Knowledge and Ignorance in a Secondary Insurance Market

Jay Bhattacharya

Stanford University

September 2008

Knowledge Aggregation in Markets Many economists have stressed the ability

of markets to aggregate local knowledge. e.g. Hayek’s famous AER essay

Recent interest in ability of markets to predict the future: Political betting markets Terrorism insurance markets Life insurance markets (e.g. Mullin and

Philipson)

Can Decentralized Knowledge Fail? The behavioral economics literature

emphasizes misperceptions and cognitive errors.There is limited evidence (except

perhaps savings behavior) whether such errors are important in real market settings with large stakes.

What if getting prices right depends upon knowledge that no one has?

Financial Times 9/8/08

“United Airlines temporarily lost most of its market value on Monday after a false report the carrier had returned to bankruptcy court surfaced on the internet.”

“A six-year-old Chicago Tribune story on United’s 2002 bankruptcy filing – spotted on a Google search by an investment newsletter – triggered a sell-off of the carrier’s shares that ended when trading was halted. The stock reached a low of $3, then rebounded once trading resumed to close down 11 per cent.”

“Investors accepted the article as news that the Chicago-based airline had once again sought protection from creditors, a scenario that had grown more feasible in the past year as jet fuel prices skyrocketed.”

Research Aims

Develop evidence from the secondary life insurance market on:The extent to which market

participants have mistaken perceptions regarding their own mortality risks.

The extent to which the market anticipates medical technological breakthroughs.

Why Secondary Life Insurance Markets? This market is a good setting to test for the

presence of cognitive errors. It requires participants to make complicated

evaluations involving their own mortality. This market is a good setting to test for

whether markets are good at predicting the future. Firms need to know whether technological

advances will turn a good deal sour.

Background on the Secondary Life Insurance Market

The Secondary Life Insurance Market The basic transaction:

“Cash out” a life insurance policy before death. The buyer of the policy (typically a 3rd party or

the life insurance firm itself) becomes the beneficiary.

Variations on the market: Viatical settlements market: the market arose in

the late 1980s in response to the AIDS epidemic. Life settlements: transactions are similar to the

viatical settlement market, except for the patient population consists of the chronically ill.

Accelerated death benefits: the life insurance company itself becomes the beneficiary.

Tracking the Viatical Settlement Market Thirty-eight states regulate transactions in the viatical

settlement market in some form. Several states require any viatical settlement firms

doing business in the state to report on all transactions nationwide.

Through FOIA requests, we have collected all available information on viatical settlement transactions from state agencies in California, Connecticut, Kentucky, NY, Texas, North Carolina, and Oregon. Because nearly all large firms sell in those states, we

have data on (nearly) the universe of VS transactions from 1995 to 2001.

We have done a lot of work to cull out duplicate entries.

Breakthroughs in Treatment of HIV Protease Inhibitors introduced in late 1995 Protease Inhibitors combined with other

ARVs (HAART) have been shown to reduce mortality in: Clinical trials (Hammer et al., 1997;

Staszewski et al., 1999 ) Observational studies (Detels et al., 1998;

Palella et al., 1998; Lucas, Chaisson, and Moore, 1999; Vittinghoff et al., 1999; Lucas, Chaisson, and Moore, 2003 )

Death rates declined initially but reached a plateau in 1998

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

1995 1996 1997 1998 1999 2000 2001

Year

AID

S D

eath

Rat

e p

er 1

00,0

00

Source: Centers for Disease Control

Average Life Expectancy of Viators from 1995-2001

15

20

25

30

35

40

1995 1996 1997 1998 1999 2000 2001

LE

(m

on

ths

)

Nominal Price of a Viatical Settlement, by Life Expectancy and Year

Life Expectancy

1995 1996-1997

1998-1999

2000-2001

<12 73.59 78.62 68.20 73.24

12-23 71.43 71.34 60.08 50.60

24-35 61.65 60.74 48.24 38.99

36-47 48.72 46.92 36.25 29.86

>=48 39.31 36.13 28.86 26.91

Size of Viatical Settlement Market 1995-2001

Year# Trans-actions

Face ValueAmount

Viaticated

1995 2,623 $229 million $148 million

1996 2,083 $182 million $121 million

1997 1,930 $213 million $104 million

1998 3,267 $398 million $174 million

1999 1,486 $194 million $84 million

2000 465 $92 million $40 million

2001 188 $81 million $23 million

Secondary Life Insurance Market Grew in the 90s

0

200

400

600

800

1000

1200

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

New HIV Treatments Introduced

Size of Secondary Life Insurance Market

$50 million

$500 million

$1000 million

Secondary Life Insurance Markets are Expanding beyond HIV

Total Life Insurance in Force in 1998

$13.2 trillion

Total held by companies offering ADB $10.3 trillion

113

215

245

0

50

100

150

200

250

300

1991 1994 1998

Life Insurance Companies Offering ADB products

Evidence of Mistaken Consumer Perceptions

Explaining the Empirical Patterns of Viatication Two models to explain who sells their life

insurance policy. A model where sellers correctly perceive

their mortality risk A model of mistaken mortality risk (MMR)

The latter model is motivated by evidence from the HRS that suggests that: Individuals early in the course of a chronic

disease are more pessimistic about their probability of death than warranted

Individuals late in the course of a chronic disease are more optimistic than warranted.

A Vanilla Model with Correct Mortality Predictions People maximize discounted expected utility

(including utility from bequests). Assets include:

(Exogenous) income in each time period A non-liquid asset that can be used to secure a

loan (such as a house) Zero premium life insurance note that pays off

at death. Income can be moved around different times and

states by borrowing/lending against the house and by selling/viaticating the life insurance policy.

Why Treat Actuarially Fair Life Insurance as Valuable Asset?

The unit price of life insurance depends on health status at the time of purchase.

For patients who suffer unexpected health shocks, the actuarially fair unit price of life insurance exceeds the original unit price.

Thus, unexpected health shocks generate a valuable new asset for the chronically ill with life insurance.

Trade-offs in Cashing Out Life Insurance

Patients have three options to finance current consumption:Spend liquid assets.Borrow against non-liquid assets such

as housing—i.e. credit market. Viaticate.

All of these potentially reduce bequests.

Complete Markets in This Context Viatical settlements and credit markets are

complementary in distributing income across time and across different states of the world (uncertain time of death).

Given an arbitrary initial allocation of income in time and in mortality-state space, it is impossible to replicate the time-pattern of consumption achievable with viatical settlements and credit markets combined using only one of these instruments. Actually, in this setting, any mortality

contingent commodity combined with any certain credit note will complete the market.

Mortality Risk and Prices in the Vanilla Model

Given a mortality risk profile, the expected net present value of the stream of returns from purchasing a viatical settlement must equal the n.p.v. of secured lending.

This is true regardless of the mortality risk of the policy holder. Healthier patients receive higher discount to the face

value of life insurance since they are more likely to die later.

This does not mean that changes in mortality risk profiles leave unchanged the incentive to viaticate rather than borrow.

Vanilla Comparative Statics In the simplest versions of this model:

Relative to healthy consumers, unhealthy consumers are more likely to sell life insurance

Healthy and unhealthy consumers with more non-liquid assets are more likely to viaticate.

Both of these comparative statics are driven by wealth effects. Increased mortality risk, increases the equity in life

insurance holdings. Unless the consumer’s portfolio is reorganized, all of the

increase in wealth would go to increased bequests. Increased wealth lead to increased consumption, which

increases both optimal viatication and borrowing.

A Model of Mistaken Mortality Risk

The true price of selling insurance is the same for both healthy and unhealthy consumers.

What if sick consumers do not correctly perceive their mortality risk?Relatively unhealthy consumers (late in

the course of disease) think they are getting a “good deal” at actuarially fair prices

Relatively healthy consumers (early in the course of disease) think they are getting a “bad deal.”

No Arbitrage Opportunity The misperception in price that this

model posits does not generate any arbitrage opportunities for third partiesMisperception does not imply

mispricingCompetition prevents VS firms from

“taking advantage” of the misperception.

Prices are right no free lunch

Favorable Perceived Terms of Trade Let be some cut-off mortality risk.

Patients with that risk perceive the same price in both credit and viatical settlement markets.

Terms favor the credit market for patients with mortality risk (healthy patients).

Terms favor the viatical settlements market for patients with risk (unhealthy patients).

a

a a

a a

Budget Constraint for the Unhealthy—Terms Favor Viatical Settlements

First Prediction Health status is negatively correlated with

the decision to viaticate. Terms of trade favor credit markets for

healthier consumers. Terms of trade favor viatical settlements

markets for unhealthier consumers. Unlike the economic model, this prediction

is not motivated by the wealth effect alone (though that is present in the model).

Changes in Non-Liquid Assets for the Healthy

Changes in Non-Liquid Assets for the Unhealthy

Second Prediction For the healthiest consumers, the decision

to viaticate is negatively correlated with non-liquid assets. Terms favor credit markets, so the healthy

substitute new borrowing for viatical settlements.

For the sickest, the decision to viaticate is positively correlated with non-liquid assets. Terms favor viatical settlement markets, so

the unhealthy increase cashing out.

Changes in Liquid Assets Increasing liquid assets allows both

healthy and unhealthy patients to substitute liquid assets for borrowing, viatication, or both.

Thus, increases in liquid assets reduces or leaves unchanged life insurance supply, as long as consumption and bequests are normal goods.

Third Prediction For all consumers, a small increase in

liquid assets will either reduce or leave unchanged the incentive to participate in the viatical settlements market.

Three Predictions for the MMR Model Prediction 1: Health status is negatively

correlated with the decision to viaticate. Prediction 2: Effect of non-liquid assets.

For the healthiest, viaticating is negatively correlated with non-liquid assets.

For the sickest, viaticating is positively correlated with non-liquid assets.

Prediction 3: Increases in liquid assets will weakly reduce the supply of life insurance.

Data HIV Cost and Services Utilization Study (HCSUS) Longitudinal sample of 2,864 HIV patients in care.

3 Waves-wave 0 (1996), wave 1 (1997), wave 2 (1998)

Information on life insurance holdings and sales, health status,income and demographics and state of residence

1,009 patients report life insurance holdings. 165 patients (16.4%) sold policies. 886 patients in states without minimum price

regulation on viatical settlement sales

Summary Statistics Patients who viaticate are more likely to:

Be maleBe whiteHave a college degreeHave income > $2,000 per monthOwn a houseHave AIDS and low CD4+ T-cell levels.

Empirical Model (1)

Let be the hazard of not selling life insurance (t=0 at the inception of the viatical settlements market or at the date of HIV diagnosis (whichever is later)).

Type of Respondent Contribution to likelihood function

Sold policy by wave 1

Sold between waves 1 and 2

Did not sell

( )Õ=

-1

1

1T

t

tl

( )tl

( ) ( )ÕÕ==

-21

11

T

t

T

t

tt ll

( )Õ=

T

t

t1

l

Empirical Model (2)

We model the hazard of not selling life insurance as:

Xit is the vector of covariates measured at time tβ is the vector of regression coefficients is the baseline logit hazard rate

( ))exp(1

10 bl

litt

iX

t++

=

)exp(1

10tl+

Asset Measurement House ownership is the only measure

of non-liquid assets that is reliably measured in each wave of HCSUS.In waves where other assets are

measured, house ownership is strongly correlated with other wealth

Income is a good measure of liquid assets.

Health Measurement Health status is measured using predicted

one-year mortality rates. Probit incorporates demographic and

health status measures, including CD4 T-cell counts and clinical stage.

The health measure binary (whether predicted mortality exceeds an arbitrary cutoff). Makes interpretation of results easier. Results are not sensitive to the cutoff

(within reason).

Predicted Viatication Probabilities

Years at risk 0 1 2 3 4 5 6 7 8 9

0

.25

.5

.75

1

(Healthy, House)

(Healthy, NoHouse)

(Unhealthy, NoHouse)

(Unhealthy, House)

Pro

port

ion

not V

iati

cate

d

Alternative Theories Viatical settlements and Medicaid

program participation Viatical settlements and taxes Adverse selection in viatical

settlement markets Differential transactions costs of life

insurance sales for healthy vs. unhealthy consumers

Viatical settlements and Medicaid

In most states, funds from a viatical settlement count against Medicaid asset limits, while life insurance holdings do not.This provides a disincentive to sell life

insurance that applies to healthy and unhealthy alike.

Typically HIV patients apply for Medicaid late in the course of their disease.Medicaid asset accounting rules most likely

deter the relatively unhealthy from selling insurance more than the relative healthy

Viatical settlements and taxes The 1996 Health Insurance Portability and

Accountability Act exempts viatical settlements from federal taxes as long as the seller has a life expectancy of 24 months or less or chronically ill.

This fact might explain the relative desirability of viatical settlements for the unhealthy, but cannot explain the pattern of observed interactions between health and non-liquid assets on the hazard of selling insurance.

Asymmetric Information What if viatical settlement firms cannot observe mortality risk? Separating equilibria may exist with welfare loss for low risk

types (relative to symmetric information). High risk types (low mortality) impose a negative externality on

low risk types (high mortality). This may make credit markets more attractive for low risk (high

mortality) types. This is inconsistent with the evidence which indicates that the

healthy are less likely to viaticate. This is a reasonable result given that good measures of life

expectancy are available for HIV patients, and patients undergo a thorough medical evaluation before viatication.

Also, there is no evidence that prices change with the face value of the policy.

Differential Transaction Costs

What if costs of borrowing are higher for the relatively unhealthy As banks anticipate transaction costs of liquidating estates of

the relatively unhealthy to collect loan payments? This is consistent with the evidence which indicates that the

unhealthy are more likely to viaticate. But this is an unlikely explanation as

Standard credit applications do not ask for health status and mortality risks

It might be illegal to discriminate (charge different loan processing fees) based on mortality risk

Search costs of finding a viatical company and negotiating a transaction might be higher for the relatively unhealthy who only have a few more months to live.

How Well Does the Market Anticipate Technological Shocks?

Nominal Price of a Viatical Settlement, by Life Expectancy and Year

Life Expectancy

1995 1996-1997

1998-1999

2000-2001

<12 73.59 78.62 68.20 73.24

12-23 71.43 71.34 60.08 50.60

24-35 61.65 60.74 48.24 38.99

36-47 48.72 46.92 36.25 29.86

>=48 39.31 36.13 28.86 26.91

Number of Viatical Firms by State from 1995 - 2001

1995 1996 1997 1998 1999 2000 2001

California 13 11 9 9 9 8 5

New York 11 10 6 9 8 4 2

Texas 11 12 9 14 13 15 5

N. Carolina 4 8 6 9 7 6 5

Oregon 5 5 2 3 0 2 1

What Explains the Declining Prices? Medical technology shock

HAART increase in life expectancy; but prices declined within life expectancy categories

Increased variance in life expectancy projections, especially for the healthy

Declining competition Identification problem: both lead to

declining prices

A Model of Viatical Settlement Prices More general than the vanilla model

Includes a risk premium due to the possibility of future technological change

Includes market power parameter Assumes constant mortality hazard in

each period.

Effect of Declining Competition on Prices

Effect of Increasing Risk Premium on Prices

Estimation

We estimate the parameters of the pricing equation using non-linear least squares with the national price database.

Inferring Cure Probabilities from the Estimates Cure probabilities are more intuitive than risk

premia We write an expression for what the price

would be assuming a constant hazard of a technological breakthrough that restores full life expectancy (without HIV) – LE(B). This expression depends on the parameters

of our non-linear least squares model, including the risk premium.

( )( ) ( )( )

1

1 1b

LE B

l l l

-=

- - -

According to the Market, How Long Until a Cure for HIV?

LE < 24 months

LE ≥ 24 months

199573.1 years

(3.2)

23.3 years

(3.5)

1996-199813.6 years

(2.6)

8.6 years

(3.0)

1999-200177.1 years

(3.8)

30.6 years

(3.2)

Evaluating the Market’s Performance Seen one way, the market did very well.

The development of HAART had a profound effect on market expectations of future breakthroughs.

HAART had a large clinical effect on low life expectancy individuals, and this is reflected in its effect on market expectations.

Seen another way, the market did very poorly The market missed the 1995 breakthrough.

Conclusions Hayek was right

The ability of the market to mobilize local knowledge is fundamental to market efficiency.

Whether the market gets things right depends upon whether such knowledge is “out there”

In the viatical settlement market: Sellers make mistakes about their true life

expectancies. Neither buyers nor sellers are good at

foretelling the technological future. Nevertheless, both sides benefit from

voluntary transactions when the market is competitive.