- how many concepts can an agent optimise in a given span of time (e.g. can I make a decision between the utility of buying coffee, eating a croissant, writing a blog post and listening to a song on the radio)
- how many, or how distant, are the contingent worlds that an agent can consider in a given span of time (e.g. can I consider my coffee-utility forty years in the future or only twenty minutes?)
- how quickly the agent receives new information about the current state-of-the-world (e.g. how do I learn a coffee is available or what attributes it has?)
- the agent's accuracy in evaluating the attributes of contingent concepts (e.g. do I correctly predict my utility from the state-of-the-world in which I have eaten one more croissant or does my guess turn out to be wrong?)
Sunday, 29 March 2009
Mark Thoma reports Robert Shiller's article on the psychology of the asset bubble and bust, and asks "how to implement this forecasting technique - one based upon a theory of the mind".
I have been working in this area for some time and can suggest the following as a possible framework. I don't know if Shiller has something like this in mind - I suspect not - but I do think it will be a step in the direction that he calls for. Note that this is not yet a fully developed model, but a proposal for how such a model might look.
While standard economic theory deals with a set of goods, I propose instead that there are a set of concepts in the world. We can imagine some of these as corresponding directly to traditional goods - for example the concept of a loaf of bread or an economics PhD. These concepts are mental constructs and not physical ones; they represent the relationship of a person in this model to the ideas of bread or PhDs.
Next, let us define concepts which represent second-level, more abstract or dereferenced thoughts about goods - for instance the concept of a loaf of bread in one year or what other people think bread is worth. These can be considered contingent concepts, in that they refer to the same concept but in some kind of contingent state-of-the-world instead of the current one (with the caveat that each agent has their own private state-of-the-world made up of their own set of concepts). One of the key features of minds is that they project themselves into alternative worlds in order to make judgments about what actions to take.
These alternative worlds are why this model can be said to incorporate a theory of mind. As well as alternative worlds such as "the world tomorrow" or "the world if I buy that car" people use the same mental tools to project into "the world as seen by Tim Geithner" or "the world the car salesman thinks he's in".
A real mind of course considers many concepts which have no analogue in economic goods, such as the concept of truth or Miami or Barack Obama. But I believe we will get more tractable results with a simpler model which does not incorporate these - or at least by assuming they have no significant effect on the predictions our model gives.
Next, we allow each individual to assign each concept a number of attributes each with its own value, specific to that individual. One of these attributes is economic utility; another is confidence in their own evaluation of this judgment; others include their memories of where they have received information about this concept, and their evaluation of the risk of unanticipated changes in the attributes.
Some of these attributes will relate in turn to other concepts; for instance if I learned about what an economics PhD is worth from Greg Mankiw, I may also be interested in where I learned what Greg Mankiw is worth.
The number of attributes that a concept can have is huge, but again I believe we will develop a limited set of standard attributes about each concept that will be incorporated into the model.
The relationships between concepts - embodied in those key attributes - will be expressed in an algebra of how concepts are linked and how they are communicated between agents. This will probably be the most important aspect of the distinction between concepts in this model and goods in conventional economics.
The final step in defining the model will be to state how agents act in response to the values of certain attributes of concepts. I anticipate that this will work by defining an action as a relationship between a current and contingent state of the world, and that the actions that take place will be determined by the difference in the utility of a concept in the current state and in the contingent state. This allows agents to optimise certain concepts, meaning that they maximise the utility they can achieve from that concept.
With the model ready, we can then try out different assumptions about the cognitive constraints of agents. Key constraints may be:
This kind of model should also allow for predictions about collective behaviour which will explain "group irrationality", or the market's departures from the behaviour of its representative agent.
Once we have the basic tools from the fundamental model it should be possible to build on them to deal with higher-level predictions, and I believe this will be where Shiller's challenge is met. There is a place in the model for expectations about asset prices - individual and aggregate - and I expect that the tools developed from this model will be able to give quantitative predictions.
This proposal is based both on modelling approaches from conventional economics, and on my experience of information modelling from building software and business models, as well as some ideas from abstract algebra and epistemology. The mathematics of developing this are likely to be fairly complex, but manageable with some knowledge of abstract algebra and basic differential equations.
I intend to build a more detailed and concrete version of this model over the coming months and test the predictions that come out of it. Anyone interested in having sight of the results as they're developed, or in collaborating on this research, please contact me on firstname.lastname@example.org.
[A final note: Roman Frydman and Michael Goldberg have taken a different approach to the same problem with their notion of Imperfect Knowledge Economics. I have not yet read their book but will be doing so soon. Although they have some quite different assumptions to mine - for example they take as a starting point the idea that economics cannot make sharp predictions - I suspect their modelling approach has similarities with the one I have proposed. The probabilistic aspect of their theory, in particular, may be a powerful addition to my model and might resolve some of the contradictions between the two approaches.]