Sunday, February 01, 2009

Useless Statistics

In my previous post I argued that the fraction of GDP due to government spending is a pretty useless statistic. It does not provide a useful measure for how big or intrusive government is. I'd like to take this opportunity to point out another statistic that has been both amazingly popular and completely meaningless. This would be the conservatives use of the fraction of all income taxes paid by some particularly wealthy fraction of the population.

For a couple of decades now I have heard conservatives trot this statistic out to indicate that the class of people being discussed is over taxed. The top 1% of all taxpayers pay 45% of all taxes (actual number were made up by me now, but he gist is accurate) indicates that those taxpayers are over taxed. There are at least two things wrong with this statistic.

  1. The fraction of all taxes payed by an individual or group pretty nearly tracks the fraction of all income earned by that group. If you are paying a large fraction of all taxes that is because you are earning a large fraction of all income. Earning a large fraction of all income is not a hardship.
  2. The statistic is comparing the fraction of all revenue taken in by the government. No rational person would asses whether a given expense was too great or too small based on the fraction of all revenue earned by the recipient. This is equivalent to comparing the value of a Honda and a Toyota based on which car comprised the greater fraction of the respective corporation's revenue. No one would care. One might well, and in business will generally, compare the amount of revenue the buyer can get from the purchase to the cost of the purchase. But the fraction of all revenue gained by the provider is irrelevant.
More attention needs to be payed to the underlying assumptions of arguments presented publicly, and much more attention needs to be payed to rebutting those assumptions where false.

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