Mortality risk, insurance, and the value of life

Daniel Bauer, Darius Lakdawalla, Julian Reif 05 November 2018

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For over 40 years, policymakers and analysts have relied on an established framework for making implicit or explicit trade-offs between money and lives (Schelling 1968). While philosophical objections sometimes arise to a theory that equates life with money, this covenant is unavoidable in the real world, where policymakers and business leaders use it to guide vital decisions. 

For example, increasing the safety of roads, nuclear power plants, and aircraft all costs money, but these investments reduce mortality. Health care is another salient illustration. Even though opportunities exist to reduce spending without harming human health, investing more in healthcare saves lives (Card et al. 2009).

Generations of economists have contributed to this analytical framework, routinely assigning monetary values to extensions in human life (Arthur 1981, Rosen 1988, Murphy and Topel 2006). 

While this economic structure has been enormously influential, it has also produced a few curious and unrealistic implications. For example, it implies that society is just as happy providing one month of life to 120 individuals in good health as it would be in providing ten extra years of life to one 50-year-old with a terminal and inoperable brain tumour. This prediction is at odds with evidence on how consumers report their own preferences over lives and money (Norde et al.1995), with the fact that societies invest significantly more resources in therapies than in prevention (Pryor and Volpp 2018), and perhaps also with common sense. Some economists have argued that this amounts to a flaw that is so fatal as to consign the entire economic theory of life-extension to the scrap heap.

Our research in Bauer et al. (2018) saves the life of this venerable framework. We show that the theory is sound and fits the facts well, provided we abandon a patently unrealistic assumption that was inserted at its birth. For simplicity, the early theorists assumed that consumers hold their wealth in a complete portfolio of annuities. Thus, instead of cash or investments in bank or brokerage accounts, each consumer possesses only a set of annuities that pay them a constant stream of income. This assumption is false and produces perverse implications for the value of life. 

A very simple example illustrates the point. Imagine a 60-year-old retiree. If she owns nothing but annuities, her annual spending remains flat at, say, $30,000 annually. If she is unfortunately afflicted with a brain tumour, she has no ability to change her annual expenditures, because the annuities force her hand. However, suppose instead that she holds all her wealth in the bank. Before the brain tumour, maybe she expected to live to 85. After it, she expects to die 20 years earlier, or more. The brain tumour will cause her to spend more of her money each year, because she has fewer years to use up her wealth. This effect is slightly mitigated if she wants to leave behind some money for her heirs, but the basic pattern remains – if she is no longer planning to live into her 80s, she will see less need to save and skimp in her 60s.

This result has an important practical implication. In the wake of a severe health event – like our example of a brain tumour – each year of life becomes more precious, because it involves a higher level of consumption and wellbeing. Conversely, when people are in healthier states, life-extension becomes less valuable.

Several policy-relevant implications follow. First, in contrast to the old adage, cures may be more valuable than prevention. That is, adding an extra year of life through preventive healthcare, like vaccines or regular exercise, may be worth less to consumers than adding that same year of life when in a severely ill state. This helps explain why it seems so difficult to use policy levers to increase preventive health investments. In effect, policymakers are ‘pushing on a string’ when trying to get consumers to participate in prevention programmes. 

Second, our findings matter for the evaluation of new healthcare technologies. A number of countries, including the UK, Canada, and Australia, explicitly use the economic framework for the value of life to decide how to allocate money to new medical treatments. Our analysis suggests this is causing them to undervalue the treatment of highly severe illnesses – like cancer – and overvalue mild ones – like hay fever. 

The UK provides an instructive example, particularly because UK health authorities hew closely to the use of economic criteria for deciding when and how to reimburse new medical technologies. Perhaps as a result, the UK has ranked down the list of developed countries in the reimbursement of drugs to treat cancer, which has motivated legislators there to provide exceptional reimbursement for such products, above and beyond what the UK health authorities dictate (Lancet 2010). Controversy has erupted within the medical, scientific, and policy community over the appropriateness of this approach, and the legislation has drawn a great deal of criticism (Lancet 2010). Yet, our analysis illuminates how the severe nature of cancer might misalign the standard economic approach with the preferences of legislators and voters. Economists’ criticism of the UK’s cancer exception might be misplaced – indeed, it may be the legislators who have a better idea about the fundamentals of economic theory.

References

Anon (2010), “New 50 million cancer fund already intellectually bankrupt”, Lancet 376(9739): 389.

Arthur, W B (1981), “The economics of risks to life”, American Economic Review 71(1): 54-64.

Bauer, D, D Lakdawalla, and J Reif (2018), “Mortality Risk, Insurance, and the Value of Life” NBER Working Paper 25055.

Card, D, C Dobkin, and N Maestas (2009), "Does Medicare save lives?", Quarterly Journal of Economics 124(2): 597-636.

Murphy, K M, and R H Topel  (2006), "The value of health and longevity", Journal of Political Economy 114(5): 871-904.

Nord, E, J Richardson, A Street, H Kuhse, and P Singer (1995), “Maximizing health benefits vs egalitarianism: an Australian survey of health issues”, Social Science and Medicine 41: 1429-37.

Pryor, K, and K Volpp (2018), “Deployment of Preventive Interventions — Time for a Paradigm Shift”, New England Journal of Medicine 378: 1761-63.

Rosen, S (1988), "The value of changes in life expectancy", Journal of Risk and Uncertainty 1(3): 285-304.

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Topics:  Frontiers of economic research Health economics

Tags:  healthcare, value of life, economic models, Cancer

Hickman-Larson Chair in Actuarial Science and Associate Professor of Risk and Insurance, Wisconsin School of Business

Director of Research at the Leonard Schaeffer Center for Health Policy and Economics at the University of Southern California

Assistant Professor of Finance and Economics, University of Illinois

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