing annuities in the

private market. Alternatively, retirees in countries adopting the pay‐as‐you‐go (PAYGO)

retirement pension system may rely, at least partially, on pension benefits whenever they

are alive. However, neither the PAYGO system nor a pure market solution seems to solve

the problem satisfactorily. On the one hand, it is well known that many developed countries

with an unfunded PAYGO system have suffered budgetary difficulties in the past few

decades. In response, some countries have already extended the pension eligibility age

and/or reduced the benefit. On the other hand, few retirees annuitize a substantial portion

of their wealth (Benartzi et al., 2011; Modigliani, 1986). A lot of researchers have analyzed

this phenomenon of “annuity puzzle,”but no consensus has been reached regarding the

underlying reasons, and their relative importance. As a result, it is hard for policymakers to

propose appropriate market regulations to mitigate the possible efficiency loss due to low

annuitization rates.

In this paper, we consider the public annuity (PA) scheme in the payout (or decumulation)

phase under a fully funded pension system, an alternative to either the PAYGO system or

private annuities. In recent decades, more countries have introduced the defined‐contribution

Individual Account system. An important policy debate for these countries is whether

appropriate financial instruments are available for retirees to solve the problem of longevity

risk. The focus on the PA scheme in this paper is motivated by two sets of factors. First,

compared with private annuity providers, the government may have a lower cost structure

(Diamond, 2004). Second, we have observed diverse practices in the PA plans in various

economies, as summarized in Section 2.1. Even though these plans generally differ in various

dimensions, there are also common features, such as the guarantee and nonescalating

payments.

On the basis of these observed PA practices, we think it is interesting to study at least the

following two aspects. First, it is not clear how to best organize and classify different public

annuitization plans. The study of the pros and cons of mandatory versus voluntary PA plans in

Lau and Zhang (2023) is an attempt in this direction. Second, the reasons of adopting several

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commonly observed features, including guarantee and nonescalating payments, by the PA

providers are not well understood. This paper aims to study the implications of these two

features by using a tractable analytical model of annuitization behavior in the presence of

adverse selection.

We find that the difference of annuitization‐weighted and unweighted averages of the

retirees' survival probabilities is a useful measure of the severity of adverse selection. On the

basis of this concept, we study whether introducing the guarantee or nonescalating payments

affects the severity of adverse selection of the annuity market. Previous empirical and

theoretical studies such as Finkelstein and Poterba (2002,2004), Davidoff et al. (2005) and

Cannon and Tonks (2016) examine whether these features affect annuity market efficiency

through changing the severity of adverse selection. A key finding of this paper is that

introducing either one of these two features leads to a decrease in the severity of adverse

selection under some conditions regarding the degree of heterogeneity in survival probabilities,

but has no effect on the severity of adverse selection when the conditions are not satisfied. (The

intuition of these results will be provided in Sections 5and 6.) Besides providing new results

regarding these issues, our paper highlight the common underlying factors for the survival‐

contingent payments only versus the guarantee component on the one hand, and the escalating

versus nonescalating payments on the other. To the best of our knowledge, previous

researchers studied these questions separately, and have not linked them through a common

lens. Moreover, the results in this paper have policy implications regarding the number and

form of the PA plans provided.

The remaining sections of this paper are organized as follows. In Section 2, we provide the

background material for this study, reviewing the PA plans in various economies, as well as

related papers in the literature. Section 3describes the model in detail. Section 4analyzes the

annuity buyers' behavior. We study how the buyer's annuitization behavior is related to her

survival probability and the annuity payout level. We also show that the difference of

annuitization‐weighted and unweighted averages of survival probabilities is a useful measure of

the severity of adverse selection of the PA plan. Both sets of results are useful for the

subsequent analysis of policy issues. On the basis of the analysis in Section 4, we consider two

policy issues relevant to the actual practices of the PA plans. Section 5discusses how guarantee

payment as a policy instrument could interact with adverse selection. Section 6examines the

issue of escalating versus nonescalating payments in the PA plan. Section 7provides

concluding remarks.

2|ANNUITIZATION POLICIES AND LITERATURE

REVIEW

In Section 2.1, we review annuitization policies in several economies, focusing particularly on

those offering PA plans. We provide literature review in Section 2.2.

2.1 |Observed PA plans

Many governments adopt annuitization policies to help retirees deal with longevity risk. We

observe a wide variety of these practices and there are differences in at least four major aspects.

First, some economies (such as the UK before 2015 and Chile) simply require the retirees to

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