Models the Armchair Economist gets wrong
Sent to MetaMed’s eventual founding CEO Michael Vassar — then president of the Singularity Institute and Alyssa’s SIAI mentor — this is a list of alternative economic models drafted while Alyssa was reading Steven Landsburg’s The Armchair Economist . The stated motivation: getting a feel for what publishable economics papers can look like, in preparation for talking to Yale econ professors when she returned to campus the following month. A list of models I invented of phenomena named in The Armchair Economist which, while not very accurate, are definitely more accurate than the (frequently nonsensical) things he discusses. 1. “When a man pays a dollar for a lottery ticket that gives him one chance in ten million of winning $5 million, we see no evidence of irrationality. People have different attitudes toward risk, and their behavior appropriately differs.” (p. 11.) This model is completely inaccurate — nobody buys a lottery ticket because they have rationally determined that it is a wise thing to do given their expected payoff and risk-aversion coefficient, and I can construct a better, experimentally verifiable, model to prove it. My model states that, above a certain amount, people’s attitudes towards probability and money no longer follow the laws of arithmetic: anything above a certain amount (fairly well approximatable as fifty times median income) in money, and below a certain amount (I would guess 1%) in probability, just gets rounded to “a lot”. Hence, if we examine state lottery data, we should see that people’s preferences over lotteries are extremely inelastic relative to the odds — people should not really care whether they’re buying a lottery ticket for $1 million at odds of 1:100,000 against or odds of 1:100,000,000 against. You could probably use this to construct a lottery ticket which has a higher expected payoff but a lower market price. 2. “Teenage concertgoers tend to follow up by buying records, T-shirts, and other paraphernalia. Adults don’t. Therefore, the promoters want teenage audiences. The way to guarantee a teenage audience is to set low prices and watch the queues grow; adults won’t camp out overnight to see the Rolling Stones.” (p. 13.) One could easily show, given access to data on profits from concerts, that the amount you could make by selling tickets at market price is far in excess of the amount you could earn from selling T-shirts. I would guess that a better model is that the producers have an idea in their head of what a ticket should cost, and will vary the actual price of the ticket plus or minus 2-3 dB from this norm depending on how popular the band is, but don’t want to charge the actual market price (which may be ten times what it “should” cost), as it would seem as “absurd” as trying to sell a laptop for $12,000 or a BlackBerry for $400. One could easily experimentally verify this by charging much higher prices for one concert, and then seeing whether you make money in proportion to the price increase. Or you could see whether the distribution of prices is a Gaussian around some mean, instead of a log-normal. Another model is that people may tend to feel that market economies are immoral, because they give preference to the rich regardless of the source of their wealth, and prefer to allocate limited resources by desire or “need” rather than money. One could also easily experimentally verify this, by charging much higher prices for one concert, and then seeing whether it’s boycotted or denounced in the media for “only letting the rich see the band play”. Alternatively, and much more generally, one could come up with some way of ranking industries by moral valence, by doing a survey of the form: “Suppose a rich businessman and a poor taxi driver walk into a store selling X. The owner of the store only has one X left in stock, and he sells the one he has to the businessman, because the businessman is able to offer a higher price. How fair, on a scale from 1 to 10, do you think it is for the owner of the store to conduct business in this way?”, for different values of X. You’d expect to get a very low value for things like “life-saving medicine” and a high value for things like “plasma-screen televisions”. You then measure the correlation between the moral valence of an industry, and the lack of economic efficiency due to government intervention. Since people are very passionate about concerts (and sports teams), they get treated with high moral valence, and so are not very efficient economically as a consequence. 3. “Hiring a celebrity to endorse your product is like posting a bond. The firm makes a substantial investment up front and reaps returns over a long period of time. A firm that expects to disappear in a year won’t make such an investment. When I see a celebrity endorsement, I know that the firm has enough confidence in the quality of its product to expect to be around for a while. This theory also makes a testable prediction: Celebrity endorsements will be more common for goods whose quality is not immediately apparent.” (p. 14.) This seems to me to be rather silly. A better model of the situation would be: “Suppose I want to buy one of good X. The quality of good X is hard to measure; it’s tricky to determine in advance which X will turn out to be the best. My brother, last year, went to buy an X of brand Y. Since he’s been using his X for a year, he should have a pretty good idea of how good it is, and he’s my brother so I’m pretty confident he won’t lie to me.” A company could therefore (in theory) do advertising by paying people’s friends and family to endorse goods, since people use their friends’ endorsements as a reliable indicator of quality. However, this would be extremely inefficient. So, what actually happens is that the company pays the celebrity to endorse the product instead; people don’t distinguish very strongly between people they know in real life and people they see on television, so it still works. The celebrity effectively serves as a stand-in for people you know who can measure the quality of a good. One could test this versus the first theory by running endorsements with, say, the former governor of Tennessee, in both Tennessee and North Dakota. The people of Tennessee are already familiar with their governor, while the people of North Dakota aren’t, so the stand-in-for-a-friend should work for those in Tennessee and not those in North Dakota. On the other hand, the original theory predicts no difference in effect between the two states: people in both states presumably have a roughly equal idea of how large a “bond” it is to pay a former governor to endorse your product. 4. “Why do men spend less on medical care than women do? Possibly because men are more likely than women to die violent deaths. The value of protecting yourself against cancer is diminished if you have a high probability of being hit by a truck.” (p. 17.) One could easily debunk this by showing that the difference in people dying violent deaths during old age (when most health-care spending occurs) is so minimal that it cannot possibly account for the difference in spending. My personal model of the situation is that women in general tend to have more trust in institutional authority, and hence in doctors (a symbol of that authority), than men, who tend to be more independent and distrustful of those in power. One could measure this by doing a survey about people with diseases, and then asking people to estimate their chance of survival with and without medical care; if my model is right, women will rate the difference between the two as being larger than men will. 5. “I have no idea why people vote.” (p. 18.) The obvious, and more classical-economic model of this, is that the value of a vote is still quite large, especially in a swing state; the odds of it making a substantial difference to the election are small, but the payoff is very large, so the total expected value is still big. The more cynical model, and the one I personally place more stock in, is that people intuitively model the country by treating it as an extrapolation of their neighborhood. If half the people you know are voting for Bush and half for Kerry, then it seems intuitively like your vote could make a substantial difference. Whereas, if all the people you know are voting for Bush, what would be the point of voting for Kerry? It seems like he’s going to lose anyway. One could easily test this by getting electoral data, and then showing that within a given state (to account for Electoral College effects), people who support Kerry in polls are less likely to turn out to vote in neighborhoods which are 75% pro-Bush than neighborhoods which are 50% pro-Bush. 6. “Without sex scandals, more candidates would enter, to the detriment of those who are already in the race. Entry would continue until being in and being out of the race are equally attractive, just as they are today.” (p. 32.) I would propose instead that (a) most high-level politicians really want to be President, and would gladly trade a 20% chance of having their careers ruined for a 10% chance at the Presidency, and (b) most high-level anything aren’t very risk-averse anyway, which is why they’re high-level. The reason more people don’t run isn’t that people don’t want to run at a 1-in-N (for N candidates) chance of winning; it’s that the chances of winning are extremely unevenly distributed. You can construct a model for this thusly: take all the senators, congressmen, governors, etc., and rank them from 1 to N in order of presidentialness. Their chance of winning is distributed exponentially: person #1 has a C% chance, person #2 a C·N% chance, person #3 a C·N²% chance, and so on, with C and N set such that the total adds to 1. This matches nicely with the empirical observations about the 2008 election in prediction markets. Now, add in the additional condition that if you run for the Presidency below some given rank (say, twenty) and lose, you immediately get labeled as a crackpot and can never run again. Classically, the people who run for President with no serious chance of winning are not those who will later run with a serious chance of winning — they’re fringe people who don’t actually expect to win ever, like Kucinich, Paul, and Gravel, so running with a low chance of winning labels yourself as a fringe person and thus sinks your future chances. Every election cycle, there are many thousands of reversals within the presidentialness ranking — people #9 and #10 become people #10 and #9, say. (A better way to model this would probably be that people have some exponentially distributed presidential “rating”, like an Elo rating, and that people randomly move up and down every year by a certain amount.) If you do out the math, if you’re a lower-ranked politician, your best strategy probably isn’t to run for President now; it’s to wait four years and hope that your rating increases, because then you’ll have a decent shot at it. 7. “Most important, they would learn that consumption and leisure, not accumulation and hard work, are what Life is really all about.” (p. 43.) This is, of course, true, but you can’t tell people that as an official policy. I don’t even need to invent a model of hyperbolic discounting, since it’s already well-established — people irrationally overvalue short-term reward at the expense of long-term reward. Telling them to overvalue short-term reward as official policy will just cause them to do it more . We already have quite enough trouble getting people to save for their own retirements as it is, even with massive government and corporate incentives, hence the necessity for programs such as Social Security. 8. “The efficiency criterion dictates that we measure all gains and all losses in terms of willingness to pay and measure one total against the other.” (p. 63.) This method of determining a collective preference is obviously broken, because money does not necessarily translate into weight over preferences. Suppose we are living in a town in ancient Rome. The local landowner is very wealthy and a member of the Senate, and so he has a huge plantation with hundreds of slaves. He and a hundred of the slaves want to decide collectively whether they should be tortured to death for his personal amusement. The landowner values his personal amusement at 200,000 sesterces, a small fraction of his total personal wealth. The slaves each have total assets of 1,000 sesterces. The standard economic interpretation of this would be that the slaves value their not getting tortured at 1,000 sesterces apiece, and that an economically efficient outcome would be for the landowner to pay the slaves 1,100 sesterces each, and then have them all tortured to death. Hence, if the Roman government intervenes on behalf of the slaves, it is an “inefficient decision”, because both sides would have “preferred” this to the actual outcome — even though this is obviously not how it actually works. As for how to actually sum people’s preferences, I would recommend the use of a utility currency which is renormalized beforehand, so that every person only ever has a fixed amount of it. 9. “The best way to see the absurdity of the allegation that a draft is cheaper is to imagine taxing the young man himself $30,000, and then offering it back to him as a wage for joining the army. Surely this proposal does not differ from the draft in any meaningful way.” (p. 66.) That is silly; of course it does. What it in fact means is that a draft is more expensive. Consider, as a more realistic model, a country with a hundred young men, half of which have a willingness to pay of $10,000 to avoid being drafted, and the other half of which have a willingness to pay of $20,000. Suppose we need an army of fifty men. If we draft them all, then presumably the draft will draw equally from each group, for a total draft cost of $10,000 × 25 + $20,000 × 25 = $750,000 (note that this is an opportunity rather than a direct cost). Now suppose the government wants to recruit volunteers. It calculates that it can recruit the 50 volunteers it needs for $10,000 apiece, and taxes each of the 100 men $5,000 to pay for it. Hence, the total cost to everyone is only $500,000, which is 33% cheaper. (To provide a more vivid illustration of this principle, what if Einstein had stayed in Germany and gone off to fight in WWI? Physics would have lost a tremendous amount of value, for virtually no gain.) What’s really going on here is that “we” (as a society) doesn’t include young men, who are treated as outside the system; losses to grandmothers, businessmen, and coal miners, in the form of taxes, are a cost to “us”, but the loss of freedom and opportunities to the young men are not, so having them bear the losses is “cheaper”. 10. “I emphatically do not care about the psychic harm that I might do to others who are morally offended by the very idea of my operating an internal combustion engine or an aerosol can. I think this distinction would be very hard to justify philosophically.” (p. 71.) I think we can treat this as a matter of (much simpler than Eliezer’s paper) extrapolated volition. Suppose I approach a primitive tribe of hunter-gatherers, the Wookieani. The Wookieani, knowing nothing of the principles behind light or camera film, have not the foggiest idea how a camera operates. However, their shaman (to consolidate his own power against those of outsiders) has decreed that having your picture taken will cause your soul to be stolen by the sun god. While most of us would be very reluctant to, say, deliberately cause the breakup of a Wookieani couple to make $100, we would be much less so to take their picture for the same amount, even if the two cause an equivalent amount of emotional distress. This is because we model, not the current volition, but the extrapolated volition, of the Wookieani: their aversion to photography predictably goes away when they become more educated, while their aversion to breakups does not. 11. “The best way to appreciate the spectacular efficiency of the competitive marketplace is to see some examples of outcomes that are inefficient. For such an example, let us make the pessimistic hypothesis that students learn nothing of any value in college.” (p. 75), followed by an excellent description of how shortening education times benefits everyone, like mutual cooperation on the Prisoner’s Dilemma, yet it is not done due to the problem of enforcing cooperation. The problem with this is, the thing he is describing is a competitive marketplace! It is a marketplace for the labor of the new workers, and college might well be compared to, say, an official grading by the CGC in the comic book market, which is an expensive way (which benefits a third party) for the seller to prove the value of their wares to the buyer. I therefore propose the following model of economics: markets are efficient, because any example of inefficiency is automatically counted as not being a market, even when it is obviously such. Hence, economists can maintain the delusion of an efficient market principle for as long as they wish. 12. “When you assume a debt, the costs and benefits cancel each other out exactly. The issues of whether to run a deficit — and if so, for how long — are of no consequence.” (p. 108.) This is true from a strict NPV perspective, but it assumes a terribly unrealistic model of human behavior. Suppose Mr. B has a monthly paycheck (after taxes) of $5,000, and basic monthly expenses (mortgage / insurance / food / utilities / etc.) of $3,000. Mr. B’s spending works as follows: he first uses his $5,000 to cover his basic expenses, because otherwise he would starve. He then goes about his business, and when he sees something that happens to interest him, he buys it out of his $2,000. He repeats this until nothing is left out of the $2,000, at which point he must stop spending. He then waits for next month’s paycheck, at which point the process begins all over again. Now, suppose I, an unscrupulous banker, come to Mr. B with a credit card. This credit card is actually pretty good — it has an indefinite zero interest rate and no credit limit. I explain to Mr. B how it works, and he runs off, delighted to know that he can now make more purchases. This month, he need not stop at $2,000; about $4,000 worth of objects strike his fancy every month, so he now continues purchasing until he has run up $4,000 worth of debt. I, the banker, demand 2% of the total balance, or $80, as a minimum payment. All other things being equal, the minimum payments would simply keep rising until there was $200,000 worth of debt and a $4,000 monthly payment, and the two are in equilibrium. However, once the payment starts going above $2,000, Mr. B’s paycheck can no longer meet basic expenses and the credit card bill simultaneously, and he must put some of his basic expenses on the credit card. Doing out the math, it is only nine years before Mr. B cannot pay his credit card bill at all, at which point he must declare bankruptcy. Hence, even though we see that the credit card is completely neutral in terms of input and output, it can still lead to financial ruin, by removing natural barriers to overconsumption. 13. “I am sure that if he wanted to press his point, Professor Breslow could list a dozen other ways for the government to get a dollar and a dozen other possible reactions by private citizens. But every one of these alternatives must result in a dollar less being spent somewhere in the economy.” (p. 121.) There is at least one interesting exception to this which I can think of — very large estates. Suppose the Lavishes, an old money family, have a net worth of $1,000,000,000, earning interest at a rate of 5%. To support their lavish lifestyle, the Lavishes spend $10,000,000 every year on caviar, fine wine, and other such luxuries. However, every year, $50,000,000 more in interest accumulates, for a total of $40,000,000. What happens to this $40,000,000? It is never spent, not now or at any time in the future — it is enough work already finding a way to spend $10,000,000 in a year, which equates to $28,000 a day . If the government taxes the Lavish inheritance at 80% — actually at 80%, without various loopholes involving trusts and offshore businesses in the Cayman Islands — the Lavishes would continue their current rate of spending indefinitely, just like they were going to originally. No one loses at all, while the government gains $800,000,000 in additional tax revenue. This is clearly a most marvelous system, which we should therefore pass into law as quickly as possible. 14. “Journalists like to use the unemployment rate to indicate the overall state of the economy. The surrounding discussion usually overlooks the fact that unemployment is something to which people aspire.” (p. 129.) This completely ignores the fact that the unemployment rate already takes into account people who aspire to unemployment (the retired and so forth), who are not counted as “unemployed”, but rather, “not participating in the labor force”. The fraction of the population that is voluntarily unemployed is a totally different number than the unemployment rate, and is of course much higher, currently around 35%. Unemployment statistics only count those who are currently looking for a job, and so presumably see their present condition of unemployment as undesirable. We could also use “cigarette unemployment”, or the percentage of people who want to smoke but are unable to afford it, as a (less accurate) measure of economic distress — even though everyone agrees that smoking is a bad thing — because such a number measures the number of people who want something they are currently not getting . 15. “Second, family breakups create a statistical illusion of poverty.” (p. 133.) I would argue that a large component of this is not merely a statistical illusion of poverty, but an actual cause of poverty; divorces frequently create poverty for everyone, as Elizabeth Warren explains. The essential problem is this: suppose that the cost of establishing an average middle-class household is $2,000/mo. (to pay for the mortgage, utilities, food for one person, and so on), but that the marginal cost of adding people to the household is only $1,000/mo., because many things can be shared between the original household member and the new household members; living in small groups is more efficient than living alone. Suppose that a household has two adults and two children, and total monthly income of $2,500 per adult; income exactly meets expenses. Now, suppose that the two adults get divorced, and one of them establishes a new household. This costs $2,000/mo., plus the cost of $4,000/mo. for the original household, for a total of $6,000/mo. However, income for both adults is still only $5,000/mo. in total, so expenses exceed income; someone’s living standard must drop to make this arrangement viable. Because not all resources can be shared, however, measuring income per household may be as disingenuous as measuring it per individual; the best statistic is probably some combination of the two. 16. “If in fact American cars are of lower quality than their Japanese counterparts, there are a lot of candidates for a good reason why.” (p. 141.) Intriguingly, one explanation that he does not give is the cost of transportation. Suppose that there are two kinds of cars, cheap cars costing $10,000 and expensive cars costing $20,000. All expensive cars and all cheap cars must be made in the same country. It also costs $2,000 to transport a car from one country to the other. Now, suppose that Americans spend an equal amount, $1,000,000, on cheap cars and expensive cars. If cheap cars are produced in Japan and expensive cars in America, then the total cost will be 100 × $12,000 + 50 × $20,000 = $2,200,000 (there’s an equilibrium involved here between the cost of a car and the number of cars bought, but this is the quick and easy and mostly accurate way of doing it). If, however, cheap cars are produced in America and expensive cars in Japan, then the total cost will be 100 × $10,000 + 50 × $22,000 = $2,100,000, which is $100,000 cheaper, so clearly producing cheap stuff in America is the more efficient option.