Tag Archives: economic theory

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

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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

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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.

Putting your money where your mouth is in policy debates

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Climate change deniers should put their money where their mouth is by buying property in low-lying coastal areas or investing in drought-prone farmland. Symmetrically, those who believe the Earth is warming as a result of pollution should short sell climate-vulnerable assets. Then everyone eventually receives the financial consequences of their decisions and claimed beliefs. The sincere would be happy to bet on their beliefs, anticipating positive profit. Of course, the beliefs have to be somewhat dogmatic or the individuals in question risk-loving, otherwise the no-agreeing-to-disagree theorem would preclude speculative trade (opposite bets on a common event).

Governments tend to compensate people for widespread damage from natural disasters, because distributing aid is politically popular and there is strong lobbying for this free insurance. This insulates climate change deniers against the downside risk of buying flood- or wildfire-prone property. To prevent the cost of the damages from being passed to the taxpayers, the deniers should be required to buy insurance against disaster risk, or to sign contracts with (representatives of) the rest of society agreeing to transfer to others the amount of any government compensation they receive after flood, drought or wildfire. Similarly, those who short sell assets that lose value under a warming climate (or buy property that appreciates, like Arctic ports, under-ice mining and drilling rights) should not be compensated for the lost profit if the warming does not take place.

In general, forcing people to put their money where their mouth is would avoid wasting time on long useless debates (e.g. do high taxes reduce economic growth, does a high minimum wage raise unemployment, do tough punishments deter crime). Approximately rational people would doubt the sincerity of anyone who is not willing to bet on her or his beliefs, so one’s credibility would be tied to one’s skin in the game: a stake in the claim signals sincerity. Currently, it costs pundits almost nothing to make various claims in the media – past wrong statements are quickly forgotten, not impacting the reputation for accuracy much.

The bets on beliefs need to be legally enforceable, so have to be made on objectively measurable events, such as the value of a publicly traded asset. By contrast, it is difficult to verify whether government funding for the arts benefits culture, or whether free public education is good for civil society, therefore bets on such claims would lead to legal battles. The lack of enforceability would reduce the penalty for making false statements, thus would not deter lying or shorten debates much.

An additional benefit from betting on (claimed) beliefs is to provide insurance to those harmed by the actions driven by these beliefs. For example, climate change deniers claim small harm from air pollution. Their purchases of property that will be damaged by a warming world allows climate change believers to short sell such assets. If the Earth then warms, then the deniers lose money and the believers gain at their expense. This at least partially compensates the believers for the damage caused by the actions of the deniers.

Volunteer work is less efficiently allocated than paid work

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In my experience, the labour of volunteers and low-wage workers is frequently wasted, just like other free or cheap resources. Unlike for expensive market work, there are no price signals to guide people to the most important tasks first. If activities are not prioritised based on how productive these are, then randomly allocating labour is likely to select work with low usefulness.

Within an organisation, competent managers of volunteers may direct them to the most productive work, but even with the best leaders managing some volunteering opportunities, it remains unclear which organisations do the most good and thus should get priority labour. There is a limited amount of work hours available, just like other resources. Even the best volunteers cannot do everything at once, so to maximise social welfare, the most helpful tasks should be done first. In market work, the employer at which a worker is most productive is generally willing to pay the most for this person’s services. Then if people follow the money, their labour gets allocated to the highest-value tasks.

Of course, markets are not perfect and the importance of some work is not accurately measured in money, but for reasonably rational agents, a noisy signal is better than no signal. Prices carry information and help efficient allocation of resources. One way to better allocate volunteer labour is to establish a pseudo-money for unpaid work: each nonprofit organisation gets a certain amount of credits initially and can spend these to “hire” voluntary workers. Credits used for one person cannot be used for another, so the organisation willing to give away the most for a given individual’s services is probably the one receiving the greatest benefit from that person. Volunteers can then use the credits offered to judge where they would be the most productive (could do the greatest amount of good).

Keeping an open mind and intellectual honesty

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„Keep an open mind” is often used as an argument against science, or to justify ignoring evidence more broadly. Let’s distinguish two cases of keeping an open mind: before vs after the evidence comes in. It is good to keep an open mind before data is obtained – no hypothesis is ruled out. In reality, all possibilities have positive probability, no matter how great the amount and quality of information, so one should not dogmatically rule out anything even given the best evidence. However, for practical purposes a small enough probability is the same as zero. Decisions have to be made constantly (choosing not to decide is also a decision), so after enough scientific information is available, it is optimal to make up one’s mind, instead of keeping it open.
Intellectually honest people who want to keep an open mind after obtaining evidence would commit to it from the start: publicly say that no matter what the data shows in the future, they will ignore it and keep an open mind. Similarly, the intellectually honest who plan to make up their mind would also commit, in this case to a policy along the lines of „if the evidence says A, then do this, but if the evidence says B, then that”. The latter policy resembles (parts of) the scientific method.
The anti-science or just intellectually dishonest way of “keeping an open mind” is to do this if and only if the evidence disagrees with one’s prior views. In other words, favourable data is accepted, but unfavourable ignored, justifying the ignoring with the open mind excuse. In debates, the side that runs out of arguments and is about to lose is usually the one who recommends an open mind, and only at that late stage of the debate and conditional on own weak position. Similarly, “agreeing to disagree” is mostly recommended intellectually dishonestly by the losing side of an argument, to attempt to leave the outcome uncertain. This is an almost logically contradictory use of “agreeing to disagree”, because it is mathematically proven that rational agents putting positive probability on the same events cannot agree to disagree – if their posterior beliefs are common knowledge, then these must coincide.

Political parties claim inconsistent patience

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If the stated preferences of politicians are taken at face value, then they have inconsistent patience across different policy areas. Left-wingers want to invest in education, infrastructure and prevention of climate change. These investments have a present cost and a long-delayed benefit, which suggests patient preferences (high discount factor, low discount rate). On the other hand, the left wants to increase borrowing, redistributive transfers and government spending in general, which have a current benefit (including electoral, but focus on societal for now) and a future cost. Preferring a current benefit and a future cost implies impatience.

For right-wing parties, these preferences are switched (impatient on education, climate, but patient on redistribution), so their inconsistency is the mirror image of the one described above. In summary, both sides of the political divide claim policy preferences that simultaneously imply patience and impatience, which suggests motives other than societal benefit. One way to reason about these other motives is described in https://sanderheinsalu.com/ajaveeb/?p=1015

Economic and political cycles interlinked

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Suppose the government’s policy determines the state of the economy with a lag that equals one term of the government. Also assume that voters re-elect the incumbent in a good economy, but choose the challenger in a bad economy. This voting pattern is empirically realistic and may be caused by voters not understanding the lag between the policy and the economy. Suppose there are two political parties: the good and the bad. The policy the good party enacts when in power puts the economy in a good state during the next term of government. The bad party’s policy creates a recession in the next term.

If the economy starts out doing well and the good party is initially in power, then the good party remains in power forever, because during each of its terms in government, it makes the economy do well the next term, so voters re-elect it the next term.

If the economy starts out in a recession with the good party in power, then the second government is the bad party. The economy does well during the second government’s term due to the policy of the good party in the first term. Then voters re-elect the bad party, but the economy does badly in the third term due to the bad party’s previous policy. The fourth government is then again the good party, with the economy in a recession. This situation is the same as during the first government, so cycles occur. The length of a cycle is three terms. In the first term, the good party is in power, with the other two terms governed by the bad party. In the first and third term, the economy is in recession, but in the second term, booming.

If the initial government is the bad party, with the economy in recession, then the three-term cycle again occurs, starting from the third term described above. Specifically, voters choose the good party next, but the economy does badly again because of the bad party’s current policy. Then voters change back to the bad party, but the economy booms due to the policy the good party enacted when it was in power. Re-election of the bad is followed by a recession, which is the same state of affairs as initially.

If the government starts out bad and the economy does well, then again the three-term cycle repeats: the next government is bad, with the economy in recession. After that, the good party rules, but the economy still does badly. Then again the bad party comes to power and benefits from the economic growth caused by the good party’s previous policy.

Overall, the bad party is in power two-thirds of the time and the economy in recession also two-thirds of the time. Recessions overlap with the bad party in only one-third of government terms.

Of course, reality is more complicated than the simple model described above – there are random shocks to the economy, policy lags are not exactly equal to one term of the government, the length of time a party stays in power is random, one party’s policy may be better in one situation but worse in another.

Golf as a cartel monitoring device for skilled services

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Many explanations have been advanced for golf and similar costly, seemingly boring, low-effort group activities. One reason could be signalling one’s wealth and leisure by an expensive and time-consuming sport, another may be networking during a low-effort group activity that does not interfere with talking.

An additional explanation is monitoring others’ time use. A cartel agrees to restrict the quantity that its members provide, in order to raise price. In skilled services (doctors, lawyers, engineers, notaries, consultants) the quantity sold is work hours. Each member of a cartel has an incentive to secretly increase supply to obtain more profit. Monitoring is thus needed to sustain the cartel. One way to check that competitors are not selling more work hours is to observe their time use by being together. To reduce boredom, the time spent in mutual monitoring should be filled somehow, and the activity cannot be too strenuous, otherwise it could not be sustained for long enough to meaningfully decrease hours worked. Playing golf fulfills these requirements.

A prediction from this explanation for golf is that participation in time-consuming group activities would be greater in industries selling time-intensive products and services. By contrast, if supply is relatively insensitive to hours worked, for example in capital-intensive industries or standard software, then monitoring competitors’ time use is ineffective in restricting their output and sustaining a cartel. Other ways of checking quantity must then be found, such as price-matching guarantees, which incentivise customers to report a reduced price of a competitor.

Star job candidates benefit from appearing to be worse

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Employers have a cost of making a job offer: filling out forms, getting approval, not being able to make other offers simultaneously in case too many job candidates accept, etc. A company who believes that it is not the top choice of candidates would want to avoid making an offer to a star applicant (one who is likely to receive better alternative offers from top employers, thus turn down the lower-ranked company’s offer).

If the star job-seeker is uncertain about the offers she or he will get, or wants a bargaining chip to use with the most preferred company, then (s)he prefers to obtain the lower-ranked employer’s offer, even when planning to reject it. A way to entice the company into offering a job is to pretend to be more attainable (have a worse outside option) by faking lower talent and potential when interviewing with lower-ranked employers. For this pretence to be (partly) credible, it must have a cost for the job-seeker, otherwise all the best candidates would pretend to be worse and increase their chance of obtaining offers from their backup employers. Then the next-best candidates would have to fake being less good to receive jobs, etc. This race to the bottom would only end once all candidates look like the worst possible, which does not seem realistic.

One potential cost is that faking lower talent has a random outcome, which may be so bad that the employer does not want to offer a job at all. This would temper the incentive to appear worse. Another cost is information leakage – if bad performance at a less desirable interview becomes known to higher-ranked employers, then the candidate may forfeit her or his most preferred interviews and jobs. It could also be that the top job-seekers cannot hide their quality, for example because their genius shines out despite their best effort, or employers base offers solely on recommendation letters, which the candidate cannot see or affect around the time of applying.