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.
Do you happen to have any references to back up your claims?
Not that I particularly care about Greenwald-Stiglitz. But in the time taken to make your point and dismiss it as irrelevant you could prevent some future helpless sap from the misfortune of being lead slightly astray!
Unfortunately, I think this is one of those instances where wikipedia can lead one (slightly) astray.
Come to think of it, I’m going to have to use this retort some day:
Well, the paper itself (referenced in the wikipedia page Wei referred to) is obviously the definitive source. The abstract reads:
This paper presents a simple, general framework for analyzing externalities in economies with incomplete markets and imperfect information. … The approach indicates that … equilibria in situations of imperfect information are rarely constrained Pareto optima.
All the other summaries I’ve ever seen also describe the result in similarly narrow terms, e.g.:
the wikipedia entry on Joe Stiglitz, which states that
Stiglitz has shown (together with Bruce Greenwald) that “whenever markets are incomplete and /or information is imperfect (which are true in virtually all economies), even competitive market allocation is not constrained Pareto efficient”.
the paper by Dixit that comes up as the first google hit for “Greenwald Stiglitz”, which states that:
It establishes a conceptual parallel between asymmetric information and technological externalities, andshows that a competitive equilibrium of an economy with asymmetric information is generically not even constrained Pareto efficient.
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.
“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 thought you were saying that the GS theorem becomes false if you weaken the hypothesis to allow other kinds of violations.
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.
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.
Do you happen to have any references to back up your claims?
Not that I particularly care about Greenwald-Stiglitz. But in the time taken to make your point and dismiss it as irrelevant you could prevent some future helpless sap from the misfortune of being lead slightly astray!
Come to think of it, I’m going to have to use this retort some day:
Well, the paper itself (referenced in the wikipedia page Wei referred to) is obviously the definitive source. The abstract reads:
All the other summaries I’ve ever seen also describe the result in similarly narrow terms, e.g.:
the wikipedia entry on Joe Stiglitz, which states that
the paper by Dixit that comes up as the first google hit for “Greenwald Stiglitz”, which states that:
subsequent papers by Stiglitz himself, e.g. The Invisible Hand and Welfare Economics, which describes the result in almost identical terms.
I expect that the statement Wei linked to is just a typo where someone accidentally substituted “perfect competition” for “perfect information”.
ETA: I actually would have edited the wiki entry myself; but I didn’t want to create the impression I’d done so just to back up my claims.
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.
I’m afraid I’m not sure what you mean by generic, nor why it’s especially relevant to my original point. Could you explain?
“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.