One of the politically hottest statistics right now is median household income, especially its slow growth. But there is a big problem with understanding what this statistic means, since it mixes up two different things: the changing composition of households and changes in incomes. If the makeup of households is altering dramatically, as it has in recent decades, median household income may be a quite misleading number.
For example, it is mathematically possible for everyone’s income to be rising, while the median household income is falling. How is that possible? The paradox is caused by counting by households, when the relationship between individuals and households keeps shifting.
To take the simplest possible case: Consider a population of one household, a married couple, each of whom has an income of $50,000. The median household income is $100,000. Their incomes each rise by 10 percent to $55,000—but they get divorced. Now there are two households. The median household income has become $55,000. The median household income has gone down by 45 percent! Obviously, we have a demographic event, not an income event.
Suppose our married couple stays married with their new household income of $110,000. An immigrant joins the population, making $20,000, which is three or four times his previous income. In this case, the median household income has become $65,000, falling 35 percent! But everybody is better off than they were before.
In what is naturally a more complicated way, just these sorts of major changes have been going on inside the statistics that count income by household. If the composition of households were unchanged, the statistics would be more straightforward. But this is obviously not the case. Until the demographic changes are untangled from the results, it’s not clear what the changes in median household income tell us.
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