Whenever we talk about income mobility, we should never forget that we’re talking about mobility in each direction. One can move down the income scale as well as up. Indeed, if we measure income mobility of households by movement from one quintile to another, it necessarily must be the case (given a fixed number of households) that for every household that moves up, one must move down. If that didn’t happen, then the apparent quintile into which more households moved than moved out of would not really be a quintile.

Because movement can be down as well up, income mobility for the bottom quintile will likely be less than for the middle three quintiles. Why? Because a household in the bottom quintile cannot move to a lower quintile. It can only stay in the same quintile or move up.

Similarly, income mobility in the top quintile is likely to be less than for the middle three quintiles. The reason: a household at the top cannot move up but can only stay in the same quintile or move down.

Here’s how Alan Reynolds put it in his excellent blog post, “Likely Sources of Obama’s Misconceptions about Income Mobility”:

The middle three quintiles are defined by both a floor and ceiling. Unlike the middle quintiles, however, movement in or out of the top or bottom income groups can be in only one direction. Anyone in a top income group in any particular year must have either been in the same or a lower group in previous years, because there is no higher group to move down from. Anyone in a bottom income group must likewise have either been in the same or higher groups in previous years, because there no lower group to move up from.

This simple mathematical distinction has led many careless observers to deplore the illusory fact that there appears to be less “mobility” among rich and poor than there is in the middle. Rather than indicating that the poor are stuck at the bottom and the rich secure at the top, this is simply the unavoidable consequence of the fact that only families at the top and bottom can move in only one direction. Like so much overheated rhetoric about inequality and mobility, this is just another example of people forming extremely strong opinions on the basis of extremely weak logic and evidence.