Is this Africa's big chance?

Planet Money just finished an amazing eight-part series on how t-shirts are made, centered around following a shirt they are selling (men’s women’s). You can find all the episodes on their podcast’s webpage or by pulling up their podcast on your smartphone. I strongly recommend you listen to the whole thing starting from Part 1 (link). They’re each only around 20 minutes long, and they might be the best reporting on microeconomics, ever. I found that the series challenged a lot of my prior notions about how the garment industry works, and that’s even with a relatively strong base of knowledge.

One theme of the series was that t-shirts are now made in Bangladesh because that is the cheapest place in the world to make them. In the segment on t-shirt factories in Bangladesh, they note that the country recently raised its minimum wage. The consensus among industry experts was that this would end up just raising prices slightly for the end consumer. This would then lead to more income for garment workers in Bangladesh, which sounds like an unmitigated good.

What’s missing from this story is the history of globalized garment manufacture, which has always had the feature that production moves to the cheapest possible place. Indeed, Planet Money discusses one of the most dramatic such moves, which was when production moved from South Korea to Bangladesh because quotas were tightened on Korean-made t-shirts. This move was actually spearheaded by Korean businessmen who actively sought out Bangladeshi partners to start factories in the other country. The argument about the current change in costs is that Bangladesh is as cheap as it gets. There is no place else to go that is cheaper (although they do allude to Cambodia being competitive on costs)

I’m not sure that’s the whole story. Sure, no other country currently offers lower costs of production right now. But when t-shirt manufacture moved to Bangladesh, it didn’t offer lower costs either. What it did offer was lower wages . And despite what NPR might tell you, Bangladesh does not have the lowest wages in the world. According to the World Bank’s excellent PovcalNet tool (which I found via this CSAE blog post), there are 15 countries that have lower average incomes than Bangladesh, based on the most recent available household survey data. This is a decent proxy for having lower wages – made more compelling by the fact that all 15 said countries have higher poverty rates than Bangladesh, meaning that they have lots of people at the low end of their income distributions.

The other thing those countries have in common? All 15 are in Africa. The rise in wages in Bangladesh creates an opportunity for other lower-cost players to step in, and Africa is home to essentially all of them. This opportunity would only really accrue to countries with the ocean ports necessary to participate in the global manufacturing economy, so Liberia, Madagascar, Tanzania, Nigeria, Mozambique, Sierra Leone, and Guinea-Bissau are legitimate candidates. The other 8 possibilities are out of luck, unless road and rail transit improve drastically, or we do something crazy like building a set of canals into the heart of Africa.

This version of the future doesn’t have to end disastrously for Bangladesh, either. Remember, Bangladesh got its start not just by gaining the low-cost lead from South Korea, but also because Korean companies went to Bangladesh to invest there. And South Korea’s fate, after that point, was to continue its spectacular rise into the ranks of the world’s richest countries. This could be the kickstart Bangladesh needs to make a move up the value chain. There are risks: some Bangladeshis will probably lose jobs, for example, especially in the short run, but the large numbers of currently un- and under-employed Africans who would stand to benefit are jut as deserving of our sympathies.

I have no way of knowing whether this is the future we’ll actually end up with, but if I were in the t-shirt business, I wouldn’t settle for keeping my manufacturing in Bangladesh and just accepting higher costs. I would be looking at making clothes on the continent with the lowest wages in the world, which faces the exact same tariff and quota structure as Bangladesh. A continent with a huge number of jobless people who would benefit hugely from more jobs, which happens to have an economy that is growing faster than anyplace else in the world. I would be looking at Africa.

In Praise of Crazy Ideas

On Sunday Amazon announced plans to deliver online purchases within 30 minutes via fleets of autonomous drones. I’ve seen various reactions to Amazon Prime Air: from excited, to claiming this is a PR stunt timed to coincide with Cyber Monday, to the aforelinked Matt Yglesias piece which argues that this is a defensive move to prevent competitors from doing the same thing. But I think everybody can agree that the idea of using thousands automated miniature helicopters in order to save consumers the effort of going to the grocery store is totally insane. I, for one, was sure this was some kind of April Fool’s joke resurrected by the internet and circulated at the wrong time. And my instinctive response, on learning that it was serious* was “that will never work”.

And there’s a good chance it won’t work – they might not even be able to secure permission to do it. But that’s fine. Crazy ideas are the mother of successful innovation. I had almost the same response back when Google announced Gmail (which actually did happen on April Fool’s Day of 2004): “A gigabyte of storage? For free? No way. Never. Well, maybe in 2014, but not now.” As it happened, they were serious, and Gmail heralded the now-familiar world where all our data is stored in the cloud and accessible anywhere for free. But for every Gmail there are untold numbers of Webvans (which was really sort of a low-tech Amazon Prime Air), most of which we’ve never heard of.

And this isn’t just a private-sector game: government-sponsored crazy ideas make the world go round. Building the Panama Canal (and for that matter the Suez) was totally nuts – but crucial to the development of the world we live in today. We put a man on the moon during an era when science hadn’t yet sorted out that smoking kills you. As a result, we now regularly hurl chunks of metal off of the Earth’s surface, with enough speed that they miss the ground – chunks of metal that then send us signals from outer space to help us find the nearest gas station. The future is awesome – thanks in large part to crazy things people tried in the past.

Indeed, I’m actually worried that the world doesn’t have enough crazy ideas to keep pushing us into the awesome, unexpected world of the future. So you can only imagine my delight when I stumbled across this op-ed in The East African by Charles Onyango-Obbo. He calls for a set of canals linking the landlocked countries in Africa to the sea:

There could a T-shaped canal that begins in Mozambique, touches the Botswana-Zimbabwe border, hugs Malawi, snakes along Tanzania’s southeast border, to Burundi, Rwanda, Uganda, then along the eastern edge of DR Congo, and to South Sudan.

Then a leg would begin from Obbia on the Somalia coast, into southern Ethiopia, connect with the southern leg in South Sudan, and then cross through CAR, Chad, Niger, run between Mali and Burkina Faso, into Guinea and end on the Atlantic Ocean.

Some of you may have heard me talking about almost the exact same idea – replicating the system of waterways that connects the American Great Lakes to the Ocean, but with their African cousins.

Now, this idea is completely nuts. The environmental consequences alone are enough to make it – probably – impossible. And where would we get all the water we’d need? This doesn’t even mention the number of locks we’d need, since the great lakes region of Africa is, topographically, more or less a single high plateau:

This would be a far bigger challenge that the Panama Canal was, or even the system of waterways connecting the American Great Lakes to the Ocean. On the other hand, the benefits would be enormous. Here is a map of where people in Africa live:

It’s not just that lots of countries in Africa are landlocked – a huge number of people live in landlocked countries, with a particularly high concentration around the great lakes. A system of canals linking those lakes to the ocean would drastically reduce the cost of shipping goods from those countries to the rest of the world – potentially making them competitive in actual manufacturing, instead of just exporting raw materials. It would also be absurdly expensive, require better international cooperation than the world has ever seen outside of wartime, and disrupt hundreds of fragile ecosystems. In short, it’s a crazy idea – the kind we need more of, because every once in a while an idea this crazy actually works out.

*I mean, probably serious. This could still be a joke for all I know.

Let's stop insinuating that just because people are poor, they are stupid. That's nonsense.

A recent BBC piece reports on sex workers in Kenya using post-exposure prophylaxis (PEP)* as a substitute for condoms, cycling through different clinics to use the drugs on a regular basis. This lets them earn a premium for unprotected sex at relatively low risk to themselves (although not without social and personal cost). The article focuses mainly on the public health ramifications, which are definitely serious. A skeptical reader might point out that the only first-person anecdote about the alleged practice is in fact a totally reasonable use of PEP: a sex worker got drunk, she made a mistake, she got worried about HIV infection, so she got her hands on some ARVs. That’s exactly what you’re supposed to do.

I want to put that aside, however, and focus on how goddamned clever the women described in this piece are. These drugs will keep me from getting HIV? Then I can use them instead of condoms – that way I can earn more money, since men will pay more for unprotected sex. You can’t get them from the same clinic more than once a year? That’s okay, I’ll give a fake name. Take pictures of the people you give PEP to? I start going to different clinics. Or I send a friend.

This isn’t an isolated case, either. Several years ago, TB-positive people in South Africa evidently started selling their saliva to other folks looking to get targeted disability grants. I remember hearing about a similar scheme involving the selling of HIV-positive blood. No matter how well you design your system, you should always expect people to find a way to game it.

Economics is often criticized for the assumption that people are rational. Obviously, the critics say, human beings are not perfect calculating machines, they make mistakes, they do things that don’t maximize profits, or whatever. The typical counterargument defends rationality by pointing out that it can accommodate mistakes, that we don’t actually think people maximize profits, and so forth – it confronts the “people aren’t rational” argument on its own terms.

I want to offer a different defense: rationality, the way it is typically used by economists, means that people are smarter than you think – even poor people. Indeed, the canonical economic model of a poor person is a rich person with less money.**  The rational choice paradigm of economics amounts to taking people’s choices seriously as legitimate choices given the options they face, and trying to understand them as such, rather than writing them off as obviously unreasonable.

*PEP is the use of a large dose anti-retroviral drugs shortly after a (potential) HIV exposure to prevent infection with the virus.
**Even most behavioral economics research that looks at poverty and poverty traps focuses on how resource constraints lead to impatience, time inconsistency, and other issues with decisionmaking. The poor make questionable decisions because they don’t have much money, not vice-versa.

Programs that raise test scores also do objective good

Economists like to use improvements in standardized tests as a measure of how well education programs are working. This commonly leads to dissent on the grounds that standardized tests don’t really measure anything of value. My go-to response to that critique has long been that these exam scores are predictive of objectively important outcomes. Change the test scores (in a meaningful way) and you will shift those outcomes as well.

A new paper by Will Dobbie and Roland Fryer, “The Medium-Term Impacts of High-Achieving Charter Schools on Non-Test Score Outcomes“, makes exactly that point. Participation in the Promise Academy (which famously raised students’ test scores in the short term, by half a standard deviation in math and a fifth of an SD in English) led to big gains in important outcomes in the medium term. Their abstract:

High-performing charter schools can significantly increase the test scores of poor urban students. It is unclear whether these test score gains translate into improved outcomes later in life. We estimate the effects of high-performing charter schools on human capital, risky behaviors, and health outcomes using survey data from the Promise Academy in the Harlem Children’s Zone. Six years after the random admissions lottery, youth offered admission to the Promise Academy middle school score 0.283 standard deviations higher on a nationally-normed math achievement test and are 14.1 percentage points more likely to enroll in college. Admitted females are 12.1 percentage points less likely to be pregnant in their teens, and males are 4.3 percentage points less likely to be incarcerated. We find little impact of the Promise Academy on self-reported health. We conclude with speculative evidence that high-performing schools may be sufficient to significantly improve human capital and reduce certain risky behaviors among the poor.

I was lucky enough to meet with Fryer when he came to Michigan to give a talk. One thing he said is that his research agenda is motivated by the robust link between racial gaps in test scores and racial gaps in outcomes. Fix the black-white gap in test scores, he said, and you could fix almost all of the gap in crime, teen pregnancy, and so forth. This is the first time, however, that I’ve seen compelling evidence that the observed relationship between test scores and overall quality of life holds up when you actually get low-scoring kids to do better in school.

Granted, a lot of other stuff could be going on. The Promise Academy surely had other effects beyond academics. But this study provides important evidence in favor of using test score improvements as a meaningful measure of improvements in education.

"Don't just give us cash"

While I have been bogged down in the insanity of the middle of the academic semester, reports have kept coming out about the staggering success of unconditional cash transfer programs in Africa. For those of you playing along at home, that means just giving cash to poor people with no strings attached. These have even hit the popular press*, and been emailed to me by non-academics, prompting me to emerge from my involuntary blogging hiatus to offer a few thoughts.

1) These programs have massive benefits. Both the GiveDirectly and Northern Uganda Social Action Fund cash transfer programs are showing increases of around 50% on earnings, several years out, from cash grants in the range of $300-$1000. People I have explained this to commonly leap to the erroneous conclusion that that has something to do with the grants being around 50% of income. Nope – these are impacts on additional income. This implies massive social returns to this kind of investment strategy: Blattman, Fiala and Martinez say they are 40% annually. Amazing.

2) They don’t have the downsides that people often assume they will. One red flag often raised with giving the poor cash is that it will be wasted on alcohol or other addictions, potentially making people worse off. The GiveDirectly RCT looks at spending on these “temptation goods”, and finds no evidence of that.

3) It’s not just white people in rich countries who are worried about cash handouts being wasted. Paolo Abarcar links to a Jishnu Das post about this concern, where he asks “Can we please stop making judgments about what poor people should and should not do with money that is redistributed to them?” I agree totally that this is fundamentally unreasonable – but poor people are worried about these problems themselves. During a conversation I had with a man from rural Malawi, I asked if it wasn’t a better idea to hand out cash to people facing food shortages, instead of trucking in maize to an area that was growing tons of it. He (a potential beneficiary of this program!) was adamant that cash was a terrible idea. People would waste it on booze. Better, he said, to give us maize.

In ongoing research with fellow UM grad student Lasse Brune, we’re taking a radical approach to the question of how to measure whether money is wasted: we’re asking people to decide for themselves. What do they buy in violation of their prior plans and budgets? What do they buy and then regret later? Which things that they bought were spur-of-the-moment purchases, or regretted? Pilot-testing these questions has revealed some surprising choices. Maybe unsurprisingly, though, among the most common selections are alcohol and unhealthy snacks. The possibility that cash transfers might be wasted on temptation goods is a concern not only to Economist readers and international development donors, but also to the very people who stand to receive the cash.

EDIT: Corrected the end of the second-to-last paragraph, which had said “to give us cash”.

*Okay, popular among bourgie college graduate types.

If you're paying someone to take your classes, pay for Bs, not As

I stumbled across this local Ann Arbor craigslist posting (since flagged for removal, and hence reproduced below) that advertises for a “ghost student” to take someone’s online master’s courses for them. Surprisingly, on the surface, the poster wants someone to earn a B average and occasionally fail classes. Why not pay for As? Potentially for a couple of reasons.

  1. Maybe you’re getting compensated for doing this masters and want to drag it out. Seems unlikely, considering how much they are willing to pay
  2. They realize the single biggest problem with faking academic credentials is getting caught, and if you want to avoid detection, it’s best to fly under the radar.

I strongly suspect that #2 is the major factor here. Carol Moseley Braun was found out within just days of misstating she had degrees from Harvard, when she merely held visiting fellow position at the school. Marilee Jones, on the other hand, claimed degrees from far less-renowned institutions, but was able to keep them on her resume for 28 years, because who is going to lie about having a degree from Union College? (You may remember Jones as the resume-padding fraud who, as dean of admissions for MIT, urged applicants not to pad their resume. Comedy gold.) Similarly, no one is going to check into your college records if you earn a B average and fail several classes. But if you are the shining star of your graduating cohort, somebody might just try to verify that you’re really taking your classes.

Full text of the ad:

What I need:
A U of M student
who is capable of good quality Masters level work
who is dependable
lives in the area
honest
will be around for 21 months or at least 9 months
knows APA formatting

To do what:
Take my online Masters Degree program for me as if they were me

For how long:
21 months

The game plan:
I need B level 3.0 work I need you to occasionally fail classes so the degree takes a little longer too

So that’s:
6 credits which is two 3 credit classes every 16 weeks, 16 weeks is one semester, one class at a time so one class every 8 weeks, total of 30 credits

When you fail:
You must participate weekly in the course discussions and submit assignments weekly and participate actively so you are not withdrawn from the course. You must write based on personal opinion and cite Wikipedia and do poor work so as to fail but actively participate the whole semester.

The pay:
$100 per week when you get the B’s. Paid to you the Monday after the Sunday night everything is due after you submit the work (I will be checking that you do the work). I can meet up with you for cash or we can arrange to set up a prepay VISA SERVE card or other such system for electronic transfer of funds or paypal so we don’t need to ever meet up and you just get paid online directly. When you fail you only get $50 a week because it’s less work. So $1,600 for the semester with B’s. $800 for the F’s or D’s.

Interested????
E-mail me with a little about yourself and why you would want to do this and how you would have the time to do the work. I will respond quickly. I need to pick someone by October 28. Please e-mail about yourself. If after a couple e-mails you sound like you’re the one. I would want to see some examples of your papers you’ve written for school to know you can do the work. Then meet up in person to give you the books and my passwords and everything.

START OCTOBER 28

Obligatory LOL at the requirement that the applicant be “honest.” But if people are going to cheat, I’d rather see them do it cleverly. Stupid cheaters are the most depressing thing in academia.

The difference between statistics and econometrics, in one graph

Planet Money recently ran an excellent story on the relationship between your college major and your eventual earnings. This is an important and generally under-appreciated aspect of the college decision. Broadly speaking, earnings are more strongly correlated with major than with school quality, but people spend a lot more time worrying about the latter. The basic relationship they are talking about is summarized in a short article entitled “The Most (And Least) Lucrative College Majors, in 1 Graph”:

I was careful to say “correlated” above because this graph highlights one of the key ways in which econometrics differs from (the rest of) statistics. Econometrics has an almost singular focus on isolating causal relationships in situations where simple correlations like the above are potentially misleading. That’s its single biggest strength, because humans are great at pattern-recognition and our tendency to jump to causality from observed correlations is hard to overcome. Think about describing this graph to a high school senior who is headed off to college. “People with engineering degrees tend to earn more than people with social work degrees” is something you can say without qualification. “Major in engineering because you will earn more money” is not.

Why not? Well, engineering degrees are hard, and you need to be very smart, diligent, and good at math to finish one. These abilities are things that, in part, you carry with you into college, and someone with that skill set will probably earn more money than someone who lacks it, even if they both choose to major in Studio Arts. The differences in the above graph will hence tend to overstate the benefits of majoring in engineering. Everyone (or at least everyone who has taken Stats 101 course) has heard the mantra that “correlation does not imply causation”.

But oftentimes correlations are causal. Econometric reasoning can help us see when they aren’t, and why. It also can give us a sense of the likely direction of the bias (upward, in this case – the effect of majoring in engineering on your wages looks bigger than it actually is) and what you might do to get better inferences (try to get your hands on pre-college measures of diligence and math ability). In its sophisticated extreme, econometrics is employed by (very clever) economists to isolate the actual causal relationship in question, say the impact of college major choice on eventual earnings.

I don’t know the right answer to the question of how much majoring in engineering will increase your earnings, but if you got a BA in counseling psychology, you can take some solace: that probably didn’t cost you a full $50,000 per year. However, it also wasn’t free, and college students should definitely pay more attention to that cost – and other associated costs, like higher unemployment rates.

The Prevalence and Correlates of Oral Sex in Malawi

The latest paper from our ongoing project on the potential of oral sex as a safer sex strategy in sub-Saharan African has been accepted for publication at the International Journal of Sexual Health. This paper, which I coauthored with Sallie Foley of the University of Michigan Graduate School of Social Work and my advisor (and study PI), economics Professor Rebecca Thornton, measures the how common oral sex is in Malawi and what factors are associated with it. Here’s the abstract:

Despite medical evidence that female-to-male oral sex (fellatio) carries a lower risk of HIV transmission than unprotected vaginal intercourse, little research exists on the practice of fellatio in Africa. We use two samples of men from Malawi, one rural and one urban, to examine the prevalence of oral sex. While 97 percent of the rural sample and 87 percent of the urban sample report having had vaginal sex, just 2 percent and 12 percent respectively say they had ever received oral sex. Only half of the rural sample, and less than three quarters of the urban sample, report having heard of oral sex. Education, exposure to newspapers and television, and condom use significantly predict oral sex knowledge after controlling for other confounding factors, while exposure to radio does not. The large gap between sexual activity and oral sex prevalence suggests that fellatio should be taken into consideration as a potential component of a HIV-prevention strategy, but further quantitative and qualitative research that includes women as well as men is needed to understand its potential benefits and drawbacks.

A copy of the final manuscript, not yet typeset, is available here. The full citation is: Kerwin, J. T., Thornton, R. L., & Foley, S. M. (in press). Prevalence of and Factors Associated with Oral Sex among Rural and Urban Malawian Men. International Journal of Sexual Health. doi:10.1080/19317611.2013.830671

We got accepted just before I left for my latest trip to Malawi (for another project), and turned in the proofs just as the fall semester was starting here at Michigan, so putting up a link to the article fell way down my to-do list. Today they sent me an email reminding me that not only is the manuscript already online, but that I also have a limited-use public link to it that people can use to access the PDF if they can’t get through the Taylor and Francis paywall. Contact me here or through my umich email address if you want the link.

The previous paper to come out of this project was called “Missing Safer Sex Strategies in HIV Prevention: A Call for Further Research”, and was published in African Population Studies. Our next step will likely be to exploit some novel data we have collected on people’s attitudes towards oral sex and sexual activity in general, which fills some of the gaps left by the just-accepted article. In particular, it includes women instead of just men, and has a qualitative component (we did a set of gender-segregated focus groups).

This is the greatest spam in history

Last week I received the most impressive spam I have ever seen. Here is the text, with identifying characteristics redacted:

Subject: GLOBAL WARMING
From: CLIMATE CHANGE AWARENESS

 Attn: Sir/Madam, View attached letter and contact Prof. XXXXXX

Thanks,
Ms. XXXXXXX

Attached as a PDF is a letter that begins:

This is to inform you that the United Nations Framework Convention on Climate Change (UNFCCC) in Collaboration with the Nelson Mandela Foundation and William J. Clinton Foundation has held an Internet Raffle Draw, and your Email Address was among the 18 Email Addresses that was picked through the computer ballot system. The United Nations Framework Convention on Climate Change/Nelson Mandela Foundation and William J. Clinton Foundation was conceived with the objective of human growth, educational and community development, and to create awareness to the dangers posed on our planet by climate change.

To celebrate the 18th anniversary of the United Nations Framework Convention on Climate Change (UNFCCC), the United Nations Framework Convention on Climate Change/Nelson Mandela Foundation and William J. Clinton Foundation in conjunction with the United Nations (UN) is giving out a yearly award of $900,000 (Nine Hundred Thousand United States Dollars Only) to 18 lucky recipients.

I’ve uploaded the letter to my personal webspace (after stripping identifiable information, which frankly is probably false anyway). The whole thing is worth reading.

What’s impressive about this is the way it plays on a prospective victim’s emotions, especially if the target is of a socially liberal persuasion. Nelson Mandela and Bill Clinton and the UN Framework Convention on Climate Change are involved. I’m being asked to help protect and save our planet! And I’ve won a grant – these big international organizations totally make grants, right? It couldn’t hurt to see where this is going. Also helping its credibility is the professional-looking email address for the “consultant” the target is referred to.

I now wonder whether there are other variants on these, targeted at different groups. For conservatives, for example, you would want to invoke religious groups, Ronald Reagan, and maybe Freedom House.

The world's most confusing lottery description

My mother passed on this excellent piece from The Week that discusses the psychology of lotteries. It’s well worth reading – it covers all of the ways that lotteries exploit our mental and emotional weaknesses. But the lead paragraph has one of the most confusing explanations of a lottery that I’ve ever seen. For context, the basic idea behind a lottery is to sell n tickets for $Z apiece, and award the winning ticket some amount $X that is much less that n times $Z. One person wins a big cash prize, and you make a tidy profit. That’s the underlying grift behind all the mind games lottery organizers play. But according to The Week (and the underlying Nautilus post) it’s not how the Powerball drawing on May 18th, 2013 worked:

To grasp how unlikely it was for Gloria C. MacKenzie, an 84-year-old Florida widow, to have won the $590 million Powerball lottery in May, Robert Williams, a professor who studies lotteries, offers this scenario: Head down to your local convenience store, slap $2 on the counter, and fill out a six-numbered Powerball ticket. It will take you about 10 seconds. To get your chance of winning down to a coin toss, or 50 percent, you will need to spend 12 hours a day, every day, filling out tickets for the next 55 years. It’s going be expensive. You will have to plunk down your $2 at least 86 million times.

Williams could have simply said the odds of winning the $590 million jackpot were 1 in 175 million. But that wouldn’t register. “People just aren’t able to grasp 1 in 175 million,” Williams says.

If the jackpot is $590 million, and the odds are 1 in 175 million, then each ticket has an expected value of $3.37. At $2 per ticket, you make a profit, on average, of $1.37 for each ticket you buy. Taken at face value, these numbers imply the folks running Powerball (a cabal with the lovely moniker of “Multi-State Lottery Association”, which is for some reason abbreviated MUSL) lost money on that drawing. There are tons of caveats here: to play the eponymous “powerball” costs an extra dollar, and taking the money all at once reduced MacKenzie’s payout to $370.8 million.* But if these details matter, then they should have been clarified. I’m assuming the real issue is an error in the probability of winning, but a lazy Google search was unable to confirm that.

Irrespective of the cause, this is an extremely telling error to make in an article about why we (foolishly) play the lottery. The author himself couldn’t do the math to see that the numbers implied that the expected profit from the example lottery was positive. This actually shows that Robert Williams is on the wrong track! It’s not just that people can’t understand small probabilities – in general, we can’t compute expected values either.

*There are also federal taxes to consider, but these would just have lowered the expected profit to lottery players, and wouldn’t change the fact that MUSL lost money.