I don’t remember the exact quote, but I do remember laughing (out loud). It was something like: “who knew there’d be three six-sigma events in one week?” This was a banker’s response to a journalist’s question about the 2008 financial crisis. It reminds me of the cult classic The Princess Bride where Vizzini yet again exclaims “Inconceivable!” and Inigo Montoya replies “You keep using that word. I do not think it means what you think it means.”
For those of you who are relatively fluent in the language of statistics, six sigma is an event that is six standard deviations away from the mean. Recall, 99.97% of events in a normal distribution will theoretically occur within 3 standard deviations (sigmas) from the mean. So, six sigma is way out there in the tails of the distribution. In other words, very very rare. Inconceivable you might say. Being conversant in the language of statistics—understanding tail risk, normal and skewed distributions, dependency among events, sample bias, etc.—is becoming an increasingly important skill set for policy makers and regulators.
Without these skills, we will keep getting it wrong. Last month, just after Hurricane Harvey hit Texas, the headline read: “Insurance providers miscalculate risks posed by big storms”. Since then, Hurricanes Irma and Maria both have caused major destruction. In that Financial Times Editorial[i], Brooke Masters tells us that “New types of investors, lured by the promise of decent returns, have been pouring into the reinsurance market [through insurance-linked securities and catastrophe bonds] driving prices down to unprofitable levels.” “...and regulators are worried that some reinsurance providers may have underestimated their risks when setting prices.” Who knew there’d be 3 major hurricanes in one month? It’s deja vu all over again. Putting aside any discussion of climate change, is it any wonder that insurers are underestimating their risks when governments continue to signal that they will cover the downside risks and bail them out if things go pear shaped...especially when pension funds are invested in these products?
There are two fundamental questions to be explored here: first, why are the risk-predicting models consistently found to be wrong? Second, what should be the relative roles of government and the market in providing insurance for a wide range of frontline risks and/or in offering some kind of reinsurance? As a corollary, what role should be left to individuals subject to these risks?
First: why are the models of risk wrong?
There are a number of reasons why risk models have often gone badly wrong.
Non-normal distributions. One common assumption is that distribution of risk (e.g., from financial markets or in devastating storms) is normal; that is to say, the classic bell curve. But fortunately, the models are getting better and there is greater recognition that there are, indeed, skewed distributions with fat tails.
Sampling error. Six sigma doesn’t actually mean that there is some certainty about how often an event will occur, it’s really more a measure of whether your sample is likely to contain that event. People, especially policy makers, want to hear simple declarative statements like “x % chance x will happen” but statisticians rightly get annoyed. Even with huge sample sizes, you may not see the event. Think of how people would have considered Secretariat’s race times had his grandfather Man of War been excluded from the sample time frame?
Dependency between events. Events are correlated in a way that these models have a hard time capturing. Dealing with correlation is difficult. The math gets harder. For example, the conditions that created Hurricane Harvey obviously also created Irma and Maria. The conditions that caused Donald Trump to win Michigan also led to him winning Pennsylvania and Wisconsin. (On his website FiveThirtyEight, Nate Silver explains how other voting models dealt with states independently and assumed they were not correlated. That’s how they got Trump’s election predictions wrong. Over the past year, much has been written about the integrity of election polling and data journalism with a particularly heated exchange between Silver and the NY Times’ Ed Rutenberg.)
Historical pattern assumptions. Predictions are based on past data. Forecasting models typically assume artificially smooth relationships that are consistent with history when, in reality, often there are ‘cliffs’ when events happen. Tipping points is the common jargon. Fixing the assumption that things move along smooth historical paths is hard but can be done (see e.g., Geweke and Keane, 2007[ii]).
Second: the relative roles of government and market
If policy makers were to undertake a systematic discussion around the question of what is government’s appropriate role in offering both insurance for frontline risks and reinsurance, they might start with a proper discussion of values. Several years ago, I was invited to give a lecture on comparative health systems. The course organiser wanted my focus to be how different health care systems reflect different national values. It was a fascinating exercise thinking about how, for example, ideas like “solidarity” and “a right to health care” were common in Europe but never used to describe the current American health care system while “profit” and “markets” were similarly absent from descriptions of many western health care systems but ubiquitous in the U.S.. It would be very fruitful to extend this thinking beyond health care by asking what values are reflected in how governments decide to handle different risks.
When there is both an upside and downside to the risk involved, the discussion is not only especially relevant, it is very politically tricky to navigate as the financial crisis showed us. If we value a market that is allowed to make a profit, shouldn’t it follow that that market should also bear the risk of loss? How much does this depend on whom the ultimate losses fall hardest? When different values are reflected in different treatment of risks, there are important distributional consequences across groups of people.
The U.S. is often thought to be relatively stingy when it comes to helping people when they face certain risks (health care events for the uninsured comes to mind). But, in reality, the government often steps up to help when bad things like natural disasters happen because they are thought to be no one’s fault. The US government spent over $100 billion on Hurricane Katrina in 2005 and $50 billion on Hurricane Sandy in 2013. For perspective, the US government spends only $60 billion each year on public housing for the entire country. The notion of how sympathetic or “deserving” (a notion articulated by Christopher Jencks[iii] so well) may explain this. We all take risks sometimes and so can appreciate when those risks don’t turn in our favour. In a way, the shared notion of who is deserving is the insurance.
Bringing this discussion to population ageing, there are several risk predicting models that we need to get right in order to make good public policy decisions around retirement and long-term care. Modelling longevity risk (i.e., the risk of living longer than your pensions and insurance expected you to) and the lifetime risk and costs of needing nursing home care are important in this regard. Competing models (see Kemper & Murtaugh[iv], 1991 and Cohen, Tell & Wallack[v], 1986) on nursing home risk are more than 25 years old now and could use updating to reflect more current trends of use. The excellent work of Michael Sherris and various co-authors in the area of longevity risk should have the considered attention of eager policy makers. How these age-related risks are treated should reflect our values with an emphasis on articulating how much burden should be borne by the individual. Should we treat longevity and the need for long-term care as catastrophes? Are older people deserving? These are questions we need to answer.
It’s risky business, indeed.
References
[i] “Insurance providers miscalculate risks posed by big storms” by Brooke Masters Financial Times September 9-10, 2017 p. 14.
[ii] Geweke, J., & Keane, M. (2007). Smoothly mixing regressions. Journal of Econometrics, 138(1), 252-290.
[iii] Jencks, C. (1991). Is the American underclass growing?. The urban underclass, 28, 37.
[iv] Kemper, P., & Murtaugh, C. M. (1991). Lifetime use of nursing home care. New England Journal of Medicine, 324(9), 595-600.
[v] Cohen, M. A., Tell, E. J., & Wallack, S. S. (1986). The lifetime risks and costs of nursing home use among the elderly. Medical Care, 1161-1172.
About the Author
Dr Laurel Hixon brings over two decades of health policy and applied health care research experience to OIPA. She has had academic research appointments in both the U.S. and Australia. She has written extensively about health and long-term care financing and reform
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Comments Welcome: We welcome your comments on this or any of the Institute's blog posts. Please feel free to email comments to be posted on your behalf to administrator@ageing.ox.ac.uk or use the Disqus facility linked below.
