There is a great vignette in the book Moneyball, illustrating the gulf between what actually happens on a baseball field and what the statistics reflect. Imagine the following situation…
Two outs. Runner on third. The pitcher throws his best pitch, fools the batter who hits a lazy fly ball towards right-center field. But the right fielder is a guy like Albert Belle — all bat, no range, no glove. The Belle-ish outfielder can’t get there and the lazy fly ball drops in for a clean single and the runner scores from third.
Now, what really happened? The pitcher succeeded. He made his pitch and got the lazy fly ball he wanted. The batter failed. His job was to hit the ball hard and he didn’t. He got fooled and hit what should have been an easy fly ball. The outfielder failed. His lack of range and bad jump on the ball caused the hit and is responsible for the run scored. The front office who decided that the bad defense was a good trade off for the big bat might be guilty too.
But what do the statistics record? The Batter gets rewarded with a hit, and with a run batted in. The Pitcher gets saddled with giving up a hit and an earned run. The front office and the outfielder get off scot-free.
This was brought to mind by James Pethokoukis’ recent post about Median Household Earnings. Does this statistic always prove illuminating? Does it give us clear picture of what is really happening? Or is there a bad outfielder getting off scot-free in there somewhere? Let’s do some thought experiments and see what can happen.
Lets begin by constructing a simple economy with five households. Here they are with their Household Earnings:
Ok. Median Household Earning is $60,000 and the gap between the top and bottom households is $80,000. Remember, this is Household Earnings.
Let’s now suppose that two things change. A). Everybody gets a 10% raise. B). Household 3, a husband and wife each earning $30,000, gets divorced. What does our income distribution look like now? Remember … from an earnings perspective, everybody is better off. They all got a 10% raise.
Old Household #3 is now two separate households — 4 and 5 — each earning 33,000. But even though everybody got a 10% raise, Median Household Income went down. Median Household Income has now plummeted to $38,500! And the gap between the top and bottom households has grown to $88,000. The statistics would have you believe that things are on an alarming downward trend.
Let’s go back to the start again and try something else. We started here…
Now suppose that things change. But what happens is that times are hard, no one gets a raise. In fact, Household #5 — the recently graduated from college child of Household #4 gets their hours cut to part-time. They now only earn $10,000. They can’t afford their apartment and move back with the parents. What does this new income distribution look like?
Ok. New Median Household Income has now grown to $70,000 and the gap between the top and bottom households has shrunk to $50,000. The statistics would have you believe things are going swimmingly!
Median Household Income statistics really have two distinct variables embedded in them — income and what we call a Household. Because we can’t tell what is going on with the Household composition, the statistic is kind of useless.