One reason why grad students find it tough to do economic theory: It takes courage to make wrong guesses. For (most) problem sets, you know ahead of time that your target theorem is true and provable. For real research, you have to guess. (1/N)
Most theorems worth proving are ex ante implausible. If your guesses often turn out right, you should aim higher. You need the emotional fortitude to make conjectures and work under uncertainty, knowing that most conjectures are wrong. (2/N)
Crucially, you often only discover whether a model is fruitful by working on the model - which means making guesses and trying to prove them or find counterexamples. Even wrong conjectures can be productive! (3/N)
To illustrate, here are some guesses that were (obviously!) wrong in hindsight, but led to theorems. Of course, I can only draw from my own experiences. (4/N)
Guess #1: Maybe we can characterize the optimal dynamic policy for matching on random graphs.
Wrong: The state space is combinatorially complex.
Theorem: We can bound the performance of the optimal policy even though we can't characterize it. (Akbarpour, Li, & Oveis-Gharan 2019)
Wrong: The state space is combinatorially complex.
Theorem: We can bound the performance of the optimal policy even though we can't characterize it. (Akbarpour, Li, & Oveis-Gharan 2019)
Guess #2: Maybe all strategy-proof matching mechanisms have extensive-form counterparts that are obviously strategy-proof.
Wrong: in so many ways.
Theorem: No OSP mechanism for top trading cycles. Thus, OSP and weak group strategy-proofness are not equivalent. (Li 2017)
Wrong: in so many ways.
Theorem: No OSP mechanism for top trading cycles. Thus, OSP and weak group strategy-proofness are not equivalent. (Li 2017)
Guess #3: Maybe the only credible auctions are first-price auctions and ascending auctions.
Wrong: There are many others.
Theorem: (under some assumptions) only first-price auctions are credible and static. only ascending auctions are credible and SP. (Akbarpour & Li 2019)
Wrong: There are many others.
Theorem: (under some assumptions) only first-price auctions are credible and static. only ascending auctions are credible and SP. (Akbarpour & Li 2019)
Reading a finished paper, you only see the eventual theorem - and not the (many) wrong guesses that led to them. Have courage to make wrong guesses! (and find coauthors who will make wrong guesses with you.) (N/N)
Addendum: here’s one more theorem that started with a wrong conjecture. Ken Arrow told my first-year PhD cohort that he started out thinking that preference aggregation was easy and a solved problem. Fin. (N+1/N)
