Dollars and Jens
Tuesday, December 19, 2006
Second derivatives commute. One of the consequences of this is that, when an incentive to X increases with Y, the incentive to Y also increases with X. As an example, take the Earned Income Tax Credit.
The EITC offers an incentive for people at the bottom of the income scale to earn some income. It is designed, however, to offer higher incentives to people with children (in fact, for the childless, the EITC is almost nonexistent); thus it also provides a higher incentive to have children to those who earn income up to its peak. Because the EITC discourages earning income above a certain point, and discourages it again most heavily among those with children, it also provides a decreasing incentive to have children as one makes enough money for the credit to phase out.
Of course, the incentives are independent of which effect is intended; whether the intended public policy was to provide more inducement to have children among those who are poor than among those with more economic means, or whether it was to disproportionately encourage people with children to spend time at work, the impact is the same. (Also, of course, such incentives may be laid upon other effects that provide either encouragement or discouragement of those ends. The result is for the effects either to amplify or partially cancel; either way, particularly on societal levels, one gets more of what is incented than one would otherwise.)
I started thinking about this a couple months ago when Greg Mankiw mentioned a discussion of which he was a part in which it was suggested that medicare be "means-tested", i.e. that its benefits phase out with rising income. "Wouldn't that essentially amount to an extra income tax imposed only on sick old people?" he asked. As with EITC, when you create a greater incentive for old people to be sick when they make less money, you also create a greater incentive for old people to make less money when they are sick.