Friday, February 03, 2012

Disagreement About the Probability of Future Events: Insurance, Moral Hazard and Climate Change

Young people who are good at math are told that being an actuary might be a good job for them.  As I understand it, actuaries take historical data and calculate conditional probabilities such as; what is the probability that a 45 year old white man will die in the next year and that such probabilities are useful for pricing products such as life insurance.  Suppose that the probability that the average 45 year old white man has a .1% chance of death (1/1000) then if the insurance industry is a perfectly competitive industry the price of $1 million dollars of insurance would be $1,000.  Why?  The expected cost to the industry =  probability of death*payout =  (1/1000)*1,000,000 = $1,000.  Note that in this case, all actuaries at different firms would have access to the same historical data and would converge on the same "best guess" of the probability that a 45 year old while man will die within the next year.

Now let's turn to climate change and suppose that climate change introduces a non-stationarity to the probability that events take place.  For example, what is the probability that there are more than 3 100 degree days in Sacramento over the next year?  Climate change raises this probability but there will be disagreement about by how much.

Let's return to disaster insurance.  Suppose that the actuaries disagree about the probability that there will be massive floods over the next year.  The optimistic actuaries who work at "Nice Firm" say that the probability is 1% while the pessimistic actuaries who work at "Nasty Firm" say that the probability is 10%.

In competition, the price of a $1 million dollar housing insurance policy will be $10,000 charged by the "Nice Firm" and $100,000 charged by the "Nasty Firm".  Suppose that the truth is that the Nasty Firm's assessment is correct.  As consumers shop for a lower price, the "Nasty Firm" will attract no customers and it will go broke. The over-optimistic firm "Nice Firm" will gain the whole market for insurance but when the true state of the world is observed it will go bankrupt because it collects $10,000 per premium but its expected losses is $100,000 so it loses $90,000 on each policy it sells!

What happens next? In our moral hazard government,  the Federal Government will bail out the home owners who will not be punished for their bad choice.  If the disaster had not taken place, the "Nice Company" would remain in business so it holds an option on when it declares bankruptcy.

This discussion is motivated by this NY Times article  about regulation of the insurance industry given the anticipation of climate change.

How would Milton Friedman address this issue?  Note that as the "Nasty Firm" offers its policy at a higher price it will be accused of price gouging just as the health insurance industry is being accused as it raises premiums. But, the interesting wrinkle in my example is the cross-sectional variation in premium prices based on differences in subjective probability assessments.

How do market equilibrium forces lead to a convergence to the true probability assessment as this target (i.e the probability of horrible flood) moves over time due to climate change?   The government would need to pre-commit to no bailouts of premiums when insurers declare bankruptcy and that the insurers would have to post a bond to commit that they can cover extreme losses. In this case, they would have the right incentives to each do their homework about predicting future dynamics of events rather than in focusing on historical data and linearly extrapolating.