The Keynesian Beauty Contest – is there any better example of an “old” concept in economics that, when read in its original form, is just screaming out for a modern analysis? You’ve got coordination problems, higher-order beliefs, signal extraction about underlying fundamentals, optimal policy response by a planner herself informationally constrained: all of these, of course, problems that have consumed micro theorists over the past few decades. The general problem of irrational exuberance when we start to model things formally, though, is that it turns out to be very difficult to generate “irrational” actions by rational, forward-looking agents. Angeletos et al have a very nice model that can generate irrational-looking asset price movements even when all agents are perfectly rational, based on the idea of information frictions between the real and financial sector.
Here is the basic plot. Entrepreneurs get an individual signal and a correlated signal about the “real” state of the economy (the correlation in error about fundamentals may be a reduced-form measure of previous herding, for instance). The entrepreneurs then make a costly investment. In the next period, some percentage of the entrepreneurs have to sell their asset on a competitive market. This may represent, say, idiosyncratic liquidity shocks, but really it is just in the model to abstract away from the finance sector learning about entrepreneur signals based on the extensive margin choice of whether to sell or not. The price paid for the asset depends on the financial sector’s beliefs about the real state of the economy, which come from a public noisy signal and the trader’s observations about how much investment was made by entrepreneurs. Note that the price traders pay is partially a function of trader beliefs about the state of the economy derived from the total investment made by entrepreneurs, and the total investment made is partially a function of the price at which entrepreneurs expect to be able to sell capital should a liquidity crisis hit a given firm. That is, higher order beliefs of both the traders and entrepreneurs about what the other aggregate class will do determine equilibrium investment and prices.
What does this imply? Capital investment is higher in the first stage if either the state of the world is believed to be good by entrepreneurs, or if the price paid in the following period for assets is expected to be high. Traders will pay a high price for an asset if the state of the world is believed to be good. These traders look at capital investment and essentially see another noisy signal about the state of the world. When an entrepreneur sees a correlated signal that is higher than his private signal, he increases investment due to a rational belief that the state of the world is better, but then increases it even more because of an endogenous strategic complementarity among the entrepreneurs, all of whom prefer higher investment by the class as a whole since that leads to more positive beliefs by traders and hence higher asset prices tomorrow. Of course, traders understand this effect, but a fixed point argument shows that even accounting for the aggregate strategic increase in investment when the correlated signal is high, aggregate capital can be read by traders precisely as a noisy signal of the actual state of the world. This means that when when entrepreneurs invest partially on the basis of a signal correlated among their class (i.e., there are information spillovers), investment is based too heavily on noise. An overweighting of public signals in a type of coordination game is right along the lines of the lesson in Morris and Shin (2002). Note that the individual signals for entrepreneurs are necessary to keep the traders from being able to completely invert the information contained in capital production.
What can a planner who doesn’t observe these signals do? Consider taxing investment as a function of asset prices, where high taxes appear when the market gets particularly frothy. This is good on the one hand: entrepreneurs build too much capital following a high correlated signal because other entrepreneurs will be doing the same and therefore traders will infer the state of the world is high and pay high prices for the asset. Taxing high asset prices lowers the incentive for entrepreneurs to shade capital production up when the correlated signal is good. But this tax will also lower the incentive to produce more capital when the actual state of the world, and not just the correlated signal, is good. The authors discuss how taxing capital and the financial sector separately can help alleviate that concern.
Proving all of this formally, it should be noted, is quite a challenge. And the formality is really a blessing, because we can see what is necessary and what is not if a beauty contest story is to explain excess aggregate volatility. First, we require some correlation in signals in the real sector to get the Morris-Shin effect operating. Second, we do not require the correlation to be on a signal about the real world; it could instead be correlation about a higher order belief held by the financial sector! The correlation merely allows entrepreneurs to figure something out about how much capital they as a class will produce, and hence about what traders in the next period will infer about the state of the world from that aggregate capital production. Instead of a signal that correlates entrepreneur beliefs about the state of the world, then, we could have a correlated signal about higher-order beliefs, say, how traders will interpret how entrepreneurs interpret how traders interpret capital production. The basic mechanism will remain: traders essentially read from aggregate actions of entrepreneurs a noisy signal about the true state of the world. And all this beauty contest logic holds in an otherwise perfectly standard Neokeynesian rational expectations model!