Tuesday, March 07, 2017

The Teaching of Economics

In 2013, with funding from the Institute for New Economic Thinking, University College London, Friends Provident Foundation, Azim Premji University (Bangalore) and Sciences Po (Paris), a group of concerned economists created CORE, the Curriculum Open-Access Resources for Economics. Wendy Carlin from University College London led the initiative, and I was fortunate enough to have been involved from the outset. The group soon grew to encompass a couple of dozen members from a broad range of countries including France, Chile, Colombia, Turkey, and India.

CORE’s vision is that economics should be an inquiry into the fundamental problems facing humanity today and the ways that economic reasoning can address them, not just a training in abstract problem solving. We sought to directly address the problem of a lack of good teaching resources consistent with this vision, and the attendant issues, including limited incentives for faculty and their teaching teams to make use of what is available. 
   
Since its launch, CORE has successfully begun to produce high-quality resources for the teaching of economics through this global collaboration of scholars, and to distribute these resources free of charge worldwide under a Creative Commons license. Our e-book The Economy, currently in beta, is being taught as the required introductory course at University College London (UCL), the Toulouse School of Economics, Humboldt University (Berlin), and other top economics departments in Europe. It is also being taught at the Lahore University of Management Sciences, Azim Premji University (Bangalore), the University of Sydney, and Universidad de los Andes (Bogota). More than 2,300 verified instructors have been cleared for access to CORE’s full range of supplementary teaching materials, and over thirty thousand students spread across 78 different countries have registered for access to the e-book.

As part of its strategy to improve the teaching of economics CORE is now seeking to expand its outreach and impact in the United States. It will do so in collaboration with Barnard College, which has just received a major award from the Teagle Foundation for exactly this purpose. My department colleagues Homa Zarghamee and Belinda Archibong will join me in directing this effort. 

At the heart of the initiative is a series of workshops involving faculty and graduate students, who will be selected through a competitive application process and provided with stipends and partial reimbursement of travel costs. These workshops will be designed to bring together instructors who already have experience with implementing CORE, and a larger group of potential adopters. The first workshop will be held at Barnard on August 17-19, 2017. We will post a call for applications soon, and are currently in the process of hiring a project manager.

Among our goals is the creation of a cadre of confident, networked, new PhDs excited about making teaching a fulfilling and central part of their career in economics. Graduate students who complete a workshop will be certified as CORE-Teagle Fellows, a designation that we hope will become a credible signal of commitment to quality teaching among employers, especially liberal arts colleges and public policy schools. We would also like this to be a signal of scholarship potential, and will accordingly screen applicants for exceptional promise in both research and teaching.

Over the longer term, we also want to identify a set of institutional partners with shared goals for the improvement of economics education and a commitment to the development and use of high quality, open access instructional content. To further these goals, we will launch the CORE Consortium, a membership program for institutions willing to enter into a long-term, multi-year commitment to support faculty and graduate students using CORE, and host workshops on a rotating basis. By the end of the 36-month period covered by the Teagle grant, we hope to have at least half a dozen institutions on board as members, as well as a leadership team and an administrative structure.

We are enormously grateful to the Teagle Foundation for funding this exciting new initiative. Further updates will follow once a project manager is in place.

Wednesday, March 01, 2017

Reigns of Error

The death of Kenneth Arrow has led lots of people to swap stories about their interactions with him. Larry Blume has posted several of these on facebook, including the following response to my own contribution (quoted with permission):
This story is not at all surprising; Ken read everything. I think I mentioned elsewhere that my last conversation with Ken, this past June, concerned The Theory of Moral Sentiments. He and Amartya Sen were taking turns quoting from it, from memory... I could recognize the quotes, but not respond in kind. Once in a conversation about Nash equilibrium and rational expectations, Ken wondered if I had read Merton on expectations - not Robert Jr.: https://www.jstor.org/stable/4609267. He also had a good stock of Shakespeare to call on.
The link is to a 1948 paper by the great sociologist Robert K. Merton (father of the Nobel-winning economist). Reading anything at all by Merton is an excellent use of one's time, so I went through this paper. It's extraordinary. Not only does Merton provide a very clear account of equilibrium beliefs, but goes on to point out that even when these beliefs are correct in a narrow sense, they can hold in place an incorrect understanding of the social world. To translate this into the contemporary language of economics, Merton points out that the play of equilibrium strategies can go hand in hand with a deeply erroneous understanding of the game.

Merton begins with an account of a Depression-era bank run that perfectly captures the multiple equilibrium logic he has in mind:
It is the year 1932. The Last National Bank is a flourishing institution. A large part of its resources is liquid without being watered. Cartwright Millingville has ample reason to be proud of the banking institution over which he presides. Until Black Wednesday. As he enters his bank, he notices that business is unusually brisk. A little odd, that, since the men at the A.M.O.K. steel plant and the K.O.M.A. mattress factory are not usually paid until Saturday. Yet here are two dozen men, obviously from the factories, queued up in front of the tellers' cages. As he turns into his private office, the president muses rather compassionately: "Hope they haven't been laid off in midweek. They should be in the shop at this hour."
But speculations of this sort have never made for a thriving bank, and Millingville turns to the pile of documents upon his desk. His precise signature is affixed to fewer than a score of papers when he is disturbed by the absence of something familiar and the intrusion of something alien. The low discreet hum of bank business has given way to a strange and annoying stridency of many voices. A situation has been defined as real. And that is the beginning of what ends as Black Wednesday -- the last Wednesday, it might be noted, of the Last National Bank.
You can see why Arrow saw in this a precursor to the concept of Nash equilibrium, the existence of which would be established just two years later. There are also echoes here of the Diamond and Dybvig model of bank runs, in which the multiple equilibrium nature of the problem finds formal expression.

But Merton doesn't stop there, he considers how the people expressing the described behavior interpret the situation they are in. And here he observes an important disparity between the manner in which the situation is viewed by the the participants themselves, as compared with its interpretation from the analytical viewpoint of the social scientist:
The self-fulfilling prophecy is, in the beginning, a false definition of the situation evoking a new behavior which makes the originally false conception come true. The specious validity of the self-fulfilling prophecy perpetuates a reign of error. For the prophet will cite the actual course of events as proof that he was right from the very beginning. (Yet we know that Millingville's bank was solvent, that it would have survived for many years had not the misleading rumor created the very conditions of its own fulfillment.) Such are the perversities of social logic.
So beliefs are correct in one sense, but at sharp variance with reality in another. Such "reigns of error" are not something we economists pay much attention to, with one very notable exception. 

In his book The Anatomy of Racial Inequality Glenn Loury discusses the manner in which negative stereotypes about a group can become self-fulfilling through the incentive effects that the stereotypes themselves create. This is the phenomenon of statistical discrimination, introduced into the economics literature by none other than Kenneth Arrow. Like Merton, however, Loury is not content to simply identify the kinds of behaviors consistent with equilibrium beliefs. He wants to know how people with these beliefs will interpret the behaviors. And here he deploys the idea of biased social cognition, which can give rise to essentialist causal misattributions.

That is, behavior arising in equilibrium through the operation of incentives can be interpreted by casual observers as being a consequence of deep differences in character. And this has enormous consequences, since biased social cognitions can "cause some situations to appear anomalous, disquieting, contrary to expectation, worthy of further investigation, inconsistent with the natural order of things---while other situations appear normal, about right, in keeping with what one might expect, consistent with the social world as we know it."

Loury has argued elsewhere that the level of mass incarceration currently prevailing in the United States could not possibly be sustained were it not for its racial character. As long as essentialist interpretations of incentive-driven actions continue to be widespread, such high levels of confinement will not be seen as anomalous or disquieting, and will not give rise to urgent calls for action.

The economic method, for all its flaws, has one very important virtue: it shines a bright light on interests and incentives, and in doing so can challenge essentialist interpretations of social reality. But if this potential is to be realized, it is important to focus not just on the characterization of equilibrium behavior, but also on the reigns of error that distort our mental models of the underlying game.

Saturday, February 25, 2017

Arrow, Edgeworth, and Millicent Garrett Fawcett

There's not much one can say about Kenneth Arrow that hasn't already been said, but there's one personal story that I can add to all the tributes and remembrances. 

I met Arrow just once, at a Stanford conference in April 2008 that he and Matt Jackson jointly organized. While everyone else was seated around the outside of a large ring of tables, Arrow was on the inside, directly in front of the speaker. He was 86 at the time.

I was first up, presenting an early version of a paper with Sam Bowles and Glenn Loury on group inequality. Arrow interrupted me within the first couple of minutes – not aggressively at all, just seeking clarification about the information structure. Then, during a coffee break after the talk, he asked if I’d read a piece by Millicent Fawcett on gender wage inequality, published in the Economic Journal in 1892. That’s not a typo – he really meant 1892. I confessed that I hadn't.

Arrow said that Fawcett’s work was extensively discussed in a 1922 presidential address by Francis Edgeworth, but while many were familiar with the Edgeworth lecture, few had bothered to read Fawcett herself. 

It’s true. Edgeworth mentioned “Mrs. Fawcett” seven times in his address, and cited three separate pieces by her. His lecture was on “Equal Pay to Men and Women for Equal Work,” and one of papers he referenced was “Equal Pay for Equal Work,” published by Fawcett in 1918. Here’s how the latter begins:



I didn’t realize it at the time, but Dame Millicent Garrett Fawcett was every bit as remarkable as Edgeworth and Arrow, and economics was the least of her accomplishments. I imagine that Arrow saw in her a kindred spirit.

Wednesday, December 14, 2016

Thomas Schelling, Methodological Subversive

Thomas Schelling died at the age of 95 yesterday.

At a time when economic theory was becoming virtually synonymous with applied mathematics, he managed to generate deep insights into a broad range of phenomena using only close observation, precise reasoning, and simple models that were easily described but had complex and surprising properties.

This much, I think, is widely appreciated. But what also characterized his work was a lack of concern with professional methodological norms. This allowed him to generate new knowledge with great freedom, and to make innovations in method that may end up being even more significant than his specific insights into economic and social life. 

Consider, for instance, his famous "checkerboard" model of self-forming neighborhoods, first introduced in a memorandum in 1969, with versions published in a 1971 article and in his 1978 book Micromotives and Macrobehavior. This model is simple enough to be described verbally in a couple of paragraphs, but has properties that are extremely difficult to deduce analytically. It is also among the very earliest agent-based computational models, reveals some limitations of the equilibrium approach in economic theory, and continues to guide empirical research on residential segregation.

Here's the model. There is a set of individuals partitioned into two groups; let's call them pennies and dimes. Each individual occupies a square on a checkerboard, and has preferences over the group composition of its neighborhood. The neighborhood here is composed of the (at most) eight adjacent squares. Each person is content to be in a minority in their neighborhood, as long as minority status is not too extreme. Specifically, each wants strictly more than one-third of their neighbors to belong to their own group. 

Initially suppose that there are 60 individuals, arrayed in a perfectly integrated pattern on the board, with the four corners unoccupied. Then each individual in a central location has exactly half their neighbors belonging to their own group, and is therefore satisfied. Those on the edges are in a slightly different situation, but even here each individual has a neighborhood in which at least two-fifths of residents are of their own type. So they too are satisfied.

Now suppose that we remove twenty individuals at random, and replace five of these, placing them in unoccupied locations, also at random. This perturbation will leave some individuals dissatisfied. Now choose any one of these unhappy folks, and move them to a location at which they would be content. Notice that this affects two types of other individuals: those who were previously neighbors of the party that moved, and those who now become neighbors. Some will be unaffected by the move, others may become happy as a result, and still others may become unhappy. 

As long as there are any unhappy people on the board, repeat the process just described: pick one at random, and move them to a spot where they are content. What does the board look like when nobody wants to move?

Schelling found that no matter how often this experiment was repeated, the result was a highly segregated residential pattern. Even though perfect integration is clearly a potential terminal state of the dynamic process just described, it appeared to be unreachable once the system had been perturbed. The assumed preferences are tolerant enough to be consistent with integration, but decentralized, uncoordinated choices by individuals appear to make integration fragile, and segregation extremely stable. Here's how Schelling summarized the insight:
People who have to choose between polarized extremes... will often choose in a way that reinforces the polarization. Doing so is no evidence that they prefer segregation, only that, if segregation exists and they have to choose between exclusive association, people elect like rather than unlike environments.
One can tune the parameters of the model: the population size and density, or the preferences over neighborhood composition, and see that this key insight is robust. And for reasons discussed in this essay, equilibrium reasoning alone cannot be used to uncover it. 

A very different kind of contribution, but also one with important methodological implications, may be found in Schelling's 1960 classic The Strategy of Conflict. Here he considers the adaptive value of pretending to be irrational, in order to make threats or promises credible (emphasis added):
How can one commit himself in advance to an act that he would in fact prefer not to carry out in the event, in order that his commitment may deter the other party? One can of course bluff, to persuade the other falsely that the costs or damages to the threatener would be minor or negative. More interesting, the one making the threat may pretend that he himself erroneously believes his own costs to be small, and therefore would mistakenly go ahead and fulfill the threat. Or perhaps he can pretend a revenge motivation so strong as to overcome the prospect of self-damage; but this option is probably most readily available to the truly revengeful
Similarly, in bargaining situations, "the sophisticated negotiator may find it difficult to seem as obstinate as a truly obstinate man." And when faced with a threat, it may be profitable to be known to possess "genuine ignorance, obstinacy or simple disbelief, since it may be more convincing to the prospective threatener."

Starting with three classic papers in the same 1982 issue of the Journal of Economic Theory, a large literature in economics has dealt with the implications for rational behavior of interacting with parties who, with small likelihood, may not be rational. While this work has focused on characterizing rational responses to irrationality, Schelling's point speaks also to payoffs, and raises the possibility that departures from rationality may have adaptive value

The methodological implications of this are profound, because the idea calls into question the normal justification for assuming that economic agents are in fact fully rational. Jack Hirshleifer explored the implications of this in a wonderful paper on the adaptive value of emotions, and Robert Frank wrote an entire book about the topic. But the idea is right there, hidden in plain sight, in Schelling's parenthetical comments.  

Finally, consider Schelling's burglar paradox, also described in The Strategy of Conflict:
If I go downstairs to investigate a noise at night, with a gun in my hand, and find myself face to face with a burglar who has a gun in his hand, there is a danger of an outcome that neither of us desires. Even if he prefers to just leave quietly, and I wish him to, there is danger that he may think I want to shoot, and shoot first. Worse, there is danger that he may think that I think he wants to shoot. Or he may think that I think he thinks I want to shoot. And so on. "Self-Defense" is ambiguous, when one is only trying to preclude being shot in self-defense.
Sandeep Baliga and Tomas Sjöström have shown exactly how such reciprocal fear can lead to a fatal unraveling, and explored the enormous consequences of allowing for pre-play communication in the form of cheap talk. And I have previously discussed the importance of this reasoning in accounting for variations in homicide rates across time and space, as well as the effects of Stand-your-Ground laws.

There are a handful of social scientists whose impact on my own work is so profound that I can't imagine what I'd be writing if I hadn't come across their work. Among them are Glenn Loury, Elinor Ostrom, and Thomas Schelling. I can think of at least five papers: on segregation, on variations in homicide across regions and communities, on reputation in bargaining, and on social norms, that flow directly from Schelling's thought. 

It may surprise some to know that Glenn Loury's Du Bois lectures are dedicated to Schelling, but it makes perfect sense to me. Here's how Glenn explains his choice in the preface:
Shortly after arriving at Harvard in 1982 as a newly appointed Professor of Economics and of Afro-American Studies, I begin to despair of the possibility that I could successfully integrate my love of economic science with my passion for thinking broadly and writing usefully about the issue of race in contemporary America. How, I wondered, could one do rigorous theoretical work in economics while remaining relevant to an issue that seems so fraught with political, cultural and psychological dimensions? Tom Schelling not only convinced me that this was possible; he took me by the hand and showed the way. The intellectual style reflected in this book developed under his tutelage. My first insights into the problem of "racial classification" emerged in lecture halls at Harvard's Kennedy School of Government, where, for several years in the 1980s, Tom and I co-taught a course we called "Public Policies in Divided Societies." Tom Schelling's creative and playful mind, his incredible breadth of interests, and his unparalleled mastery of strategic analysis opened up a new world of intellectual possibilities for me. I will always be grateful to him.
As, indeed, will I.

Wednesday, November 02, 2016

The Prediction Market Paradox

There’s a reason why campaigns are eager to publicize polls that show them ahead, while downplaying those in which they happen to be trailing. The perception that a candidate is losing can depress donations and volunteer effort, and lower morale and turnout among supporters. Hence polls that show tightening of a race are often advertised as indicators of momentum by the trailing party, and as outliers by the leader. The actual likelihood of victory is not independent of beliefs about this likelihood.

This gives rise to what might be called a prediction market paradox. If prices are widely believed to accurately reflect underlying probabilities, then there is an incentive for deep-pocketed partisans to try and manipulate these prices at the margin. But if the possibility of manipulation is salient and prices are treated with skepticism, then incentives to manipulate are weakened and prices will in fact be quite accurate reflections of underlying beliefs.

An interesting illustration of this phenomenon is  the recent decision by PredictIt to post an electoral college map, updated by the minute, that aggregates probabilities derived from all its state level markets. Here's what the map looks like at the moment:


There are seven categories: the safe, likely, and leaning states for each candidate and one toss-up category. States shift across categories as prediction market prices cross the relevant thresholds. This way, a broad range of probability assessments is mapped onto a much coarser set that is easy to visualize and process.

But this creates the possibility that small changes in price, of the order of one cent, can lead to reassignments across categories that generate a very different picture. The incentives to manipulate prices is amplified whenever such categorical switches are feasible.

Of course these incentives apply to both sides of the market, with some traders wishing to shift states to the left while others are pushing to the right. As a result, an unusually large number of states may be expected to bounce back and forth across boundaries, and to remain within a narrow band of prices close to those selected (somewhat arbitrarily) by the exchange as thresholds.

This seems to be what we are seeing. The boundary between the lean and likely Clinton states is determined by a 75% threshold, and we see four states (Wisconsin, Michigan, Colorado, and Pennsylvania) all within a point or two of this. Here are those above the threshold:


And those below:


New Hampshire is not far from the boundary either. 

All this could be just coincidence, but if one looks at probabilistic forecasts from other sources, there is no such pattern. The New York Times conveniently collects six probabilistic forecasts including it's own, with the current picture looking like this:


These forecasts (from the Times, FiveThirtyEight, Huffington Post, Predictwise, Princeton Election Consortium and Daily Kos respectively) don't appear to be clustered around the PredictIt thresholds at all.

Still, the evidence is anecdotal at best, and a proper analysis would have to look for a discontinuity in prices around the time that the map was created, with a clustering of prices around boundary points that could not be accounted for by random chance alone. 

Meanwhile, some caution is probably warranted in interpreting prediction market data. This is a case in which the ease of visualization, aggregation and dissemination of data can have an impact on the underlying measurements themselves, and indeed on the objective probabilities that the measures are intended to reflect.

Friday, September 23, 2016

Thine Every Flaw

There’s a verse in America the Beautiful that I absolutely adore; it represents for me the very best traditions of my adopted country:
America! America!
God mend thine ev’ry flaw,
Confirm thy soul in self-control,
Thy liberty in law.
I’ve been thinking about these words a lot over the past year or so, as the election season has revealed just how divided and how lacking in common purpose we are as a nation.

It's glaringly obvious that international trade, migration, and technological progress have brought enormous benefits to many of us. Our handheld devices are more powerful than the computers that launched our first satellites into orbit. Our system of higher education remains a magnet for eager students from every corner of the world, in part because we have attracted and retained the finest research talent. We are on the verge of a revolution in transportation and urban form as driverless cars make their presence felt. Our cultural products—movies and music among them—continue to attract strong global demand. And our Olympic medal winners encompass many different identities, religions, and countries of origin.

But globalization and technological progress have also left in their wake economic devastation and social disintegration across large swathes of the country that were previously prosperous and stable. The kind of deprivation once confined to inner cities—and tolerated for decades by the rest of society—is now pervasive in once-thriving industrial areas. In his recent and acclaimed memoir, JD Vance laments the decline of Middletown, Ohio from a proud and bustling steel town to "a relic of American industrial glory," with abandoned shops and broken windows, derelict homes, druggies and dealers, and places to be avoided after dark.

Anne Case and Angus Deaton have reported a startling increase in midlife mortality among white Americans without a college degree, "largely accounted for by increasing death rates from drug and alcohol poisonings, suicide, and chronic liver diseases and cirrhosis." Stratification by sex reveals that this phenomenon has hit white working class women especially hard. Trends in criminal justice tell a similar story: the incarceration rate for white women has risen by a staggering fifty percent since 2000, while that for black women has fallen more than 30%. Similar, but much less striking trends are in evidence for males.

All this has led to what Dani Rodrik calls the politics of anger. In its American incarnation, this anger has lifted to the helm of a major political party a man who has apparent contempt for the greatest of our traditions: due process even for those accused of the most heinous crimes, the prohibition of cruel and unusual punishment, and freedom from discrimination on the basis of religion or race. He lacks the self-control for which the verse above pleads, and his appeal to liberty and law is opportunistic and entirely self-serving.

This has been too much for some in his own party to stomach. Meg Whitman, a Republican candidate for Governor of California as recently as 2010, has been actively campaigning for Hillary Clinton. And if unconfirmed reports are to be believed, former president George H.W. Bush intends to vote for her too.

But even if we manage to dodge this bullet in November, the conditions that have fueled Trump's rise will remain in place, and the anger will intensify rather than abate. Something has got to be done to prevent our social fabric from fraying further. But what?

Perhaps protectionist and exclusionary policies can provide some measure of short term relief, but much of the dislocation that results from globalization is also a consequence of technological progress, and giving up on the latter is a recipe for economic suicide. Targeted interventions that support retraining and transition to growing sectors of the economy have to be part of the solution, but these are piecemeal efforts with varying effectiveness and the potential for bureaucratic mismanagement.

An alternative approach is to target inequality and poverty directly, through cash transfer schemes such as a universal basic income or a negative income tax. But payments such as these are not contingent on the performance of the economy as a whole, and therefore provide no incentives for people to support policies that are beneficial in the aggregate but impose costs on them as individuals.

What we need is a distributive mechanism that allows for all to benefit when the country benefits. Debraj Ray has recently proposed something along these lines, a universal basic share. This is simply a share of nominal GDP,  the value of which will ebb and flow with the nation's aggregate income. Aside from some obvious advantages relative to a basic income, such as the absence of any need for indexation, this would give all citizens a stake in the prosperity of the country as a whole.

How might such a scheme be implemented? I have previously proposed the creation of individual accounts at the Federal Reserve for every citizen, including minors, which could be credited with the profits of open market operations. These profits are currently transferred to the Treasury. Any shortfall relative to the basic income share would then have to be made up by transfers from the Treasury to the Fed. One considerable benefit of such accounts is that they would do away with the need for deposit insurance, and would remove at a stroke the implicit subsidy that such insurance provides for proprietary trading at commercial banks. 

Policies of this kind already exist. For instance, the Alaska Permanent Fund collects and invests a portion of the revenue from mineral leases, and periodically distributes dividends to all qualified residents of the state.

The hope is that an initiative such as this can distribute more evenly the benefits from policies that raise aggregate incomes, whether through trade, migration, or technological progress. This ought to mitigate the political obstacles to the implementation of such policies. And perhaps the sense of common ownership will help bridge some of the deep divisions that have become so salient during this electoral season.

Through his rhetoric, Donald Trump has emboldened and empowered some of the most virulently racist and anti-Semitic elements in our society. Just take a look, for instance, at the messages received on twitter by the political theorist Danielle Allen, in response to her concerns about a Trump nomination. They are disheartening in the extreme.

But Trump has the support of about 40% of registered voters, which in my estimation is about 88 million people or 36% of the adult population. While many of them may hold views on some matters that are immensely distasteful and deeply hurtful to others, I think that JD Vance is right to point out that it is "difficult in the abstract to appreciate that those with morally objectionable viewpoints can still be good people." 

I have been an American for just six years, and it is far too soon for me write off so substantial a fraction of my fellow citizens. Call it the naive optimism of the newly naturalized if you like, but I really do think that we can get past this. With or without divine intervention, we can mend our individual and collective flaws.

Thursday, July 21, 2016

A Fallacy of Composition

Peter Moskos is a sociologist by training, a professor at John Jay College of Criminal Justice, and a former Baltimore City police officer. In responding to the shooting of Philando Castile, he had this to say:
Honestly, in this shooting, with this cop, in this locale, I don't think there's a chance in hell Castile would have been shot had he been white. 
Nor did he think this was an entirely isolated incident; it reminded him of the (non-fatal) shooting of Levar Jones by Sean Groubert at a traffic stop in South Carolina. I had exactly the same reaction when I saw the Castile video, as did others. Even the Governor of Minnesota conceded that the shooting "probably would not have happened if he were white."

And yet, Moskos was unsurprised by Roland Fryer's recent claims of an absence of racial bias in police shootings:
I was not surprised by Fryer's conclusions... if one wishes to reduce police-involved shootings... there are good liberal reasons to de-emphasize the significance of race in policing.

Jonathan Ayers, Andrew Thomas, Diaz Zerifino, James Boyd, Bobby Canipe, Dylan Noble, Dillon Taylor, Michael Parker, Loren Simpson, Dion Damen, James Scott, Brandon Stanley, Daniel Shaver, and Gil Collar were all killed by police in questionable to bad circumstances... What they have in common is none were black and very few people seemed to know or care when they were killed. 
Moskos is not arguing here that the police can do no wrong; he is arguing instead that in the aggregate, whites and blacks are about equally likely to be victims of bad shootings. 

How can these two views be reconciled? If there is bias in individual incidents, ought it not to show up in aggregate data? Doesn't the congruence between the racial composition of arrestees nationwide and the racial composition of victims of police killings indicate an absence of bias, as Sendhil Mullainathan claimed a few months ago?

I have argued previously that it does not, because of systematic differences in the qualitative nature of encounters. If police initiate more encounters with blacks that are not objectively threatening (but may in some cases be subjectively perceived to be threatening) then parity in killings per encounter can indicate the presence rather than absence of bias. As Andrew Gelman put it at the time, it's all about the denominator

But Moskos offers another, quite different reason why bias in individual incidents might not be detected in aggregate data: large regional variations in the use of lethal force. 

To see the argument, consider a simple example of two cities that I'll call Eastville and Westchester. In each of the cities there are 500 police-citizen encounters annually, but the racial composition differs: 40% of Eastville encounters and 20% of Westchester encounters involve blacks. There are also large regional differences in the use of lethal force: in Eastville 1% of encounters result in a police killing while the corresponding percentage in Westchester is 5%. That's a total of 30 killings, 5 in one city and 25 in the other.

Now suppose that there is racial bias in police use of lethal force in both cities. In Eastville, 60% of those killed are black (instead of the 40% we would see in the absence of bias). And in Westchester the corresponding proportion is 24% (instead of the no-bias benchmark of 20%). Then we would see 3 blacks killed in one city and 6 in the other. That's a total of 9 black victims out of 30. The black share of those killed is 30%, which is precisely the black share of total encounters. Looking at the aggregate data, we see no bias. And yet, by construction, the rate of killing per encounter reflects bias in both cities. 

This is just a simple example to make a logical point. Does it have empirical relevance? Are regional variations in killings large enough to have such an effect? Here is Moskos again:
Last year in California, police shot and killed 188 people. That's a rate of 4.8 per million. New York, Michigan, and Pennsylvania collectively have 3.4 million more people than California (and 3.85 million more African Americans). In these three states, police shot and killed... 53 people. That's a rate of 1.2 per million. That's a big difference.

Were police in California able to lower their rate of lethal force to the level of New York, Michigan, and Pennsylvania... 139 fewer people would be killed by police. And this is just in California... If we could bring the national rate of people shot and killed by police (3 per million) down to the level found in, say, New York City... we'd reduce the total number of people killed by police 77 percent, from 990 to 231!
This is a staggeringly large effect. 

Additional evidence for large regional variations comes from a recent report by the Center for Policing Equity. The analysis there is based on data provided voluntarily by a dozen (unnamed) departments. Take a close look at Table 6 in that document, which reports use of force rates per thousand arrests. The medians for lethal force are 0.29 and 0.18 for blacks and whites respectively, but the largest recorded rates are much higher: 1.35 for blacks and 3.91 for whites. There is at least one law enforcement agency that is killing whites at a rate more than 20 times greater than that of the median agency.

On the reasons for these disparities, one can only speculate:
I really don't know what some departments and states are doing right and others wrong. But it's hard for me to believe that the residents of California are so much more violent and threatening to cops than the good people of New York or Pennsylvania. I suspect lower rates of lethal force has a lot to do with recruitment, training, verbal skills, deescalation techniques, not policing alone, and more restrictive gun laws. 
Moskos expands on these points in a recent conversation with Glenn Loury.

All of this must be interpreted with caution, since the information we have available is so patchy and deficient. As I wrote in a recent opinion piece with Willemien Kets, there is a desperate need for better data, collected and distributed in a comprehensive and uniform manner. Without this we are just groping in the dark.