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Unexpected spikes to demand for products during pandemics or natural disasters often create shortages. A salient example is at the beginning of the Covid-19 pandemic, when there was a shortage of masks, toilet paper, and other goods. Consumers suddenly wanted these things immediately at much higher quantities than suppliers were expecting, and production capacity needed time to adjust to demand. When such shortages happen there is often policy debate about whether firms should be allowed to raise prices until the market clears or if they should instead face price caps. The advantage of allowing prices to rise is that it creates profit incentives for firms to increase their productive capacity in order to sell to consumers at the prevailing high prices. In contrast, price caps can diminish the payoff for incumbent firms from increasing their capacity and deter entry from new firms. The two policies also allocate the existing stock of goods differently. High prices allocate scarce goods to people with the highest willingness to pay for them, while under price caps the number of people wishing to buy the good exceeds the available supply, resulting in some sort of rationing. Allocating goods to the people with the highest willingness to pay would be efficient if we believed the marginal dollar has the same value to rich and poor people, but obviously if we think it is unfair or morally inefficient to allocate scarce vital goods predominantly to rich people then we might not be happy with allowing prices to rise without restriction during shortages.

While price restrictions are the predominant policy proposal argued about during shortages, they are not the only option for governments, and alternative mechanisms may do a better job of balancing investment incentives and inequality concerns. Suppose for simplicity that there are a number of firms producing homogeneous masks in a Cournot game, with no possibility of entry by other firms into the market.¹ Suddenly there is a large and unexpected spike in demand for masks, and firms cannot adequately adjust mask supply in the short run because of capacity constraints in their factories. Each firm can produce at most Y masks. In order for firms to increase their capacity for producing masks beyond Y, they must first pay some fixed cost X. 

Consider the following policies mulled by the government:

Policy A: Price cap

Imposing a price cap can result in a more equitable allocation of goods. However, it also runs the risk of making it unprofitable for firms to pay the fixed cost X to increase capacity since the return on investment is low. If firms decide it is not worth it to increase capacity then there will be rationing and underprovision of masks. 

Policy B: Unrestricted pricing

High prices result in larger incentives for firms to pay the fixed cost X in order to increase their capacity and sell masks to marginal consumers, who are willing to pay a lot to receive the good. However, it also results in masks getting allocated initially only towards people with the highest willingness to pay, who may be predominantly high income. As a result there could be equity concerns with this policy.

Policy C: Partial price cap

Consider instead imposing a price cap on the first p fraction of goods sold, while the remaining 1-p fraction of goods can be priced at the firm’s discretion. That is, for each firm, pY goods get sold under a price cap, while (1-p)Y goods do not face a price cap. Reserving p fraction of units to be sold at low prices results in rationing of those goods, resulting in potentially greater allocation towards low income consumers compared to Policy B. The remaining 1-p fraction of goods get allocated towards the leftover consumers who have the highest willingness to pay. Notice that the share of high willingness-to-pay consumers who get masks under this policy is lower than under Policy B because of the partial price cap and rationing. That means the marginal consumer under this policy has an even higher willingness to pay than under unrestricted pricing in Policy B, since only the most valuable 1-p share of consumers who got allocated the good under unrestricted pricing get the good under this scheme. As a result, incentives to pay the fixed cost X are higher under this policy than under Policy B. The additional consumers who would be captured by expanding capacity are more valuable than they would be under unrestricted pricing. 

The above discussion shows that Policy C results in an allocation that is both more equitable and provides better investment incentives than Policy B. The reason this works is because it recognizes that firms price and make investment decisions on the margin. Reallocating a set fraction of goods towards low income consumers makes the marginal residual consumer even more valuable than under unrestricted pricing.

Policy C is clunky to implement in practice, but a similar policy could work nearly as well. In the United States, the government could for example use the Defense Production Act to procure some number of masks from companies at the pre-shortage price level and ration them to citizens for free. It could commit to otherwise not interfering with prices. This would create essentially identical allocations and investment incentives as Policy C.

I do not claim that Policy C or its variants are the optimal policy. In particular, it could discourage firms from investing in capacity even before a shortage occurs because they anticipate partial price caps will prevent them from receiving the windfall from meeting the sudden spike in demand. Whether or not these dynamic concerns are actually relevant at all in practice, it would be worthwhile for economists and policymakers to consider more creative policies than the binary choice between price caps and unrestricted pricing.

Academics can become frustrated by government policies captured by political considerations. Proposals can get floated by policymakers with evident shortcomings, and yet they get implemented anyway either because of interest group lobbying, horse trading, or private interests. Why do we often get second- and third-best policies from the government even when domain-experts readily agree on what would be the first-best design?

Of course, sometimes the first-best is not feasible, or people cannot agree on what it is. In the case of optimal taxation, reallocation of resources towards those most deserving is constrained by citizens’ ability to inefficiently adjust their behavior to avoid taxes. People can move their income towards uses that avoid taxes, or adjust the amount they work and invest. The government can only do so much to limit these distortions because it lacks information about people’s true abilities and preferences. While the aim may be to redistribute resources to those disadvantaged by conditions of their birth or other turns of bad luck, the government can only observe proxies for disadvantage like income. Since income is a consequence of disadvantage, preferences, and choices such as effort and distortionary adjustments, redistributive taxation faces a tradeoff between supporting those disadvantaged through bad luck and encouraging inefficient transfers and adjustments. Economists who study optimal taxation consider the problem of redistribution and revenue generation subject to these costs from distortion caused by limited information and enforcement.

However, few people would argue that the tax system in countries like the United States comes close to approximating the best system subject to these constraints, even if they disagree on the appropriate levels of redistribution. The question is why governments cannot institute efficient policies given known constraints on citizens’ economic behavior–the policies that academic economists may choose if given license to design them themselves, the “technocratic solutions.” The above discussion of optimal tax rates subject to distortionary behavior of citizens ignores another constraint that is less frequently modeled in technocratic solutions–checks on distortionary behavior of a policymaker acting without society’s legitimacy. Giving a policymaker free reign to implement technocratic solutions risks future abuses of power for self-enrichment and personal inclinations. Optimal policymaking should recognize the incentive constraints of both the citizens and the policy maker. Even a benevolent policymaker acting unchecked can miscalculate and create policies the citizens do not want. Without checks on policymaking by society, governments may be slow to realize mistakes.

Balancing the state’s capacity to institute technocratic solutions versus capture by politicians that have too much unchecked power might present a tradeoff. Nondemocratic states have fewer checks imposed by society. On the one hand this may enable technocratic elites to impose large-scale policies without excessive deliberation and delay. Examples include the industrial and scientific advances of the USSR in the mid-20th century, such as in space exploration. However, there are countless examples of unchecked state power leading to disastrous consequences, either because of corrupt pilfering of revenues, elite infighting, or crazed technocracy and despotic subjugation. Excessive discretion over provision of social services can lead to widespread corruption, as in South Africa under Jacob Zuma; it can also lead to widespread famine, as in China during the Great Leap Forward or in colonial states prior to independence. Constant power struggles between elites can lead to instability and inefficient zero-sum competition. One example is in Stalin’s Soviet Russia, where over half of the Politburo members appointed between 1919 and 1952 were murdered or committed suicide. The most crazed and despotic states commit genocidal acts even against their citizens. While limited checks on the government can lead to faster and more ambitious policy-making, such benefits do not arise in many social and historical contexts, with capacity either hobbled by elite capture or used for devious ends.

Distributing power broadly in society, such as by guaranteeing rights to protest and criticize the government, can limit such excesses. So can fundamental rights that protect minority groups from subjugation. However, catering to the needs of various interest groups can force undesirable tradeoffs and dysfunction in governance. In recent years democratic elections in some countries have led to the rise of incompetent leaders fomenting zero sum games between segments of the electorate, limiting the ability for consensus and sensible technocratic policymaking. Convincing a majority of society to consent to policy changes, especially when they have disparate interests or may not be well-informed, is a daunting task and can lead to deviations from first-best policies. Indeed, interest groups may reject technocratic solutions precisely because they want to limit the capacity of the state in order to protect their own privileges and rights from future encroachment, lest politicians gain too much discretion. Issues where this seems practically relevant in the US include taxation and guns on the right, and policing and surveillance on the Left. While social deliberation and electoral incentives can limit the capacity of the state to implement optimal policies, they distribute power away from technocrats and politicians and towards citizens. The policies the society is left with may not seem very good relative to the optimal subject to constraints on the behavior of citizens, but they may be better relative to the optimal subject to constraints on behavior of both the citizens and the state.¹ Limiting the power of the state prevents it from exerting arbitrary control over citizens. 

The correct tradeoff between technocratic capacity and checks on arbitrary power depend on the social and cultural conditions of a society. Often state capacity and empowerment of society can grow in tandem over time, as happened in the early 20th century as many countries extended the franchise and extended social programs.² With a well-functioning society holding the state in check, policies that deviate from the first-best may be better than they appear. 

Non-economists sometimes view policies widely accepted by economists as foreign and even distasteful. In my view, much of the divide can be explained by contrasting perspectives on the primacy and normativity of preferences. In standard models economists take preferences as given, while non-economists often view preferences as moral objects that are malleable. While the economic method has important explanatory and practical power, the non-economist’s approach offers imaginative and in some cases empirically relevant perspectives on ideal societies.

In non-cooperative theoretical models of behavior standard in much of economics, individuals choose actions they view as optimal given their preferences and the actions of other agents they interact with. Modeled preferences frequently capture elements beyond pure self interest. Modern approaches often incorporate into preferences the well-being of other people or desires for fairness and altruism when such tastes have meaningful predictive power in behavior. However the model specifies preferences, these preferences are typically taken as given when individuals choose their optimal actions. Such approaches have enormous positive (i.e., non-normative) power when trying to understand how the world operates. When extending the approach to make normative judgments, the standard method is to consider allocations or regulations that best accommodate these preferences, though most papers consider heterogeneity analysis that evaluates how different segments of the population have their preferences satisfied under policy counterfactuals. 

In my view, much of the popular discourse views the defining challenges of organizing society not in the lens of allocative efficiency taking preferences of individuals as given. Instead, critiques of institutions are often framed in terms of failures of moral uprightness. As an example, one way to frame difficulties with dealing with climate change is that collective action is challenging when nations have their own self interests that stifle coordination for the common good. These are the constraints that economists consider when trying to address the problem through mechanism design or regulation. However, another way to frame inaction on climate change is that failure to coordinate reflects a moral failing of world leaders. If individuals, and in particular people in power, had preferences that aligned with the common good instead of their own interests or those of the constituencies that provide legitimacy to their authority, then climate change, and other global ills, would be solved. The problem is primarily people and leaders who are insufficiently morally upright and competent to resolve these collective action problems, not the intricacies of the collective action problems taking self-interests as given.

In the non-economist’s lens, social change and revolution are often viewed as movements for greater individual and collective morality. It is useful to consider twentieth social movements from this perspective. Moral and social change, both within the individual and in the collective society, were central in the political philosophy of many leaders of India’s anti-colonial movement in the first half of the twentieth century. Gandhi famously sought a radically decentralized economic system with self-sufficient communal living and curtailment of wants. He did not draw a distinction between economics and ethics, and viewed excessive consumer appetites as harmful to human dignity. The ideal society was one in which people’s desires and preferences were altered to be minimal, not the one that allocated goods most efficiently given the prevailing material preferences that existed at the time. Nehru and Ambedkar also sought fundamental changes in human relations, though they viewed a centralized state as the best means of enacting changes in behavior. Gyan Prakash writes, “Implicit in Ambedkar’s view was the project for a powerful pedagogic state, tutoring India in constitutional morality, freeing it from the inherited burdens of history, and ushering in social change.” In writing the Constitution he sought to create explicit legal institutions and state power that would alter “essentially undemocratic” hierarchical relationships that stifled social well-being.¹²

The experience in post-colonial India I believe is emblematic of social movements in other countries—the moral uplifting of the people was on par in importance with the specific economic policies pursued by governments and activist groups. These efforts often did result in meaningful social change. Explicit discrimination on the basis of race, gender, religion, and caste is viewed by a substantial share of the world as socially distasteful and morally abhorent. The world is not equal by any means, but the doctrines of equality taught by twentieth century social movements have affected the political, social, and economic preferences of many people. Moral views and preferences are malleable, even if the ideal state remains beyond reach. 

The economic approach is in my view a highly useful one for most practical problems and for the general pursuit of science. Explaining how and why people interact as they do matters for understanding behavior and for designing policies that accommodate individuals’ incentives. Ignoring these constraints and blaming all social ills on moral failing typically lacks rigor and useful policy guidance. It is in a sense vacuous to attribute everything to insufficient morality. However, moral lobbying does matter, and in some ways is an optimistic and idealistic exercise. It imagines what humans could be through self-improvement. It considers possibilities ruled out by taking preferences as given, which matters both normatively and empirically given the variation in moral outlooks across time and space.

(kind of technical)

I recently finished Invisible Women by Caroline Criado Perez. This is an amazingly researched and ambitious book that documents disparities in outcomes between men and women in transportation access, leisure, workplace accessibility, venture financing, product selection, health, safety, political access, disaster relief, and many other facets of life. Criado Perez attributes such discrepancies in part to “male-unless-otherwise-indicated” modes of research and thinking that fail to account for women, despite them constituting roughly half of humans.

A particularly egregious example of this is the large share of drug trials conducted disproportionately or entirely on male animals and human subjects, even for certain diseases that are more female-prevalent. Further, when both sexes are included in studies, results are often not sex-disaggregated, which prevents researchers from measuring heterogeneous effects for males and females.¹ 

Such discrepancies can cause both false positives and false negatives for women—drugs on the market may not be as effective in women as suggested by trials, and many potential drugs that would have worked for women may be discarded because they do not work on men. Women consequently have 50% more adverse drug reactions than men, including high incidence of drugs not working at all.²

Social science research is not exempt from such disparities. I have noticed papers, particularly older papers in the field of labor economics, that conduct analysis exclusively on men. Papers that include both men and women often do not sex-disaggregate results, despite it being fairly low effort in many cases.

There are statistical justifications that may be made for such practices, but I would argue they are misguided. Women and men had different labor market trajectories over the latter half of the twentieth century as women’s labor force participation increased. Suffice to say this should not justify looking only at male outcomes without some very strong a priori justification for doing so (such as the study measuring an intervention that can only plausibly have effects on men–likely not a common scenario). 

Not reporting sex-disaggregated data is a trickier case. Pooling data often increases statistical power and can lead to more precise estimates. Likewise, sex-disaggregating the data reduces sample sizes and can lead to more variable results that fail to replicate in other studies. A cash-strapped researcher running an RCT may not have the resources to recruit a large enough sample size for reliable estimation of sex-disaggregated results.³

However, the consequence of not reporting such estimates at all can stymie scientific progress. Accumulated underpowered sex-disaggregated results can be analyzed in meta-analyses and literature reviews, which are more appropriate ways of evaluating parameter estimates than relying on individual studies anyway. As long as journal publication outcomes do not select on such underpowered estimates (specifically, underpowered estimates should be interpreted in the text with appropriate caution, should often belong in appendices, and should not drive journal acceptances), such practices should improve the stock of scientific knowledge and help reduce data disparities. 

Of course, disaggregating data and reporting heterogeneous treatment effects matters for more than just gender differences. Such considerations also apply for other dimensions–including but not limited to race, income, and geography–along which our priors should suggest plausibly different effects of policies.⁴ Even considering heterogeneous treatment effects across all these variables may still mask policy-relevant heterogeneity; a nice method for measuring heterogeneous effects in a data-driven way is to use causal forests.⁵

Such research practices may be a drop in the bucket relative to many of the policy issues raised in the book that disadvantage women, but they are a pretty low cost way for social scientists to help address disparities.

Commenters have decried the erosion of democratic norms over the past several years in various countries around the world. The discussion raises interesting related questions: Why do norms matter? Should norms substitute for rule and enforcement of codified law? If norm violations are not legally sanctioned, what compels officials to ever follow norms at all? Microeconomic theory offers a useful lens for thinking about all of these questions. 

Imagine a brand new country just being born that needs to draft a constitution. For the sake of argument, assume the drafters of the constitution are all totally benevolent social planners who are all aligned in wanting what is best for the welfare of all future generations. They are not self-interested individuals looking to loot the state or consolidate power. The constitution they draft will codify the laws that govern the country for all future time periods. One way to think about the constitution is as a contract that governs the allocation of rights in future disputes that may arise. For example, the First Amendment of the United States states that “Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.” In any future time when a dispute over freedom of religion or speech or the press may occur, the First Amendment specifies the allocation of property rights in the dispute–each citizen owns the right to follow whatever religion they want, etc., and the ownership of this right supersedes other claims of legal ownership.¹

The drafters of the new constitution want to create the best possible constitution to foster the well-being of citizens. To think about this problem, it is first useful to define a state of the world. For my purposes, a state of the world is all of the information that describes what is happening at a given time and place that is pertinent to resolving a dispute over ownership of political rights. For example, in a dispute over freedom of religion, the following information may constitute the state of the world: who are the parties involved in the dispute; where and when is the dispute taking place; which of the interested parties most benefits from their rights superseding the others’; what does the public think about the dispute; what precedent has been established in previous years on related disputes; what are the consequences of the decision on future disputes; how did the relevant parties register their grievances; etc. The state of the world can at least in theory incorporate infinitely many factors that a benevolent arbiter might find remotely pertinent to resolving the dispute. 

Returning to the problem of drafting the best possible constitution, if the drafters are all-powerful, all-knowing beings, then constructing the optimal constitution is actually relatively straightforward, conceptually if not practically. The optimal constitution is just a document that lists the correct allocation of rights in any possible state of the world. Concretely, one such line in the document may say, “if the year is 2020, and there is a global pandemic, and it rained the previous day in Barcelona, and in three days hence a baby will be born at 1:15pm in Singapore, then Bharat has ownership of the right to practice whatever religion he chooses that supersedes any other claims that deny his right to do so.” The constitution maps all possible states of the world to an allocation of rights. 

The first-best, optimal constitution is of course not possible, for many, many reasons. The benevolent drafters face constraints in drafting their document. For simplicity, suppose we can summarize those constraints by saying that the constitution has a word limit. I still assume that the drafters are all-knowing for now, but now they have to do the best they can given their document has to be short enough to be useful. 

When going from the optimal unconstrained constitution to the optimal constitution with a word limit, the drafters lose something. They can no longer exactly specify the correct allocation of rights in any possible state of the world; they can only specify a short and finite set of rules that apply generally and approximate a good outcome to the extent possible.

As the world evolves over time, there will inevitably be some point in the future in which the rules of the constitution poorly approximate the state of the world and fail to offer enough guidance. The constitution can only include finite information when there is a word limit, but the world is infinitely complex and evolving. When the rules fail to provide guidance, citizens of the state will have to decide what to do. The rule of law fails to offer a solution in such states of the world because of incomplete contracting that arises from constraints on the complexity of the codified law.² 

Norms of behavior matter when the constitution does not have much to say about how to resolve a dispute in some state of the world. If formal laws cannot constrain behavior, people rely on informal codes of conduct. But why would anyone feel compelled to adhere to norms? Altruistic intentions are an important motivator. Another incentive to follow appropriate behavior follows from a beautiful result in game theory called the Folk Theorem. 

As mentioned, when the constitution has a word limit, there will eventually be a gap in formal legal boundaries. Going one step further, gaps will happen repeatedly. There will always be another time when the constitution fails to legally constrain behavior. Every time the legal doctrines fail to be useful, the citizens of the state will have to informally decide what to do. The problem of resolving these disputes repeatedly over time is called a repeated game in game theory. 

The Folk Theorem gives conditions under which cooperation can be sustained between self-interested parties in a repeated game. Informally, if the individuals involved in the repeated game care enough about future outcomes relative to the present, then mutually beneficial cooperation is possible. As an example, consider a standard Prisoner’s Dilemma problem. Two prisoners are separately approached by authorities and asked to betray the other. If both betray, they both get 10 years in prison. If neither betray, they both get two years in prison. If one betrays and the other does not, the betrayer gets one year in prison, while the betrayed gets 15 years. If the game is played only once, then the famous result is that purely self-interested actors must betray each other, even though they would both be better off if neither betrayed. If the game is played repeatedly infinitely many times, then the Folk Theorem shows that cooperation in all periods is possible. The logic behind the result is that if initially the agents cooperate, but at some point one of the agents betrays, then the other one punishes them in the future by also betraying in all subsequent periods. The repeated play enables agents to punish each other for bad behavior by withholding future rewards. If the agents care enough about those future rewards, fear of retaliation causes them to cooperate. 

The Folk Theorem is one way to understand how norms can substitute for a fully specified written rule of law. When imperfect constitutions fail to guide behavior, we have to rely on informal structures like future punishments or altruism to sustain a well-functioning state. 

Why do norms break down? There are many possible explanations. One reason could be that political agents may not be sufficiently invested in the future functioning of the state to care about possible punishment for bad behavior. Some research suggests that term limits on holding political office may result in worse politician behavior because the long-term consequences of losing an election are lower when politicians can only hold office one or two times anyway.³ However, if norm violations have indeed gotten worse over the past several years, disinterest in future outcomes is not the most obvious explanation. It is not clear why politicians might care less about the future now than in past years. Another possible explanation is that the world may have become more complex, and it has become murkier to figure out whether something actually is or isn’t a norm violation. In a similar vein, there could be intense disagreement between different citizens about what proper norms are, and these disagreements could erode cooperation. 

I do not hope to give a definitive explanation for the cause of norm violations here, but the microeconomic theory is at least one useful frame for thinking about these problems, their causes, and possible solutions. 

P.S.

Institutions, Institutional Change and Economic Performance by Douglass North touches on many of these themes. He discusses limitations of interpreting norm-adherence through tools like the Folk Theorem and instead presents a theory of institutions and institutional change.

A set of statements is logically consistent if they can all be true at the same time. In forming theories about how or why things are as they are, many people seek theories that are logically consistent and reject ones that are logically inconsistent. For example, believing that all fruits are sweet and that tomatoes are fruits is logically inconsistent, so someone who cares about logical consistency would reject this set of beliefs in favor of some alternative–perhaps not all fruits are sweet, or tomatoes are not fruits, or neither claim is true.

There is satisfaction in holding beliefs that are logically coherent, both for factual or scientific claims and for moral stances.¹ It’s certainly easier to defend viewpoints when they don’t contradict each other. However, I argue that logical consistency is only one criterion for evaluating an argument, and it is not appropriate for many reasonable circumstances. It is a highly constraining condition to put on the set of beliefs a person can hold. In fact, in an uncertain world, a rational person’s beliefs may be almost certainly logically inconsistent. 

Imagine there are three balls in a bag, one green, one red, and one blue. Two of the balls will be drawn at random. For each ball, a risk-neutral gambler is offered a bet that pays them one dollar if the ball is drawn and takes one dollar away if it is not. The gambler decides which of the three bets to take before any balls are drawn.

It should be clear that the gambler should accept all three bets. Each of them has an expected payoff of ⅓ since there is a ⅔ chance of getting paid a dollar and a ⅓ chance of losing a dollar. However, the probability of winning all three bets is 0 since only two balls are drawn. In choosing which bets to take, the gambler cares only about the expected outcome of each individual event given the information available, not about the joint outcome of all three events.² I argue the same type of reasoning can hold for beliefs about the world more generally, leading a rational individual to have stances on various individual issues that contradict each other jointly.

Consider debates about the minimum wage. Economist James Buchanan once said “The inverse relationship between quantity demanded and price is the core proposition in economic science, which embodies the presupposition that human choice behavior is sufficiently rational to allow predictions to be made. Just as no physicist would claim that ‘water runs uphill,’ no self-respecting economist would claim that increases in the minimum wage increase employment.” Theories of monopsony power had long existed by the time Buchanan said this, first developed by Joan Robinson in 1933, and such theories do predict that increases in a minimum wage can sometimes increase employment. A burgeoning empirical literature now suggests near-zero average employment effects of minimum wages increases, at least close to current minimum wage levels.³ 

Purely for the sake of argument–both since it is beyond my expertise to evaluate the minimum wage literature and because settling the issue is not central to my point–consider a person choosing a set of beliefs to hold about the two following claims: 

• Claim A: price increases cause reductions in quantity demanded 
• Claim B: increases to the minimum wage decrease employment

As a gross oversimplification, assume that each of these claims is simply true or false. Specifically, rejecting Claim A requires believing price increases do not cause reductions in quantity demanded, and rejecting Claim B requires believing that increasing the minimum wage does not decrease employment. This rules out more complex beliefs, reducing stances on each issue to a binary yes or no decision.⁴ A disciple of Buchanan would view both of these claims as true, which would be logically consistent. What should the disciple do when shown the recent empirical evidence about employment effects of the minimum wage?

To maintain logical consistency, they must either reject the claim that price increases cause reductions in quantity demanded, or they must reject the empirical evidence. Maintaining logical consistency constrains the possible beliefs this person can hold regarding claims A and B. In this toy example, it is simply not logically consistent to believe that price increases cause reductions in quantity demanded and simultaneously that increases to the minimum wage do not decrease employment.

Suppose this person is rational–they seek to form the best set of beliefs possible given the information they have. However, they have a strong conviction that claim A is true, that price increases reduce quantity demanded. Given their theoretical reasoning, lived experience, and other empirical work they have read, they do not think the findings about the effect of the minimum wage on employment are enough to shake their conviction on this point. Suppose we approach this person and ask them whether a new increase of the minimum wage in Illinois will decrease employment. What should they respond?

If they force themselves to have logically consistent beliefs, they must answer that the minimum wage increase will decrease employment since this is the only stance that coheres with their stance on Claim A. However, without the constraint of logical consistency, it could be perfectly reasonable and rational to answer that the minimum wage increase would not decrease employment. A rational person can alter their beliefs in the face of contrary evidence on one issue without shifting their beliefs about everything else–believing that a minimum wage increase will most likely not decrease employment does not require entirely upending one’s view about the effect of price on quantity demanded. The rational choice in predicting the effect of the minimum wage is the one that best fits the evidence for the minimum wage, not the one that most suitably reconciles stances across all of the issues this person can possibly have an opinion about.

Perhaps the assumptions in this simple example are excessively unrealistic since it rules out more nuanced beliefs, but the intuition is still instructive for more general and genuine cases. Imagine forming beliefs not about just Claim A and Claim B, but about the infinitely many things we can form beliefs about. Forming logically consistent beliefs across all of the issues in the world given only our limited lived experience is a very difficult problem. Further, it likely requires an elaborately twisted and convoluted set of beliefs, so overfit to the tiny slice of the universe we see that it would be basically useless for making meaningful predictions on any given issue. It may also result in rejection of novel information that defies our priors, leading to excessive dogmatism.

This matters especially when some issues are bigger or more important than others. Consider a new claim:

• Claim C: increases to the minimum wage decrease employment at the McDonald’s on East 52nd street and South Lake Park Ave in Chicago

Suppose now the problem is to choose a set of beliefs to hold only for Claims B and C. If the overall evidence overwhelmingly suggests Claim B is false in general, but the specific evidence for the McDonald’s in Chicago indicates Claim C is true, forcing logically consistent beliefs at worst risks warping beliefs about large and important issues to cohere with evidence for small and trivial issues. In this case, it might require rejecting Claim B entirely because it does not fit with Claim C. 

Logical consistency is important for answering specific types of questions, in particular when asked to give the most coherent general worldview that jointly explains several different phenomena. Consider again guessing which balls will be drawn from the bag, but with a different betting scheme. Now the gambler gets paid $2 if they guess exactly which balls will be drawn from the bag and loses $1 otherwise. Obviously, it does not make sense to guess that all three balls will be drawn since that happens with probability 0. In this case, since the problem is to guess the joint outcome for the three balls rather than separately choosing the outcome for each ball individually, choosing a logically inconsistent outcome violates rationality. Similarly, when asked to specify our most coherent complete worldview that reconciles our beliefs about a variety of issues, we should aim for logical consistency, even if we would give different answers if asked to evaluate each issue individually.

I do not think the point I raise in this piece is particularly novel, mathematically⁵ or philosophically, but it is one I myself only started to consider seriously recently. In my experience at graduate school and especially in undergrad, clean logical reasoning has been the standard for intellectual inquiry. Given the limits it places on beliefs, perhaps it should not be such a vaunted standard after all. 

In this post I summarize a few papers with extremely surprising and important results about social learning. Suppose you have some news that you need as many people to learn about as possible. A topical example is disseminating Covid-19 prevention measures. What’s the best way to spread the message?

It seems obvious that if the goal is to get as many people to learn as possible, you should just broadcast the news as widely as you can, making sure everyone gets the memo. Shockingly, this is not always true: spreading information widely can result in less learning than sharing it with only a few people. Two recent papers confirm this both theoretically and experimentally.

How could spreading information more widely result in less learning? The proposed culprit is the desire to not look dumb. When everyone gets the same information, and everyone knows that everyone gets the same information, asking for help concedes that you couldn’t figure things out on your own when other people could. That means you might choose to stay silent instead of asking your neighbors for help, hindering your learning.

Chandrasekhar, Golub, and Yang (2019), which I’ll refer to as CGY, study two channels through which aversion to looking dumb hinders learning: signaling and shame.¹ When you ask someone for help, that person might infer that you are not smart. This penalty to your reputation constitutes the signaling channel. Admitting your own inability to learn might also be painful in and of itself irrespective of the reputational consequences. The unpleasantness of admitting and confronting your weaknesses in front of another person is the shame channel.

CGY run an experiment across villages in Karnataka, India to test how these two forces affect learning. Participants are split into seekers and advisors. Seekers participate in a game where they guess which of two boxes contains a cell phone. If they guess correctly they get to keep the phone. The key is that seekers get clues about which box has the phone. In the first arm of the experiment, the number of clues a seeker gets is either completely random or based on their score on a cognitive test, with a higher score resulting in more clues. Seekers get paired with an advisor from their village whom they can ask for help in collecting potentially more clues, but the caveat is that by seeking help they reveal to their advisor information about the number of clues they got initially. This should make no difference in seeking decisions when the number of clues is random, but when clues are based on the cognitive test the seeker may fear stigma from drawing attention to their low score. In this arm of the experiment, seekers with low scores are 55% less likely to ask their advisor for help when the number of clues is based on test scores instead of randomly assigned. This demonstrates that social stigma can have huge effects on decisions to ask for help.

This arm on its own does not separate stigma into signaling and shame. The second arm addresses this by varying whether test scores get automatically revealed to advisors. If the advisor already knows the seeker’s score, the seeker does not signal anything about their ability by asking for help. That means revealing the score to the advisor shuts down the signaling channel and isolates the shame channel. CGY find that both shame and signaling have a substantial effect on seeking decisions, but, imposing some assumptions, they find the signaling effect is eight times bigger on average than the shame effect. 

However, the magnitudes depend a lot on social proximity between the advisor and the seeker. When the advisor and seeker are socially proximate (e.g., friends or of the same caste), shame can have a large effect and signaling is negligible, but when the advisor and seeker are socially distant, signaling dominates shame. This suggests there is less scope for reputational damage among close acquaintances who know each other well already. On the other hand, shame seems to matter more among close acquaintances since the emotional stakes are higher around people we interact with frequently.

Banerjee, Breza, Chandrasekhar, and Golub (2019), which I’ll refer to as BBCG, study the effects of stigma on learning in a high stakes setting—the 2016 Indian demonetization. The 2016 demonetization was markedly chaotic. In the seven weeks after the announcement that all Rs. 500 and 1000 notes would be demonetized, there were over 50 rule changes, resulting in widespread confusion and misinformation. BBCG ran an experiment across villages in India to test different methods for diffusing accurate information. They provided pamphlets with official details about demonetization to village members but varied how the information was delivered. There were two levels of randomization: the number of people given information, and whether the dissemination was common knowledge. In half the villages, every person received a pamphlet with information about demonetization, while in the other half only five villagers were given pamphlets. BBCG then randomized whether people knew who in the village had received a pamphlet. In the “Common Knowledge” treatment, everyone was notified which villagers had received a pamphlet, while in the “No Common Knowledge” treatment, people were not told who received a pamphlet. 

As I mentioned, the intuitive expectation is that sharing information with everyone in the village should result in more learning than sharing it with only five people. Because of stigma, this turns out not to be true. When the dissemination strategy is common knowledge, villages where only five people receive information about demonetization experience a lot more learning than villages where everyone receives information. When everyone receives a pamphlet and this is common knowledge, they avoid discussing details with each other out of fear of looking dumb or lazy, and as a consequence know less about demonetization in ways that demonstrably result in poor decisions. In contrast, when only five individuals receive information, people do not feel as much inhibition about asking for help, resulting in more learning and better decisions. Maybe even more surprisingly, the treatment where everyone is given a pamphlet but there is no common knowledge results in the best outcomes. When everyone receives a pamphlet but no one knows that everyone else got one too, people can still ask their neighbors for help without fear of stigma.

These two papers show that stigma is remarkably important in hindering how people learn, and they compel researchers to think about how to foster social environments that mitigate signaling and shame.

Many airlines are offering zero change and cancellation fees for flights booked in March. Why are they doing this?

One story: consumers are risk averse and don’t know the severity of the crisis. They fear booking a flight and then being unable to travel because of quarantine, illness, or risk of getting sick while abroad. There are always risks in deciding to book a flight, but all of a sudden consumers face a lot more uncertainty than they did before. This should create an increase in the demand for insurance.

Airline companies can absorb the risk their customers face from bad virus-related outcomes by offering zero change and cancellation fees. In order to bear this risk, they will likely raise their prices relative to the counterfactual in which they did not offer zero change fees. It’s going to be hard to see this in the time series because of concurrent ongoing negative demand shocks from the virus (plus March is generally a cheap time to fly anyway). There also aren’t great historical data on flight prices that are easily publicly available, especially at the airline level. But theoretically, this policy change should come with higher prices.

The problem with this insurance market is that correlated outcomes make risk pooling difficult. In a car insurance market, an accident in Miami is not at all predictive of whether there will be an accident in San Francisco. By offering insurance plans to lots of different people, an auto insurer can break even with high probability since on average good and bad risk outcomes will even out.

In contrast, with epidemics adverse outcomes are highly correlated. There seems to be a lot of uncertainty about how bad the coronavirus is going to be. If it turns out really badly, then a lot of people will look to cancel their flights at the same time. This means airline companies face the prospect of flying a lot of nearly empty planes, or just canceling flights entirely.

Airlines may be willing to accept this risk for a few reasons. Perhaps they are so profitable that even if things turn out badly they don’t face excessive downside risk. This means they are basically risk-neutral, and it’s efficient for them to absorb consumers’ uncertainty. Even if they have to fly empty or cancel flights for a few months, they can continue to pay off debts and weather the storm pretty easily.

Alternatively, it could be that without zero cancellation fees, they would have seen a huge drop in demand in the next few weeks and months as consumers grappled with uncertainty, regardless of whether the coronavirus turned out really badly or not. From the airline’s perspective, this certain bad outcome may have been worse than the uncertain prospect of offering everyone insurance, with some risk that a lot of people cancelled. Such incentives might be stronger because of limited liability. People don’t seem too worried right now that the big airlines will go bankrupt, but for some airlines, a few months of hugely depressed demand could result in bankruptcy as funds stop coming in to pay off debts. Such firms may face bankruptcy with certainty if they continue to enforce change fees, or bankruptcy with some probability less than 1 if they waive them. The worst case is the same in both scenarios, so the firm may as well waive change fees and hope for the best. 

Firms may also face limited liability if the government eventually decides to support the economy and bail out struggling firms, taking on the risk that airlines absorbed from consumers by offering no cancellation fees. This may matter for large firms especially if they deem the government would prevent them from failing. 

Glen Weyl and I just completed revisions on our paper, “Quadratic Voting in Finite Populations.” Quadratic voting (QV) is a voting rule proposed by Glen in which individuals purchase votes by paying the square of the votes they buy using some currency. QV has been written about extensively, most notably in Glen’s book Radical Markets with Eric Posner. I give an overview of QV here, but there are many other places online that explain it well if you would like to read more¹. Among our contributions in this paper is that we show QV leads to desirable social choices even in small groups of people, giving formal justification for experimenting with QV in real-world, smaller-scale settings.

A fundamental problem societies face is making collective decisions, such as who to choose as representatives, how much tax to levy, or what rights should be guaranteed to minorities. As just one example, societies decide whether to allow same-sex marriage. A particularly common method for making collective decisions is majority voting, or one-person-one-vote: whichever option is favored by the most people becomes law. In the United States, prior to the Supreme Court’s ruling in Obergefell v. Hodges in 2015, several states put the decision of whether to allow same-sex marriage to direct popular vote. In 2008, California voters rejected same-sex marriage by a 52% to 48% margin; in Maryland, on the other hand, voters approved same-sex marriage in 2012 by a 52% to 48% margin.

The limitations of one-person-one-vote have been understood for thousands of years. It can lead to “mob rule” or “tyranny of the majority,” scenarios in which the strong interests of the minority are trampled by the majority. Many modern states have various institutions to prevent tyranny of the majority, among them written constitutions, bicameral legislatures, and judiciaries. In the US, the Supreme Court ultimately ensured minority LGBT individuals would have the right to marry across the country.

However, the institutions that the state uses to protect minorities have many flaws. The Supreme Court, for instance, concentrates a large amount of power among a few unelected officials. Further, there is no guarantee that any of the above-mentioned institutions will actually act in the interest of the minority when needed, or that the benefits they generate outweigh the inefficiencies they cause.

Designing better mechanisms to make desirable collective decisions is an old, critical open problem in the social sciences. I cannot hope to list all of the mechanisms proposed over the years or discuss their merits². Quadratic voting is a relatively recent contribution to the field, proposed by Glen originally in 2012.

Under QV, each individual in the society can purchase votes in an election, either for or against a resolution passing; in the near- and medium-term, most applications will likely use artificial currency distributed equally to each member and which can be spent only across each election the society faces. Individuals can purchase as many votes as they would like in an election (as long as they still have money left), but each additional vote they buy in an election increases in cost. The total cost paid is the square of the number of votes purchased, so 1 vote costs $1, 2 votes cost $4, 2.5 votes cost $6.25, etc. In the case of artificial currency, buying more votes in one election leaves less money left over to spend on other elections. The resolution passes if the total votes purchased for the resolution exceeds the total votes purchased against the resolution. Since individuals can buy more than one vote, they can choose to vote more in elections they really care about and vote less in elections that are not as important to them. On the other hand, the increasing cost of voting prevents individuals with extreme preferences from dominating the election. Buying a lot of votes becomes costly quickly.

Each individual either prefers that the resolution passes or that it fails. If we make (quite strong) assumptions about people’s preferences, then how strongly they feel about their preferred outcome can be measured by the amount of currency they would be willing to pay to get it. If someone in favor of the resolution is indifferent between having it fail and having it pass but giving up $10, then their value for the outcome as measured by willingness to pay is $10. Lalley and Weyl (2019) give conditions under which, when there are many people taking part in the election, QV gives the outcome that maximizes total willingness to pay. In fact, the squared cost of votes in QV is the unique cost function that accomplishes this feat in the election framework Lalley and Weyl consider. If everyone in favor of the resolution passing would be willing to pay $1000 in total, and everyone opposed would be willing to pay $900 in total, then the resolution would pass under QV under the conditions outlined by Lalley and Weyl³.

To see why maximizing willingness to pay could be a desirable outcome, consider a simple, extreme example. Suppose voters are voting between candidate A and candidate B. 49% of voters really dislike candidate A. They would be willing to pay $10,000 each to prevent A from winning. The other 51% of voters are mostly indifferent, but would each be willing to pay $1 to have candidate A win. Under one-person-one-vote, since the majority of people favor candidate A, candidate A would win. Under QV, the total willingness pay is clearly higher for the side that favors candidate B, who would end up winning. Thus, QV allows people to express how much they care, whereas one-person-one-vote behaves as if everyone cares the same amount. Under QV, the minority shows that they really want B to win by spending more of their scarce voting resources to prove it.

How often is there tyranny of the majority? It is difficult to quantify exactly (not least because modern elections and polling fail to measure intensity of preference well), but the case of same-sex marriage offers one case study. It seems quite likely that the people with the strongest preferences in the 2008 same-sex marriage referendum in California were LGBT individuals. LGBT voters constituted about 4% of the population of California in 2010. Since the ban on same-sex marriage passed, a small majority of non-LGBT voters must have been in favor of the ban. While we do not have hard numbers on people’s intensity of preference, it is easy to imagine this as a case where the weak preferences of the majority against same-sex marriage dominated the stronger preferences of the minority in favor of same-sex marriage. This is a case where QV could have allowed the minority to have greater voice in the election and swing it in their direction.

However, as I mentioned previously, Lalley and Weyl (2019) only show that under their conditions QV maximizes willingness to pay when there are very many people voting in the election. The reason they require a lot of people is that having many voters resolves uncertainty that could muddle analysis of possible outcomes. One way to think about this is to imagine randomly drawing 5 people from California to take part in the election. When there are only 5 voters, the direction of total willingness to pay for and against the resolution can vary depending on which 5 voters are drawn, which means each individual voter has a meaningful chance of swinging the outcome by themselves. The outcome can vary a lot depending on how much each person votes. Accounting for the possible outcomes in such an election is hard to model mathematically. Instead, if every voter in California takes part, there is little chance any one individual will be influential enough to swing the election themselves. As a result, there is much greater certainty over which outcome will receive the most votes and how this relates to total willingness to pay⁴.

In real-world applications in the near future, it is hard to imagine QV being tested in elections with millions of people. This creates a dilemma: how can we test if QV actually works in the real-world if the theory only makes predictions about its efficacy in massive elections we should be hesitant to experiment in? Answering this question is a major contribution of our paper. Through simulation, we show that even in small-scale elections QV usually leads to the outcome that maximizes total willingness to pay in a broad number of scenarios. In fact, it very often outperforms one-person-one-vote.

There are intuitive reasons one-person-one-vote should actually do well in small-scale elections. As a toy example, suppose there are only two people, and they need to decide whether to go to Chipotle or Qdoba for lunch. For the sake of argument, suppose most people in society prefer Chipotle, but the minority of people who prefer Qdoba are very passionate that it’s better and have greater willingness to pay to go to Qdoba on average. If the two individuals both are in favor of Chipotle or are both in favor of Qdoba, then one-person-one-vote will definitely choose the outcome that maximizes total willingness to pay. Either of these scenarios should happen with fairly high probability. Instead, if the two people disagree about going to Chipotle or Qdoba, then suppose the tie is broken via a coin flip. The correct outcome will still be chosen half the time. Thus, in small groups, one-person-one-vote can often lead to the right outcome just by chance, even if in the overall society the minority has higher total willingness to pay. As the society gets larger, these chance beneficial outcomes become more and more unlikely if the minority has greater total willingness to pay, leading to tyranny of the majority. In a group of 20 people, it is likely people who prefer Chipotle outnumber people who prefer Qdoba, but people who prefer Qdoba have greater total willingness to pay.

A similar, but stronger, logic occurs for QV. Similar to one-person-one vote, the total willingness to pay for each side will frequently coincide by chance. However, unlike one-person-one-vote, QV also allows people to spend more or less of their budget depending on how much they care. People can express how intense their preferences are. In the case with two voters, instead of relying on a coin flip to break ties, we rely on the number of votes purchased by each side, which should almost certainly break the tie in favor of the side with stronger intensity of preference. We show that in elections with approximately 2 to 15 voters, QV almost always chooses the side that has greater willingness to pay.

We believe our findings give formal basis for experimentation with QV in smaller-scale elections. In all cases we simulate, QV chooses the wrong outcome only a small fraction of times, and typically only when the willingness to pay on both sides is nearly equal (10% is the largest inefficiency for QV we found in any setting). Numerous real-world experiments with QV have in fact already occurred, and so far give promising results⁵. Our work gives intuition for why QV can do well in these cases, and provides software for researchers to test it out on their own and explore conditions where QV can do especially well or poorly. We hope our results encourage more people to experiment with QV in the future.

My paper “The Drivers of Social Preferences: Evidence from a Nationwide Tipping Field Experiment” with Uri Gneezy, John List, and Ian Muir is now out as an NBER working paper. We analyze over 40 million tipping outcomes on the Uber app in the summer of 2017 to study tipping behavior and social preferences in the field. The immensity of the data set, both in terms of the number of observations and the number of features about each individual outcome we can observe, helps us determine facts about tipping behaviors and norms that were difficult to assess in previous studies. 

As a first fact, roughly 16% of trips were tipped on Uber at the time.¹ In the four weeks of data we collected, 60% of riders who took at least 10 trips never tipped. Conditional on tipping, people tip a little more than $3 on average (about 26% of the fare), so the average tip, including cases where the rider did not tip, is about $0.50. Tipping frequency on Uber is lower than tipping frequency in other contexts like restaurants. This could be a consequence of different norms and cultural expectations in the two settings–Uber did not encourage riders to tip in the earlier days of the app. It could also be because the tipping decision is made privately on Uber after the ride is over, whereas in many other contexts the tipping decision is more public, adding social pressure to the decision. Across cities, tips are lowest in large cities, especially in California and in the Northeast, and highest in less densely populated areas. 

A key result is that rider characteristics are about 3 times as informative of the amount tipped as driver characteristics. Knowing who the rider is on a trip is much more predictive of the tip amount than knowing who the driver is. We show this to be true in various cities across the United States.

A rider’s rating is especially predictive of how much they will tip. Higher rated riders tip more, after controlling for a large number of other factors like the time and location of the trip. Riders also tip more after they just joined Uber, and then start tipping less as they get more experience taking rides. One possible explanation is that initially they overestimate tipping norms on Uber, and as they get more experienced they adjust their tipping downwards. Using a proxy for the gender of a rider constructed from their first name, we find that women tend to tip less than men. We also find that riders who use a default app language other than English tip less. We do not speculate on reasons in the paper, but it is possible that perceived tipping norms or perceived pressure to tip vary by demographics. 

On the driver side, we similarly find high ratings and less experience are associated with higher tips. Declines in tips with experience could suggest that drivers try especially hard on their first few trips before getting comfortable, or that they decide tips are not worth the effort. Drivers whose default app language is not English get tipped less as well. 

Women get tipped more than men on average. In particular, younger women get tipped more than younger men, with the gap shrinking with age. 

Both male and female riders tip women more, but male riders are much more responsive to the age of female drivers than they are to the age of male drivers. Men tip younger women about seven cents more on average than older women (roughly a 14% increase, give or take), while they tip younger men about 3 cents more than older men. Female riders tend to not vary tips as much based on the age of the driver. 

Tips also vary based on characteristics of where riders and drivers are from. Riders from ZIP codes that are high income and have a lower share of African American or Hispanic residents tend to tip more. Drivers from low income areas and areas with a higher share of Hispanic residents get tipped less on average. 

Finally, tips seem to be positively correlated with several dimensions of trip quality. Picking up a rider on time is associated with getting higher tips, as is having fewer hard brakes and accelerations on the ride.

In addition to uncovering these facts, we explore some aspects of social preferences in the field. First, we look at repeated interactions between a rider and a driver. It is not common for a rider to match with the same driver twice, but our dataset is large enough that we still observe a substantial number of tip outcomes on repeat interactions. Riders tip on average 27% more the second time they see the same driver than they do the first time. 

There are two reasonable explanations: strategic reciprocity, or some kind of behavioral or norms response. Under the strategic reciprocity explanation, when a rider matches with the same driver twice, they realize that repeat interactions happen more frequently on Uber than they originally thought. As a result, they should tip all of their drivers more to avoid bad or awkward encounters in the future. A testable implication of this model is that riders should tip other drivers more too. This is not borne out in the data–only the single trip with a repeat interaction gets tipped more. This gives evidence for some kind of behavioral response instead, like social connection built between the rider or driver, or different norms governing repeat interactions and single encounters. 

We might reasonably think that riders and drivers build social connection by spending more time with each other and having a conversation. If the rider or driver is less comfortable using English, then we might expect conversation to be less likely, which could hinder social connection and mitigate the repeat interaction effect. However, we find that even when the rider or driver uses a default app language other than English, repeat interactions result in an increase in tips on par with the effect in the general pool of Uber users. If higher tips happen on repeat interactions because of social connection, this is at least suggestive evidence that conversation is not the mechanism through which social connection is built.

Finally, we look at the effect of default tip options on tipping levels. Riders can always enter a custom tip, but most people tend to choose one of the default options when they do tip. Uber ran an experiment early on varying the default options shown to riders. While we show that higher defaults did lead to slightly higher tips, we show the effect of defaults are much smaller on Uber than what the literature suggests for taxis.² On Uber, tips happen privately, while on taxis tips happen in front of the taxi driver. Our results suggest that defaults can be more influential in setting tipping norms when the tipper is monitored. That is, norm setting through defaults and monitoring of the tipper complement each other in boosting tip levels. 

This paper is long and packed with results, some of which I did not have space to discuss here. I hope you take a look at the full paper if you are interested in learning more.

If you like econometrics, also check out my other newly released paper, “Design and Analysis of Cluster-Randomized Field Experiments in Panel Data Settings,” with Ali Hortacsu, John List, Ian Muir, and Jeffrey Wooldridge. We use simulation to study best practices for analyzing cluster-randomized field experiments with panel data.