Doing Discounting Wrong

By James Kwak

Ezra Klein focuses on this passage from  John Judis’s review of regulatory policy in the Bush and Obama years:

“Bush stopped weighing the costs and benefits of deregulation and issued an executive order allowing OIRA to intercede before agencies made their initial proposals, thereby providing industry lobbyists with a back door to block regulations. OIRA also instructed agencies to discount the value of future lives in constructing cost-benefit analyses by 7 percent a year, so that 100 lives in 50 years would only be worth 3.39 current lives. (Such logic can be used by conservatives to argue that the present cost of regulating greenhouse gases outweighs the future benefits of stopping climate change.)”

There is a normative argument against valuing lives in cost-benefit analysis; some people think it’s just wrong. I don’t agree with that; I think that in practice, you either value lives implicitly or you do it explicitly, and so you might as well do it explicitly. And for what it’s worth, the practice of valuing lives is firmly entrenched in our legal system; the amount you pay in damages if you kill someone negligently depends primarily on that person’s future earning potential, and also on the monetary value of the benefits that other people gained from his or her life.

There is another argument against discounting future lives, however. The basic premise of discounting is that money in the future is worth less than money today. This has two components. One is the time value of money: $100 with certainty one year from now is worth about $99 today, because you can invest $99 in an FDIC-insured account at about 1% and get back $100 in a year. The second is risk: Future events are not certain, and the less certain they are to occurthe less valuable they are to you.

Does this apply to lives, however? If a regulatory agency says, this rule will cost industry $1 billion in present-value terms, but it will save 1,000 lives twenty years from now, is that any different from saying it will save 1,000 lives today? That seems wrong to me; you can’t take, say, 900 lives now, put them in the bank, and get back 1,000 lives in twenty years. I can see the counterargument, though: once you’ve agreed to value lives in monetary terms, you can translate those 1,000 lives twenty years in the future into some amount of money twenty years in the future, and you can discount that back to today.

But if we’re going to do that, let’s at least do it right. A discount rate of 7 percent?

I assume that’s a real discount rate, not a nominal one, since anyone doing this kind of spreadsheet over decades would use real terms to avoid inflation uncertainties.* A discount rate of 7 percent means that 100 lives in ten years are worth roughly 50 lives today. Is that justified?

By the time value of money theory, the government (or industry) could put aside money in an account today and use it to pay benefits to the survivors of dead people at some point in the future when the deaths occur. But if we’re going to use that logic, we need to look at the risk-free rate of return. Over the last five years, the ten-year Treasury yield has generally been between 4 and 5 percent. Call that 4.5 percent. Inflation has been in the low 2 percent range, so at best this is a risk-free return of 2.5 percent.

But it gets worse than that, because the real value of lives is continually increasing. This is because GDP grows faster than inflation, and faster than inflation plus population growth. The rest of GDP growth is productivity growth, which means that people produce more and, on average, they earn more (even if the median workers doesn’t). Since the legal value of a life is primarily based on future income, this means that the real value of a life increases roughly with productivity. Productivity growth runs at about 2% per year. So if you are getting 2.5 percent on your risk-free investment, 2 percentage points of that just goes to make up for the fact that the people your policy is killing are getting more expensive, which means your discount rate should be 0.5 percent. (The numbers don’t quite add up here, since I think population growth is actually around 1% per year. So let’s say your discount rate should be 1 percent — still a lot less than 7 percent.)

But that’s just the time value of money — shouldn’t we also be discounting for risk? But I think that’s wrong. In the corporate finance model, you look at the volatility of the expected cash flows. Let’s say you have an investment that has an expected return of $1 million in ten years with some probability distribution around $1 million. The textbook says you should adjust your discount rate based on that probability distribution — the wider the distribution (the riskier the investment), the higher the discount rate. This makes sense because of basic risk aversion. In the financial context, the more risky the project, the higher the expected return has to be to justify it.

Now let’s translate this into lives. Say you have a policy that is likely to kill 1,000 people in ten years, but it might kill more or it might kill fewer. Should that be counted as fewer lives than a policy that is certain to kill 1,000 people in ten years? In other words, does risk aversion mean that we should prefer policies that kill variable numbers of people to policies that kill certain numbers of people? That doesn’t make sense to me, and hence discounting for risk doesn’t make sense to me in the lives context.

That leaves us with a discount rate of 1 percent, not 7 percent. And instead of 3.39 lives today, you get 60.80 lives today. That’s a big difference.

(If the 7 percent is nominal instead of real, you don’t deduct inflation from the 10-year Treasury yield; however, then the value of lives grows because of both productivity and inflation, so you end up roughly in the same place.)

* It might make sense to use nominal terms if some of your future values were fixed in nominal terms. But in a situation like this, where all of your future values are fixed in nominal terms, I can’t see any reason to do the calculations in nominal terms.

47 thoughts on “Doing Discounting Wrong”

  1. In other words, does risk aversion mean that we should prefer policies that kill variable numbers of people to policies that kill certain numbers of people? That doesn’t make sense to me, and hence discounting for risk doesn’t make sense to me in the lives context.

    ???

    Of course it makes sense. A policy that might kill 1000 people in 10 years is preferable to a policy that definitely will kill 1000 people in 10 years.

    That seems wrong to me; you can’t take, say, 900 lives now, put them in the bank, and get back 1,000 lives in twenty years.

    Of course you can, if you accept that the value of someone’s life today “depends on their future earnings potential”. You “put 900 lives in the bank” today by allowing them to earn for the next 20 years. The earnings they produce is “worth” 1000 lives 20 years from now.

    There is simply nothing wrong with these analyses once you accept the premise — as you claim you do — that a life can have a dollar figure attached to it. Everything you are attacking follows directly from that premise.

    In your heart, I suspect you want to reject that premise. So please just do so, and stop constructing tortured arguments trying to avoid the logical consequences of the premise.

  3. OK, I take back that first part… But I still think the “right” way to do this analysis is to follow through on the assumption that a life equals the present value of its future cash flows.

    What discount rate does a court use in a manslaughter case, for instance? Any argument you make here will apply equally to that situation as well.

    And in any event, it seems a little odd that the value we place on future lives today should depend on the current market price of 20-year TIPS. In my heart, I want to reject the whole premise…

  4. Well, in rough terms, the U. S. reproduction rate is around replacement, so saving 1,000 lives today means there will be about 1,000 equivalent people in 50 years that there would not otherwise be. But since we do not know when they die, say that there is about a 60% chance that they have already replicated. So saving 1000 people today means saving only about 400 people 50 years from now. ;)

  5. No, don’t take it back. That’s the whole premise of prospect theory — we humans are risk-averse when it comes to potential gains, & risk-loving when it comes to potential losses. It’s *normal* to prefer a policy that might kill more or less than 1000 to a policy that will definitely kill 1000.

    So discounting for risk does make sense; the only question is how much, & is the move from 1 to 7% really justified.

  6. A policy that might save N people is certainly better than one that might save N people? it’s all a matter of perception, don’t you think?

  7. There is a normative argument against valuing lives in cost-benefit analysis; some people think it’s just wrong. I don’t agree with that; I think that in practice, you either value lives implicitly or you do it explicitly, and so you might as well do it explicitly. And for what it’s worth, the practice of valuing lives is firmly entrenched in our legal system; the amount you pay in damages if you kill someone negligently depends primarily on that person’s future earning potential, and also on the monetary value of the benefits that other people gained from his or her life.

    Well, yes. Once one accepts the monetization psychopathy, then this does follow.

    My thinking it’s wrong follows from my condemnation of the whole system.

    I don’t think anyone is ever going to “discount” in good faith. Majestically impartial technocracy is no more achievable today than when Plato envisioned it.

    So we can dispense with the notion that any government or corporation is ever going to make any such decision based upon good Benthamite utilitarian principles.

    Every decision will be based upon projected larcenous profit, and if the numbers look like something will kill more people, they’ll simply be falsified (assuming “real” numbers ever exist in the first place instead of just purely fabricated ones).

    So the moral of the story is that whatever they say is most life-preserving will really be what’s expected to be the most profit- and power-maximizing.

    Any actual healthiness will be strictly coincidental.

    Exhibit A: Obama’s rejection of single-payer, projected by all independent authorities to be both the healthiest and socially the least expensive system, even as he lies and says he seeks health care reform.

  8. The useful span of a human life (age 20-70) is 50 years. The inverse of 50 is 2%, so I would apply a 2%/year discount in the calculation. I think one would need to assume a constant nominal value for a human life, else the calculation becomes somewhat silly, kind of like when advocates of a certain spending program calculate the return on investment by factoring in a fudge factor for all of that money that they estimate will work it’s way into the secondary and tertiary economies.

  10. Do any non-economists here wonder where these people who thought this up buried their bludgeoned humanity?

  11. In normal risk adjusting, the risk is that actual return falls short of expected return. So to make up the difference the investor will ask for a higher nominal rate of return (which essentially increases the expected value of the return).

    In the case of lives, the “risk” is that the number of people killed by a policy choice will _exceed_ the expected value. Therefore, to adjust for this risk we should reduce the nominal rate (here, the discount rate) so that the initial expected value is lower than the non-risk-adjusted value.

    Thus, the 1% estimate put forth by Prof. Kwak must actually be adjusted _down_ to account for the potential risk of “costing” more lives than expected.

  12. Nemo,

    Small point, but we probably can not say whether we prefer a risky policy to a certain policy with the same expected outcomes. The risk of losing 900 people versus 1000 is obvious, but its risky – it could as easily be 1100 people that are lost which is obviously worse. I think your framing of the question was inconsistent with the concept of risk.

    Maybe nitpicking- but as an admirer of your posts, i have come to expect more from you.

  13. “It is difficult to get a man to understand something when his job depends on not understanding it.” — Upton Sinclair

    Equally true when speaking of morality.

  14. Cost/benefit analyses of this sort also have the problem that earnings expectations over x period may well reflect profoundly skewed remuneration rates. For example, an investment banker may be expected to earn xx thousands over 20 years but a nurse in a hospice will certainly earn a fraction of that. Nancy Folbre wrote several works that examined how this country discounts ‘caring work’ (e.g. nursing, geriatric, mothering). These are only an example. What is certain is that who puts a price on ‘earnings’ is imputing a range of values that get hidden in the premises where they don’t get examined -brought to scrutiny.

  15. When one talks about discounting money, one is talking about *the same money* now and in the future. “If you were to take *this* money and invest it, this same money, together with its associated returns would be x.” Not so with lives, which in any case are (should not be) fungible.

    Let’s take a more concrete example: “Either you shoot these 3.39 old men right now, or you can slaughter 1,000 babies in 50 years. Your choice. It’s all the same to us.” A baseline should be established, and individual lives rated against it. A 70-year-old man who requires the use of a cane would be worth, say, .15 of a 35-year-old man with a BA. I realize all of this calculation and adjustment gets in the way of all the important killing that needs to get done, but right is right.

    Finally, if you’re going to talk about inflation when it comes to lives, the only relevant metric is population growth, possibly adjusted for the availability of resources necessary to sustain/nurture it.

    (And shouldn’t a proper comparison be like-for-like? Money investments compounding interest with a real rate of return is a good thing. Couldn’t this be about saving lives? Yeesh.)

    Loxy

  16. One is the time value of money: $100 with certainty one year from now is worth about $99 today, because you can invest $99 in an FDIC-insured account at about 1% and get back $100 in a year.

    I disagree. It is *because* $100 in a year are worth less than $100 today (even adjusting for inflation, etc.) that banks have to pay an interest on your deposits. They might just as well be *charging* you for the convenience of not having to stash your cash under your mattress, but they don’t and instead pay *you* because they need to induce people to forgo current consumption.

    It is time preferences that cause interest rates to be positive, not the opposite!

  18. I love your analyses. This one is perfect!

    It seems like so many people, particularly in the financial sphere, are devoid of any ethical and moral foundation.

    Here is a link to a lengthy, but excellent, interview with Jim Sinclair (who is intimately involved with the financial sphere – note: his father and business partner was legendary trader Bert Seligman.) Jim Sinclair appears to agree that the government is now “owned” by the predominantly amoral financial sector.

    http://www.kingworldnews.com/kingworldnews/Broadcast_Gold+/Entries/2010/2/15_Jim_Sinclair.html

  19. Implicitly or explicitly, attaching a solely monetary value to human life is obscenity. Just because it is done everyday does not make it any more palatable. Explicitly put then, Mr. Blankfein ought to be allowed, if he wishes, to eat a quadriplegic for dinner every so often since the sum total of the quadriplegics expected future earnings are smaller than than Mr. Blankfein’s; the only point of contention would be the exact number of quadriplegics he may eat per day.

    That might be a world that some might like, and that might actually be the world that we live in. Nevertheless I hold that such a world is an evil world.

  20. A really cogent example is shooting X teenage breeders now to avoid the present value inducing a growth multiple of future generations.

    I have a great example. My maternal grandparents had seven children between 1910 and 1920. Three of the seven are still alive. The other four all died in accidents but bred progeny. The seven though together bred progeny which as near as I can determine now exceed 350 people.

    So, if cost benefit analyses utilizing discounting is proper for humans then we reach the ultimate question. Aldous Huxley’s Brave New World Revisited was linked today on Baseline Scenario.

    This is from Chapter II.

    ” We know the pursuit of good ends does not justify the employment of bad means. But what about those situations, now of such frequent occurrence, in which good means have results which turn out to be bad?”

    I was a student when ” Revisited” was published and the question has been with me ever since.
    So , absolutely, the world has suffered terribly from good means the last 52 years since Huxley asked the important question.

    My brother and I have no progeny in the 350 plus kinfolk generated since the fifties.

  21. You can watch animals make those tactical calculations — by conscious process or dna programming is hard to know — for example whether to defend their young or abandon them in the face of various threats — my point being that such calculations are natural. But the animals are calculating life/life. The thing to reject, perhaps, is calculating lives against dollars when those dollars do not equate to anyone’s survival, but only a bit more comfort or luxury for the well off.

  24. Putting aside the humanity issue, the ability to value lives is important as long as we must live with these models. So let’s get real with the costs. Thanks James, this is a real contribution.

    But there is another issue that sometimes get lost in the calculation, I think. These 1000 people who will die in 20 years do not go off like some unwanted dog and die in the wilderness. They die in costly institutions or after expensive treatments. If they contact a desease as a result of some practice or policy (pollution, on-the-job safety or exposure, etc.), their end of life experiences imposes real costs on everyone, particularly if they are like most victims of bad policies and practices, i.e. uninsured. But even if they are lucky enough to have health insurance (e.g. a unionized mineworker), we all still pay in the end. Most importantly, real folks like families, friends, co-workers (to say nothing of society in general) pay for such losses because they cheapen life and deprive us of associates and their potential contributions.

  26. I don’t understand your objection. You seem to be objecting to the second argument in my post — and I concede your point there. I say that once you translate things into dollars, you can discount — and then the rest of the post is about how you discount. So what exactly are you criticizing me of?

  27. Even if psychologically we are risk-loving when it comes to bad outcomes, is that a good thing and should we base policy on it? I find it hard to come up with a policy argument for why a policy that kills 900 or 1100 people with even odds is better than a policy that kills 1000 people with certainty. I also find it hard when converted into financial terms. With positive financial gains, the benefits of certainty are obvious. With financial losses, it seems to me that the benefits of certainty are still obvious; as an insurance company, for example, I would much prefer to know exactly when my payouts will occur, because then it will be cheaper to plan for them. Having to deal with volatility, even volatility of bad outcomes, creates costs.

  28. There is another perspective on this, which is applied in health-care cost-effectiveness research.

    First of all, whether we like the idea or not, it is impossible to avoid placing some monetary valuation on life. Suppose aliens came and kidnapped a terminally ill person who was bound to die in the next hour or two anyway and demanded 100 years of global economic output as ransom. Would anybody pay it? Of course not. So, an hour or two of a person’s life is worth less than 100 years of global economic output. If the ransom were only $1, pretty much everyone would agree to pay it. So somewhere in between, there is a point of indecision that defines our value of an hour of (poor quality) life, by willingness to pay. It doesn’t feel good to acknowledge this, but that’s the way it is.

    Now, as for discounting, first some technical points. Inflation is not part of it because we deal in real rather than nominal values in our work. We also don’t vary our discount rate for uncertainty: we look at the expected value (or, in some situations, the entire distribution) of present values and act on those. The discounting proceeds at a single rate for all outcomes at all times, and uncertainty appears when we take expectations or map distributions.

    Finally, you have to discount lives at the same rate you discount money or you end up with some clearly fallacious results. Consider an influenza vaccine campaign. Let’s simplify reality a bit to make the point clearer: pretend that there is an influenza epidemic every year, and that each year’s epidemic is just as severe as every other year’s. (Fairly far off the mark, actually.) Assume that vaccine given in any year is ineffective in future years (not exactly true, but close enough). Now suppose that we have figured out that our community considers it fair value to spend $X to vaccinate those at high risk for death from influenza. If we discount money but not lives, then we can reason as follows: rather than doing the campaign this year, we should postpone it for a year. Next year’s vaccination campaign will save just as many lives, but its cost, being postponed, will be lower by our discount factor. In fact, we can iterate this argument and conclude that we should postpone the vaccination campaign forever. The only way to block this absurdity is to discount the saved lives in the future so that they lose value just as the costs of saving them do.

    By the way, for what it’s worth, most health care cost-effectiveness analysis uses a 3% per annum discount rate (and applies it to lives as well as money). Personally, I’ve never found the 3% rate particularly convincing, but it’s become a standard practice.

  29. Don’t take the criticism personally. When you construct an elaborate mathematical refutation of a nonsensical premise, you pretty much deserve what you get. Comparing financial savings to corporations with an expected loss of human life is too idiotic to discuss in terms other than the rarefied mathematical. Also, don’t forget the life side of the equation is completely faked, even before you start discounting, which of course makes no sense since a death fifty years from now is not less important than a death tomorrow, except to a politician. Figures don’t lie but liars figure.

  30. There are some interesting posts here notably CBS from the West explanation of discount factors as applied to healthcare, but I too have a problem with this statement on the vexed issue of the environment. ” There is a normative argument against valuing lives in cost-benefit analysis; some people think it’s just wrong. I don’t agree with that; I think that in practice, you either value lives implicitly or you do it explicitly, and so you might as well do it explicitly.” Th cost-benefit model here seems to break down. How do you assign an appropriate discount rate? The one thing we know is that we don’t know- consensus science is anything but that. Hence the risk of catastrophic events, storms /crop failures etc. cannot easily be measured ecept for individual events. If climate change and changing biodversity results in systemtic instability, we do not know whether it is reveresible or not. This is not soe closed loop and touches on chaos theory. There is no guarantee that there is an actual cylical effect or whether an ecosystem goes unstable and remains so. So ascribing a discount rate is groping in the dark by definition. I think this is misapplied mathematical techniques which require there toi be a lot less “unknowns”. This is unhelpful to the argument, but recognising it might be better than some notion of specious accuracy

  31. Thanks to James Kwak for a thought-provoking post.

    The concept of — discounting the value of future lives in constructing cost-benefit analyses — is new to me. This may be a useful tool in certain scenarios … but as Ezra Klein points out it was “gamed” to produce desired outcomes … Deregulation.

    I can’t help feeling there is something wrong with reducing human lives to a mere number value. There are intangible values to human life that cannot be quantified.

    Indeed, there might be something — irrational —about reducing human life to a mere number value. Eg, according to Akerloff and Shiller there are “irrational spirits” that drive an economy. It seems to me this theory embraces a fuller understanding of economic forces.

    I’ve also been thinking about something D. Christopher Leonard wrote in a previous post. Something about how Descarte got it wrong and current theory has moved beyond his concept of rationality.

    If DCL catches my comment perhaps he could expand on his previous comment about Descarte.

  33. Funny thing about Decarte — He said “I think therefore I am” — but he died of food poisoning. He “thought” it was good and therefore he was not.

  34. sorry about typo — I always think he put de cart before de horse. Gotta remember we are connected to de horse.

  36. The Information Age was characterized by the ability of individuals to transfer information freely by having instant access to knowledge that was previously difficult or impossible to find. The digital economy transmitted information via a 2-D (length and width) non-linear net. People learned by observing and analyzing. A major differentiator between the epochs was that assets employed in the creation of value depreciated with usage in the Industrial Age, whereas they appreciated from usage in the Information Age.

    Three dimensional models drive economies of span and speed to expand enterprise parameters in the Conceptual Age. Capital market policymakers, however, too often chose overly simplified responses. These responses were formulated within the context of a relatively narrow, two-dimensional perspective resulting in unintended consequences (i.e. SOX). Policymakers must either segment the current one-size-fits-all governance paradigm into predictable, probabilistic, and uncertain regimes in a single 3-D governance model or, they should apply 2-D matrices and schematics in a coordinated 3-D metric. The pathways are different, but the end result is the same. A 3-D conceptual change must take place in order for the US capital market to remain competitive in a global economy.

    Reference: “We’re All Screwed: How Toxic Regulation Will Crush the Free Market System” p 140 – 141

    http://w-apublishing.com/Shop/BookDetail.aspx?ID=D6575146-0B97-40A1-BFF7-1CD340424361

    Before you think outside the box, you have to transition thinking to think outside the square.

  37. If I read you correctly, you’re assuming that having lots of progeny is a bad thing. I’d argue that it’s a good thing…even though my great-grandfather, born in the 1850’s or so, has only 11 living biological descendants.

  38. @ Stephen Boyko. I understand the point that regulation may have to be/will have to be non-linear and that we have to change our mindsets in the digital age but I find your post impenetrable. It is redolent of the overly complex attempt to control the banks via Basel II. Far too complex, late and subject to endless consulatation and delays. If you apply this as your book blurb purports to suggest to a wide field of activities -education etc.we are again entering a world of multi-dimensional Alice through the Looking Glass thinking. There are IMHO simpler and effective ways to achieve the objectives. Simplicity used to regarded as a virtue in most theories, this looks like a recipe for confusion and endless academic debate. We need a fix and now. I fear we are not going to get it like this. One of the attractios of the Volcker ruke, no matter how disliked was that it was straightforward, easily understood and delivered a veritable missile to the banking system. I don’t think we need quantum theory type regulation

  39. Here is a process to resolve the dispute on discounted present value of human life. You take all the think tank experts on each side of the political spectrum and put them in a room with just enough space for a chair for each of them(though standing would be better). You then seal the room so no oxygen exchange can take place. You will have consensus in about 10 minutes although just like Congress, the minute they escape they will deny they agreed to anything.

  40. Let’s establish foundational guidelines

    1.Does “uncertainty” exist in the capital market to a material degree?
    2.Is “uncertainty” different from rather than a higher form of risk?
    3.If “yes”, can it be regulated by one-size-fits-all deterministic governance?

  41. …projected larcenous profit,…

    A profit (larcenous or otherwise) is what gets well over half (and growing!) of the people in this world out of bed in the morning.

  42. this was my first thought exactly!… I ctrl+f’d sandel and was very pleased to know I’m not the onlyh one out there who would be able to share this with other. Cheers mate!

  43. Even if you use a 1% discount rate, 5 million lifes are worth nothing in 500 years.

    I have just justified the cost-benefit ratio of eugenic campaign to purify a race of supermen for a 1000 year reich.

    Its time Classical Economists start talking about the moral assumptions embedded in their “scientific” mathetized models, and the distortion and immorality that economic ideology can justify using “rational” cost/benefit analysis. People are taught these theories are “rational truth” and a guide to finding “the good”, instead of acknowledging it is an ideology, which like all ideology has blind spots.

  44. Yup. Once one accepts this logic, he can’t just condemn something like the Holocaust out of hand.

    He has to say the Nazis’ projections were economically irrational, and therefore their discounting was misconceived, and that’s why it was an incorrect policy.

  45. So the Bush-era OIRA used Enron-style accounting standards to get the results they wanted?

    Well, color me surprised.

  47. The value of a human life is not calculated using the discounted value of future earnings. Is your mother worth nothing because she didn’t have a job? The value of a human life is better estimated based on what people will pay to reduce the risk of death — preferably their own deaths. EPA estimates the Value of a Statistical Life at something like $7 million, which is much higher than the present value of earnings.

    I fully agree with your point that explicit statement of value is much better than implicit. I’m not quite sure why you lose your nerve when it comes to discounting. A low discount rate for human life is really the equivalent of a low rate of return on saving human life. In other words, you’re really saying that saving lives is a bad investment.

    By the way, seven percent real is a pretty good rate for lots of decisions. It’s about the real return from the stock market overall, so it’s a reasonable measure of the opportunity cost of consumption. In other words, if you want to extract money from me in taxes for some public health project, you better be able to get at least as good a return as I could get myself. And please, no talk about public health spending being low risk and so justified at a lower discount rate. It ain’t so!

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