Knowledge and Ignorance in a Secondary Insurance Market



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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

  • Source: Centers for Disease Control

Average Life Expectancy of Viators from 1995-2001

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

  • 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 Value
  • Amount 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

  • 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
  • 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 parties
    • Misperception does not imply mispricing
    • Competition 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).

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.
  • 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 male
    • Be white
    • Have a college degree
    • Have income > $2,000 per month
    • Own a house
    • Have 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

Empirical Model (2)

  • We model the hazard of not selling life insurance as:
  • Xit is the vector of covariates measured at time t
    • β is the vector of regression coefficients
    • is the baseline logit hazard rate

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.
  • 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

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.

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

  • LE < 24 months
  • LE ≥ 24 months
  • 1995
  • 73.1 years
  • (3.2)
  • 23.3 years
  • (3.5)
  • 1996-1998
  • 13.6 years
  • (2.6)
  • 8.6 years
  • (3.0)
  • 1999-2001
  • 77.1 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.


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