I have now seen this paper presented twice and I really like it.  It’s Gul, Pesendorfer, and Strzalecki modeling the implications of limited attention on asset prices.  They show how competitive equilibrium requires large fluctuations in prices in extreme states of productivity.

Their model is very simple and the logic can be explained in a few sentences. Output in the economy is stochastic so that there are high productivity and low productivity states.  There is one simple behavioral assumption:  each agent is limited in his cognition, (or attention, or flexibility) so that he must partition states into a small number of categories.  His limitation is modeled by a constraint that his consumption must be the same in all states belonging to the same category.

Qualitatively, the results of the paper follow almost immediately now. Consider the very small probability event that productivity is at the extreme low end. Agents will lump these states together with other states and so they will not be able to reduce their consumption in response to the very low output.  So in order for the market to clear there must be some agent, or small set of agents, who do pay attention to these states and reduce their consumption exactly when output is this low.

Think about these agents. They are committing their scarce resource, namely attention, to this rare event.  Its very unlikely that this use of their attention will pay off.  In order to give them enough incentive to do this, the reward must be very large.  And the way to reward them is to make the price extremely high in these low productivity states.  The ability to sell at these extreme high prices is the necessary incentive.

A similar logic explains why prices must be extremely low in high productivity states.  Overall there are large price fluctuations, larger than in a standard economy without the need for these incentives.

The paper is a beautiful example of the value of abstraction.  Rather than getting into details about how complexity/attention constraints actually work, it is enough to model their essential implication, namely the partition.  This keeps the canvas clean for the economic logic to stand out.

There is one conceptual point that I haven’t been able to come to terms with. It has to do with feasibility.  In competitive equilibrium, feasibility–the assumption that total consumption equals the total endowment– is just a way of modeling market clearing.  And market clearing is the essential assumption of competitive equilibrium.

If markets didn’t clear then there would be excess demand and supply and the resulting competitive pressures would cause prices to adjust so that market clearing was restored.  That’s the usual story behind competitive equilibrium. But it doesn’t work here, at least not in the usual way.

For example, suppose that nobody was paying attention to the lowest state. All traders are grouping it with higher productivity states and so they are planning to consume more than the total output in this lowest state.  There will be excess demand.  That can’t be a competitive equilibrium, therefore someone must be paying attention to the lowest state.

But notice we cannot explain this “equilibration” by the textbook story of how prices adjust to clear markets.  No matter how much the price adjusts, since nobody is paying attention to this lowest state, nobody can change their behavior in response to changes in prices.

Instead, the story has to work something like this.  If nobody is paying attention to the lowest state, the price in that lowest state has to rise so that somebody starts paying attention to it.  That is, it’s as if there is some ex ante stage where everybody is paying attention to every state, and on the basis of all that information they decide which states to then stop paying attention to.

Probably this is taking the model too literally and there is an as if interpretation that doesn’t sound so convoluted.  I am still trying to find that.

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