Tag Archives: incentives

On the optimality of self-quarantine

Is self-quarantine early in an epidemic optimal, either individually or for society?

Individual incentives are easier to analyse, so let’s start with these. Conditional on catching a disease, other things equal, later is better. The reasons are discounting and the advances in treatment. A delay of many years may increase the severity conditional on infection (old age weakens immunity), but such long time intervals are typically not relevant in an epidemic.

Conditional on falling ill within the next year (during which discounting and advances in treatment are negligible), it is better to catch the disease when few others are infected, so hospitals have spare capacity. This suggests either significantly before or long after the peak of the epidemic. Self-quarantine, if tight enough, may postpone one’s infection past the peak.

Another individually optimal choice is to get infected early (also called vaccination with live unattenuated virus), although not if immunity increases very little or even decreases. The latter means that one infection raises the probability of another with the same disease, like for malaria, HIV and herpes, which hide out in the organism and recur. Cancer displays similar comebacks. For viral respiratory diseases, as far as I know, immunity increases after infection, but not to 100%. The optimality of self-quarantine vs trying to be infected early then depends on the degree of immunity generated, the quality of the quarantine, whether the disease will be eradicated soon after the epidemic, and other details of the situation.

Individual optimality also depends on what the rest of the population is doing. If their self-quarantine is close to perfect, then an individual’s risk of catching the disease is very low, so no reason to suffer the disutility of isolation. If others quarantine themselves moderately, so the disease will be eradicated soon, but currently is quite infectious, then self-isolation is individually optimal. If others do almost nothing, and the disease spreads easily and does not generate much immunity, then an individual will either have to self-quarantine indefinitely or will catch it. Seasonal flu and the common cold (various rhinoviruses and adenoviruses) are reasonable examples. For these, self-quarantine is individually suboptimal.

Social welfare considerations seem to weigh in favour of self-quarantine, because a sick person infects others, which speeds up the epidemic. One exception to the optimality of self-quarantine comes from economies of scale in treatment when prevalence is not so high as to overwhelm the health system. If the epidemic is fading, but the disease increases immunity and is likely to become endemic, with low prevalence, then it may be better from a social standpoint to catch the disease when treatment is widely available, medical personnel have just had plenty of experience with this illness, and not many other people remain susceptible. This is rare.

Herd immunity is another reason why self-quarantine is socially suboptimal for some diseases. The logic is the same as for vaccination. If catching chickenpox as a child is a mild problem and prevents contracting and spreading it at an older age when it is more severe, then sending children to a school with a chickenpox epidemic is a smart idea.

Reducing the duration of quarantine for vulnerable populations is another reason why being infected sooner rather than later may be socially optimal. Suppose a disease is dangerous for some groups, but mild or even undetectable for most of the population, spreads widely and makes people resistant enough that herd immunity leads to eradication. During the epidemic, the vulnerable have to be isolated, which is unpleasant for them. The faster the non-vulnerable people get their herd immunity and eradicate the infection, the shorter the quarantine required for the vulnerable.

For most epidemics, but not all, self-quarantine is probably socially optimal.

Affirmative action, unequal contests and incentives for effort

Firms using affirmative action policies may perform better because of a welcoming work environment, better candidates, peer effects in diverse teams, but also because of stronger incentives that are targeted better. Unequal standards in contests, such as a lower bar for promotion for historically underrepresented groups, may motivate greater effort than equal ones. The reasoning is as follows.

If people expect to have unequal performance, then equal standards may demotivate everyone, because the high performers think the promotion or bonus is almost assured even without further effort, and the low performers believe the prize is unattainable, so no point in trying. In this case, setting a higher bar for the better-performing group can incentivise both groups, like different divisions in sports. The result that equalising a contest motivates greater effort is fairly general in game theory. Contests may even motivate overprovision of effort relative to the socially efficient level.

A similar effort-increasing effect of unequal standards occurs even if the groups have equal performance, provided their preferences differ. For example, if men value winning a contest (for evolutionary or other reasons), then they exert greater effort in a competitive environment where some but not all can get promoted. If women care little about winning and focus on absolute compensation, then promoting all of them does not significantly reduce their work incentives. An employer who does not internalise the full cost of the employees’ effort wants them to overwork, thus in such an environment optimally sets a high bar for the promotion of men, but a low bar for women.

On the other hand, if there is a limited number of promotion slots, then it may be optimal to give all these to men, because this increases total effort in the firm the most, and use other compensation (salary, bonuses, flex-work) to motivate women.

Free food for health and the environment

To motivate choosing vegan or environmentally friendly or healthy food, one option is to provide it for free. If people have eaten their fill, they are less likely to buy extra, whether meat or unhealthy. There are tradeoffs of course – any free resource tends to be overused.

For free food to be environmentally friendly, it should not be wasted and disposable utensils should be avoided. Food waste can be reduced by providing small portions to be eaten on the spot, with unlimited free refills of these small portions. All-you-can-eat restaurants already use this strategy by providing only small plates and bowls. The oversight of the food servers and other eaters and their disapproval of wasting food is a social deterrent.

The use of disposable dishes may be reduced by not providing any, requiring people to bring their own utensils, but some will then bring disposable and some will substitute away from the free food toward buying (unhealthy, delivered) meals in disposable containers. It is an empirical question whether the potential use of disposables outweighs the benefit of switching people to healthy and environmentally friendly eating. A dishwasher next to the food station eases the use of reusable kitchenware. Handheld foods (buns, sandwiches, wraps, whole fruit) do not require dishes.

Free food may lead to overeating and increase obesity. Any free resource tends to be over-used, especially if in limited quantity or available for a limited time. The latter overuse motives are eliminated by making the free food continuously available, but this exacerbates potential overeating. The obesity effect can be reduced by offering only healthy food without the somewhat addictive additives sugar, salt and monosodium glutamate. Foods like celery, iceberg lettuce, whole linseeds that provide fewer calories than it takes to chew and digest them (given inefficient human digestion, as opposed to the calories measured by the burn method) may actually reduce obesity when distributed for free. Again, it is an empirical question whether the potential costs of overeating and obesity neutralise the benefit of substituting towards healthier and environmentally friendlier foods.

Given how cheap basic healthy foods are (rice and other dry grains under a dollar per kilo, cabbage, bananas, lemons, dry peas and lentils two dollars per kilo), the social benefit of providing these for free may outweigh the deadweight loss of taxation to finance their purchase. In this case, the government would actually save money in the long run (over the average life expectancy) by offering free food. Cooking the foods would increase the costs slightly, but not much if it is done continuously in bulk by machines (rice cookers, bread machines). No need to wash the cookers if a new batch goes in within hours and the heat sterilises the machine. Or the machine can wash itself if it is connected to a water supply, a drain and a soap dispenser and either has a mixing blade in it like a blender or the water supply has sufficient pressure to flush out the soap residue.

Prefereeing increases the inequality of research output

Why do top researchers in economics publish almost exclusively in the top 5 journals? Random idea generation and mistakes in the course of its implementation should imply significant variance of the quality of finished research projects even for the best scientists. So top people should have more of all quality levels of papers.

Nepotism is not necessary to explain why those at top universities find it easier to publish in top journals. Researchers at the best departments have frequent access to editors and referees of top journals (their colleagues), so can select ideas that the editors and referees like and further tailor the project to the tastes of these gatekeepers during writing. Researchers without such access to editors and referees choose their projects “blindly” and develop the ideas in directions that only match gatekeeper tastes by chance. This results in much “wasted work” if the goal is to publish well (which may or may not be correlated with the social welfare from the research).

In addition to selecting and tailoring projects, those with access can also better select journals, because they know the preferences of the editorial board. So for any given project, networking with the gatekeepers allows choosing a journal where editors are likely to like this project. This reduces the number of rejections before eventual acceptance, allowing accumulating publications quicker and saving the labour of some rounds of revision of the paper (at journals that reject after a revise-and-resubmit for example).

A similar rich-get-richer positive feedback operates in business, especially for firms that sell to other firms (B2B). Top businesspeople get access to decisionmakers at other organisations, so can learn what the market desires, thus can select and tailor products to the wants of potential customers. Better selection and targeting avoids wasting product development costs. The products may or may not increase social welfare.

Information about other business leaders’ preferences also helps target the marketing of any given product to those predisposed to like the product. Thus successful businesspeople (who have access to influential decisionmakers) have a more popular selection of products with lower development and marketing costs.

On the seller side, firms would not want their competitors to know what the buyers desire, but the buyer side has a clear incentive to inform all sellers, not just those with access. Empirically, few buyers publish on their websites any information about their desired products. One reason may be that info is costly to provide, e.g. requests for product characteristics reveal business secrets about the buyer. However, disclosure costs would also prevent revealing info via networking. Another reason buyers do not to publicly announce their desired products may be that the buyers are also sellers of other products, so trade information for information with their suppliers who are also their customers. The industry or economy as a whole would benefit from more information-sharing (saving the cost of unwanted products), so some trading friction must prevent this mutually beneficial exchange.

One friction is an agency conflict between managers and shareholders. If managers are evaluated based on relative performance, then the managers of some firms may collude to only share useful information with each other, not with those outside their circle. The firms managed by the circle would benefit from wider sharing of their product needs, because outside companies would enter the competition to supply them, reducing their costs. However, those outside firms would get extra profit, making their managers look good, thus lowering the relative standing of the managers in the circle.

Directing help-seekers to resources is playing hot potato

In several mental health first aid guidelines, one of the steps is to direct the help-seeker to resources (suggest asking friends, family, professionals for help, reading materials on how to cope with the mental condition). This can provide an excuse to play hot potato: send the help-seeker to someone else instead of providing help. For example, the therapist or counsellor suggests seeing a doctor and obtaining a prescription, and the doctor recommends meeting a therapist instead.

The hot potato game is neither limited to sufferers of mental health issues, nor to doctors and counsellors. It is very common in universities: many people „raise awareness”, „coordinate” the work of others or „mentor” them, „manage change”, „are on the team or committee”, „create an action plan” (or strategy, policy or procedure), „start a conversation” about an issue or „call attention” to it, instead of actually doing useful work. One example is extolling the virtues of recycling, as opposed to physically moving recyclable items from the garbage bin to the recycling bin, and non-recyclable waste in the other direction. Another example is calling attention to mental health, instead of volunteering to visit the mentally ill at home and help them with tasks. Talking about supporting and mentoring early career academics, as opposed to donating part of one’s salary to create a new postdoc position, thereby putting one’s money where one’s mouth is.

All the seeming-work activities mentioned above allow avoiding actual work and padding one’s CV. Claiming to manage and coordinate other people additionally helps with empire-building – hiring more subordinates to whom one’s own work can be outsourced.

To motivate people to do useful work, as opposed to coordinating or managing, the desirable outcomes of the work should be clearly defined, measured, and incentivised. Mere discussions, committee meetings and action plans should attract no rewards, rather the reverse, because these waste other people’s time. More generally, using more inputs for the same output should be penalised, for example for academics, receiving more grant money should count negatively for promotions, given the same patent and publication output.

One way to measure the usefulness of someone’s activity is to use the revealed preference of colleagues (https://sanderheinsalu.com/ajaveeb/?p=1093). Some management and coordination is beneficial, but universities tend to overdo it, so it has negative value added.

Gambling deterrence mechanism

Compulsive gambling is driven by the hope of winning a large amount, so one way to deter gambling addiction is to forbid paying out winnings to people registered as having this problem. In a one-shot interaction, casinos and lottery organisers clearly have an incentive to keep both the stakes and the winnings, but problem gambling is repeated. Sufficiently patient casinos are motivated to establish a reputation for paying out winnings, if the punishment is small or unlikely enough, because such reputation attracts other gamblers, which increases the long-run expected profit of the casino. The gamblers are not interested in reporting the casino for illegally paying out, because they benefit from the payout, and the closure of the establishment would prevent them from satisfying their craving.

However, the gamblers’ desire for big winnings, even with very low probability, can be used to motivate them to report – the law can offer a large sum to anyone who proves that a casino made an illegal payout. The reward can be financed from an even larger fine levied on the law-breaking casino. The reward should of course be in addition to any winnings of the whistleblower if the latter is a patron of the casino, because a gambler should not lose money by reporting. Gamblers are impatient, unlike casinos, so the repeated interaction with an establishment does not outweigh an immediate payout, even if collecting the payout leads to less opportunity to gamble in the future.

Overbidding incentives in crowdfunding

Crowdfunding campaigns on Funderbeam and other platforms fix a price for the shares or loan notes and invite investors to submit the quantity they want to buy. If demand exceeds supply, then the financial instruments are rationed pro rata, or investors requesting quantities below a threshold get what they asked and others receive the threshold amount plus a pro rata share in the remaining quantity after the threshold amounts are allocated. Rationing creates the incentive to oversubscribe: an investor who wants n shares and expects being rationed to fraction x of her demanded quantity will rationally put in the order for n/x>n shares to counteract the rationing. For a mechanism not to invite such manipulation, the amount allocated to a given bidder in the event of oversubscription should not depend on that bidder’s bid quantity. For example, everyone gets the minimum of their demanded amount and a threshold quantity, where the threshold is determined so as to equate demand and supply. If there are s shares and all m investors demand more than s/m, then each gets s/m.

If some investors demand less than s/m, then the allocation process is recursive as follows. The i1 investors who asked for less than s/m each get what they requested. Their total t1 is subtracted from s to get s1 and the number of remaining investors reduced to m1=m-i1. Then the i2 investors asking for less than s1/m1 get what they demanded (t2 in total), and the new remaining amount s2=s1-t2 and number of investors m2=m1-i2 determined. Repeat until the number of investors asking for less than sj/mj is zero. Divide the remaining amount equally between the remaining investors.

An alternative is to let the market work by allowing the price to adjust, instead of fixing it in advance. Everyone should then submit demand curves: for each price, how many shares are they willing to buy. This may be too complicated for the unsophisticated crowdfunding investors.

However, complexity is probably not the main reason for the inefficient allocation mechanism that invites overbidding. The crowdfunding platform wants to appear popular among investors to attract companies to raise funds on it, so wants to increase the number of oversubscribed campaigns. Rationing is a way to achieve such manipulation if the fundraisers ignore the investors’ incentives to overbid and do not compare the platform to competing ones with similar allocation mechanisms. If fundraisers are irrational in this way, then they do not choose competing platforms without overbidding incentives, because funding campaigns there seem to attract less investor interest. Competing platforms with more efficient allocation mechanisms then go out of business, which eliminates comparison possibilities.

Privacy reduces cooperation, may be countered by free speech

Cooperation relies on reputation. For example, fraud in online markets is deterred by the threat of bad reviews, which reduce future trading with the defector. Data protection, specifically the “right to be forgotten” allows those with a bad reputation to erase their records from the market provider’s database and create new accounts with a clean slate. Bayesian participants of the market then rationally attach a bad reputation to any new account (“guilty until proven innocent”). If new entrants are penalised, then entry and competition decrease.

One way to counter this abusing of data protection laws to escape the consequences of one’s past misdeeds is to use free speech laws. Allow market participants to comment on or rate others, protecting such comments as a civil liberty. If other traders can identify a bad actor, for example using his or her government-issued ID, then any future account by the same individual can be penalised by attaching the previous bad comments from the start.

Of course, comments could be abused to destroy competitors’ reputations, so leaving a bad comment should have a cost. For example, the comments are numerical ratings and the average rating given by a person is subtracted from all ratings given by that person. Dividing by the standard deviation is helpful for making the ratings of those with extreme opinions comparable to the scores given by moderates. Normalising by the mean and standard deviation makes ratings relative, so pulling down someone’s reputation pushes up those of others.

However, if a single entity can control multiple accounts (create fake profiles or use company accounts), then he or she can exchange positive ratings between his or her own profiles and rate others badly. Without being able to distinguish new accounts from fake profiles, any rating system has to either penalise entrants or allow sock-puppet accounts to operate unchecked. Again, official ID requirements may deter multiple account creation, but privacy laws impede this deterrence. There is always the following trilemma: either some form of un-erasable web activity history is kept, or entrants are punished, or fake accounts go unpunished.

Committing to an experimental design without revealing it

Pre-registering an experiment in a public registry of clinical trials keeps the experimenters honest (avoids ex post modifications of hypotheses to fit the data and “cherry-picking” the data by removing “outliers”), but unfortunately reveals information to competing research groups. This is an especially relevant concern in commercial R&D.

The same verifiability of honesty could be achieved without revealing scientific details by initially publicly distributing an encrypted description of the experiment, and after finishing the research, publishing the encryption key. Ex post, everyone can check that the specified experimental design was followed and all variables reported (no p-hacking). Ex ante, competitors do not know the trial details, so cannot copy it or infer the research direction.

Avoiding the Bulow and Rogoff 1988 result on the impossibility of borrowing

Bulow and Rogoff 1988 NBER working paper 2623 proves that countries cannot borrow, due to their inability to credibly commit to repay, if after default they can still buy insurance. The punishment of defaulting on debt is being excluded from future borrowing. This punishment is not severe enough to motivate a country to repay, by the following argument. A country has two reasons to borrow: it is less patient than the lenders (values current consumption or investment opportunities relatively more) and it is risk-averse (either because the utility of consumption is concave, or because good investment opportunities appear randomly). Debt can be used to smooth consumption or take advantage of temporary opportunities for high-return investment: borrow when consumption would otherwise be low, pay back when relatively wealthy.

After the impatient country has run up its debt to the maximum level the creditors are willing to tolerate, the impatience motive to borrow disappears, because the lenders do not allow more consumption to be transferred from the future to the present. Only the insurance motive to borrow remains. The punishment for default is the inability to insure via debt, because in a low-consumption or valuable-investment state of affairs, no more can be borrowed. Bulow and Rogoff assume that the country can still save or buy insurance by paying in advance, so “one-sided” risk-sharing (pay back when relatively wealthy, or when investment opportunities are unavailable) is possible. This seemingly one-sided risk-sharing becomes standard two-sided risk-sharing upon default, because the country can essentially “borrow” from itself the amount that it would have spent repaying debt. This amount can be used to consume or invest in the state of the world where these activities are attractive, or to buy insurance if consumption and investment are currently unattractive. Thus full risk-sharing is achieved.

More generally, if the country can avoid the punishment that creditors impose upon default (evade trade sanctions by smuggling, use alternate lenders if current creditors exclude it), then the country has no incentive to repay, in which case lenders have no incentive to lend.

The creditors know that once the country has run up debt to the maximum level they allow, it will default. Thus rational lenders set the maximum debt to zero. In other words, borrowing is impossible.

A way around the no-borrowing theorem of Bulow and Rogoff is to change one or more assumptions. In an infinite horizon game, Hellwig and Lorenzoni allow the country to run a Ponzi scheme on the creditors, thus effectively “borrow from time period infinity”, which permits a positive level of debt. Sometimes even an infinite level of debt.

Another assumption that could realistically be removed is that the country can buy insurance after defaulting. Restricting insurance need not be due to an explicit legal ban. The insurers are paid in advance, thus do not exclude the country out of fear of default. Instead, the country’s debt contract could allow creditors to seize the country’s financial assets abroad, specifically in creditor countries, and these assets could be defined to include insurance premiums already paid, or the payments from insurers to the country. The creditors have no effective recourse against the sovereign debtor, but they may be able to enforce claims against insurance firms outside the defaulting country.

Seizing premiums to or payments from insurers would result in negative profits to insurers or restrict the defaulter to one-sided risk-sharing, without the abovementioned possibility of making it two-sided. Seizing premiums makes insurers unwilling to insure, and seizing payments from insurers removes the country’s incentive to purchase insurance. Either way, the country’s benefit from risk-sharing after default is eliminated. This punishment would motivate loan repayment, in turn motivating lending.