Monday, 28 October 2013

On The Use of Rational Expectations



Lars Syll has a couple of posts (here and here) on rational expectations.  Of the various assumptions underlying microfounded macro this one is, for many heterodox economists, the most preposterous.

In my view, though, it is wrong to dismiss rational expectations out of hand.  I would not suggest it is embraced whole-heartedly with other concepts pushed aside if they don't fit neatly with it.  However, I do think it is important that economists appreciate the way that expectations shape results and in this respect, I think paying proper attention to the implications of rational expectations is an important discipline.

When constructing models, it's often necessary to say something about expectations.  In saying how people act in aggregate, we need to make some assumption about what their average expectations are.  This is particularly so when modelling financial markets.  The results we get from our model will then depend on the assumptions we have made.

In a sense, we have two choices when deciding how to model expectations.  We can either assume that people get it right or that they get it wrong.  Now, it's quite reasonable to suppose that people will almost invariably get it wrong.  The problem, though, is that it's not enough simply to say that people will get it wrong.  Unfortunately, if we don't want to use rational expectations, we have to make a further assumption about the precise manner in which people will get it wrong.  How confident can we be that this further assumption is the right one?

I think it is legitimate to make assumptions that involve people making systematic expectations error.  More than that, I think we have to make such assumptions to understand certain behavioural patterns that occur in the real world.  It is quite clear that people do make expectations errors and consequences follow from this.  These are things we need to be able to explain as economists and they cannot be explained by appealing to rational expectations.

However, what I think is really important is that we understand the extent to which our results depend on our assumptions about expectations formation.  It may be appropriate to assume that people make systematic errors, but we should still have some idea of how the model would perform under rational expectations.   This will inform us on the extent to which our result depends on these assumptions.  This is important, as any assumption we make about expectations is unlikely to be reliable.

Of course incorporation of rational expectations into models is not straightforward.  In many cases, expectations can be self-fulfilling, so use of that assumption can lead to indeterminate solutions.  Furthermore, adapting the structure and other assumptions of the model simply so that it can solved whilst preserving the preferred expectations theory, is not really a helpful approach.  We might decide that rational expectations just doesn't work in our model.  But that's not a good reason to abandon the model.

So we should always ask ourselves how the model would perform under rational expectations.  If we conclude then that our result depends purely on an expectation error, that doesn't invalidate the result.  But it is something we need to know and understand.

11 comments:

  1. Nick,

    Nice post.

    p = p^e_-1 is that rational expectations for price?

    (^ for superscript; _ for subscript.)

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    1. My previous comment seems simplified and not make sense. In other words, if use the template of G&L models, is it even possible to assume something like that?

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    2. Thank you. I was a bit worried I was going to alienate some people with this. But, whilst I'm definitely on the PKE side of the fence, I've always seen great value in trying to find useful bits from different sides, simply because it's all fumbling in the dark really, trying to get a bit of a grasp on something that's terribly complicated.

      You can apply rational expectations to G&L type models, but I think you'd generally have to use iterative processes like Fair-Taylor. This basically solves a long future path, then feeds it back into a new simulation as expectations and keeps going till it all fits.

      So of those models might not have solutions though.

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    3. I see.

      Yeah even I try to get some bits. I found some expectations modeling in a book Exchange Rate Economics by Ronald MacDonald interesting. It uses bandwagon, adaptive and regressive expectations. Fancy words but simple when written in analytic form. Also the exchange rate market micro-structure by Richard Lyons is nice.

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    4. Also, I didn't mean to suggest it is necessary to try and run every model with an RE assumption. Often, it's really tricky to get it to solve. It's more of a question of just thinking through the impact of the expectation assumption.

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  2. Nick,

    The problem is not so much with rational expectations as with "model consistent" expectations and assuming that everyone has the same model and knows about it. Not just that people know all the states of the world but that they assign the same probability to those states. In other words, the structure is completely known. There is no "learning" per se. Ken Binmore has beautifully argued this point in his essay about large world and small world uncertainty.

    That is why you get such strong, crisp results, that are so heavily dependent on minute changes in long-run outcomes, when in practical life people will routinely ignore such minute differences in the distant future.

    People's behaviors when faced with known state-space is radically different from when faced with unknown state-space. Look at the subgame perfect equilibria of caterpillar or other games and how they routinely violate our intuitions and are routinely violated in experiments. I dont think RE is that useful as a "benchmark." That said, I do think that we should be cognizant of the fact that expectations matter and to what extent our results are driven by particular assumptions about expectations.

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    1. Whether it's "model-consistent" expectations or rational expectations, I think it is useful benchmark, simply because it is the zero error outcome. Every other assumption about expectations involves people making an error and the results will then depend on that error.

      However, I absolutely agree that it is not how people work in the real world and thinking about how people do really form expectations is important and useful work. I am certainly not arguing that we should prefer an RE hypothesis to any alternative.

      I think part of the problem is that the crisp results are a function, not just of the use of rational expectations, but also of various other questionable assumptions.

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  3. Nick,

    Yes, it is a combination of assumptions--all of which are routinely violated--including expected utility. Many do not realize that Ricardian equivalence stems from the transversality condition. If you dont impose it, even with ratex you can get all kinds of results.

    I am not suggesting that we ignore expectations or the fact that they are often forward looking. I just dont think that ratex is helpful at all in thinking about it. I have problem with using something as a "benchmark" that is so far removed from reality--example the backward induction result for the caterpillar game. In social sciences it is not very helpful to start with models. Rather start with observed facts (Stylized facts??) and try to think of mechanisms--a la Elster. This is the opposite of what Nick Rowe would suggest. The problem with the Nick Rowe approach is that you can build all kinds of toy models to show all kinds of things that are not very useful at all (see his demonstration of public debt as a burden).

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    1. Maybe think about it this way. Suppose we run a model with a different assumption about expectation formation, say some form of adaptive expectations. This will give us a set of results, including a series for the expectation error. It is reasonable now to ask ourselves to what extent the results depend on that error. Not because we think people don't make errors, but because it's useful to understand what the results are contingent on. To be able to answer this question, we need to have an idea what the result would be if the expectation error is zero.

      But I think we're on the same page in how to think about modelling and building up from stylized facts. If you're seen other stuff I've written here, you'll know that's very much my approach. And I know what you mean about Nick Rowe. I think his mini models can sometimes be rather misleading, but actually that's why I like them - I find it interesting to try and spot exactly what I think is wrong about them

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  4. Nick,

    Btw, Tom Palley has some things to say about Rational Expectations here: http://www.boeckler.de/pdf/p_imk_wp_121_2013

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    1. Thank you. I was aware of that paper, but I hadn't really read it properly, so I hadn't noticed the comments on rational expectations. I think the view he's implying there is in line with what I'm saying.

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