Statistics of Inequality and Discrimination

36-313, Fall 2021

Many social questions about inequality, injustice and unfairness are, in part, questions about evidence, data, and statistics. This class lays out the statistical methods which let us answer questions like Does this employer discriminate against members of that group?, Is this standardized test biased against that group?, Is this decision-making algorithm biased, and what does that even mean? and Did this policy which was supposed to reduce this inequality actually help? We will also look at inequality within groups, and at different ideas about how to explain inequalities between and within groups. The class will interweave discussion of concrete social issues with the relevant statistical concepts.

Pre-requisites

Learning Objectives (accreditation bureaucrats look here)

• Calculate standard measures of within-group inequality, such as the Gini index, apply them to data sets, and interpret the results
• Recognize, describe and estimate heavy-tailed distributions of income, wealth, etc., and articulate how heavy tails relate to levels of inequality
• Calculate standard measures of between-group inequality, apply them to data sets, calculate the statistical significance and uncertainty of these measures, and interpret the results
• Adjust measures of between-group inequality for differences in the characteristics of various groups (using regression or other, related techniques), and explain the pros and cons of doing so
• Relate statistical measures of between-group inequality to legal concepts of "disparate treatment", "disparate impact" and discrimination
• Calculate standard measures of intergenerational mobility, and explain their implications for the persistence of inequality
• Calculate and interpret standard measures of spatial segregation;
• Calculate, distinguish and apply widely-used concepts of "fairness" and "bias" for decision-making algorithms and for mental tests;
• Assess studies of social programs against commonly-accepted standards of experimental and observational study design
• Understand models of social dynamics in which categorical inequalities form and/or perpetuate themselves, even in the absence of prejudice, and distinguish situations where these models do apply from those where they do not

Course Mechanics

• Lectures
  • No Recordings
• No textbooks, lots of readings
• Assignments
  • Exercises
  • Homework
• Time Expectations
• Grading
  • Grade changes and regrading
• Canvas, Gradescope and Piazza
• Office Hours
• Collaboration, Cheating and Plagiarism
• Accommodations for Students with Disabilities
• Inclusion and Respectful Participation

Lectures

No Recordings: I will not be recording lectures. This is because the value of class meetings lies precisely in your chance to ask questions, discuss, and generally interact. (Otherwise, you could just read a book.) Recordings interfere with this in two ways:

1. They tempt you to skip class and/or to zone out and/or try to multi-task during it. (Nobody, not even you, is really any good at multi-tasking.) Even if you do watch the recording later, you will not learn as much from it as if you had attended in the first place.
2. People are understandably reluctant to participate when they know they're being recorded. (It's only too easy to manipulate recordings to make anyone seem dumb and/or obnoxious.) Maybe this doesn't bother you; it doesn't bother me, much, because I'm protected by academic freedom and by tenure, but a good proportion of your classmates won't participate if they're being recorded, and that diminishes the value of the class for everyone.

Recording someone without their permission is illegal in many places, and more importantly is unethical everywhere, so don't make your own recordings of the class.

(Taking notes during class is fine and I strongly encourage it; taking notes forces you to think about what you are hearing and how to organize it, which vhelps you understand and remember the content.)

No textbooks, lots of readings

You will see, when you look at the class schedule below, that there are usually no more than two (shorter) readings per class. There are also however a lot of optional readings. I don't expect you to do all those readings, but they do give you pathways to go deeper into particular subjects, to explore the history of ideas about some matter, or point you at related topics. You may notice that lots of the readings aren't about statistics; this is because doing good statistics about any subject requires knowing lots about the subject-matter.

Assignments

1. Practice. Practice is essential to developing the skills you are learning in this class. It also actually helps you learn, because some things which seem murky clarify when you actually do them, and sometimes trying to do something shows you what you only thought you understood.
2. Feedback. By seeing what you can and cannot do, and what comes easily and what you struggle with, I can help you learn better, by giving advice and, if need be, adjusting the course.
3. Evaluation. The university is, in the end, going to stake its reputation (and that of its faculty) on assuring the world that you have mastered the skills and learned the material that goes with your degree. Before doing that, it requires an assessment of how well you have, in fact, mastered the material and skills being taught in this course.

To serve these goals, there will be two kinds of assignment in this course.

After-class comprehension questions and exercises

Following every lecture, there will be a brief set of questions about the material covered in lecture. Sometimes these will be about specific points in the lecture, sometimes about specific aspects of the reading assigned to go with the lecture. These will be done on Canvas/Gradescope, and will be due the day after each lecture. These should take no more than 10 minutes, but will be untimed (so no accommodations for extra time are necessary). If the questions ask you to do any math (and not all of them will!), a scan or photograph of hand-written math is OK, so long as the picture is clearly legible. (Black ink or dark pencil on white paper helps.)

Homework

Most weeks will have a homework assignment, divided into a series of questions or problems. These will have a common theme, and will usually build on each other. Each problem set will involve some combination of (very basic) statistical theory, (possibly less basic) calculations using the theory we've gone over, and analysis of real data sets using the methods discussed in class.

All homework will be submitted electronically through Gradescope/Canvas. Most weeks, homework will be due at 6:00 pm on Thursdays (Pittsburgh time). There will be a few weeks, clearly noted on the syllabus and on the assignments, when this won't be the case. When this results in less than seven days between an assignment's due date and the previous due date, the homework will be shortened.

Time Expectations

Grading

Grades will be broken down as follows:

• Homework: 90%. All homeworks will have equal weight. Your lowest 3 homework grades will be dropped, no questions asked. If you turn in all homework assignments on time, for a grade of at least 60% (each), your lowest four homework grades will be dropped. Accordingly: Late homework will not be accepted for any reason.
• After-class questions: 10%. All sets of questions will have equal weight. The lowest 5 will be dropped, no questions asked, with the lowest 6 dropped if you turn in every set of questions with a minimum grade of 60%.

Grade boundaries will be as follows:

A	[90, 100]
B	[80, 90)
C	[70, 80)
D	[60, 70)
R	< 60

To be fair to everyone, these boundaries will be held to strictly.

Grade changes and regrading: If you think that particular assignment was wrongly graded, tell me as soon as possible. Direct any questions or complaints about your grades to me; the teaching assistants have no authority to make changes. (This also goes for your final letter grade.) Complaints that the thresholds for letter grades are unfair, that you deserve a higher grade, that you need a higher grade, etc., will accomplish much less than pointing to concrete problems in the grading of specific assignments.

As a final word of advice about grading, "what is the least amount of work I need to do in order to get the grade I want?" is a much worse way to approach higher education than "how can I learn the most from this class and from my teachers?".

Canvas, Gradescope and Piazza

We will be using Piazza for question-answering. You will receive an invitation within the first week of class. Anonymous-to-other-students posting of questions and replies will be allowed, at least initially. Anonymity will go away for everyone if it is abused. During Piazza office hours, someone will be online to respond to questions (and follow-ups) in real time. You are welcome to post at any time, but outside of normal working hours you should expect that the instructors have lives.

Office Hours

Collaboration, Cheating and Plagiarism

Except for explicit group exercises, everything you turn in for a grade must be your own work, or a clearly acknowledged borrowing from an approved source; this includes all mathematical derivations, computer code and output, figures, and text. Any use of permitted sources must be clearly acknowledged in your work, with citations letting the reader verify your source. You are free to consult the textbooks and recommended class texts, lecture slides and demos, any resources provided through the class website, solutions provided to this semester's previous assignments in this course, books and papers in the library, or legitimate online resources, though again, all use of these sources must be acknowledged in your work. (Websites which compile course materials are not legitimate online resources.)

In general, you are free to discuss homework with other students in the class, though not to share or compare work; such conversations must be acknowledged in your assignments. You may not discuss the content of assignments with anyone other than current students, the instructors, or your teachers in other current classes at CMU, until after the assignments are due. (Exceptions can be made, with prior permission, for approved tutors.) You are, naturally, free to complain, in general terms, about any aspect of the course, to whomever you like.

Any use of solutions provided for any assignment in this course, or in other courses, in previous semesters is strictly prohibited. This prohibition applies even to students who are re-taking the course. Do not copy the old solutions (in whole or in part), do not "consult" them, do not read them, do not ask your friend who took the course last year if they "happen to remember" or "can give you a hint". Doing any of these things, or anything like these things, is cheating, it is easily detected cheating, and those who thought they could get away with it in the past have failed the course. Even more importantly: doing any of those things means that the assignment doesn't give you a chance to practice; it makes any feedback you get meaningless; and of course it makes any evaluation based on that assignment unfair.

If you are unsure about what is or is not appropriate, please ask me before submitting anything; there will never be a penalty for asking. If you do violate these policies but then think better of it, it is your responsibility to tell me as soon as possible to discuss how to rectify matters. Otherwise, violations of any sort will lead to severe, formal disciplinary action, under the terms of the university's policy on academic integrity.

On the first day of class, you will be assigned a "homework 0" on the content of these policies. This assignment will not factor into your grade, but you must complete it before you can get any credit for any other assignment.

Accommodations for Students with Disabilities

Inclusion and Respectful Participation

The university is a community of scholars, that is, of people seeking knowledge. All of our accumulated knowledge has to be re-learned by every new generation of scholars, and re-tested, which requires debate and discussion. Everyone enrolled in the course has a right to participate in the class discussions. This doesn't mean that everything everyone says is equally correct or equally important, but does mean that everyone needs to be treated with respect as persons, and criticism and debate should be directed at ideas and not at people. Don't dismiss (or credit) anyone in the course because of where they come from, and don't use your participation in the class as a way of shutting up others. Don't be rude, and don't go looking for things to be offended by. Statistical methods don't usually lead to heated debate, but the subjects to which we'll apply the methods notoriously do. If someone else is saying something you think is really wrong-headed, and you think it's important to correct it, address why it doesn't make sense, and listen if they give a counter-argument.

The classroom is not a democracy; as the teacher, I have the right and the responsibility to guide the discussion in what I judge are productive directions. This may include shutting down discussions which are not helping us learn about statistics, even if those discussions might be important to have elsewhere. (You can have them elsewhere.) I will do my best to guide the course in a way which respects everyone's dignity as a human being, as a scholar, and as a member of the university.

Detailed course calendar

Readings will be finalized a week before each course meeting. Links on readings point to electronic versions accessible through the university library. (You may need to authenticate yourself with the library and/or use the VPN, if you're trying to access them from off campus.) Optional readings really are optional, but the non-optional ones really are not optional. Readings marked with one or more stars (*) are, as it were, especially optional, because of some combination of being long, difficult, old, etc.

The order of topics after about October 15 is currently somewhat tentative. The due dates for assignments, however, are fixed.

Lecture 1 (Tuesday, 31 August): Introduction to the course

• Overview of course topics, goals and mechanics. Lighting review of essential probability and statistics: populations, distribution within a population, distribution functions, models for distributions, comparison of distributions across populations or sub-populations, samples and inference from samples.
• Notes for lecture 1 (.Rmd file, showing how to do all the calculations and make all the figures using R Markdown)
• Homework:
  • Homework 0 assigned (on Canvas)
  • Homework 1: assignment, handout on propagation of error

Lecture 2 (Thursday, 2 September): Describing income and wealth inequality within a single population

• What does the distribution of income and wealth look like within a population? How do we describe population distributions, especially when there is an extreme range of values (a big difference between the rich and poor)? Measures of central tendency (median, mode, mean), of dispersion and of skew. Trends over time in median vs. mean income and wealth. Where do you fall in the distribution if you make $10,000 a year, or $50,000, or $1,000,000? How much do you need to make to be better off than 50% of the population? Than 90%? Than 99%? Where did the idea of "the 1%" wealthy elite come from? Trends over time in typical values vs. high percentiles. Measures of concentration of income and wealth: ratios, the Lorenz curve, the Gini coefficient. Time permitting: other summary measures of concentration and inequality besides the Gini coefficient.
• Notes (.Rmd)
• Readings:
  • Suresh Naidu, Rajiv Sethi and Sarah Thomas, A World of Differences: An Introduction to Inequality [This is a short document that's written as a supplement to a free, online introductory economics textbook, and works through examples of things like calculating the Gini coefficient. You don't really need to know economics to read it.]
  • Robert M. Solow, "Thomas Piketty Is Right: Everything you need to know about Capital in the Twenty-First Century", The New Republic 22 April 2014 [This is is a review and summary of Piketty book, written for a general audience by one of the great economists of the 20th century]
  • Optional reading:
    • (*) Michele Alacevich and Anna Soci, "The Statistical Drift of Inequality Studies", ch. 3 in Inequality: A Short History (Washington, D.C.: Brookings Institution Press, 2018)
    • (**) Thomas Piketty, Capital in the Twenty-First Century (Cambridge, Massachusetts: Harvard University Press, 2014; translated by Arthur Goldhammer from Le capital au XXI siècle, Paris: Éditions du Seuil, 2013)

Lecture 3 (Tuesday, 7 September): Income and wealth inequality: modeling I

• The concept of "heavy tails", where the largest values in a population are orders of magnitude larger than typical values. Specific kinds of distributions adapted to heavy-tailed data; log-normal and power law (Pareto, Zipf) distributions. Calculating measures of inequality from theoretical distributions.
• Notes (.Rmd)
• Reading
  • Mark E. J. Newman, "Power laws, Pareto distributions and Zipf's law", Contemporary Physics 46 (2005): 323--351, arxiv:cond-mat/0412004, sections I, II, III (skipping or skimming sub-section F), IV (skipping or skimming sub-sections E and F)
  • Optional reading
    • (*) Barry C. Arnold, Pareto Distributions, 2nd edition (Boca Raton, Florida: CRC Press, 2015)
    • (**) Vladimir Hlasny, "Parametric representation of the top of income distributions: Options, historical evidence, and model selection", Journal of Economic Surveys 35 (2021): 1217--1256

Lecture 4 (Thursday, 9 September): Modeling wealth and income distributions II

• Fitting distributions to data, using summary statistics and/or maximum likelihood. Checking goodness of fit. Explanations and origin myths: positive feedback, multiplicative growth and "cumulative advantage" processes.
• Reading:
  • Continue reading Newman (2003)
  • Optional reading:
    • (*) Aaron Clauset, Cosma Rohilla Shalizi and M. E. J. Newman, "Power-law Distributions in Empirical Data", SIAM Review 51 (2009): 661--703, arxiv:0706.1062
    • (*) Michael Mitzenmacher, "A brief history of generative models for power law and lognormal distributions", Internet Mathematics 1 (2004): 226--251
    • (***) Elliott W. Montroll and Michael F. Shlesinger, "On 1/f noise and other distributions with long tails", Proceedings of the National Academy of Sciences (USA) 79 (1982): 3380--3383
    • (***) Herbert A. Simon, "On a Class of Skew Distribution Functions", Biometrika 42 (1955): 425--440
    • (**) John Sutton, "Gibrat's Legacy", Journal of Economic Literature 35 (1997): 40--59 [ungated copy]
• Homework:
  • Homework 0 due
  • Homework 1 due
  • Homework 2: assignment, uswealth.csv data file

Lecture 5 (Tuesday, 14 September): Speed-run through social and economic stratification

• Reminders (?) about social-scientific concepts used to describe differences between people, and how people describe others and themselves. Types of qualitative, categorical differences: class, order, caste, race, ethnicity, nationality, citizenship, sex, gender. More-or-less dimensions of differentiation: age, status, prestige, income, consumption, wealth, other resources --- "human capital" or skills, "cultural capital", "social capital". The compound measure "socioeconomic status". Education. The distinction between "ascribed" and "attained" social conditions. The legal notion of "protected categories". Individual and inter-generational mobility; transmission of inequality. Endogamy and informative, but uninfluential, genetic differences.
• Readings
  • Lisa A. Keister and Darby E. Southgate, "Social stratification and opportunities", ch. 1 in Inequality: A Contemporary Approach to Race, Class, and Gender (Cambridge, England: Cambridge University Press, 2012)
  • Optional reading
    • Kwame Anthony Appiah, The Lies That Bind: Rethinking Identity (New York: W. W. Norton, 2018)
    • (*) Kwame Anthony Appiah, Lines of Descent: W. E. B. Du Bois and the Emergence of Identity (Cambridge, Massachusetts: Harvard University Press, 2014)
    • Luigi L. Cavalli-Sforza, Genes, Peoples, and Languages (New York: North Point Press, 2000)
    • (*) Luigi L. Cavalli-Sforza, Paolo Menozzi and Alberto Piazza, "Demic Expansions and Human Evolution", Science 259 (1993): 639--646
    • (*) John Dollard, Caste and Class in a Southern Town (3rd edition Garden City, New York: Doubleday Anchor, 1957; first edition New Haven, Connecticut: Yale University Press, 1937), especially ch. V ("Caste and Class in Southertown")
    • Ernest Gellner, Nations and Nationalism (Ithaca, New York: Cornell University Press, 1983)
    • Alondra Nelson, The Social Life of DNA: Race, Reparations, and Reconciliation After the Genome (Boston: Beacon Press, 2016)
    • (*) W. G. Runciman, The Social Animal (London: HarperCollins, 1998)
    • (*) Charles Tilly, Durable Inequality (Berkeley: University of California Press, 1998)
    • (*) Adam P. Van Arsdale, "Population Demography, Ancestry, and the Biological Concept of Race", Annual Review of Anthropology 48 (2019): 227--241
    • (*) W. Lloyd Warner, "American Caste and Class", American Journal of Sociology 42 (1936): 234--237

Lecture 6 (Thursday, 16 September): Income (and wealth) disparities: comparing central tendencies and typical values

• How does income (and wealth) differ across groups? How do we compare average or typical values? Permutation tests for differences in mean (and other measures of the average). Resampling (the bootstrap) for finding the range of differences compatible with the data, and/or margins of error around an estimate of the difference.
• Notes (.Rmd file, containing code you may find useful in the homework)
• Reading:
  • Andrew S. Zieffler, Jeffrey R. Harring, and Jeffrey D. Long, Comparing Groups: Randomization and Bootstrap Methods Using R (New York; John Wiley and Sons, 2011), chs. 6 ("Randomization and Permutation Tests"), 7 ("Bootstrap Tests") and 9 ("Bootstrap Intervals and Effect Sizes"). Of these, chs. 6 and 9 are most important, and you can skim or even skip sections 6.8, 7.4--7.7, 7.12--7.13, 9.5--9.6, 9.8--9.10
  • Optional readings:
    • (**) A. C. Davison and D. V. Hinkley, Bootstrap Methods and their Applications (Cambridge, England: Cambridge University Press, 1997)
    • (**) Bradley Efron, "Bootstrap Methods: Another Look at the Jackknife", Annals of Statistics 7 (1979): 1--26
    • (*) Tim Hesterberg, "What Teachers Should Know about the Bootstrap: Resampling in the Undergraduate Statistics Curriculum", arxiv:1411.5279 (2014)
    • (*) CRS, Advanced Data Analysis from an Elementary Point of View, ch. 6
    • CRS, "The Bootstrap", American Scientist 98 (2010): 186--190
• Homework:
  • Homework 2 due
  • Homework 3: assignment; the data file and descriptive "codebook" are on Canvas, and shouldn't be shared outside this class.

Lecture 7 (Tuesday, 21 September) Income (and wealth) disparities: comparing whole distributions

• The "analysis of variance" method: decomposing the over-all variance into variance within groups versus variance between groups. Some ANOVA models, i.e., linear regressions with only categorical predictor variables. Fitting ANOVA models. Trends in global income inequality, between-country and within-country inequality. Q-Q plots for comparing distributions. Stochastic dominance. The "relative distribution" method of comparing populations.
• Notes (.Rmd)
• Readings:
  • Mark S. Handcock and Martina Morris, "Relative Distribution Methods", Sociological Methodology 28 (1998): 53--97
  • Optional readings:
    • (**) Patrick Bayer and Kerwin Kofi Charles, "Divergent Paths: Structural Change, Economic Rank, and the Evolution of Black-White Earnings Differences, 1940--2014", Working Paper 22797, National Bureau of Economic Research (2016)
    • (*) Mark S. Handcock and Martina Morris, Relative Distribution Methods in the Social Sciences (New York: Springer-Verlag, 1999)
    • (**) R. A. Fisher, Statistical Methods for Research Workers (Edinburg: Oliver and Boyd, 1925), chs. 7 and 8
    • (***) R. A. Fisher, "The Correlation Between Relatives on the Supposition of Mendelian Inheritance", Transactions of the Royal Society of Edinburgh 52 (1918): 399--433 [Available via the R. A. Fisher Digital Archive]
    • Branko Milanovic, Global Inequality: A New Approach for the Age of Globalization (Cambridge, Massachusetts: Harvard University Press, 2016)

Lecture 8 (Thursday, 23 September) No class meeting due to instructor illness

• Homework:
  • Homework 3 due
  • Homework 4: assignment

Lecture 9 (Tuesday, 28 September): Explaining, or explaining away, inequality I

• To what extent can differences in outcomes between groups be explained by differences in their attributes (e.g., explaining differences in incomes by differences in marketable skills)? How should we go about making such adjustments? Is it appropriate to treat discrimination as the "residual" left unexplained? Using regression models to "control for" or "adjust for" multiple variables when comparing mean outcomes. (Time permitting: equivalent adjustments in relative-distribution comparisons.)
• Notes (.Rmd)
• Readings:
  • Optional:
    • (*) Philipp Bach, Victor Chernozhukov, Martin Spindler, "Closing the U.S. gender wage gap requires understanding its heterogeneity", arxiv:1812.04345
    • Walter Benn Michaels and Adolph Reed, Jr., "The Trouble with Disparity", Nonsite 32 (10 September 2020)
    • (*) Jacob Mincer, Schooling, Experience and Earnings (New York: Columbia University Press, 1974)

Lecture 10 (Thursday, 30 September): Explaining, or explaining away, inequality II

• Deciding what to adjust for. explanation, and when is it "explaining away" discrimination? Using graphical models to represent causal relations between variables. How to use graphical models to decide what should and what should not be controlled for. The causal models implicit in decisions about controls.
• Notes (.Rmd)
• Reading:
  • Main reading: none
  • Optional reading
    • Clark Glymour, "What Went Wrong? Reflections on Science by Observation and The Bell Curve", Philosophy of Science 65 (1998): 1--32 [Ungated PDF copy via Prof. Glymour]
    • Maya Sen and Omar Wasow, "Race as a Bundle of Sticks: Designs that Estimate Effects of Seemingly Immutable Characteristics", Annual Review of Political Science 19 (2016): 499--522
• Homework:
  • Homework 4 due
  • Homework 5: Assignment

Lecture 11 (Tuesday, 5 October): Detecting and interpreting inequalities in hiring, admissions, etc.

• Do employers hire members of different groups at different rates? (Or: do schools admit members of different groups at different rates?) How can we tell? Statistical tests for differences in proportions or probabilities. Comparing hiring rates per applicant by group vs. comparing those hired to some reference population. Audit studies. When are differences in hiring rates evidence for discrimination? How do statistical perspectives on this question line up with legal criteria for "disparate treatment" and "disparate impact"? The economists' concepts of "taste-based" and "statistical" discrimination.
• Reading
  • Main reading: none
  • Optional readings
    • (*) Marianne Bertrand and Sendhil Mullainathan, "Are Emily and Greg More Employable Than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination", American Economic Review 94 (2004): 991--1013 (also Working Paper 9873, National Bureau of Economic Research [2003])
    • (*) Michael Feldman, Sorelle Friedler, John Moeller, Carlos Scheidegger, Suresh Venkatasubramanian, "Certifying and removing disparate impact", arxiv:1412.3756
    • (**) Patrick M. Kline, Evan K. Rose and Christopher R. Walters, "Systemic Discrimination Among Large U.S. Employers", Working Paper 29053, National Bureau of Economic Research (2021)
    • Devah Pager, "The Mark of a Criminal Record", American Journal of Sociology 108 (2003): 937--975
    • (*) Lincoln Quillian and Arnfinn H. Bidtboen, "Comparative Perspectives on Racial Discrimination in Hiring: The Rise of Field Experiments", Annual Review of Sociology 47 (2021): 391--415

Lecture 12 (Thursday, 7 October): Inequalities in health, disease and mortality

• Quantifying differences in the incidence of diseases. Issues of adjustment and explanation again. Death rates, life expectancy and survival curves. Survival modeling. Focus: The "deaths of despair" controversy.
• Reading
  • Main reading: Anne Case and Angus Deaton, "Life expectancy in adulthood is falling for those without a BA degree, but as educational gaps have widened, racial gaps have narrowed", Proceedings of the National Academy of Sciences (USA) 118 (2021): e2024777118
  • Optional readings
    • Anne Case and Angus Deaton, "“Rising Morbidity and Mortality in Midlife among White Non-Hispanic Americans in the 21st Century", Proceedings of the National Academy of Sciences (USA) 112 (2015): e201518393
    • Anne Case and Angus Deaton, Deaths of Despair and the Future of Capitalism (Princeton, New Jersey: Princeton University Press, 2020)
    • Christopher J. Ruhm, "Deaths of Despair or Drug Problems?", Working Paper 24188, National Bureau of Economic Research (2018)
    • One Nation Under Stress (documentary film, 2019)
• Homework:
  • Homework 5 due
  • Homework 6: assignment, due on Wednesday, 13 October to accommodate mid-semester break (and shortened accordingly)

Lecture 13 (Tuesday, 12 October): Mobility and Transmission of Inequality

• Definitions: changes in absolute income (or wealth) within a lifetime; changes in relative income (or wealth) within a lifetime; education and occupations of children compared to parents; income and wealth of children as compared to parents. Measurement issues. Large-scale patterns in inter-generational mobility in recent decades. Social mechanisms for transmitting advantage from one generation to the next; social mechanisms for increasing inter-generational mobility. "The iron law of meritocracy".
• Reading
• Raj Chetty, Nathaniel Hendren, Patrick Kline and Emmanuel Saez, "Where is the Land of Opportunity? The Geography of Intergenerational Mobility in the United States", Quarterly Journal of Economics 129 (2014): 1553--1623 [Preprint version of the paper, data files, etc.]
• Optional reading
  • (*) Samuel Bowles and Herbert Gintis, Schooling in Capitalist America: Educational Reform and the Contradictions of Economic Life (New York: Basic Books, 1976)
  • (*) Raj Chetty, Nathaniel Hendren, Maggie R. Jones, Sonya R. Porter, "Race and Economic Opportunity in the United States: An Intergenerational Perspective", Quarterly Journal of Economics 135 (2020): 711--783 [Preprint version, data files, etc.]
  • (*) Raj Chetty and Nathaniel Hendren, "The Impacts of Neighborhoods on Intergenerational Mobility I: Childhood Exposure Effects", Quarterly Journal of Economics 133 (2018): 1107--1162
  • (*) Raj Chetty and Nathaniel Hendren, "The Impacts of Neighborhoods on Intergenerational Mobility II: County-Level Estimates", Quarterly Journal of Economics 133 (2018): 1163--1228
  • Richard Thompson Ford, "The Harvard Ruling Misses the Point", Boston Review 1 October 2019
  • Robert D. Putnam, Our Kids: The American Dream in Crisis (New York: Simon and Schuster, 2016)
  • Richard V. Reeves, "The Dream Hoarders: How America's Top 20 Percent Perpetuates Inequality", Boston Review 30 May 2017
  • Richard V. Reeves, Dream Hoarders: How the American Upper Middle Class Is Leaving Everyone Else in the Dust, Why That Is a Problem, and What to Do About It (Washington, D.C.: Brookings Institution Press, 2017)

Wednesday, 13 October

Thursday, 14 October: NO CLASS

Enjoy the mid-semester break.
• Homework:
  • Homework 6 was due on Wednesday, 13 October
  • Homework 7: assignment, mobility.csv data file

Lecture 14 (Tuesday, 19 October): Measuring Spatial Segregation and Its Consequences

• What do we mean by "segregation"? Segregation in law ("de jure") and segregration in fact ("de facto"). Different ways of measuring de facto segregation. Trends in de facto racial segregation since the end of de jure racial segregation. Why different measures of segregation give different results. Segregation by income. Segregation by political partisanship. Consequences of segregation. Inter-generational transmission again.
• Reading
  • Optional reading
    • (**) Jeremy E. Fiel, "Decomposing School Resegregation: Social Closure, Racial Imbalance, and Racial Isolation", American Sociological Review 78 (2013): 828--848
    • Salim Furth, "Is Diversity 'Segregation'?", Market Urbanism 5 July 2021 (Commentary on an application of the work of Roberto, below)
    • (**) Douglas S. Massey and Nancy A. Denton, "The Dimensions of Residential Segregation", Social Forces 67 (1988): 281--316 [also JSTOR]
    • (*) Elizabeth Roberto, "The Divergence Index: A Decomposable Measure of Segregation and Inequality", arxiv:1508.01167
    • (*) Robert J. Sampson, Great American city: Chicago and the Enduring Neighborhood Effect (Chicago: University of Chicago Press, 2011)
    • (*) Patrick Sharkey, Stuck in Place: Urban Neighborhoods and the End of Progress toward Racial Equality (Chicago: University of Chicago Press, 2013)
    • (**) Henri Theil and Anthony J. Finizza, "A note on the measurement of racial integration of schools by means of informational concepts", The Journal of Mathematical Sociology 1 (1971): 187--193
    • William Julius Wilson, When Work Disappears: The World of the New Urban Poor (New York: Alfred A. Knopf, 1996)

Lecture 15 (Thursday, 21 October): Algorithmic Bias and/or Fairness

• Notions of "fair" prediction or automated decision-making: not using "protected categories" or features; parity of error rates across groups; calibration of prediction. "Inference" issues: using features that carry information about protected features. Trade-offs between different forms of fairness. Trade-offs between forms of fairness and accuracy. Some critiques of these notions of "fairness".
• Notes (.Rmd)
• Reading
  • Sam Corbett-Davies and Sharad Goel, "The Measure and Mismeasure of Fairness: A Critical Review of Fair Machine Learning", arxiv:1808.00023
  • Optional reading:
    • Julia Angwin, Jeff Larson, Surya Mattu and Lauren Kirchner, "Machine Bias", ProPublica 23 May 2016
    • (**) Alexandra Chouldechova, "Fair prediction with disparate impact: A study of bias in recidivism prediction instruments", arxiv:1610.07524
    • (*) Simon DeDeo, "Wrong side of the tracks: Big Data and Protected Categories", pp. 31--42 in Cassidy R. Sugimoto, Hamid R. Ekbia and Michael Mattioli (eds.), Big Data Is Not a Monolith (Cambridge, Mass.: MIT Press, 2016), arxiv:1412.4643
    • (*) Michael Feldman, Sorelle Friedler, John Moeller, Carlos Scheidegger, Suresh Venkatasubramanian, "Certifying and removing disparate impact", arxiv:1412.3756
    • (***) Sharad Goel, Jake M. Hofman, M. Irmak Sirer, "Who Does What on the Web: A Large-Scale Study of Browsing Behavior", Sixth International AAI Conference on Weblogs and Social Media [ICWSM 2012] [Preprint via Prof. Goel]
    • Michael Kearns and Aaron Roth, The Ethical Algorithm: The Science of Socially Aware Algorithm Design (Oxford: Oxford University Press, 2019), especially ch. 2 (but really the whole book is relevant)
    • (***) Ninareh Mehrabi, Fred Morstatter, Nripsuta Saxena, Kristina Lerman, Aram Galstyan, "A Survey on Bias and Fairness in Machine Learning", arxiv:1908.09635
    • Cathy O'Neil, Weapons of Math Destruction (New York: Crown Books, 2016), especially chs. 1, 5, 6 and 8
• Homework:
  • Homework 7 due
  • Homework 8: assignment, compas_violence.csv data file

Lecture 16 (Tuesday, 26 October): Admissions tests

• Are standardized tests for school admission biased against certain racial groups? What does it mean to measure qualifications, and how would we know whether tests really are measuring qualifications? Predictive validity. What does it mean for a measurement to be biased? When do differences across groups indicate biases? Differential validity. (Also, disparate impact again.) Why correlating outcomes with test scores among admitted students may not make sense. "Conditioning on a collider". The "compared to what?" question.
• Reading
  • Brent Bridgeman,Laura McCamley-Jenkins, and Nancy Ervin, "Predictions of Freshman Grade-point Average from the Revised and Recentered SAT I", ETS Research Report Series 2000:1 (2000): 1--16
  • Optional reading
    • (*) A. J. Alvero, Sonia Giebel, Ben Gebre-Medhin, anthony lising antonio, Mitchell L. Stevens and Benjamin W. Domingue, "Essay Content is Strongly Related to Household Income and SAT Scores: Evidence from 60,000 Undergraduate Applications", Working Paper No. 21-03 (2021), Stanford Center for Education Policy Analysis
    • Daniel Koretz, Measuring Up: What Educational Testing Really Tells Us (Cambridge, Massachusetts: Harvard University Press, 2008)
    • (*) D. Kortez and M. Langi, "Predicting Freshman Grade-Point Average from Test Scores: Effects of Variation Within and Between High Schools", Educational Measurement: Issues and Practice 37 (2018): 9--19
    • (*) Report of the University of California Academic Council Standardized Testing Task Force (January 2020)
    • (*) Rebecca Zwick, "Disentangling the Role of High School Grades, SAT scores, and SES in Predicting College Achievement", ETS Research Report Series 2013:1 (2013): 1--20
    • (*) Rebecca Zwick and Igor Himelfarb, "The Effect of High School Socioeconomic Status on the Predictive Validity of SAT Scores and High School Grade-Point Average", Journal of Educational Measurement 48 (2011): 101--121

Lecture 17 (Thursday, 28 October): Intelligence tests

• Are intelligence tests biased? Before that: How do we measure latent attributes? How do we know the latent attributes even exist? What would it mean for there to be such a thing as "general intelligence", that could be measured by tests? Correlations between scores on tests of particular abilities or skills; factor models as explanations for correlations; estimating factor values from tests; alternatives to factor models. What, if anything, do intelligence tests measure? What rising intelligence test results (the Flynn Effect) tell us?
• Homework:
  • Homework 8 due
  • Homework 9: Assignment

Lecture 18 (Tuesday, 2 November): NO CLASS