The New York Times has an amusing "Budget Puzzle" that allows you to select various options for budget cuts and tax increases at the federal level, in an attempt to close the anticipated US federal deficits for 2015 and 2030. The visible math is basic addition and subtraction, but hidden below the projected results of each option are various unstated assumptions. Many of these assumptions will be economic in nature, and economists have been known to make some entertaining assumptions. (Do you remember that bit in Econ 101 about the ideal production level for a firm being the quantity where marginal cost equals marginal revenue? Do you recall any mention of a capacity limit?)

Also missing from the NYT puzzle are projections of indirect costs for any of the options. If we reduce our military presence in Afghanistan drastically, will we subsequently need to make an expensive redeployment there? If we increase taxes on employer-paid health care policies, will employers reduce the availability of those policies and, if so, will that indirectly impose greater health care costs on the federal government?

It's obvious why the Times puzzle does not go into those considerations -- they're involve considerable uncertainty, and they would probably make the puzzle too complicated to be entertaining. As OR people, we're used to making assumptions (frequently designed to simplify a real-world mess into a tractable problem); but we should also be acutely aware that the puzzle contains many unstated assumptions, and not attach too much credibility to the results.

Incidentally, I balanced the budget with 34% spending cuts and 66% tax increases, and I consider myself to be a fiscal conservative (but a realist, at least in the relative topology of mathematicians).

## Wednesday, November 17, 2010

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I looked at that puzzle and considered writing an optimization model for it. My idea was to have binary variables for each option indicating whether or not you choose it. It would have to have logical constraints saying things like "you can only pick one out of these", or "if you pick this, you cannot pick that", etc. Then I thought of maximizing the expected value of your actions using as probabilities the chances that a certain choice would be approved by the congress/senate. That could take into account someone's knowledge of how (un)popular the choices are. Then there are also bundling effects of the type: if you get away with A and B, then getting away with C on top of that is very unlikely, although you might have been able to get away with C only. I gave up due to lack of time, but I think this would be a nice problem to study further (very much cross-disciplinary).

ReplyDelete@Tallys: That's an entertaining idea! The parameters for the objective function would be hard to estimate, and the objective would be highly nonlinear (although, since it involves binaries, it could always be linearized by adding more binaries).

ReplyDeleteI also think you might have to introduce a time (or at least sequence) dimension. You're right that each measure you enact could cost "karma credits" that would make the next one harder to pass, in which case the order you enacted them might matter (get the least popular one out of the way first?).

There might also be an opposite effect: passing a budget cut (tax increase) might raise the likelihood of passing a subsequent tax increase (budget cut), since the opposition and perhaps moderates would see it as a kind of balancing.

I doubt we could get any sort of meaningful probability assessments, but the notion is intriguing.

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ReplyDelete