Percents of Percents

If you heard your income tax was going to rise (or fall) by 5%, what would you assume? Would you think that 5% more (or less) of your total income would be taken by government? Or perhaps, if you understand the marginal structure of the progressive income tax, that 5% more (or less) of your last dollar of income would be taken by government? I suspect that these answers are what most people would think, assuming they thought about it at all. But often, the percentages are actually percentages of percentages, so that the effect (whether from an increase or decrease in taxes) is actually much smaller than it appears.

Most recent example: this article from Citizens for a Sound Economy, an organization I once interned for and generally admire, says that New York Mayor Michael Bloomberg recently signed into law an 18.5% increase in the property tax. Now, I don't know how high property taxes are in NYC, but I can't imagine they're high enough for that figure to be a percentage of actual property values, which tells me that it must be a percentage of a percentage. If, say, the property tax just rose from 5% to 6%, that would be about a 20% increase in the percentage (6% minus 5% divided by 5%).

The article doesn't actually claim that we're talking about 18.5% of your property value being taken by government, so the article isn't grossly misleading. And in any case, CSE is just following the general practice of politicians, journalists, and think tanks in discussing tax changes and proposals. But unless I'm terribly underestimating the American public, I'll bet that a lot of people are misled by statements like this. And at least sometimes, I think the deception is intentional. For instance, when a Republican politician wants to reduce the top marginal tax rate from 35% to 30%, Democrats will say, "The Republicans want to reduce rich people's taxes by over 14 percent [5 as a percentage of 35]"; they will almost never say, "The Republicans want to reduce rich people's taxes by 5 percentage points." (Of course, even the latter statement is misleading, as it overlooks the marginal tax structure - but that's not the point I'm getting at here.) Take note: using percentages of percentages is an equal-opportunity deception: those who want lower taxes will use it to overstate the size on an increase, while those who want higher taxes will use it to overstate the size of a decrease.