Category: Statistics

Why avoid panel data in examining social mobility?

Last week at Politics and Prose, I had the opportunity to hear Robert Putnam’s book talk for Our Kids: The American Dream in Crisis. In his book, he focuses on data that purport to show a growing divide in income inequality and social unraveling.

Putnam told a personal anecdote about his deteriorating home town in the Rust Belt. If Putnam were able to prove that the shrinking economy from the loss of manufacturing jobs in the Rust Belt proportionately reflected the larger economy in all other sectors, he might have a strong data point, but a personal anecdote is not enough. The availability heuristic is not strong evidence.

So much of the talk concerning income inequality pertains to an unstated premise about social mobility. The widespread fear is not just that the rich are getting richer, but that the rich are getting richer at the expense of the poor. The mental model assumes some fixed share of wealth that exists in the world should be divvied up fairly so as to avoid predation by the strong on the weak. Often, the evidence presented for a “fixed pie” theory is to show the shrinking share of income among the lower quintiles and the growing share of income among the higher quintiles. The problem with this methodology is that it doesn’t actually account for social mobility. To prove that capital is flowing from individuals in the bottom quintile to individuals in the top quintile, we need panel data.

If we don’t analyze with panel data, we might observe the top quintile, profiting from some entirely new high-tech sector, drastically increasing their income by 20% while lower quintiles still increase at 2%. More wealth generated at the top wouldn’t imply material loss for the bottom quintile.

In the Q&A, I pressed Professor Putnam on his methodology, specifically, to what extent he used panel data to show decreased social mobility. After his book signing, he elaborated for me.

Putnam claimed that there was some good panel data for income, but that it couldn’t be used to show current trends in social mobility.

We might suppose that the relevant panel data to measure social mobility would include income, y_{it} for i=Poor, i=Rich, t=20, t=40.

At t=40 or so, we might expect people to be generating the most amount of income for their life.

The methodological issue Putnam pointed out was that individual incomes over a lifetime are highly nonlinear. If you were to track a random sample of individuals starting at t=20, very different kinds of individuals would look very similar, but both would appear in the bottom quintile. Specifically, y_{Rich,20} could be -$100,000 for a Harvard pre-law student who’s taking out student loans, and y_{Poor,20} could be $16,000 for a minimum wage job. However, y_{Rich,40} might be $450,000, while y_{Poor,40} might be something like $25,000.

Putnam pointed out that because of how this panel data is measured, the data is always intrinsically 30-40 years out of date. Wait, is this a cop out? Is this methodological laziness?

Just because any one particular study requires 40 years doesn’t mean that we couldn’t observe multiple concurrent staggered studies, with different individuals to show panel data over time. We can imagine Study A starting in 1945 with a batch of individuals at t=0, Study B that tracks t=0 at 1950, Study C that tracks t=0 at 1955, and so on and so forth. Then, despite nonlinearity in lifetime earnings, we would still be able to see trends in how individuals are or aren’t moving up, out of their birth quintiles.

Racist ignorance of prior probabilities, explained with Venn diagrams

Last year, in reference to the Trayvon Martin case, Matt Yglesias wrote a great short explanation of how racism is a kind of ignorance of Bayesian updating. In short, racists justify their racism by neglecting base rates. It’s a fallacious form of the availability heuristic.

Bayesian reasoning can be difficult to understand when it’s presented formally with equations and formulas, so let’s illustrate the concept with Venn diagrams.

Consider two populations, white and black. The white population is larger than the black population.


Assume that the amount of crime that occurs in the two populations is roughly proportional to the size of each, represented by the red circle below.


Assume that police attention, due to institutional racism, is disproportionately focused toward black criminals, as represented by the blue ellipse below.


The population of convicted criminals would be represented by the purple shading below.


A racist observing racial discrepancies between the inmate population and the general population is myopically only seeing the purple shading. The racist sees that blacks make up a disproportionately large fraction of the purple shading while falsely assuming the inmate population is an unbiased sample. The racist neglects what the true parameter is.

Disproportionately punishing criminals in minority communities would be horrible in and of itself, but the War on Drugs has subverted the criminal justice system in an even worse way, and exacerbated institutional racism. How?

Conducting the War on Drugs requires the violation of civil liberties. Why? Whereas victims of crimes cooperate with police and offer evidence to bring criminals to justice, victimless crimes produce no such cooperative victims. Without victims pointing toward any kind of offender, the primary method to catch violators of victimless crimes is to preemptively assume some fraction of a population is criminal and use sweeping powers to arbitrarily detain and search.

Without any victims, from where would probable cause originate? Terry v. Ohio paved the path for Arizona v. Johnson, and now the police act on “reasonable suspicion,” which in practice has turned into arbitrary officer discretion, far beyond the original scope of the standard to ensure officer safety. “Reasonable suspicion” is a lesser degree of certainty than probable cause, and as such, was always obviously unconstitutional.

If a police department were already predisposed to target a black community, instructing them go after victimless crimes would intensify their biased policing, giving them cover to target whomever they already were going to target.

Not only does the War on Drugs erode the potency of the Constitution, it erodes the trust between the public and law enforcement. Whereas the public might, in ideal theory, primarily rely on law enforcement for protection from criminals, the War on Drugs has subverted the relationship, and given the public a reason to fear the police. The War on Drugs distracts the police with incentives to maximize drug arrests, drawing their focus drawn away from putting away the harmful elements of society.

The War on Drugs produces a more disturbing Venn diagram.

Assume a majority white population and a minority black population.


Assume that victimless crimes in the two populations are occurring proportionally to their populations, because the drive to alter consciousness is a human universal.


Assume that a smaller amount of crimes with victims are occurring in the two populations proportionally.


The encouragement of police attention to victimless crimes gives the police cover to disproportionately target the black community.


Racists incorrectly infer biased police attention as a proxy for societal harm, failing to distinguish between malum in se and malum prohibitum. The purple shading below represents an entire group of people who are being oppressed by a criminal justice system that is consistently and repeatedly violating Mill’s harm principle.