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Our condition here is stronger than mere income mobility. Mobility means that someone can become rich. The no absorbing barrier condition means that someone who is rich should never be certain to stay rich.
How important are these effects? One way to find out is to follow the same people over time. When you follow the same people over time, you get very different results about the impact of the economy on the poor, the middle, and the rich.
But the people in the snapshots are not the same people. These snapshots fail to correct for changes in the composition of workers and changes in household…