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Douglas_Knight comments on The Second Best - Less Wrong
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Unfortunately, I think this is one of those instances where wikipedia can lead one (slightly) astray. Greenwald-Stiglitz is not quite as far-reaching as all that. (Though it is pretty far-reaching, hence my initial comment being a nitpick.) Contra wikipedia, Greenwald-Stiglitz applies to two specific violations of perfect competition: information asymmetry and incomplete risk markets. These do not exhaust the space of possible violations of perfect competition, hence, there may be violations of perfect competition that nonetheless allow Pareto efficiency (at least in theory; in practice, information asymmetry and incomplete risk markets are pretty pervasive).
One (unrealistic) example of a non-perfectly competitive economy that is nonetheless pareto efficient is a centrally-planned economy where the government (magically) imposes exactly the same set of prices/quantities as would naturally arise in the perfectly competitive economy. Another is if two externalities (magically) exactly offset each other. Another is if a government imposes a tax that exactly offsets an externality.
Again, I do not claim that these are especially empirically relevant. My point was a fairly pedantic technical one.
ETA: your wikipedia link has a colon at the end that shouldn't be there.
I don't know the literature, but I thought the generic violations theorems covered more ground that that. Can you give an example that is generically Pareto efficient? Your cancelling externalities example is not generic. The other example doesn't seem well-posed enough to talk about genericity.
Why does my original point require genericity?
Logic appears to side with you on this one.
"Generic" is in the statement of the Greenwald-Stiglitz theorem, as quoted by Wei-Dai. It means, roughly, probability 1. The theorem does not say that information asymmetry leads to Pareto inefficiency, only that it does unless there is a numerical coincidence.
I thought you were saying that the GS theorem becomes false if you weaken the hypothesis to allow other kinds of violations. But your examples seemed to also strengthen the conclusion from generic efficiency to efficiency for all parameter values. If you strengthen the conclusion without weakening the hypothesis, it's already false.
Sorry about the deletion. I thought I'd got in quick enough. Clearly not!
I was saying that as far as I knew, the quotation misrepresented the scope of the GS theorem, which did not make claims about other types of violations. You are right that my offsetting externalities counter-example did not rely on this though.
The counter-example I had always been given as evidence that a non-perfectly competitive economy could theoretically achieve Pareto efficiency was that of a perfectly informed, benevolent central planner. However, I readily confess that this does seem something of a cheat. In any event, whether it's technically correct or not, the point is practically irrelevant, and probably not worth wasting any more time on.
I apologise for the diversion.