Tag Archives: cost and benefit

Contraception increases high school graduation – questionable numbers

In Stevenson et al 2021 “The impact of contraceptive access on high school graduation” in Science Advances, some numbers do not add up. In the Supplementary Material, Table S1 lists the pre-intervention Other, non-Hispanic cohort size in the 2010 US Census and 2009 through 2017 1-year American Community Survey data as 300, but Table S2 as 290 = 100+70+30+90 (Black + Asian + American Indian + Other/Multiple Races). The post-intervention cohort size is 200 in Table S1, but 230 in Table S2, so the difference is in the other direction (S2 larger) and cannot be due to the same adjustment of one Table for both cohorts, e.g. omitting some racial group or double-counting multiracial people. The main conclusions still hold with the adjusted numbers.

It is interesting that the graduation rate for the Other race group is omitted from the main paper and the Supplementary Material Table S3, because by my calculations, in Colorado, the Other graduation rate decreased after the CFPI contraception access expansion, but in the Parallel Trends states (the main comparison group of US states that the authors use), the Other graduation rate increased significantly. The one missing row in the Table is exactly the one in which the results are the opposite to the rest of the paper and the conclusions of the authors.

Food refused by the most people

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Which food would the greatest fraction of the world population refuse to eat? To make the question interesting, focus on widespread food items, not „interesting” local specialties like surstromming, fermented shark, maggot cheese. My guess is that pork and beef would be the most widely refused, by Muslims and Hindus respectively. Meat in general is considered objectionable by more people than vegan dishes. Refusal of plant-based food is mostly due to allergies, so soy and wheat would be the least popular. In light of this, it is interesting that the main components of the British Airways snack box on 17 May 2020 were made of wheat and pork (Jamon Iberico and a spread made of 57% bacon and 18% pork jowl). The box replaced the usual airline meal. According to British Airways, the reason was to reduce food heating on the plane during the Covid-19 pandemic. I am not sure how reducing cooking is supposed to avoid infection, but even supposing that, the pork-based snacks do not seem optimal by any criterion.

Vegan food is generally cheaper, and among animal-source foods, chicken is the cheapest, followed by turkey. So price cannot be the reason for serving pork. Airlines may try to signal wealth or that they care about passengers by offering „premium” foods, e.g. meat, and not the cheapest kind. However, this signal is undermined by the plastic boxes for the meals, the sloppy mixture of foods in the main box and the small quantities. The goal is clearly not to feed people or to keep them healthy. It does not seem reasonable for the airline to expect that it will give passengers a good taste experience.

Investing time to gain lifetime

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Exercising lengthens lifespan, but the return is diminishing in the amount of exercise. From zero physical activity, one extra hour of exercise per week gains about one year of life expectancy (doi:10.1371/journal.pmed.1001335.t003). Thus investing 1/168 of total weekly hours, or about 1% of the waking hours that are not spent on the quickest possible eating or hygiene, adds about 1/80 of lifespan in developed countries. This time investment has a positive return, because the percentage of lifetime spent on sports is less than the percentage gained.

Exercising may be optimal even for someone who intensely dislikes exercise, because one way to think about this investment is as choosing a year of being dead or a year of exercising plus some extra time living and not exercising. If doing sports is weakly preferred to being dead, then the first few hours of exercise per week are a positive-return investment.

One criticism of the above logic is that the lifetime gained is at the end of life, but the time doing sports is spread evenly throughout life. If extra time when old is worth much less than when young, then investing time in one’s youth to gain years of life in retirement may not be optimal. However, the question then becomes why is time less valuable when old. If the reason is lower ability to enjoy life (due to chronic diseases, cognitive decline, decreased libido, etc), then counterarguments are that exercise increases healthspan (quality-adjusted years of life) and the progress of medicine increases the quality of life in old age over time. If technological progress becomes fast enough to lengthen average lifespan by more than one year each year, then life expectancy becomes infinite. Increasing one’s lifespan to survive until that time then has an infinite return.

If life expectancy does not become infinite in the 21st century, then the diminishing return to exercise in terms of lifespan implies that there is a finite optimal amount of exercise per week, unless one’s utility increases in exercise no matter what fraction of time is spent on it. At 10 hours of physical activity per week, one needs to add about 10 more hours to gain one year of life (doi:10.1371/journal.pmed.1001335.t003). Spending 10% more of one’s waking time to gain 1/80 of lifetime is a negative-return investment in pure time terms, but may still be rational for the increase in health and quality of life.

In the research, exercise is defined as moderate- or vigorous-intensity activities: those with an intensity level of at least three metabolic equivalents (METs) according to the Compendium of Physical Activities. In other words, the energy cost of a given activity divided by the resting energy expenditure should be at least three (the approximate intensity of a brisk walk). The relevant weekly hours of moderate- or vigorous-intensity activity and the years of life gained are in the table below.

Physical Activity Level:0 0.1–3.74 3.75–7.4 7.5–14.9 15.0–22.4 22.5+

Years of life gained: 0 1.8 2.5 3.4 4.2 4.5

More efficient use of rooms and equipment during the shutdown

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Instead of the labs, gyms and other rooms standing empty during the shutdown, the same isolation of people could be achieved by allocating each building or other resource to one person. Equipment from gyms or labs could be lent out for the duration of the shutdown, of course keeping a database of who borrowed what and making the borrower liable for its safe return. If only one person uses each object or building the whole time, then there is no cross-contamination or infection-spreading.

Excess demand could be rationed by lottery. Only the winner of the lottery for a resource would be allowed to use the resource, with large penalties for sharing. This would improve efficiency slightly, because one person instead of zero would be using each resource.

If the heat, water and electricity were turned off during the shutdown, then it might be more efficient to let the buildings stand empty, instead of having the utilities on and one person in each building or room. However, the lights in MIT buildings are still on at night, just like before the shutdown (and it seemed wasteful back then already).

Popularity inequality and multiple equilibria

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Suppose losing a friend is more costly for a person with few contacts than with many. Then a person with many friends has a lower cost of treating people badly, e.g. acting as if friends are dispensable and interchangeable. The lower cost means that unpleasant acts can signal popularity. Suppose that people value connections with popular others more than unpopular. This creates a benefit from costly, thus credible, signalling of popularity – such signals attract new acquaintances. Having a larger network in turn reduces the cost of signalling popularity by treating friends badly.

Suppose people on average value a popular friend more than the disutility from being treated badly by that person (so the bad treatment is not too bad, more of a minor annoyance). Then a feedback loop arises where bad treatment of others attracts more connections than it loses. The popular get even more popular, reducing their cost of signalling popularity, which allows attracting more connections. Those with few contacts do not want to imitate the stars of the network by also acting unpleasantly, because their expected cost is larger. For example, there is uncertainty about the disutility a friend gets from being treated badly or about how much the friend values the connection, so treating her or him badly destroys the friendship with positive probability. An unpopular person suffers a large cost from losing even one friend.

Under the assumptions above, a popular person can rely on the Law of Large Numbers to increase her or his popularity in expectation by treating others badly. A person with few friends does not want to take the risk of losing even them if they turn out to be sensitive to nastiness.

Multiple equilibria may exist in the whole society: one in which everyone has many contacts and is nasty to them and one in which people have few friends and act nice. Under the assumption that people value a popular friend more than the disutility from being treated badly, the equilibrium with many contacts and bad behaviour actually gives greater utility to everyone. This counterintuitive conclusion can be changed by assuming that popularity is relative, not a function of the absolute number of friends. Total relative popularity is constant in the population, in which case the bad treatment equilibrium is worse by the disutility of bad treatment.

In order for there to be something to signal, it cannot be common knowledge that everyone is equally popular. Signalling with reasonable beliefs requires unequal popularity. Inequality reduces welfare if people are risk averse (in this case over their popularity). Risk aversion further reduces average utility in the popular-and-nasty equilibrium compared to the pooling equilibrium where everyone has few friends and does not signal (acts nice).

In general, if one of the benefits of signalling is a reduction in the cost of signalling, then the amount of signalling and inequality increases. My paper “Dynamic noisy signaling” (2018) studies this in the context of education signalling in Section V.B “Human capital accumulation”.

Identifying useful work in large organisations by revealed preference

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Some members of large organisations seemingly do work, but actually contribute negatively by wasting other people’s time. For example, by sending mass emails, adding regulations, changing things for the sake of changing them (and to pad their CV with „completed projects”) or blocking change with endless committees, consultations and discussions with stakeholders. Even if there is a small benefit from this pretend-work, it is outweighed by the cost to the organisation from the wasted hours of other members. It is difficult to distinguish such negative-value-added activity from positive contributions (being proactive and entrepreneurial, leading by example). Opinions differ on what initiatives are good or bad and how much communication or discussion is enough.
Asking others to rate the work of a person would be informative if the feedback was honest, but usually people do not want to officially criticise colleagues and are not motivated to respond thoughtfully to surveys. Selection bias is also a problem, as online ratings show – the people motivated enough to rate a product, service or person are more likely to have extreme opinions.
Modern technology offers a way to study the revealed preferences of all members of the organisation without taking any of their time. If most email recipients block a given sender, move her or his emails to junk or spend very little time reading (keeping the email open), then this suggests the emails are not particularly useful. Aggregate email activity can be tracked without violating privacy if no human sees information about any particular individual’s email filtering or junking, only about the total number of people ignoring a given sender.
Making meetings, consultations and discussions optional and providing an excuse not to attend (e.g. two voluntary meetings at the same time) similarly allows members of the organisation „vote with their feet” about which meeting they find (more) useful. This provides an honest signal, unlike politeness-constrained and time-consuming feedback.
Anonymity of surveys helps mitigate the reluctance to officially criticise colleagues, but people may not believe that anonymity will be preserved. Even with trust in the feedback mechanism, the time cost of responding may preclude serious and thoughtful answers.

Disagreement over policy due to preferences vs beliefs

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Disagreement about the best policy is due to different preferences or beliefs, or both. Believing that different preferences cause the opinion differences discourages debate (no point arguing over taste after all), leads to polarisation and partisanship. For example, right-wingers may believe that left-wingers prefer to disincentivise entrepreneurs with high taxes, and left-wingers may believe that right-wingers prefer to harm the poor by reducing government transfers. To put it starkly: the other side just prefers evil policy by nature.

By contrast, believing that disagreement over what should be done is caused by differing beliefs assumes that the other side is good-hearted, but mistaken. For example, left-wingers may believe that right-wingers mistakenly believe that transfers to the poor disincentivise them from working or finance their addictions. Right-wingers may believe that left-wingers mistakenly believe that entrepreneurs are not discouraged by higher taxes – being entrepreneurial by nature, they start companies because it is interesting, not out of greed. Mistaken opponents’ opinions can be corrected using data and logic, patience and understanding.

Even if policy disagreement is interpreted as coming from divergent preferences, some such differences are interpreted as less evil than others. For example, impatience is perceived as better than selfishness. Many policies trade off non-simultaneous benefits and costs: invest in infrastructure now to use it after some years, mitigate climate change now to reduce harm to future generations. Paying a current cost for a future benefit may be optimal for patient people, but not for impatient, causing a policy disagreement. The same opinion difference may be due to altruistic people wanting to invest to help others (future users of the infrastructure or the environment), but selfish ones preferring to keep the money now. Believing the same disagreement to be due to selfishness polarises people more than perceiving unequal patience as the cause.

Social welfare functions derived from revealed preference

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The social welfare functions used in policy evaluation typically put more weight on poorer people, justifying redistribution from the rich to the poor. The reasoning is that the marginal benefit of a unit of money is greater for the poor than the rich. However, people with a greater marginal value of money are more motivated to earn and save, other things equal, so more likely to become rich. In this case, the rich have on average a higher marginal benefit of money than the poor, or a lower marginal cost of accumulating it. If the justification for redistribution is an interpersonal utility comparison, then revealed preference suggests a greater Pareto weight for richer people, thus redistribution in the opposite direction to the usual.

If the marginal utility of money decreases in wealth or income, then people earn until the marginal benefit equals the marginal cost, so the comparison between the rich and the poor depends on their marginal cost of earning, evaluated at their current wealth and income. The cost and benefit of earning may both be higher or lower for richer people. In a one-shot model, whoever has a greater benefit should receive redistributive transfers to maximise a utilitarian welfare criterion. Dynamic indirect effects sometimes reverse this conclusion, because incentives for future work are reduced by taxation.

Those with a high marginal utility of money are more motivated to convince the public that their marginal utility is high and that they should receive a subsidy. The marginal utility is the difference between a benefit and a cost, which determine whether the poor or the rich have a greater incentive to lobby for redistributive transfers. The marginal cost of an hour of persuasion equals the person’s hourly wage, so depends on whether her income is derived mostly from capital or from labour. For example, both rentiers and low-wage workers have a low opportunity cost of time, so optimally lobby more than high-wage workers. If lobbying influences policy (which is empirically plausible), then the tax system resulting from the persuasion competition burdens the high-wage workers the heaviest and leaves loopholes and low rates for capital income and low wages. This seems to be the case in most countries.

A tax system based on lobbying is inefficient, because it is not the people with the greatest benefit that receive the subsidies (which equal the value of government services minus the taxes), but those with the largest difference between the benefit and the lobbying cost. However, the resulting taxation is constrained efficient under the restriction that the social planner cannot condition policy on people’s marginal costs of lobbying.

On military bravery

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All countries and armed groups emphasize the bravery of their soldiers for propaganda purposes. Such claims are made regardless of whether there is any actual valour. Going to a dangerous situation or even certain death is not necessarily courageous, in particular if there is no knowledge of the danger or no choice. Are sheep going into a slaughterhouse brave? They are calmly walking to certain death, after all. But usually this is not ascribed to courage, but to ignorance. Analogously, soldiers used in early tests of the physiological effects of radiation exposure who were marched through an area of a recent nuclear explosion are not considered brave. They did not know the cancer risk.

If there is no choice, which usually means there are only perilous choices, then putting oneself in danger is not usually accounted brave. Jumping out of a burning building offers a higher probability of survival, so people do it despite the substantial risk of falling to death. When a sufferer of a painful terminal disease chooses euthanasia, this early death is commonly not considered brave. Some cultures even believe suicide to be a sign of cowardice. If a military has a well organized system for catching deserters and administering the death penalty to them (and their family in some regimes), then a soldier charging enemy machineguns is merely maximizing his survival probability. The enemy might miss, the firing squad rarely does.

The greater the probability of victory for one’s own side, the less attractive desertion becomes, because being caught is more likely. This explains the propaganda emphasis on own victories and the punishment of “defeatist talk” in wartime. The greater the military advantage of a party in an armed conflict, the less bravery its soldiers need.

Genuine bravery exists, but it is rare. Evolution favours cowardly bullies who attack the weaker (prey) and run from the stronger (predators). People who face no compulsion to fight in a war and know the dangers, yet still join, are brave. Freedom fighters (insurgents from the other side’s viewpoint) against a dictator qualify. With the caveat that only joining the fight initially requires bravery – after that, losing would mean being tortured to death by the dictator, so continuing the war is the safer option. Similarly, volunteering for the military requires some bravery (the more the greater the likelihood of being sent into danger), but once military law applies, desertion is usually more dangerous than the duty.

Military courage is proved for those who start the war as a weaker side against a stronger, if a continuing peace is not a slow death. Peasant revolts were often driven by hunger, meaning the participants may have perceived the probability of death from starvation as higher than the probability of being killed by the aristocrats.

People who have never faced an informed choice between a safe and a dangerous option may be “latently brave”, in the sense that given such a choice, they may exhibit courage. They are not proved brave, however, until they have made the choice. There are likely to be some latently brave people in the world’s militaries and armed groups. Probably a greater percentage than among the general population.

There are some proven brave folks even in the militaries of powerful countries, but the proof requires knowingly choosing a dangerous option when there is no future punishment for cowardice. For example, when nobody would know of the choice.

A topical question is whether suicide terrorists and other fighting religious fanatics are brave. Their behaviour may be driven by the fear of punishment either in the afterlife or by their fellow fanatics. It may also be due to ignorance – believing in an afterlife is like believing that one cannot really die and thus the danger is not real. In both cases, no courage is required for choosing death.

The belief in the impossibility of dying may even be literal – W.E.B. Griffin had a story of a witch doctor convincing the fighters of his tribe that his magic had made them immune to bullets. Great was the fighters’ surprise later… Their charge with spears against guns was not due to bravery, however.

Research articles may have negative value

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Falsified, plagiarized or plain junk research is not considered here. The effort of the author and the cost to the funders are considered sunk and similarly ignored.

After a research article is published, it may still have negative value for humanity. How is this possible if the cost of creating it is considered zero and the results are not junk? Doesn’t every discovery, however small, contribute a little to the corpus of knowledge? It does, but the cost it imposes on other researchers may outweigh this. Every publication increases the number of articles that researchers of related topics have to look at, however briefly, to write their literature review and check that their idea is not already taken. It may take a few seconds to read the title and decide that the article is irrelevant to one’s work, but this small cost is paid by many. If the publication makes a small enough contribution to knowledge, then the total cost to other academics outweighs the benefit from this contribution. The researchers whose time the article wasted could have done something useful with that time.