Bogus Complaints about the use of Discrete Variables

Orazio Attanasio and Valérie Lechene (A&L) have an excellent article in the latest Journal of Political Economy that exploits the randomized rollout of PROGRESA to test the collective model of household consumption. Their analysis rests of the fact that once we condition on total consumption, the only way PROGRESA should plausibly affect the shares of consumption allocated to specific goods is through increasing women’s bargaining power (PROGRESA transferred money directly to children’s mothers). They make a similar argument for another variable, the relative strength of the two spouses’ family networks – these two variables, which affect consumption shares of different goods only through bargaining power, are called “distribution factors”. The collective model of household consumption states that however resources are allocated within the household, there is no waste; this is equivalent to saying that there is a unique index, called the Pareto weight or the sharing rule, that governs how all the distribution factors affect the shares of spending allocated to different goods. All distribution factors, then must enter the demand system proportionally, so we can effectively condition on one of them and explain away all the others. If demand shares still depend on a second distribution factor after we appropriately condition on the first, we can reject the collective model. They find that the collective model does not fail this test, while the simplistic unitary model is easily rejected (since PROGRESA changes consumption patterns, conditioning on total expenditure).

A&L exemplifies what we want to accomplish through conducting field experiments in economics: they combine a deep understanding of the institutional and cultural context of the experiment with an equally thorough analysis of what various economic models tell us about what should happen. As a result, A&L aren’t just estimating a parameter consistently or measuring the impact of a program, they are advancing our knowledge of how consumers make decisions – and in an empirically credible fashion. It’s also extremely well-written; I can hardly do it justice via a brief summary.

The only arguable shortcoming of the paper is that they make much of the fact that one of the distribution factors they rely on, the relative strength of the two spouse’s family networks, on is continuous. Continuity of at least one distribution factor is a formal requirement for the mathematics of their argument to go through. The problem with this claim is that it is false. The number of family members has only a finite number of points of support, thus leading to a finite number of potential values for the variable. The same even applies to their alternative measure, which uses the total consumption of each spouse’s family network. Money is “more” continuous than counts of people, sure – but it is not actually continuous.  This doesn’t really undermine their argument, which is that you can’t use the PROGRESA treatment if a continuous variable is needed. PROGRESA treatment is, by definition, binary, and hence discrete. It definitely seems more valid to use something that is arguably a discretized proxy for an underlying continuous variable: although we observe only discrete ratios of numbers of people, that in principle could be measuring a variable that is actually continuous.

Unfortunately, stating that their alternative variable seems more valid is about as far as I think we can go. I’m not aware of any proof that having a “mostly continuous” variable is “good enough”, nor even that having things be “more continuous” is “better”.* This is a very general problem: most of economic theory, and most of the math underlying econometrics, technically requires the variables we are working with to be continuous. But all of the variables actually used in empirical economics are discrete: the minimum granularity of money is cents (or arguably mills); for time, we never measure anything below seconds.**

None of this means that the mathematical and statistical tools we use don’t work. On the contrary, they seem to work just fine even when things are obviously discrete. The canonical example of ignoring discreteness is the “linear probability model”, which has been rehabilitated in the eyes of economists (in particular Josh Angrist). We seem to have learned, as a discipline, that if the marginal effects computed by a probit are meaningfully different from those that come out of an LPM, the solution is to fix your specification rather than to trust that the error term is normally-distributed. I’ve personally learned that pretending things are continuous is also fine in other contexts – for example by learning how to implement a count model on some of my data only to find that its estimates of marginal effects were identical to OLS to the 4th decimal place.

Pointing out discreteness as a statistical concern, or an issue with someone’s model, is usually just a cheap “gotcha”. Yes, it’s technically a problem. But it’s technically a problem with every economics paper that uses continuity – which is a lot of papers. As a discipline, economics seems to be strikingly inconsistent on whether we worry about continuity. We usually ignore it when working with discrete quantities like money or hours worked or years of education or test scores,  and nobody complains. There’s no good reason to criticize the use of variables that are discrete at the level of whole numbers while not objecting equally to the use of variables that are discrete at the level of hundredths of a whole number.

* That doesn’t mean that there is no such proof. However, if such a proof exists, Attanasio and Lechene don’t cite it, and neither do other researchers who insist that relatively more-discrete variables are more problematic.
** Broadly-informed readers might also note that according to the best of our knowledge, almost nothing is actually continuous, which doesn’t do much to limit our ability to use calculus to understand the physical world.
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Why are we so obsessed with existing national borders – especially in Africa?

Chris Blattman asks why Russia’s annexation of Crimea is such a terrible thing, triggering responses focused mostly on a possible slippery slope (is Putin in 2014 the same as Hitler in 1939?) and the unacceptable procedure by which the annexation was accomplished.

Defending the legitimate application of democratic norms is important, and so is making sure that we don’t pull a Neville Chamberlain. But I don’t think that’s why the West has reacted so strongly to the Crimea situation. I’m convinced it’s because people around the world are committed to the existing boundaries of nation-states – even when they make absolutely no sense.

We justify that commitment partly through legitimate fears about credibility and potential future invasions and annexations by other powers, but there seems to be a visceral, emotional component to it as well. This is especially obvious in Africa: the African Union’s charter enshrines “the principle of the respect of borders existing on achievement of national independence”, a principle reaffirmed repeatedly through other agreements and resolutions. Those borders make no sense. Everyone knows they make no sense, and that they were for the most part constructed by a bunch of foreign colonizers through negotiation and war. They divide ethnic groups and language families arbitrarily, and leave tens of millions of Africans living in countries with no access to the sea. And the AU is absolutely committed to defending them. This is a fairly general problem: many countries around the world are too small and poorly thought-out geographically. As Lant Pritchett has argued, strictly-enforced national borders make small countries susceptible to devastating spatially-correlated shocks.

I am no fan of the Crimean annexation’s democratic basis and am legitimately worried about Putin invading other countries. Those are valid concerns – but they aren’t the whole reason that everyone objects to this invasion. A large part of it comes from a popular belief in the legitimacy of nationalism – a sense that the status quo, as established in roughly 1945, is the natural state of the world and that it is inherently harmful to change it, especially by combining states.

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The moral obligation to haggle in developing countries

In explaining why she haggles with vendors when shopping in Tanzania, Aine McCarthy hits on one reason in particular that strikes me as very important:

3. Price inflation externality. Or, “if you pay full price, all the prices will slowly go up.” The only time I experienced this was when I went to the most touristy market in Arusha and tried to make a few few vendor friends the day before all my Americans friends arrived in Tanzania. Generally, though, I’m not under the impression that my individual bargaining has that much of an impact on prices. Not extremely likely.

Aine is talking specifically about buying souvenirs at craft markets, but when I travel to Africa, my most important interactions with vendors are actually regarding supplies and services for my projects. These are big transactions, and they add up to a large chunk of local economies when you extrapolate them across the entire development sector. In those negotiations, driving a hard bargain is necessary in order to keep the project under budget – but it also has important externalities. I’m not usually a fan of trying to solve collective action problems through individual choices, but I think development projects need to coordinate on agreeing to haggle with vendors, for the overall good of local economies.

This won’t be easy. It’s a lot more pleasant to just pay up. For most people, haggling kind of sucks: it eats up a lot of time, it can be stressful (especially if you feel like you’re getting ripped off), and it’s hard trying to talk the line between paying the Mzungu price and screwing over the person working at the market. One thing I find particularly tough is even figuring out what the market price should be. In Malawi, when a vendor gets wind of the fact that an Mzungu is involved in a project, prices go up by a lot. I had one experience where my employee agreed on a contract to rent a car, only to have the vendor double the asking price when I came into the picture to pay.

So we’re overpaying. So what, right? We can afford it – and as Aine points out, don’t Africans need the money more than we do? Not so fast. First off, it’s important to keep in mind who you are negotiating with. If it’s craft vendor or a rural shop owner, then that logic is certainly accurate. The guy renting you a 4×4 or the full-time professional survey supervisor, however, comes from much higher up the permanent income distribution. It’s still probably true that, if we are willing to compare such things across people, their marginal utility from money is higher than yours – but the difference is much smaller. In fact, in my experiences better-off vendors have been more likely to try to rip me off.

Second, the social welfare impact of huge amounts of windfall income is fairly ambiguous. We know that giving lots of money to poor people improves their lives and has few negative effects on the goods they buy, but also that in at least some places giving cash to men makes them more likely to have unprotected sex, with women experiencing the opposite effect. If a guy makes twice as much as his wife expects, that might be extra money he can use to have risky sex.

Most important, however, is that overpaying encourages the perverse misallocation of resources and especially human capital in developing-country economies that is induced by . I have previously argued that in Malawi many of the smartest and most talented people work in development, with potentially serious consequences for the overall economy. These are people who would be entrepreneurs and run businesses in an undistorted economy, creating positive externalities in the lower part of the human capital distribution. That is, we have made driving SUVs for the UN into arguably the best job in Malawi, and the people who do that might otherwise start firms that would employ tons of other people and bring benefits to the rest of society. The same pattern also holds in Northern Uganda: smart people make the best move for themselves personally and work for NGOs, rather than doing something more beneficial to the overall local economy.

Unfortunately this problem seems to be getting worse over time. The raises given out by the richest development organizations in Malawi have, in my casual estimation, far outstripped even official inflation rates.* I’ve also directly experienced positive price shocks due to huge organizations signing overpriced contracts for vehicles. We are already distorting economies by redirecting resources toward development work – by failing to haggle, we are making the problem even worse.

*As an aside, I have many doubts about Malawi’s official inflation figures, which heavily weight the price of maize. Maize is subject to huge annual fluctuations due to growing conditions, and net purchases of maize aren’t likely to be very large since almost everyone in Malawi grows it themselves (people often sell it soon after the harvest and buy it back later). Computing inflation myself using the wholesale prices I paid for sugar and soap, I get an an inflation rate of ~10%/year during 2012, when the headline figure was around 30%.
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I bless the crazy hailstorms up in Uganda

A Skype meeting for our project was interrupted today by what sounded like the loudest rainstorm I had ever heard. Then I looked outside, and saw this:


A hailstorm in Africa – add that to the list of things I never expected to see. Rain on the iron-sheet roofing common in nicer homes in Lira can be pretty loud, but hailstones are completely deafening. Not only couldn’t we hear the Skype call (and in any case the storm quickly knocked out the power and internet), but I could barely hear people who were right in front of me. We got a nice accumulation of hail, too:


I also learned my new favorite home remedy: the Mango Tree employees at the office told me that if a kid wets the bed, eating hailstones will cure them. Therefore, I was told, all kids around here are forced to eat hail when it comes down during a storm. And indeed, when I stepped outside the gate, I saw a bunch of kids rushing around gathering the ice off the ground.

I even ate a couple of the least dirty ones myself. Honestly? Not too bad.

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Save your money at the local bar and earn a 30% return

Last Friday I was at a bar near Mango Tree’s offices in Lira – I’m not sure what its name is, but it’s about a block away. I was trying in vain to buy a beer when two gentlemen interceded with the bartender – apparently she was doing something non-work related, and should have prioritized me as a customer. Or maybe not, and these guys were just asserting my priority as a white person on my behalf. That’s an uncomfortable gray area I find myself in a lot here, so I will almost always just stand politely until noticed rather than try to get the attention of e.g. a clerk at a store.

In any case, they were really nice guys and we ended up talking about what they were doing at the bar. They were there with their savings group, they said, making their weekly contributions to the savings pool. The group meets each Friday and everybody chips in. They got the idea, they said, when they realized they were spending 200,000 shillings as a group on drinks each Friday, so they had to be able to save a decent amount as well. So they merged the incentive of drinking socially with the goal of saving money. Then they lend money out to members of the group who want loans and have a decent plan for the money.

I absolutely love this group, for multiple reasons. Reason number 1 for that is that they started this themselves, rather than having some NGO come in and explain how they should have a savings group that will promote all kinds of socially-valuable buzzwords. The guys I talked to might have been bullshitting me, but if anything the tendency in Lira is to play up your ties to NGOs rather than playing them down: NGOs are where the good jobs and money are. This home-brewed nature makes me think the whole scheme is much more likely to last: there is more impetus behind it, and it’s something the members clearly want.

A second reason is that they save their money at the bank, instead of focusing entirely on trying to loan out money to group members. They talked me through the fees they pay, and they amount to something like 1-2% of their capital per year, whereas the interest rate they earn is 19%. Just speculating offhand, I assume that one benefit of their group is to get a good interest rate and low fees, by having a lot of money in one account. Consumer banking in developing countries tends to be a raw deal of high and poor interest rates, so it’s heartening to see people getting a good deal from one.

Third, they have a clever interest rate system for their borrowing members that I have never heard of before. If you want to borrow money, the monthly interest rate is 10%, which is an annual interest rate of over 200%. But that’s only for the first month – for later months, the interest rate goes down to 5%. The group members I talked to described this as a penalty, when it kind of sounds like a discount, but it makes some sense in context: if you want to borrow $20, you have to pay back $22 within a month. If you take longer than a month, you will have to pay more. People don’t like paying more than they should, so that penalty probably has teeth – but it is less likely to trap borrowers in a spiral of odious, unpayable debt.

Finally, they say that the overall savings fund earned 300,000 shillings last year on an investment of 1 million. Granted, we were discussing this over Nile Specials at 10 on a Friday, not in a corporate boardroom. And even if they really did earn a 30% return per year, that’s not going to scale up. It’s largely a function of the fraction of group members who want to borrow money, and they have a limited number of projects to invest in, so foreign investors are probably not going to flood into this asset class. Still, it’s not too shabby for something a bunch of folks came up with at the local bar.

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Incomplete Markets in Snack Foods and Condiments in Rural Africa

I spent most of this past week out in Amolatar town, headquarters of Amolatar district, which is located on a peninsula that juts out between two lakes on the Victoria Nile. This is a pretty remote area: it took us around 4 hours to drive there from Lira, which is itself a 5 or 6 hour drive from Kampala. One of the most popular ways of getting to Amolatar is to take a ferry across the lake. In this map from Wikipedia, Amolatar is the peninsula snaking down into what is marked Lake Kyoga (the upper part of the lake is technically Lake Kwania):590px-Rivers_and_lakes_of_Uganda

On the other hand, compared to other places I’ve been to in rural Africa, Amolatar town is pretty built up. While most of the way here was along dirt roads, they’re decently maintained (lots of washboarding but limited potholes). The town has electricity, and I could get internet on my iPhone via MTN. More of a pleasant surprise was that it also has piped water and sewage. Here’s a picture of what Amolatar town looks like:


The biggest limitation to Amolatar’s development that I noticed was actually its dearth of snack foods. I was working long hours, involving lots of manual labor (moving around supplies for the project) and often wanted small snacks to keep me going, or things to eat after the restaurants had closed for the night. But the shops in Amolatar sold almost no snack foods: just two kinds of basically-flavorless biscuits* enticingly branded “Glucose”, and one or two kinds of candy. At first I thought this was due to a strange, non-representative sample, but I then actually went to every single shop in Amolatar when I thought the project was going to run short of pencils. Not only were there no savory snacks on sale in the whole town,  nobody even seemed to know what the word “crisps”** meant. I found this a strange contrast with Southern Malawi, where even in very small and remote villages there is a far wider selection of available snacks, including multiple savory options.

My theory for Amolatar’s peculariar lack of snacks comes down to the available options for actual food. Lots of the Ugandans I interact with, if they hear that I’ve also spent time in Malawi, want to know which country I like better. There’s obviously no general answer to this question: I’ve only been to a small part of each country, and they differ in countless ways, big and small. But one area where Northern Uganda clearly does better than Southern Malawi is in terms of food: simply put, in Amolatar I could get everything I ate in Jali, but also a whole bunch of other things. The diet in Southern Malawi is absolutely dominated by maize, eaten in the form of nsima (sort of like a thicker version of grits). In Northern Uganda, they eat that too, but also a wide range of other carbs, from matooke (a kind of plaintain) to nsima-like foods made with millet, to sweet potatoes. This region also has more variety in terms of the protein people eat, as well as more sauces and stuff I can’t even really place (boyo, for example, is a something between a sauce and a standalone carb that is made of peanuts and greens and goes amazingly well with rice).

That’s far from the end of the story. Malawi has the best hot sauces of anyplace I’ve ever been to. Beyond their amazing national champion brand, Nali***, there are other nationwide brands of hot sauce as well (Osman Foods makes another great one). Lots of restaurants also make their own artisanal hot sauces, and there are great small batch producers that produce sauces for sale, along with people growing their own heritage varieties of the bird’s eye pepper for people to add directly to their food. Uganda, meanwhile, has a single hot sauce brand that I’ve encountered, called Top Up, and it’s pretty much terrible. This is intimately related, I think, to the limited variety in food: if there are lots of options for dinner, it’s less worthwhile to invest in ways of (literally) spicing it up. Likewise, expanding your basic menu of food options is less worthwhile if you have a kickass hotsauce to throw on your food.

The same logic probably applies to snacks: tasty snack foods and tasty meals are, to some extent, substitutes in consumers’ utility functions. Given the cost and risk of bringing in new goods and trying to develop markets for them, Northern Uganda and Southern Malawi are stuck in different equilibria in the markets for snack foods and condiments. This leaves consumers in a tough spot: if the market could support the initial cost of bringing in more variety, I am sure that Malawians would like eating more different kinds of starch, and that Ugandans would come to appreciate a decent hot sauce – just as Americans have grown to enjoy a wide variety of ethnic foods in the last couple of decades.

* In the British sense – to Americans they are cookies.
** Chips, for Americans.
*** Lest you think I am just throwing Malawi a bone here, I should note that I literally bring cases of Nali home with me every time I come back from Malawi, and carefully dole them out to friends and family as patronage. It’s that good.
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Timothy Kalyegira commits the rarely-seen inverse self-Godwin

In any debate on the Internet, the probability of a comparison to Hitler or the Nazis approaches 1 as the length of the debate increases. This truism is known as “Godwin’s Law“, and in some circles bringing Hitler up in an unrelated debate is known as “Godwinning”. Godwinning is almost always 1) done in a negative sense, since, you know, the Nazis were bad and stuff; and 2) used against one’s opponents, i.e. comparing whatever/whomever you are arguing against to Hitler, rather than yourself.

Timothy Kalyegira, in a Daily Monitor op-ed about President Museveni’s imminent signing of a bill banning homosexuality*, has achieved a rare form of Godwinning, painting Nazis in a fairly positive light and comparing his own side of the debate to them:

This is what I don’t like about the way the gay agenda is being thrust at Africa. A determined and well-organised minority can wreak havoc on a majority.

It is this frenzy, the will to power, the assertion of a collective ego by the gay rights movement that I find suspect. It is the obsession with pushing the rights of tiny minorities and fringe groups into the mainstream and making the mainstream guilty about not embracing these minority rights.

It is this precise attitude of hysterical activism that led to the rise of the fascist movements in Europe in the 1930s. The Nazi in Germany and Italy’s Brown Shirts fascists started out as extreme nationalist groups, usually scorned and their leaders often in jail. But they skilfully worked up the sentiments of their disillusioned and frustrated populations until they became part of the mainstream and eventually rose to power.

The gay lobby needs to think seriously about the aggressive way they are going about their campaign. It might bring them disaster in future. (“The coming backlash against homosexuals”, February 23rd 2014).

In the leadup to the signing of the bill, the Ugandan media has been littered with ridiculous arguments against homosexuals and in favor of banning them, but this inverse self-Godwin is simultaneously the most ridiculous and the most terrifying point I have ever seen made in a political debate. Even casting it in the most favorable possible light, Kalyegira is telling homosexuals to watch out and keep quiet or they face genocidal retribution.**

None of this is to say that all of the op-eds on the topic have been ridiculous and anti-gay: in another op-ed in the same issue of the Monitor, Bernard Tabaire eloquently makes the point that demolishing free speech and the rights of minorities is a dangerously slippery slope:

Standing up for the rights of all Ugandans is as important today as it ever was. The government has no right to tell us who to sleep with and how; what to wear; which films to watch; what to protest for or against in a group. Otherwise we will soon be told what to think.

Unfortunately, given what Kanyegira is willing to openly write about homosexuals, reasonable people like Tabaire face a tough slog in fighting for minority rights in Uganda.

EDIT: The link to the Kalyegira piece above (which was the top hit I found on Google) for some reason omits the end of the op-ed, which is by far the most disturbing section. Here is the full text – note that the lion’s share of the scariest part is on the second page. I’ve excerpted it here in case it gets taken down:

I foresee a demagogue like Adolf Hitler, sensing the silent resentment in society at this agenda. He will seize the moment. He will be courageous or reckless enough to disregard public opinion. It will take an unconventional man at the margins like that to snap the West out of its present state.

He will form a far-right party and make the core of his agenda that of restoring traditional Christian values. At first, he will shock many by daring to challenge the taboo of not speaking out against gays.

He will be denied TV studio time, but like the rapidly-rising Far Right political parties in Europe in the 1930s and today, he will be, like Hitler, a man with nothing to lose. He will be tenacious and persist with his radical agenda of calling for the elimination of homosexuals from society.

Eventually, to the disbelief of many, he will be elected by an enthusiastic majority, tired of being made to feel guilty about feeling there is something wrong with homosexuality.
Then hordes of once-suppressed majorities will descend on gays in their neighbourhoods, work places and villages and they will be jailed or worse. History is full of such backlashes.

*Scheduled to happen about 2 hours ago as of the writing of this post.
**A less favorable interpretation might note that, among other things, he seems to blame the Jews for the Holocaust.
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