Tag Archives: economic theory

Paying pharmaceutical firms for capacity is problematic

Castillo et al. 2021 (doi:10.1126/science.abg0889) make many valid points, e.g., vaccine production should be greatly expanded using taxpayer money because the quicker recovery from the pandemic more than pays for the expansion. Castillo et al. also suggest paying pharmaceutical manufacturers for the capacity they install instead of the quantity they produce. The reasoning of the authors is that producers are delaying installing capacity and the delivery of their promised vaccine quantities to save costs and to supply higher-paying buyers first, because the penalties for delaying are small. Producers refuse to sign contracts with larger penalties.

What the authors do not mention is that the same problems occur when paying for capacity. In addition, the capacity needs to be monitored, which is more difficult than checking the delivered quantity. Before large-scale production, how to detect the „Potemkin capacity” of installing cheap production lines unsuitable for large quantities? The manufacturer may later simply claim technical glitches when the production line does not work. Effective penalties are needed, which in turn requires motivating the producer to sign a contract containing these, just like for a quantity contract.

Paying in advance for capacity before the vaccine is proven to work insures firms against the risk of failure, as Castillo et al. say. The problem is that such advance payment also attracts swindlers who promise a miracle cure and then run with the money – there is adverse selection in who enters the government’s capacity contract scheme. Thus capacity contracts should be restricted to firms with a good established reputation. However, vaccines from innovative entrants may also be needed, which suggests continuing to use quantity contracts at least for some firms. If the law requires treating firms equally, then they should all be offered a similar contract.

Dilution effect explained by signalling

Signalling confidence in one’s arguments explains the dilution effect in marketing and persuasion. The dilution effect is that the audience averages the strength of a persuader’s arguments instead of adding the strengths. More arguments in favour of a position should intuitively increase the confidence in the correctness of this position, but empirically, adding weak arguments reduces people’s belief, which is why drug advertisements on US late-night TV list mild side effects in addition to serious ones. The target audience of these ads worries less about side effects when the ad mentions more slight problems with the drug, although additional side effects, whether weak or strong, should make the drug worse.

A persuader who believes her first argument to be strong enough to convince everyone does not waste valuable time to add other arguments. Listeners evaluate arguments partly by the confidence they believe the speaker has in these claims. This is rational Bayesian updating because a speaker’s conviction in the correctness of what she says is positively correlated with the actual validity of the claims.

A countervailing effect is that a speaker with many arguments has spent significant time studying the issue, so knows more precisely what the correct action is. If the listeners believe the bias of the persuader to be small or against the action that the arguments favour, then the audience should rationally believe a better-informed speaker more.

An effect in the same direction as dilution is that a speaker with many arguments in favour of a choice strongly prefers the listeners to choose it, i.e. is more biased. Then the listeners should respond less to the persuader’s effort. In the limit when the speaker’s only goal is always for the audience to comply, at any time cost of persuasion, then the listeners should ignore the speaker because a constant signal carries no information.


Start with the standard model of signalling by information provision and then add countersignalling.

The listeners choose either to do what the persuader wants or not. The persuader receives a benefit B if the listeners comply, otherwise receives zero.

The persuader always presents her first argument, otherwise reveals that she has no arguments, which ends the game with the listeners not doing what the persuader wants. The persuader chooses whether to spend time at cost c>0, c<B to present her second argument, which may be strong or weak. The persuader knows the strength of the second argument but the listeners only have the common prior belief that the probability of a strong second argument is p0. If the second argument is strong, then the persuader is confident, otherwise not.

If the persuader does not present the second argument, then the listeners receive an exogenous private signal in {1,0} about the persuader’s confidence, e.g. via her subconscious body language. The probabilities of the signals are Pr(1|confident) =Pr(0|not) =q >1/2. If the persuader presents the second argument, then the listeners learn the confidence with certainty and can ignore any signals about it. Denote by p1 the updated probability that the audience puts on the second argument being strong.

If the speaker presents a strong second argument, then p1=1, if the speaker presents a weak argument, then p1=0, if the speaker presents no second argument, then after signal 1, the audience updates their belief to p1(1) =p0*q/(p0*q +(1-p0)*(1-q)) >p0 and after signal 0, to p1(0) =p0*(1-q)/(p0*(1-q) +(1-p0)*q) <p0.

The listeners prefer to comply (take action a=1) when the second argument of the persuader is strong, otherwise prefer not to do what the persuader wants (action a=0). At the prior belief p0, the listeners prefer not to comply. Therefore a persuader with a strong second argument chooses max{B*1-c, q*B*1 +(1-q)*B*0} and presents the argument iff (1-q)*B >c. A persuader with a weak argument chooses max{B*0-c, (1-q)*B*1 +q*B*0}, always not to present the argument. If a confident persuader chooses not to present the argument, then the listeners use the exogenous signal, otherwise use the choice of presentation to infer the type of the persuader.

One extension is that presenting the argument still leaves some doubt about its strength.

Another extension has many argument strength levels, so each type of persuader sometimes presents the second argument, sometimes not.

In this standard model, if the second argument is presented, then always by the confident type. As is intuitive, the second argument increases the belief of the listeners that the persuader is right. Adding countersignalling partly reverses the intuition – a very confident type of the persuader knows that the first argument already reveals her great confidence, so the listeners do what the very confident persuader wants. The very confident type never presents the second argument, so if the confident type chooses to present it, then the extra argument reduces the belief of the audience in the correctness of the persuader. However, compared to the least confident type who also never presents the second argument, the confident type’s second argument increases the belief of the listeners.

Investing time to gain lifetime

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

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.

Ebay should allow conditional bids

Ebay should allow buyers to bid for a single item across multiple auctions: make a bid for one item, then if outbid, automatically make the same bid on the next identical (as defined by the buyer) item and so on. This increases efficiency by joining multiple auctions for identical items into one market with many sellers and buyers. It also reduces selling times, because a buyer who just wants one unit does not have to wait until being outbid before bidding for the next identical item. Buyers generally are not continuously watching the auction, so there is a delay between being outbid and manually making the next bid. Buyers are willing to pay to reduce the delay, as evidenced by purchases at “buy it now” prices greater than the highest bids in the auctions.

More generally, bids conditional on being outbid would help merge auctions into markets, gaining efficiency and speed. For example, a buyer has different values for used copies of the same item in different condition and wants just one copy of the item. Conditional bids allow the buyer to enter a sequence of different-sized bids, one for each copy, with each bid in the sequence conditional on the preceding bids losing.

Linking the bids is not computationally difficult because Ebay already sends an automatic email to a buyer who has been outbid. Instead of an email, the event of being outbid can be used to trigger entering a bid on the next copy of the item.

Faster selling times benefit everyone: sellers sell faster, buyers do not have to waste time checking whether they have been outbid and then making the next bid, Ebay can charge higher fees to appropriate part of the increased surplus from greater efficiency. Ebay can also use the data on which items buyers consider similar enough to classify products and remove duplicate ads.

A browser extension or app can provide the same functionality: an email with title containing “You have been outbid” triggers code that logs in the user (with the credentials saved into a password manager or the browser) and types in a bid on the next copy of the item.

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.

Popularity inequality and multiple equilibria

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”.

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.

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.