It doesn’t take much to win a tennis match no matter how strong your opponent is. It’s enough to win just one point, the last one.

There is an analogous saying about economics research, I heard it originally attributed to Roger Myerson. The paper is finished as soon as you have the right notation. This is exactly right because economic theory is about crafting the model and assumptions to highlight just the point you are trying to convey, nothing more nothing less. There is a continual back and forth between formulating assumptions, proving results, changing the setup, checking how the results are affected, etc. until you have it just exactly perfect (Don’t get cynical now.) How the notation is chosen, i.e. which concepts in the model get their own basic symbol and which concepts are expressed as derivatives, is a key linchpin. By grouping the right concepts with well-chosen notation you can turn an opaque argument into one that transparently lets the main idea through, i.e. just exactly perfect.

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July 6, 2011 at 8:50 am

Lones SmithFor most theory papers, this is surely true. We tend not to be Andrew Wiles in a lonely Princeton attic struggle proving the Taniyama-Shimura conjecture and thus Fermat’s Last Theorem.

But I had my notation and assumptions for my assortative matching and search paper in 1994. I struggled for another two years and 2000 hours on it, never knowing if I could solve for existence (MasCollel once conjectured to me I would not) for two more years. That struggle resulted in no new assumptions, just a slow journey through a dark and lonely logical world of math. The struggle did, however, guarantee that I was going to lose my MIT job, so it was one associated with fear.

I often find myself in similar struggles, but now with the wisdom of age, I would not venture again down such a dark road, nor do so by myself. But my coauthors Axel Anderson, Jussi Keppo, Peter Sorensen, and Giuseppe Moscarini so far can attest to more than year long struggles to prove a theorem — sometimes much more.

Bottom line: I wish it was just about crafting the model and assumptions, with the target theorem in mind, because I actually think I’m occasionally good at that stuff. But theory is not like empirical work, and the struggle can actually be so hard that it defeats a valid conjecture formulated with the right notation and assumptions.

July 6, 2011 at 12:31 pm

kI wish stuff like this could be told to grad students at the beginning of their phd rather than discovering it at the very end

Would save a lot of effort

July 10, 2011 at 12:41 am

karl” It’s enough to win just one point, the last one.”

Is it any wonder that regular folk like me have no use for economists? The fewest points you must win to emerge victorious from a tennis match is 48: four points per game, 6 games per set, two sets. Forty-eight points, not one. I swear, you people are worse than useless — you interfere with the truth.

As for economic theory and notation I have no opinion (or clue).

July 11, 2011 at 10:37 pm

jeffI love you karl.