## Hoisted from Comments on Comments Hoisted from Comments: Informationally-Inefficient Markets Edition

I think Robert means: "as Sandy Grossman and Joe Stiglitz proved when they were in nursery school"…

Robert Waldmann:

Hoisted from Comments: Information Externalities from Visible Trades: You are kind to Andy Harless. Yes his argument is worthy of attention. It isn't something which is ideally ignored entirely. However, as you proved when you were in junior high (maybe high school) such trades require irrationality. It isn't enough for different agents to have different information (as you know this is a mathematical result).

It is necessary for some agent to be overconfident. This is usually modelled by including agents which trade based on no information so their confidence should be zero. But it is quite general.

So the position is that we can learn about the world by observing irrational people. This is not an absurd claim. However, the case that the outcome is better than the outcome without such trades is based on the assumption that the traders are rational. This is absurd. It is also the state of research….

I can certainly write down a model in which such trade is socially useful (this is a special case of my claim that, for any result you want, I can write down a model to give you that result -- this is a challenge which has been open for years)…. The way to get an example of good trade is to get a model in which agents get private information about the mean of a variable and third parties care only about the mean:

Agents last three periods:

- In the first they invest in a safe asset and a risky asset.
- They consume in period 3.
- Agents have CARA utility.
- Some agents get no information and are rational.
- Other agents get a signal and are irrationally optimistic: agent i gets a signal equal to the 2nd period value of the risky asset plus epsilon_i, and epsilon_i is normal with mean zero and independent across agents.
So far we have an equilibrium with no trading…. But now assume that agent i misperceives the variance of i to be half what it really is, and correctly perceives the variance of epsilon_j for all j other than i. In this case, informed agents demand the risky asset proportional to i. Then the market closes.

This means that in period 2 agents know exactly what the risky asset will pay in period 3. in period 2 agents can convert safe to risky asset and back with a quadratic adjustment cost.

In this model, trade based on asymmetric information and subjective overconfidence is good….

[Alternatively] the risky asset can pay high with probability p or low with probability 1-p. One agent guesses and is sure that his guess is right. He is trusted by the others so he borrows and invests allllll the money in the risky asset if he is sure it will pay high. So horrible things happen with probability 1-p….

The point is: if everyone is rational than [irrational information-revealing trades] can't happen. The argument that [when such trades] happen [they] must be good because everyone is rational[--that] is schizo finance.