1

Prof. Martin Boyer, Ph.D. Professeur CEFA en Finance et assurance

Directeur du (GR)2R2P2

Fellow CIRANO

HEC Montréal

En collaboration avec Franca Glenzer (Goethe Universität Frankfurt)

Québec, Mars 2015

2

1. Motivation 2. Model Setup 3. Full-information Contracts 4. Asymmetric Information 5. Simulation and Empirical Analysis 6. Discussion and Conclusion

3

In old age, individuals face two main financial risks:

Long-term care (LTC) risk: the risk of having a chronic medical condition that requires medical attention, either at home or in an institution (nursing home)

Longevity Risk: The risk of outliving ones savings

4

The need for long-term care increases with an ever-aging population

The costs for long-term care can be substantial, up to downright catastrophic for many individuals, especially if needed over a long period: ◦ US$21 on average per hour for a home health aide ◦ US$6,235 on average per month for a semi-private room in a

nursing home

Estimated cost for LTC in Canada over the next 35 years: $1.2 trillion

Very low insurance penetration

Source: US Department of Health and Human Services, 2010

5

Two systems for insuring against longevity risk: ◦ Defined Benefit (DB) Plan: Determines the amount to be paid out

to the retiree

◦ Defined Contribution (DC) Plan: Determines the payments into the the pension plan. Benefit payments to the retiree depends on the investment outcome

Recent development: shift from DB to DC (i.e. shifting of risk to the savers/retirees)

6

7

What is more beneficial from the individual perspective? It depends… ◦ On income ◦ On the ability to compensate for a potentially bad investment

outcome and a lower annuity payment under a DC scheme ◦ On consumption needs upon retirement ( LTC!!!) ◦ On bequest motives

Despite the shift from DB to DC, DC is not always better

than DB (Cocco and Lopes, 2011; Brown, 2014)

So when is a DB plan better than a DC plan, and vice versa – considering the risk of needing long-term care?

8

Who knows what when Individuals often have private information about their risk

characteristics ◦ Asymmetric information problem ◦ Potentially: adverse selection and market failure

Here: very particular situation because ◦ Contracts (pension plan and LTC insurance) are very long-term ◦ Young individuals have no experience concerning their future

health/disability status (abstracting from genetic conditions), but they do learn about it over time

Our hypothesis: Whether an individual prefers a DB or a DC plan will depend on her risk type and the timing of the insurance purchase (and I’ll explain why).

9

1. Motivation 2. Model Setup 3. Full-information Contracts 4. Asymmetric Information 5. Simulation and Empirical Analysis 6. Discussion and Conclusion

10

An individual either survives until old age or not

Upon old age, the individual is either in need of LTC or in good health

Different individuals ◦ differ wrt their longevity risk, but

◦ all have the same probability of needing care given that they

reach old age

11

Live in nursing home

Live healthy

Die

p

1-p

1-q

q

Live

DB DC +LTC

Info

rmat

ion

acqu

isiti

on

12

1 2

Individuals choose between a DC or a DB plan; If DB, retirement contract is written

Individuals learn about their health status

Individuals may purchase long-term care insurance; Purchase of annuities for those who chose DC

Nature chooses between three states of the world: Die, Live healthy, Live in nursing home

Payoffs are distributed

3 4 5

13

An individual has a von Neumann-Morgenstern utility which depends on when insurance is purchased:

We assume competitive markets, i.e. insurance companies make zero profit. The premia thus are:

14

1. Motivation 2. Model Setup 3. Full-information Contracts 4. Asymmetric Information 5. Simulation and Empirical Analysis 6. Discussion and Conclusion

15

Independent of the risk type,

Individuals buy full insurance on the LTC insurance market

And annuitize 100% of their lifetime income (perfect

income smoothing)

Result from classic insurance economics for policies with fixed loading and risk-averse individuals

16

1. Motivation 2. Model Setup 3. Full-information Contracts 4. Asymmetric Information 5. Simulation and Empirical Analysis 6. Discussion and Conclusion

17

Live in nursing home

Live healthy

Die

p

1-p

1-q

q

Live

DC +LTC

Info

rmat

ion

acqu

isiti

on

18

Two risk-types in the longevity risk-dimension, H and L, with pH>pL

The maximization problem is then

In an economy where individuals privately know their type and where insurers are restricted to make zero profit for each of the types (i.e., the Rothschild-Stiglitz world), we find that ◦ Both risk types purchase full LTC insurance ◦ The high-risk type receives first-best allocation (perfect income

smoothing) ◦ The low-risk type must signal his type by choosing less-than-perfect

income smoothing

19

Live in nursing home

Live healthy

Die

p

1-p

1-q

q

Live

DB LTC

Info

rmat

ion

acqu

isiti

on

20

Two risk-types in the longevity risk-dimension, H and L, with pH>pL

The maximization problem is then more complicated since agents must anticipate, when choosing their retirement contract, what their long-term care insurance contract will look like.

… and has no longer an analytic solution

21

1. Motivation 2. Model Setup 3. Full-information Contracts 4. Asymmetric Information 5. Simulation and Empirical Analysis 6. Discussion and Conclusion

22

The optimal allocations under a DC-like scheme are such that both agents have full long-term care insurance.

The optimal allocations under a DB-like scheme are such that each agent purchases partial long-term care insurance, and more so for the high risk agent.

2015-10-08 23

LTC

insu

ranc

e ch

oice

Inco

me

smoo

thin

g

Preference

2015-10-08 24

Inco

me

smoo

thin

g

Preference

LTC

insu

ranc

e ch

oice

25

We varied the model parameters to see what pension scheme individuals will prefer…

The greater is… The more likely is…

DC

DB

DB

DB

DC

Risk aversion DB

26

1. Motivation 2. Model Setup 3. Full-information Contracts 4. Asymmetric Information 5. Simulation and Empirical Analysis 6. Discussion and Conclusion

27

Risk Full information

DC DB

Low risk LTC 100%

100%

<100%

Longevity 100%

100%

High risk LTC 100%

100%

<100%

Longevity 100%

<100%

28

Quel avenir pour l’assurance de soins longue-durée? ◦ Soyons optimistes

Quels dangers à l’horizon? ◦ Soyons pessimistes