Ask a Nobel Laureate: Can Everyone Benefit from Universal Mandate?

Lecture 2: Public Finance III @ Stanford University

In this lecture, Professor Perrson tackles the problem of asymmetric information. We will see two Nobel-winning models, and discuss ways to detect adverse selection. This lecture has 55 slides, and I will condense it into a 7 min read for you.

Introduction

Imagine you’re running an insurance company. How would you turn a profit?

As in any other business, you have to price your product right: the price has to be low enough to entice enough customers, but high enough for you to earn a healthy profit. To strike the balance, we would need to know our customers’ risk profile really well.

There are two obstacles, however.

In reality, companies can’t perfectly observe a person’s risk profile. If you’re underwriting a health insurance, you can’t tell if a person is at high or low risk of needing expensive care, without ordering the most comprehensive healthcare. In many countries, it is now illegal to screen people out based on pre-existing condition anyway. Without knowing the likelihood and the expected amount you would need to pay, it is impossible for you to price your healthcare contract right. Sure, there are data about the general population’s medical expenditure. But you suspect that most people who purchase healthcare voluntarily are sicker than the rest. This is what economist refers to as the adverse selection problem.

Moreover, people behave differently once they are insured. When you sign up for car insurance, you want the insurance company to believe that you’re a safe driver, so that you get charged a lower monthly fee. But the moment you get your car insurance, you might be tempted to speed or rush a yellow light, since the insurance company would pick up most of the tab if you ran into someone else’s car. This is what economist refers to as the moral hazard problem.

Adverse Selection: The Need for Universal Mandate

In a world where people have different risk profiles that cannot be perfectly observed, how would companies price their insurance product?

This is a Nobel-worthy question. Professor Stiglitz received the Nobel laureate in Economics in 2001 for “ laying the foundations for the theory of markets with asymmetric information” with George Akerlof and Michael Spence.

In this section, we will discuss the seminal paper by Michael Rothschild and Joseph Stiglitz in 1977.

Set-up

• For simplicity, assume we have 2 types of people: high risk & low risk.
• Assume that the insurance market is perfectly competitive.

Equilibrium

The market reaches equilibrium when:

• Each person has found the best contract for himself;
• Each company does the best for itself.

If Company Can Tell People Apart…

To discuss how asymmetric information mess with us, we need to first pin down the equilibrium under perfect information. (i.e. the case where insurance company can tell people’s risk perfectly.)

Result: Rothschild-Stiglitz proves that insurance companies would offer different contracts to people with different risk profile at different price @ the expected cost of servicing a particular risk type.

Proof Sketch: Leave a comment or PM me if you’re interested :)

If Company Can’t Tell People Apart…

Now imagine that the insurance company can’t tell people’s risk at all.

Result: Rothschild-Stiglitz proves that insurance companies would offer the same contract to everyone. Price would be set @ the expected cost of servicing an individual.

Proof Sketch: Again, leave a comment or PM me if you’re interested :)

Key Insight

You must be yawning at this point. Companies offer 2 contracts when they can tell high risk apart from low risk, and 1 contract when they can’t. This is common sense. Why is it Nobel worthy?

Take a closer look at the prices. When companies can tell people apart, people have to pay their expected medical cost within the covered period. This is great if you’re young and healthy. Not so great if you have pre-existing condition, or at high risk of developing some severe illness.

This is ironic because insurance is supposed to help high risk people. If they are paying their expected medical price, then the insurance contract isn’t helping them much.

This is the original inspiration for universal mandate.

Akerlof Model

This model is developed by another Nobel laureate, George Akerlof. This model shows how the insurance market can unravel, in the absence of a universal mandate; and why universal mandate can’t make everyone better off.

Set-up

• In this model, insurance companies are perfectly competitive, risk neutral, and offer a single insurance contract.
• Risk averse consumers decides whether to buy it or not.
• Insurance companies cannot deny coverage on an individual basis.
• Consumers are identical, except for the probability of getting sick.

Death Spiral

• This graph illustrates how the insurance market can unravel. “AC” stands for average cost; “MC” stands for marginal cost.
• In this graph, we sort customers by their willingness to pay in a descending order. Those with the highest willingness to pay have the highest risk, and are illustrated on the left side of the demand curve.
• Suppose the most efficient solution is Q = 1. At that point, the insurance company has to charge the average cost to break even. Unfortunately, the average cost is higher than the last customer’s willingness to pay (as read from the demand curve). Thus the last customer at Q=1 drops out.
• We then move on to the second to last customer. In response to the last customer dropping, insurance companies have to increase their prices, because the remaining customers have higher risks than the dropout. This price increase prompts the second to last customer to drop out.
• This process continues, until the insurance market completely unravels.

A Mandate Can’t Make Everyone Better Off

What happens when the government steps in, and mandate that everyone has to buy insurance?

• Price would be set at P_mandate. This is given by the average cost of covering everyone.
• At this price, insurance companies would break even.
• Consumers with the lowest willingness to pay (i.e. the segment of demand curve below P_mandate) would be unhappy with the mandate.

Key Remarks

• Universal mandate is a candidate solution to prevent the insurance market from unraveling.
• But it does create winners and losers.
• Ultimately, we need to ask ourselves: is it fair to force someone to purchase the insurance in the name of greater good? If not, how can we make it up to them?

Data Analysis: Adverse Selection

Detecting Adverse Selection

It is very hard to test whether you’re attracting the high risk crowd directly. So we have to come up with some clever ways to do it.

The first test is the “positive correlation” test. It’s a very simple idea — conditional upon observable characteristics, those who buy more insurance makes more claims down the road.

But this test is not conclusive — for it is also consistent with the moral hazard story: people who buy more insurance makes more claims, not because they are inherently riskier, but because insurance makes they behave riskier.

Is Adverse Selection a Big Deal?

To calculate the welfare loss due to adverse selection, we need to compute the triangle CDE.

In order to compute CDE, we need to estimate demand curve, average cost curve, and have some exogenous change in prices. A study by Einav, Finkelstein and Cullen (2010) did this exercise, and concluded that welfare loss due to adverse selection is not a big deal. It corresponded to $9.55 per person.

There are some caveats however. Einav, Finkelstein and Cullen’s paper is based upon one company. This is because the “exogenous change in price” criteria is usually not satisfied; but a weird company policy by Alcoa made it a reality. Thus, the generalizability of the study has been questioned.

Moreover, many critics argue that markets with severe adverse selection simply unraveled, and we have no data to study them. Thus the $9.95 estimate could be a serious underestimation of adverse selection problem.

Studying Non-Existing Markets

Hendren (2012) attempted the impossible.

Hendren used panel data from the health and retirement study to study three markets: long term care insurance, life insurance and individual health insurance. He found that rejectees would have to pay a markup of 40%-80% depending on the market, high enough to explain the non-existence of insurance markets.

What Have We Learned Today?

Theory

• Adverse selection may lead to unraveling of the insurance market.
• If insurance company can observe everyone’s risk perfectly, high risk people need to pay a lot more, which violates the spirit of insurance.
• Universal mandate can stop the market from unraveling, but creates winners and losers in the process.

Data

• Start with the positive correlation test, but note that it’s a joint test of adverse selection and moral hazard.
• Even if adverse selection is estimated to cost little in existing market, it doesn’t mean that adverse selection is not a real problem. In markets where adverse selection is severe, they might have unraveled, and left us with no data to study.

Next Time

In the presence of adverse selection and moral hazard, what does an “optimal” insurance contract looks up? Stay tuned!