Health and Mortality Delta: Assessing the Welfare Cost of Household Insurance Choice

• Author: MOTOHIRO YOGO,STIJN NIEUWERBURGH,RALPH S.J. KOIJEN
• DOI: http://doi.org/10.1111/jofi.12273
• Published date: 01 April 2016
• Date: 01 April 2016

THE JOURNAL OF FINANCE •VOL. LXXI, NO. 2 •APRIL 2016

Health and Mortality Delta: Assessing the

Welfare Cost of Household Insurance Choice

RALPH S.J. KOIJEN, STIJN VAN NIEUWERBURGH, and MOTOHIRO YOGO∗

ABSTRACT

We develop a pair of risk measures, health and mortality delta, for the universe of

life and health insurance products. A life-cycle model of insurance choice simplifies

to replicating the optimal health and mortality delta through a portfolio of insurance

products. We estimate the model to explain the observed variation in health and

mortality delta implied by the ownership of life insurance, annuities including private

pensions, and long-term care insurance in the Health and Retirement Study. For the

median household aged 51 to 57, the lifetime welfare cost of market incompleteness

and suboptimal choice is 3.2% of total wealth.

RETAIL FINANCIAL ADVISORS and insurance companies offer a wide variety of in-

surance products that includes life insurance, annuities, and long-term care

insurance. They offer each of these products in a full range of maturities and

payout structures. Examples include term life insurance with guaranteed term

∗Koijen is with London Business School and CEPR. Van Nieuwerburgh is with New York Uni-

versity,NBER, and CEPR. Yogo is with Princeton University and NBER. The authors acknowledge

financial support from Netspar, and Koijen acknowledges financial support from the European Re-

search Council (grant 338082). The Health and Retirement Study is sponsored by the National

Institute on Aging (grant U01-AG009740) and is conducted by the University of Michigan. The

authors declare that they have no relevant or material financial interests related to the research

in the paper. For comments and discussions, we thank three referees, Peter Bossaerts, Jiajia Cui,

Frank de Jong, Liran Einav, Michael Gallmeyer, Ben Heijdra, Deborah Lucas, Robin Lumsdaine,

Alexander Michaelides, Olivia Mitchell, Theo Nijman, Radek Paluszynski, Sam Schulhofer-Wohl,

Kenneth Singleton, Pascal St-Amour, Mogens Steffensen, and Mark Warshawsky. We also thank

seminar participants at APG, Australian National University,Columbia University, Erasmus Uni-

versity,Federal Reserve Bank of Chicago, Federal Reserve Bank of Minneapolis, Financial Engines,

Georgetown University, Georgia State University, Maastricht University, New York University,

Northwestern University,Princeton University, Tilburg University,University of Chicago, Univer-

sity of Minnesota, University of New South Wales, University of TechnologySydney, University of

Tokyo, University of Utah, Vanderbilt University, 2011 Netspar International Pension Workshop,

2011 SED Annual Meeting, 2011 UBC Summer Finance Conference, 2011 Conference on Economic

Decisionmaking, 2012 AEA Annual Meeting, 2012 Utah Winter Finance Conference, 2012 LAEF

Conference on Health and Mortality,2012 Wharton Conference on Household Portfolio Choice and

Investment Decisions, 2012 NBER Summer Institute Economics of Household Saving Workshop,

2012 EFA Annual Meeting, 2012 Systemic Risk Conference: Economists Meet Neurologists, 2012

NBER-Oxford Sa¨

ıd-CFS-EIEF Conference on Household Finance, 2012 Q-Group Fall Seminar,

2013 NBER Personal Retirement Challenges Meeting, and 2014 AFA Annual Meeting. The views

expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank

of Minneapolis, the Federal Reserve System, or the National Bureau of Economic Research.

DOI: 10.1111/jofi.12273

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958 The Journal of Finance R

up to 30 years, universal and whole life insurance, immediate annuities, and

deferred annuities whose income is deferrable for a year or longer. This variety

begs for a risk measure that allows households to assess the degree of com-

plementarity and substitutability between various products and ultimately

choose an optimal portfolio of products. Such risk measures already exist in

other parts of the retail financial industry. For example, beta measures an

equity product’s exposure to aggregate market risk, while duration measures

a fixed-income product’s exposure to interest rate risk. The existence of these

risk measures, based on sound economic theory,has proven to be tremendously

valuable in quantifying and managing financial risk for both households and

institutions.

In this paper, we develop a pair of risk measures for the universe of life and

health insurance products, which we refer to as health and mortality delta.

Health delta measures the differential payoff that a product delivers in poor

health, while mortality delta measures the differential payoff that a prod-

uct delivers at death. A life-cycle model of insurance choice implies optimal

consumption as well as optimal health and mortality delta, which are deter-

mined by household preferences and state variables (i.e., age, birth cohort,

health, and wealth). An optimal portfolio of insurance products, not neces-

sarily unique, aggregates health and mortality delta over individual products

to replicate the optimal health and mortality delta predicted by the life-cycle

model.

Using our risk measures, we assess how close the observed demand for pri-

vate insurance is to the optimal demand, given the provision of public insurance

through Social Security and Medicare. For each household in the Health and

Retirement Study, we calculate the health and mortality delta implied by its

ownership of term and whole life insurance, annuities including private pen-

sions (i.e., defined benefit plans), and long-term care insurance. We estimate

household preferences, allowing the bequest motive to vary across households,

to minimize the welfare cost implied by the deviations of observed demand

from the optimal demand predicted by the life-cycle model. We achieve sharp

identification of relative risk aversion, the average bequest motive, and the

complementarity of consumption and health. Insurance choice, which embeds

the desired path of wealth in future health states, is much more informative

than the realized path of savings for identifying these preference parameters.

The life-cycle model explains 68% of the variation in observed health delta

and 83% of the variation in observed mortality delta. Consistent with economic

intuition, we find that married households and those with living children have

stronger bequest motives. We also find stronger bequest motives for more ed-

ucated and wealthier households. Overall, these household characteristics ex-

plain 66% of the variation in bequest motives.

Although the life-cycle model explains most of the variation in observed

health and mortality delta across households, it fails to explain the variation

within a household over time. The model prescribes that households decrease

their health and mortality delta over the life cycle by rebalancing from life

Health and Mortality Delta 959

insurance to annuities. Observed health and mortality delta are much more

persistent than the predictions of the life-cycle model, due to the default path

of annuitization from private pensions and the lack of rebalancing. We uncover

a new puzzle that is distinct from the “annuity puzzle,” which concerns the low

level of annuitization relative to a life-cycle model with no bequest motive. The

unexplained within-household variation in the degree of annuitization, rather

than the average level of annuitization, is puzzling from the perspective of

life-cycle theory.

For each household, we estimate the welfare cost of deviations from the op-

timal demand, which we interpret as the joint cost of market incompleteness

(due to private information, borrowing constraints, or other frictions outside

the model) and suboptimal choice. For the median household aged 51 to 57,

the lifetime welfare cost is 3.2% of total wealth, defined as the sum of finan-

cial and housing wealth and the present value of future income minus out-

of-pocket health expenses. Our estimate is an order of magnitude larger than

the welfare cost of underdiversification in stock and mutual fund portfolios

(e.g., Calvet, Campbell, and Sodini (2007) estimate it to be 0.5% of dispos-

able income for the median Swedish household). Most of the welfare cost is

explained by the deviations from optimal mortality delta, instead of the devia-

tions from optimal health delta. In other words, choices over life insurance and

annuities have a much larger welfare impact than choices over long-term care

insurance.

This paper is not the first attempt to understand the demand for life insur-

ance (Bernheim (1991), Inkmann and Michaelides (2012)), annuities (Brown

(2001), Inkmann, Lopes, and Michaelides (2011)), or long-term care insurance

(Brown and Finkelstein (2008), Lockwood (2013)). Relative to the previous

literature, an important methodological contribution is to examine insurance

choice comprehensively as a portfolio-choice problem, instead of one product

at a time. By collapsing insurance choice into a pair of risk measures, we ex-

plicitly account for the complementarity and substitutability between various

products. In particular, annuities and private pensions can partially substi-

tute for long-term care insurance, by insuring that households have sufficient

income to cover late-life health expenses as long as they live. Therefore, one

cannot study the demand for long-term care insurance without simultaneously

thinking about annuities and private pensions.

The remainder of the paper proceeds as follows. In Section I, we develop a

life-cycle model in which households face health and mortality risk and choose

from a complete set of insurance products that includes life insurance, annu-

ities, and supplemental health insurance. In Section II, we derive the opti-

mal demand for insurance and a key formula for measuring the welfare cost

of deviations from the optimal demand. In Section III, we calibrate the life-

cycle model based on the Health and Retirement Study. In Section IV,we

estimate household preferences and compare the observed demand to the op-

timal demand predicted by the life-cycle model. We also estimate the welfare

cost of deviations from the optimal demand. In Section V, we illustrate how a

portfolio of existing insurance products can replicate the optimal health and