Firm‐Driven Management of Longevity Risk: Analysis of Lump‐Sum Forward Payments in Japanese Nursing Homes

• DOI: http://doi.org/10.1111/jems.12183
• Date: 01 February 2017
• Author: Shinya Sugawara
• Published date: 01 February 2017

Firm-Driven Management of Longevity Risk: Analysis

of Lump-Sum Forward Payments in Japanese Nursing

Homes

SHINYA SUGAWARA

Department of Information Science and Technology

University of Tokyo

Hongo, Bunkyo, Tokyo, Japan; andNihon University

Gobancho, Chiyoda, Tokyo, Japan

sugawara_shinya@ci.i.u-tokyo.ac.jp

This study analyzes a unique economic circumstance of longevity risk management in the Japanese

private nursing home market. This circumstance takes the form of a lump-sum forward payment

of lifetime rent by residents, which leaves most longevity risk to be covered by homes. To analyze

this circumstance, I construct a structural econometric model of industrial organization for this

market. For the underlying structure of longevity risk, I assume that both individual consumers

and nursing homes utilize the subjective evaluation. My empirical analysis detects excess pay-

ments that can be compensated for only by an unrealistically long stay in nursing homes. This

finding implies the existence of the exaggerated evaluation of longevity by economic agents. Thus,

appropriate government intervention to help hedge longevity risk might improve social welfare.

1. Introduction

Despite worldwide population aging, longevity risk remains one of the largestuninsured

risks. Many researchers have attempted to explain the small market size for insurance-

like products that address longevity risk, such as Finkelstein and Poterba (2004) for

annuities, Brown and Finkelstein (2009) for private long-term care insurance (LTCI),and

Davidoff and Welke(2006) for reverse mortgages. This study contributes to the literature

by investigating the unique firm-driven mechanism of longevity risk management in

the Japanese private nursing home market.

The mechanism takes the form of an economic circumstance, wherein residents

need to make a lump-sum forward payment to cover the rent over a prespecified expira-

tion period in addition to a monthly fee for daily living expenses. The resident can stay

beyond the expiration period without having to pay additional rent. On the contrary,

when a resident leaves the home before the expiration period, the rent for the remaining

period is refunded. Therefore, this forward payment functions as a lifetime rent without

I thank Yasuhiro Omori, Jiro Nakamura, Yuji Genda, Katsumi Shimotsu, Naoya Sueishi, Hirokazu Ishise,

Mototsugu Fukushige, YuichiroKanazawa, Naoto Kunitomo, Akimichi Takemura, Munenori Ando, Yasusada

Murata, Ryo Okui, Yoichi Nishiyama, Alexander Karmann, and seminar and workshop participants at the

University of Tokyo, Nihon University, Kyoto University, Okinawa International University, ISBA, JuBES,

JEA, JJSS, JYSG, and NASM for their helpful comments. The remaining errors are my responsibility. This

work is supported by the Research Fellowship No. 11J09741 from the Japanese Society for the Promotion of

Science, the Grant-in-Aid for Research Activity start-up No. 25885021, the Grant-in-Aid for Young Scientists

(B) No. 15K17070, and the Grant-in-Aid for Scientific Research(A) No. 21243018 from the Japanese Ministry of

Education, Science, Sports, Culture and Technology and JST CREST. The computational results are obtained

using Ox version 6 (Doornik, 2011).

C2016 Wiley Periodicals, Inc.

Journal of Economics & Management Strategy, Volume26, Number 1, Spring 2017, 169–204

170 Journal of Economics & Management Strategy

a burden to consumers, regardless of the realized lifetime. This price mechanism thus

serves as a relief for risk-averse elderly people who have limited income, mainly com-

posed of a public pension. However, this circumstance forcesa nursing home to assume

most of the longevity risk of its residents. Thus, a rational home must recover the risk

premium through a distinct channel, specifically a higher monthly fee, to manage the

burden of longevity risk.

To analyze this economic circumstance,I construct a structural econometric model

for the Japanese private nursing home market. Owing to considerable sunk costs and

regulation policies that act as barriers to entry, nursing homes are likely to encounter

incomplete competition. To model this situation, I adopt the approach of Berry et al.

(1995) (BLP hereafter), which simultaneously formulates the demand and supply sides

of an economy with monopolistic competition on the supply side.

This study extends the BLP model to capture the risk management mechanism

in the Japanese circumstance. I assume that not only individual consumers but also

homes are risk averse, contrary to the conventional assumption that only consumers are

risk averse. In addition to the adverse selection problem, which is common for many

economic risks, longevity risk management is typically difficult because death can occur

long after the contract, whereas it is uncertain how medical technologies will develop,

as discussed by Cutler (1996), even for large insurance companies. This is particularly

true for elderly people in Japan, who are shown in such demographic studies as Yong

and Saito (2009) and Saito et al. (2015) to still have an increasing trend of disabled life

years in recent years. Furthermore, risk management is more difficult for nursing homes

than for insurance companies, because the small scale of nursing homes prevents them

from canceling out the longevity risk among residents through the law of large numbers.

Therefore, for the nursing home market, it seems more suitable to avoid the conventional

assumption of risk neutrality on the supply side of an insurance-like product.

To extend the BLP model, it is difficult to utilize a conventional methodology

based on risk-averse utility and profit functions, such as a constant relative risk aversion

function, because of the dynamic nature of the situation.1Instead of conventional risk-

averse utility modeling, I assume that both consumers and homes utilize their subjective

prediction for longevity. Then, risk aversion can be characterized as a loose subjective

prediction by economic agents.

I empirically analyze real data taken from a list of nursing homes in 2010 (Mook,

2011). To complement the information from my data set, I also show several pieces of

supplementary information from surveys conducted by the nursing home association.

The descriptive statistics show that homes with short expiration periods assign large

monthly payments. This finding suggests that when nursing homes cover most longevity

risk, the burden of risk is compensated for by the monthly payment. Based on the

descriptive analysis, I construct a model of price setting that includes consumer sorting

by homes with respect to the longevity risk of consumers.

For the estimation, I utilize a nonparametric Bayesian method that can conduct

flexible simulation analysis. The estimation results report reasonable estimates for the

model parameters. As a result of the presented simulation study, I find that the circum-

stance induces a large increase in total payments by residents, except for those who

1. The risk-averse utility function represents utility in each time period. On the other hand, longevity,

which serves as the horizon in the dynamic optimization, is uncertain in the nursing home market. Thus, it is

difficult to capture the risk in the nursing home market by using a conventional approach based on a specific

functional form of utility.

Firm-Driven Management of Longevity Risk 171

have unrealistically long lifetimes. This finding implies the existence of the exaggerated

evaluation of longevity by economic agents. Thus, intervention by the government,

which is a risk-neutral economic agent, can be justified.

This study contributes to the literature on the industrial organization of the nursing

home market. A primary stream of the literature is summarized by Norton (2000), which

analyzed the effects of long-term care policies in the United States, such as the certificate-

of-need (CON) (Scanlon, 1982) and Medicare reimbursement (Nyman, 1985) policies,

by using reduced-form methods. Recently, several authors have conducted structural

analyses of nursing homes that are closely related to those of this study. Specifically,

Ching et al. (2015) utilized the BLP model to capture the US situation, in which excess

demand exists. Lin (2015) empirically analyzed quality choices by homes, using the

dynamic game model to grasp the strategic interaction on the supply side. In comparison

with these previous studies, the explicit aim of the present study is to model longevity

risk management, thereby providing a new perspective on the important factors that

influence the nursing home market.

The rest of the paper is organized as follows. Section 2 provides a brief review of

the Japanese private nursing home market and describes my data set, whose descriptive

statistics clearly show a peculiarity of the market. Section 3 introduces the econometric

model and statistical methodology used in this study. Section 4 applies the proposed

method to real data. Finally, Section 5 concludes.

2. Background and Data

2.1. The Nursing Home Industry in Japan

A nursing home is defined as an institution for permanent elderly care. In Japan, there

are public and private nursing home sectors,2where the latter is the target of my study.

Public and private homes are both covered by the social program of the LTCIestablished

in 2000. Public homes are mostly financed by the LTCI and provide uniform care at

uniform prices for those who cannot leave their beds by themselves. For private homes,

the social insurance covers only those fees strictly categorized as care costs. Care costs

are not included in ordinary payments, but instead are treated as a person-specific

additional payment. Thus, private homes provide divergent care at various prices and

accept various residents.

Until the 1990s, most residents in private homes were wealthy, whereas residents

in public homes were less well-off and solitary elderly people targeted by the welfare

program. Several luxury private homes attracted wide attention in the Japanese “bubble”

economy in the late 1980s. However, since the launch of the LTCI in 2000, the private

home industry has grown rapidly. Private homes increased their capacity from 32,302

in 1999 to 183,245 in 2009, whereas public homes showed slower growth from 283,822

2. The terms “public nursing home” and “private nursing home” are translations of the Japanese words

“Tokubetsu-Yougo Roujin Houmu”and“Yuuryou Roujin Houmu,” respectively.Tamiya et al. (2011) used the term

“private nursing home” for “Yuuryou Roujin Houmu,” but there is no consensus among researchers on this

English term. For example, Ikegami and Campbell (2000) referred to a private nursing home as “residential

care with private-pay.”In this study, private homes aretreated as a form of nursing home and juxtaposed with

public homes for two reasons. First, their function matches that of the standard definition of a nursing home,

namely to provide general long-term care without specializing in medical carefor those who permanently live

in an institution. Second, the Japanese term “Roujin Home,” which means nursing home, is commonly found

in such words as “Tokubetsu-Yougo Roujin Houmu”and“Yuuryou Roujin Houmu.” This represents the fact that

Japanese people perceive these institutions as similar service goods.