## Monday, April 2, 2012

### When do Incentives Coerce?

The current mantra among economists is that incentives matter. Incentives matter a lot. But, can incentives matter so much that using them to nudge behavior actually becomes unconstitutional? That seems to be the question the states wanted the Supreme Court to consider when they presented their argument against the Medicaid expansion contained in the health care law.

Consider the following situation (model follows the break):

The central government is offering each state $B$ dollars in benefits if the state agrees to participate in a particular program. A state may want to fund a different program instead. Possibly these programs are designed to achieve the same end, but the state prefers one method and the central government another. Or maybe the state and central governments have different preferences over what programs should be enacted. The cost to the state to comply with the central government if it accepts the money and participates in the central government's program is $C$ dollars ($C$ can be different for different states). Assume the government must have a balanced budget, so the money it pays out in total must match total taxes collected uniformly from the states.  Let $t$ denote the amount of money the central government taxes a state, $S$ be the total number of states, and $n$ be the number of states that accept the benefit and participate in the program. Then the government will tax the states such that $Bn=tS$.

What will a state do? A state is large, and it understands its decision to accept or reject the central government's offer affects how much tax it actually will pay. A state cannot affect the decision of other states to accept or reject the government's offer, and it understands the government's budget constraint, so the state understands if it accepts the offer, it will pay $B/S$ more in taxes than if it rejects the offer. Thus, the state will accept the offer if $B-C-B/S \ge 0$ which is equivalent to $B(\frac{S-1}{S})\ge C$. Thus, the state will accept the government's offer if the cost of compliance is not too large.

What would a state have done in the absence of the offer of benefits from the central government? Without the money from the central government, the state would have participated in the central government's program if and only if $C \le 0$. This can happen if, for example, there are economies of scale to a program and the costs go down as more people participate in it.

If $C$ is between $0$ and $B(\frac{S-1}{S})$, the offer of money from the central government changes the state's decision on whether to participate in the program. Has the central government coerced the states? Maybe it depends on how large $B$ is, like Paul Clement argued on Wednesday in front of the Supreme Court? He said the Medicaid expansion in the health care bill "crossed the line" into coercion. But notice that there exists a range of costs where a state changes its behavior regardless of how large $B$ is -- even if $B$ is one dollar and there is more than one state. States are incentivized to participate and optimally choose to participate or not when the amount is small or large. When does the incentive become coercive? That is, when does a cost-benefit analysis turn into a ridiculous "your money or your life?" situation? Is the central government allowed to incentive at any level? Or is the central government not allowed to incentivize at all? That would call into question tax breaks such as cash for clunkers, the mortgage deduction, highway funding, and all sorts of other federal programs. One possible legal line of demarcation that was brought up in the Supreme Court arguments was the idea that the central government should not be allowed to "coerce" the states into doing something through the tax code that the central government could not just dictate. But even then, if this rule were adopted, it would still call into question all sorts of existing programs.

One further note: in this analysis states are not asked to match funds. The "problem" -- if you can call it that -- is coming from the fact that the central government is using the states' own money to fund the program and the states are simply picking the best option available to them.