## Wednesday, May 4, 2011

### The Use of Knowledge in Society...

I first came across this paper while doing a bit of outside reading during the MSc.  It is one of my all-time favorites, and has strongly influenced my interests in the complex systems approach to economics in general, and networks in particular.

I quote my favorite passage:
"The problem is in no way solved if we can show that all the facts, if they were known to a single mind (as we hypothetically assume them to be given to the observing economist), would uniquely determine the solution; instead we must show how a solution is produced by the interactions of people each of whom possess only partial knowledge.  To assume that all the knowledge to be given to us as the explaining economists is to assume the problem away and to disregard everything that is important and significant in the real world."
What I take from the above passage is that it is not enough to show that an equilibrium exists, what is needed is to show a process of dynamic adjustment that describes how such an equilibrium can be reached given that agents have only partial knowledge of the world.  I remember as an MSc student being deeply skeptical of the utility of the Arrow-Debreu general equilibrium framework because it showed only that an equilibrium existed and did not specify a dynamic process of through which that equilibrium was obtained.  Needless to say, I was very excited when I came across this paper as it indicated to me that I was not alone in my concern.

On a related note, for those interested in a another way of modeling the price system, I highly recommend Growing Artificial Societies.  The book is slightly dated now (most of the work was done in the late 1980's early 1990's).  The authors use a computational model/simulation to show how (and under what conditions) market prices in an economy consisting of heterogeneous agents, operating under only limited knowledge of their environment, can converge to something resembling an equilibrium prices.  Perhaps even more interestingly they delve into when prices should not be expected to converge.  NetLogo has a version of the model that replicates most (all?) of the results from the book.

Upon reflection, I think the economics of Keynes and Hayek are in many respects closer than people think.  This is particularly true if one's knowledge of the differences between Keynes and Hayek comes from the following two rap videos from YouTube.

1. "The Use of Knowledge in Society" is a great article, but as far as I can see, it does not explain how the price system solves the economic problem. Hayek does explain how, IF prices change in response to external shocks, e.g. a new opportunity for the use of tin, then changes in prices give people all the information they need to coordinate on a new plan. But he does not explain how prices change in response to external shocks - how the information gets into prices' - in the first place. Indeed, he seems to assume the law of one price holds (cf. "the mere fact that there is one price for any commodity"), which suggests there are no disequilibrium price dynamics going on.

2. No it certainly does not explain how the price system solves the economic problem. In my opinion Hayek is implicitly assuming that the price system aggregates the dispersed information of economic information in such a way as to give people all of the information necessary for them to coordinate a new plan. How the price system aggregates this information he does not say. Nor does he comment on whether, or under what circumstances, this aggregation should be presumed to be correct...although I assume that Hayek assumes that the aggregation via the market price system is correct (or at least the best obtainable estimate).

I have always assumed that information gets into prices through exchange of goods. This is why I always thought it odd to think that trade only occurs at equilibrium prices in the Walrasian model.

To me at least it seems patently obvious that agents with different marginal rates of substitution between two goods, who thus want to trade, will trade at non-equilibrium prices (insert here your favorite bargaining process to divide surplus...I don't know whether or not your choice of bargaining process matters).

Such trade will narrow the agent's marginal rates of substitution slightly, which would alter the price of any future trade of the same to goods. If you repeat this process enough times with enough agents, then as long as marginal rates of substitution converge, prices will converge as well.

This is the path that Epstein and Axtell follow in the book. The question I would immediately pose is why should we believe that agents' marginal rates of substitution are stationary over time? I suspect that they are not, particularly when you allow for the continual creation of novelty (i.e., new products, commodities etc).

3. I see - this is the approach Axtell takes in his Complexity of Exchange' paper, and it is also similar to a couple of papers written in the 1970s.

My problem with this approach is that it is not obvious that agents who can gain from trade will in fact trade, when there's imperfect information. In many (all? I think the Myerson-Satterthwaite theorem suggests all, but I don't understand it well enough to be sure) games of bargaining under incomplete information, it is possible that no mutually improving trade takes place. If I'm selling you some commodity and I don't know whether you value it high or low, I may charge a high price on the off chance you happen to value the good highly - but this means some of the time, there will be no trade.

I've tried to extend the Axtell model to allow for this kind of strategic behavior, and one needs to impose some assumptions about how people's beliefs (about the surplus or markup they get from trade) change in response to the outcome of trade. (If I demand a ridiculously high price for my good and no-one ever buys it, clearly one must impose that I revise my expectations down in response to this failure to sell, otherwise we'll never get to equilibrium.)

The other issue with the Axtell model is it assumes goods are nonperishable (or they perish at a much slower rate than exchange takes place) but that's less of a concern.

4. Yes, I neglected to mention that Axtell and Epstein do assume that agents truthfully reveal their marginal rates of substitution (i.e, preferences) to one another when they trade. I had forgotten about that, rather large, assumption (which is highly relevant given the nature of our discussion!).

The role of expectation formation/updating is an important one...that, come to think of it, I have not seen really dealt with in the computational/agent-based literature (although it has been a while since I really looked to see what was going on in that area!)