July 10, 2013

• It’s time to get rid of “willingness to pay”.

  JDN 2456484 EDT 09:35.

   

  Most laypeople, if you asked them what economics is about, would probably answer with one word: “money”.

  This could hardly be more wrong; it’s like saying that physics is about computer readouts and medicine is about needles on the dials of blood pressure cuffs. But I can forgive the mistake, because it is one that a large number of economists seem to make on a regular basis.

  You’ll actually hear economists say things like: “The tsunami killed 300,000 people, equaling an estimated cost of $30 billion.” They literally try to assess the value of lives in terms of dollars. (And then wonder why people think they are cold-hearted psychopaths?) This is exactly backward; the value of dollars is and has always been what they can do for people’s lives.

  A lot of this glaring and disturbing error can be traced to one methodology in particular: “willingness to pay”, or WTP. Economists are accustomed to valuing just about everything in terms of what someone would be willing to pay for it.

  This seems relatively harmless for consumer goods; when asked, “What would you be willing to pay for a laptop?” or “What would you be willing to pay for a sandwich?” one can give a fairly consistent, precise, meaningful answer.

  There are already problems with even this simple case, but most of them seem tractable, and neoclassical models do try to take some of them into account. It depends on your financial circumstances: Maybe you’d pay $5 for the sandwich and $500 for the laptop; or maybe you really like sandwiches and would pay $15; or maybe you need a very nice laptop and have enough extra money that you’d pay $2000. If your wage goes up, your willingness-to-pay for most things will rise. We also need to adjust for inflation; $500 isn’t worth as much now as it was in 1950, so a WTP of $500 in 1950 isn’t the same thing as a WTP of $500 today.

  Also, the answer you’d state—or pay in real life—is actually anchored to current market prices and conditions; you say you’d be willing to pay $5 for that sandwich, but that’s because you know you can buy a reasonably good sandwich for $5 at Subway or Jimmy John’s. Now suppose you’re stranded in a desert, starving, and someone is offering to sell you a sandwich; you’d be willing to pay quite a bit more, wouldn’t you? $1,000? $10,000? Maybe even $100,000, if you could find some way to come up with it? But then, what is your true WTP? Is it $5, what you’d answer on a survey or pay at Subway? Or is it $100,000, the amount you’d pay if you were starving in a desert? In the sense economists really mean, the value of the sandwich to you, I think it’s actually the latter. A sandwich is life or death. That means your consumer surplus upon buying a $5 sandwich is enormous; you gain $99,995 in consumer surplus when you buy that sandwich at Subway. But I think that’s right; you really do gain something that could save your life for the cost of a few minutes of work at middle-class wage. That’s how amazing our lives are in the modern world. Of course, standard WTP analysis ignores this entirely, using the price you’d pay in a real-world market. (On that measure, life seems quite bleak indeed: Something is only worth what you pay for it, so whenever you buy something you’re really no better off. The game is zero-sum. Finance really is like this most of the time; but consumer goods most certainly are not.)

  An even worse problem is one that only cognitive economists recognize this far; willingness to pay, WTP, and willingness to accept, WTA, are not the same. They should be, in an ideal efficient market; if something is really worth $500 to you, you should be willing to buy it for $500 or less and willing to sell it for $500 or more. If it’s worth $600 to someone else, you should sell it to them, presumably for about $550; that way you gain $50 (you get paid $550 for something that was worth $500 to you) and they gain $50 (they get something that’s worth $600 to them for a price of $550). That’s how markets are supposed to allocate resources efficiently; goods go to those who value them the most. If WTP and WTA aren’t equal, this system falls apart. If WTA is less than WTP, then you’ll throw money away, buying something for $600 and then selling it for $500. Fortunately that rarely happens. But what does happen, indeed happens most of the time, is that WTA is more than WTP. It’s called “endowment effect”; you value things more once you already have them. (Ironically, our aphorisms say otherwise: “The grass is always greener on the other side.” No, actually, the grass usually seems greener on your own side.)

  By the way, the “neoclassical explanation” on that Wikipedia page is utter nonsense. Your willingness to pay is not an abstract distance between indifference curves; it’s a quantity of wealth. When asked your willingness to pay to go from X0 of the good and Y0 wealth to X1 amount of the good, that shifts you along the same indifference curve, to a point where you have X1 of the good and Y1 of wealth. The difference between Y0 and Y1 is your WTP. And when asked your WTA, you’re contemplating going back to X0 and Y0, so indeed they should be the same, because, obviously, Y1-Y0 = -(Y0 – Y1).

  Now, you might be thinking: “If it’s mine, I can use it and customize it how I like.” For instance, it makes sense that my computer is worth more to me now then it was when I bought it; I’ve customized it how I like, installed a bunch of programs, and most importantly, stored a great deal of files, which include things as important as my financial records, my resumes, and my writing (which is basically my livelihood). My financial records aren’t worth much to other people, now are they? All this is true—and important; my laptop is worth far, far more than its replacement cost, especially if we include my backups—but it doesn’t solve the problem. Endowment effect appears immediately, even before you’ve had time to make any changes to the product. Most people would be willing to pay $700 for the laptop when they buy it, and then if you offer to buy it back immediately, would expect $800.

  You might think this wouldn’t apply to sophisticated financiers, who surely know better; oh, but it does. Indeed, there’s a well-known phenomenon in the stock market called the “bid-ask spread”; bid is the price people are willing to pay for a stock (that is, WTP), while ask is the price people are willing to accept to sell it (that is, WTA). In an ideal efficient market, those two would be equal. But in real-world markets, there’s usually a small but significant gap, the aforementioned “spread”; and in market crises, the gap can widen to extreme levels, destroying liquidity in the market and often exacerbating the crisis. You might be thinking: If ask exceeds bid, how do stocks ever sell? Well, these are averages, so for small spreads, you can usually find someone whose ask is lower than your bid and vice versa (and one of the few real services brokerage firms provide is finding such matches). Also, many buyers and sellers place “market orders”, which promise to pay or accept whatever the market price may be, with no limits placed (this is generally a bad idea, though oddly my online brokerage tries to encourage it, issuing warnings when your limit is above the current market price. Yes, you idiot, I was willing to pay that price. My limit is in case it gets bigger before my bid clears. Then again, market orders make the brokerage’s job easier… so is this a conflict of interest?). But if the spread gets big enough and nobody places market orders, the distributions stop overlapping, and the market mechanism really does break down.

  Endowment effect may also explain why people get the Monty Hall Problem wrong so often; even if they thought the odds were 50/50, they should still be willing to flip a coin to decide (and thus win, indeed, 50% of the time). That would be an especially good idea if you have any uncertainty about your probability estimate; flipping a coin is a robust strategy that will always win 50% of the time, whether the odds are really 50/50 or something else, even as extreme as 0/100. But in fact the majority stay with their first choice [link], which doesn’t even make all that much sense if the odds are 50/50; it’s as good as flipping a coin if you’re exactly right, and not as robust if you’re wrong. In fact, they aren’t 50/50, they’re 33/67, so you should switch, winning 67% of the time. Endowment effect would explain this: You over-value your current choice.

  It also probably has something to do with another effect found in cognitive economics, loss aversion. You’re willing to expend more effort and bear more risk to avoid a $100 loss than you would to get a $100 gain; indeed, a $100 loss and a $200 gain seem to be about equal for most people [link], which nicely explains how we came up with the aphorism “A bird in the hand is worth two in the bush.” (This aphorism is an empirically valid statement in cognitive economics!) This also could explain why people won’t switch: Suppose the prize is $100. Then you’re comparing a 50% chance of losing $100 with a 50% chance of gaining $100, and the loss hurts more, so you don’t take the chance.

  Are loss aversion and endowment effect contrary explanations? No, I really think they’re part of the same phenomenon. You over-value what you have, so you’re afraid to lose it. They were discovered separately, but really they are part of the same cognitive process.

   

   

  So, from the above, there are already a lot of problems with WTP even in the apparently sensible cases.

  But now, let’s consider the more extreme cases: What are you willing to pay for a liver transplant? (A lot, yes?) What would you be willing to accept to have your liver taken out right now? (Is there any amount you’d take!?)

  What does willingness to pay even mean if the result of the transaction would be your death without heirs? Maybe then your WTA would be infinite? But surely there are things you’d be willing to do even if it meant dying without heirs—unless you’re a complete psychopath, you’d rather die yourself than let everyone else in the world die but you. (Just how many it would take is a difficult question, to be sure: 2? 10? 50? Don’t make it too low, for we all must make many choices every day that indirectly may cause or prevent deaths. Statistically, we are all heroes and murderers; and which we are on average, I honestly can’t say. I hope heroes. I hope.)

  What are you willing to pay to save a child from being tortured? What would you be willing to accept to have a child tortured? These kinds of questions are offensive to most people; they seem immoral to even ask. And most economists can’t fathom why; they seem to think people are just being irrational and sentimental (which apparently they can only be when they take surveys, but not when they make market judgments? I still can’t understand how any economist can believe that markets are rational; it’s kind of like believing the sky is green.).

  I, on the other hand, understand completely. This sort of question is morally backward; it values dollars instead of people, and completely ignores human dignity and agency. In what bizarre circumstances would I be paid to torture a child? Who is doing this payment, and why aren’t we killing him and confiscating all his wealth? (He tortures children. If anything merits capital punishment, it’s that.)

  Moreover, saving a child from being tortured is very good; but it is in fact not as good as torturing that child would be bad. Hurting and letting be hurt,killing and letting die aren’t the same; double effect is a moral principle that almost everyone believes in [link], and one of the best arguments against classical utilitarianism is that it doesn’t allow for it. (More sophisticated rule utilitarianism does, and that is a big part of why I am a rule utilitarian.)

  In these sorts of cases, WTP seems to break down entirely. That doesn’t stop economists from trying to use it; indeed, even cognitive economists, for I worked on a research project a few years ago where surveys asked questions like “How much money would you be willing to accept in order to 1. strangle a puppy 2. rig an election 3. publicly deny your religious beliefs” (yes, really). They also measured eye movements of people taking the survey. I will say one thing in their favor: They did offer “no amount of money would be enough” as an option, which neoclassical economists would scoff at.

  And then there’s the fact that when economists try to estimate the WTP or WTA of human lives, the results they get vary absurdly depending on how they are measured.

  If you determine how much we value life based on auto safety, consider that Americans own about 200 million cars, with an average value of about $10,000; that’s $2 trillion. We probably spent 10% of that on safety features. The Institute of Highway Safety reports that auto safety features save about 100,000 lives per year. The average US car is 10 years old (yes, really!), so we’re spending an average of $20 billion per year on safety features, to prevent 100,000 deaths. That’s a price of $200,000 per life saved.

  Now compare how much we spend on medical care; that’s about $3 trillion. How many lives do we save that way? A lot, to be sure; but there are also a lot of people who just aren’t sick. So let’s say about 10 million lives per year, meaning our medical system extends average lifespan by about 30 years compared to what it would have been. That’s $300,000 per life.

  If you determine how much we value life based on what we spend fighting terrorism, you conclude that even assuming we prevented another 9/11 (which is dubious), we have net lost 1000 American lives—and young, healthy American lives, no less—by the wars in Iraq and Afghanistan, which cost us $1.4 trillion; so apparently we value American lives at a price of -$1.4 billion per person!? Even if you (insanely) discount the lost soldiers, that’s only 3000 lives saved for $1.4 trillion, a whopping $466 million per life. Now do you see why I think we need to spend more on healthcare and less on war?

   

  But it’s one thing to say that WTP is flawed; it would be much more useful if I could actually propose a viable alternative.

  Fortunately, I can: Quality-Adjusted Life Years (QALY).

  QALY are already in fairly wide use in medicine. They don’t need to be inflation-adjusted; a QALY in 1950 (or 50 BC!) is the same as a QALY in 2013.

  The “life years” part is fairly straightforward; if an intervention saves lives, you can estimate how many people it saves, and how old they would be, and what their life expectancy now is. This is why we can use it easily in medicine; a lot of medical interventions straightforwardly save lives.

  But what about the “quality-adjusted” part? That’s obviously a lot more difficult. It requires you to ask questions like, “How many years of your life would you give up to get rid of your migraines?” and “How nice would a house have to be for it to be worth losing a year of your life?”

  One might think that these questions are just as difficult—or just as absurd—as questions like “How much money would I have to pay you to torture a child?”; but there are some important differences that make QALY better than WTP.

  First and foremost, QALY isn’t immoral. It actually makes sense to weigh lives against other lives; ethical philosophy already does ask questions like “How many people would I have to save for it to be worth killing this person?” And when just assessing your own QALY, there’s nothing obviously immoral or irrational about choosing to die a year sooner rather than suffer in chronic pain.

  Secondly, there are already some obvious applications. Malaria treatment and prevention obviously has a higher QALY per dollar ratio than derivatives trading, so as a society it would be worthwhile to take some of the money from derivatives trading and put it into malaria prevention. We can compare the QALY losses due to marijuana use to the QALY losses due to imprisonment, and invariably find that prison is worse, not only for the users but also for the taxpayers. The latter would be hard to do with WTP, and the former would be utterly impossible; the WTP for derivatives is simply the price of the derivatives, and the WTP of malaria treatment would be very high except for the fact that most of the people dying of malaria have hardly any money.

  Indeed, it is perhaps precisely because they use WTP that neoclassical economists can still convince themselves that markets are rational. If the price of everything is its value, then sure enough, everything is selling for its proper value! The First Rule of Tautology Club is…

  Krugman calls this “ketchup economics”, but that’s not nearly harsh enough. A 40-ounce bottle of ketchup doesn’t actually sell for twice as much as a 20-ounce bottle, and that makes sense because some people don’t want a 40-ounce bottle of ketchup because they won’t use it all before it spoils. And ketchup, actually, is worth some QALY. Not a lot, mind you; I love ketchup, and I’d give it up forever to get even 2 more years of life; so assuming I average 50 mL a day for my whole life, and live to be 80, that 1.46 cubic meters of ketchup (a lot of ketchup!) is worth only 2 QALY, meaning that the QALY value of ketchup is 1.37 QALY/m^3, or 1.37 milliQALY per liter. Since a liter of ketchup is about $3 (or $5 if you buy organic), I’m paying $2200 to $3700 per QALY, which is actually pretty good. I’m sure I’ve paid far more than that in ineffective migraine treatments—and possibly even in effective ones. In fact, I may even be getting a better deal than that, since the lycopene and vitamins may be extending my life. Then again, there’s also the salt and sugar, and even for me ketchup is a small part of my diet, so the assumption that ketchup has net zero effect on lifespan seems pretty reasonable.

  QALY can also explain very nicely why you shouldn’t smoke; heavy smoking shortens your life by as much as 20 years, and a pack of cigarettes is about $5 and will last a heavy smoker about a day; so in your lifetime of 60 years (instead of 80), you’ll have spent about $100,000 on cigarettes, which means you are purchasing QALY at a rate of negative $5500 per QALY—you are paying to kill yourself. Put another way, not smoking is like being paid to stay alive.

  Of course, that ignores any potential benefits of smoking (it feels good?), so let’s try factoring that in. How QALY-dense must smoking be in order to be worth it? Let’s say we price each QALY at the same level as organic ketchup, $3700 per QALY. That means that from this lifetime of smoking you must gain 27 QALY, in addition to the 20 QALY you lose by killing yourself; so that means that those cigarettes have to produce 47 QALY of pleasure. That’s 20,000 packs, so you’re asserting 2.35 milliQALY per pack, meaning you get twice as much pleasure from a pack of cigarettes than I get from an entire liter of ketchup. Even eating it at every meal, I could probably spread that liter over a month, so now imagine spreading that pack of cigarettes over two months. You now have a cigarette once every five days, and you’re telling me you get more happiness out of that than I would by having ketchup at every meal. I don’t buy it.

  But see, if we’d used WTP, you pay as much for the pack of cigarettes as I do for the liter of organic ketchup ($5), so it must be worth the same. Never mind that one product kills you while the other may extend your life; The Market Has Spoken.

  Likewise, I had an economics textbook argue, yes, I kid you not, and I quote: “Based on market principles, a professional basketball player is worth more than a neurosurgeon.” This is what happens if you conflate how much something costs with how much it is worth.

  Indeed, on this sort of market-fundamentalist view, it becomes impossible to even assert that something is not worth what we’re paying for it. What we’re paying is what it’s worth, by definition. This would make markets Pareto-efficient, as neoclassicists hope; it would also make them zero-sum. No matter what we do, we’ll have the same outcome. A nuclear war is as good as a malaria vaccine. Surely that is not what you meant to say? (It shouldn’t be hard to see that the QALY figures come out quite a bit different.)

   

  I don’t mean to suggest that QALY are perfect, or even that they’re easy; they aren’t, and in some ways they may even be harder to measure than WTP. But as in the Parable of the Lamppost, sometimes you want to look at what’s actually important, instead of just what’s easy to see.

   

   

   

   

   

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