*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.

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

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

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

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.

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)