Posts tagged with class

#### Chances of US Blacks, Hispanics, Poor, Women, Men, Whites, Rich to reach the middle class by middle age.

by Isabel Sawhill, Scott Winship, and Kerry Searle Grannis

SWG define the US middle class as 3 times the poverty level. That’s

• at least \$35 000 / year for a single person
• or at least \$71 000 / year for a family of four (multiple family members can work toward that).

Middle age they take to begin at 40.

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You can also see the 40% who do not make it to the middle class in Catherine Mulbrandon’s picture:

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SWG find “rungs” on the ladder to prosperity, such that within their dataset,

• achieving today’s rung increases the odds of achieving tomorrow’s rung,
• and failing to achieve today’s rung decreases the odds of achieving tomorrow’s rung.

(The weakest link is from basic reading & maths skills + social & emotional skills → to high school graduation + non-criminality. The strongest link is from acceptable pre-reading & pre-maths + school-appropriate behaviour → to basic reading & maths + social-emotional skills.)

That is a Markov or AR(1) at each step, but changing 2×2 matrices (pass-through probabilities) each time.

The poor outcomes for low-birthweight black poor youths are then understood, within the paper, as the composite effect of passing through the several gates.

For example low birth weight, poor parents of the wrong race starts the child off in the disadvantaged category. 40% of those are off track when school starts. Then 55% of (not just the `0-disadvantaged ∩ 1-disadvantaged`, but all of the) stage-1-disadvantaged continue to advance to the next stage on the losing track.

In this way the eventual low success-rate of the adults from poor families is seen as the product of a succession of gates.

In matrix terms each 2×2 matrix “shuffles beads from gate to gate”. For example the first matrix is

$\dpi{300} \bg_white \begin{bmatrix} 72\% & 28\% \\ 59 \% & 41\% \end{bmatrix}$

and the product (composite) of the first two is this matrix product:

$\dpi{200} \bg_white \large \begin{bmatrix} .72 & .28 \\ .59 & .41 \end{bmatrix} \cdot \begin{bmatrix} .82 & .18 \\ .45 & .55 \end{bmatrix}$

In the product matrix the red entry is the fraction of babies born disadvantaged (`0-loser`) who end up `2-disadvantaged` after 2 matrices `M₁bull;M₂` have been applied—entering middle childhood.

$\dpi{200} \bg_white \large \begin{bmatrix} .72 & .28 \\ .59 & .41 \end{bmatrix} \cdot \begin{bmatrix} .82 & .18 \\ .45 & .55 \end{bmatrix} = \begin{bmatrix} \colorbox{red}{\color{white}{71\%}} & 29\% \\ 67\% & 33\% \end{bmatrix}$

If you wanted to compute the overall numbers from the bar chart at the top you would need also a starting vector `X₀` saying how many babies start off already at a disadvantage. (The fraction who don’t start off disadvanaged is not a free parameter.)

(Source: brookings.edu)

hi-res

by Rachel Johnson, Urban-Brookings Tax Policy Center Microsimulation Model

Reading about the early meanings of the phrase “middle class” it clearly refers to:

…someone with so much capital that they could rival nobles….. professionals, managers, and senior civil servants.

and not to “the broad shoulders" holding up society, which should properly be called "the working class".

In other words, not “normal” or “typical” people at all (typical being \$21k/year)—the “middle class” could accurately refer in the U.S. only to those making over \$100k/year. I.e., “possessing significant human capital” which allows them not to just have a job at a successful corporation and be a line-item on that corporation’s budget, but to extract significant wages from the economy.

(Source: The New York Times)

hi-res

people at three different socioeconomic levels in Mumbai

(Source: video.ft.com)

## Gender Studies & Mathematics, #2

I’m totally convinced that ∃ more connections between mathematics and the humanities than the university culture I once stewed in would suggest.

Probably due to personality differences, but also lack of familiarity with each other’s subject matter, I never saw inter-departmental collaborations and—as I’ll discuss in another post—even the idea of data is seen as a four-letter word in the gender studies department. (Likewise, ethnography and anecdote are four-letter words within the economics field, and statisticians also concern themselves only with structured data.)

Nevertheless I see mathematical shapes all over cultural analysis, and I mean to record them. (However typing up a coherent few paragraphs, let alone adding drawings, takes several orders of magnitude more time than simply thinking a thought.)

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After reading her essay crowing that millennials do not see themselves as special, I went on to read more of Phoenix and the Olive Branch, which talks about rehabilitation from “Quiverfull” fundamentalist upbringing—particularly gender issues that arose as a Quiverfull young woman.

(Relevant to the “value of liberal arts" question, Sierra writes that "College literally saved my life"—without the critical thinking skills—not science or programming skills—that she learned at college, her mind and heart and … uterus would have remained ensnared in the “Quiverfull” fundamentalist mindset she grew up in. Just an interesting sidelight.)

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Sierra has a very logical way of describing a flaw with sexist views:

Check out this gem from “Reclaiming the Mind”:

You see, when people are truly committed and consistent egalitarians, they have to defend their denial of essential differences. In doing so, they will advocate a education system in the home, church, and society which neutralizes any assumption of differences between the sexes. In doing so, men will not be trained to be “men” since there is really no such thing. Women will not be encouraged to be “women” since there is no such thing. The assumption of differences becomes a way to oppress society and marginalize, in their estimation, one sex for the benefit of the other. Once we neutralize these differences, we will have neutered society and the family due to a denial of God’s design in favor of some misguided attempt to promote a form of equality that is neither possible nor beneficial to either sex.

As a truly committed and consistent egalitarian, yes, yes I do deny “essential” differences. You know why? My essential nature is not “woman.” My essential nature is me. Sierra. It’s who I am. …[M]y best friend[’s] essential nature [is] not identical to mine. It might have similar colors and shapes, but so would mine and my fiance’s. Because people are different. “Men” are not more different from women than they are from other men.

In statistical or mathematical language, I would interpret this as saying "The fact that `gender==Woman` is not entirely determinate of everything about me.”

If I were writing a computer program to mimic the kind of sexism Sierra is talking about, it would take one input for `gender` and, if the answer is `male`, then prompt for further details on the personality, achievements, background, interests, thoughts. `Elsif gender == female`, then the only questions worth asking are “`Fat? Hot?`" Otherwise, `break`; because there is no `else`.

Not that the "Being a minority is determinate of everything and only males can show variation” is limited to gender. On Reddit we find:

"I can’t imagine a black guy saying ‘anywho’"

as if blackness is somehow so determinate of behaviour. Charmed, I’m sure.

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In statistics the paradigm is that data go into a model and a couple numbers come out. Some of the numbers parameterise the model. But other numbers tell us how good the explanation is. There are numbers to tell us how well individual parts fit, how well the overall whole fits, and several numbers that are warning indicators for various types of traps that can make the other numbers mess up.

Thinking that everything about a minority is determined by their minority status is a bit like ignoring all the model-fit numbers.

If we explored some data with a large number of linear models, progressing from coarse (few terms) to fine (many terms), we would probably see gender differences as a significant term among coarse models. But those models would also have a low specificity and explanatory power. Then as we added more explanatory terms (finer models), those other explanators—correlates of gender/race, but not gender/race itself—would start to steal explanatory power away from the gender  dummy variable.

To give a physical example, 100m sprint times show differences across male/female, but training is more determinate of the sprint time. If we could measure personality and thoughts and the kinds of traits that Sierra might say define her as a person, we would probably be left with very little t-value on the gender dummy.

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One more mathematical parallel. The idea that “minorities show no variation; only the privileged group can be variable” is isomorphic to Jim Townsend’s mathematical-psychology model of racism. Substitute “minority” with “other group” and “privileged group” with “self" or "my group" and you have the same model of a negatively curved metric space:

So you thought postmodernism was opposite to science? Here is Derrida’s “privileged hierarchy” where “one term dominates the other” — at least one mathematical interpretation of those words.