Rational expectations and independence of what is forecasted

Economics Economics Questions
1

I’m not a trained economist, so apologies if this really falls into the ‘newbie’ section. I may be making some very naive statements here…

I’m creating computer simulation models of economic systems and was trying to position some of the ideas therein more formally within economics theory. But there’s an aspect of rational expectations theory which I’m unsure of, so here goes…

The old topic on this forum here (https://forum.freecapitalists.org/t/critique-of-rational-expectations/15245) covers some critiques (and I liked edward_1313’s long ‘real-world example’). However, all this discussion would seem to assume that what is being forecasted is independent of the actions of those doing the forecasting. What are the limits of RE theory in this regards?

I’ve read stuff such as Arthur’s Santa Fe Bar Problem, where he illustrates how ‘rational expectations can break down’ when agents are estimating outcomes which are entirely dependent on their responses to such estimates.

Let’s use an equity price as an example. How does an RE theorist fit RE to such a process (if they do), where the actions of investors based on their price estimates (partly/largely) determines the price?

Hope this makes some sense. I’m happy to be pointed to good textbook explanations of the principle and concepts, though I haven’t found anything remotely useful in the various textbooks I’ve seen.

Regards,

Stuart

(monsieurrigsby)

2

I know little of the specifics of the practice of RE, but it appears to me the problem is “What is my estimate” and “What is my estimate of my estimate” are completely different questions. Confusing these questions to be the same will break your self-consistency.

The key to handling this is keeping the levels separate: Where did my estimate come from? What are the exact cognitive gears behind its formulation? What you need for a model to predict prices is a model of the gears, not a self-referential list of individual estimates.

3

Azure,

Thanks for the response. I agree that the two questions are different, but I don’t think I’m confusing them. I probably should have attempted to explain better initially…

From my understanding, the RE ‘hypothesis’ relates to the assumption that the expected value of predictions is equal to the actual outcome. Thus, it is true if this mathematically holds for the model/system in question.

So, if we modelled my equity price example with agents making predictions, and then buying some amount of stock based on some fixed stochastic function of that prediction, then RE would hold if it could be shown analytically that this maths results in an expected value of predictions which equals the actual outcome price. To do this, most models would involve the agents ‘knowing’ the underlying model by which the price is computed from, say, historic price data and the bought quantities of agents (whether this sub-model is economically plausible is irrelevant). Which is why, in the modelling literature, talking about a model as an RE model tends to be synonymous with a model where agents know the underlying outcomes calculation model. (That is, this is used loosely when there isn’t necessarily any correspondence of the mean prediction to the outcome.)

(Of course, you could still have an agent prediction model totally separate from the actual outcomes model which still satisfied the RE property, but it would be very hard to imagine such a model!)

This (perhaps!) makes sense in theory, but I guess my question is how well developed such analysis is for systems where the outcome is not independent of the predictions. Are there ‘canonical’ examples where RE is shown to hold? (Or conversely, known limits to when RE definitely doesn’t apply, such as the Santa Fe Bar Model?). And, of course, any corrections to my logic above, which may well be faulty :slight_smile:

BTW, for anyone interested in the Bar Problem (also known as the El Farol Bar problem), there’s a Wikipedia page: http://en.wikipedia.org/wiki/El_Farol_Bar_problem

Arthur’s papers are obviously better for a more detailed consideration; e.g., his American Economic Review paper “Bounded Rationality and Inductive Behavior (the El Farol problem)”, available from his Web page: http://tuvalu.santafe.edu/~wbarthur/Papers/Papers.html

4

I would say that RE simply does not hold - it is a too strong assumption.

In reality, expectations of some persons land closer to the real outcome, and these guys reap the entrepreneurial profit. Other guys miscalculate, and are left with losses.

If you need a fancy explanation, the real world is too chaotic to be predicted by humans (or any other intelligence for that matter).

5

One important consideration here is where the information came from. It’s a very big assumption to say everyone always knows the correct model to make reasonably accurate predictions, and always has access to the relevant information needed. People don’t have perfect information, and what information they don’t have is a huge factor. To assume it away is a big enough leap, I think, to make RE unfounded outside of some very special cases.

Still, if you have to keep working with RE for employment reasons, the best way to save it is to work under your agents having divergent models of each other’s behavior, in exactly the right way such that none of them are reliably able to make predictions as invididuals, but their collective squared error is 0. Still pretty unrealistic, but better the alternative.

Two models coincide if their procedures are computationally isomorphic. You can easily calculate how much lift an aircraft will generate using formulas much simpler than the ones reality actually uses at the quantum level.