On (rational) expectations

Reading Simon's defence of rational expectations made me wonder: what's the empirical evidence here?

One obvious data source is the Bank's survey of households attitudes to inflation. Every three months it asks people what they think the inflation rate has been in the last 12 months, and what they think it'll be in the next 12. My chart shows the median answers to these two questions.

It's clear that there's a close link between the two; the simple correlation coefficient since data began in 1999 is 0.88. Regressing inflation expectations upon current inflation gives us the equation: 0.87 + 0.6 x past inflation. Whilst this might be consistent with some rational expectations, it's also consistent with a simple rule of thumb: expect inflation to be what it is now, but adjust down if inflation is unusually high, and up if it's unusually low.

This in turn is consistent with Paul Ormerod's claim (pdf) that we should model behaviour as if agents used rules of thumb rather than full maximization.

So, is Simon wrong? Not necessarily. Look what happened in the recession. Inflation expectations then were lower than you'd expect from this rule of thumb. In exceptional circumstances, then - by which I mean the cases of most interest - agents form expectations in some other way.

How? Rational expectations are certainly one possibility. Another (non-exclusive) possibility is that, as Chris Carroll has described, expectations spread in much the same way diseases do: if enough people have (say) low expectations for inflation, they'll infect others.

This leaves me in an awkward position. On the one hand, agents sometimes (often) seem to have what Simon calls "naive" expectations. But on the other, they don't always have them.

Which brings me to something I've said before - that we should think not just about models, but mechanisms. We should ask: what is the mechanism by which inflation expectations are formed? It is perhaps reasonable to suspect that in ordinary times, the mechanism is a backward-looking rule of thumb. After all, in stable times, folk have better things to do than think about inflation. In abnormal times, however - such as recessions or high inflation - the costs of being wrong about inflation become higher, which leads people to abandon  rules of thumb in favour of something else.

Now, this is much easier said than modeled; it leads us into Markov-switching models and other stuff I don't understand. And it might not be much use for forecasting purposes: can we tell in advance whether the expectations formation process will shift? Maybe the real world is more complicated - nay, complex - than any single model would suggest.

Comments

[Szczepan Stachura]

What I think the chart is showing is adaptive inflation expectations vs. basis of its forming. It’s only my opinion: but don’t know, why you consider inflation expectations as a measure of rational expectations, and not adaptive expectations.

[Luke]

Over my head here, but wouldn't the rational person say "I have no idea what inflation will be in the future"? What that does for models I don't know. I'm guessing rules of thumb, but I have no idea. (IIRC, "same as today" is a pretty good method of weather forecasting.)

[Ralph Musgrave]

Wiki in defining rational expectations says “Rational expectations theory defines this kind of expectations as being identical to the best guess of the future (the optimal forecast) that uses all available information.”

The idea that households and firms use “all available information” is plain bonkers. Only academics, more concerned with getting their models published than with solving the problems of the real world could make that sort of assumption.

I.e. Chris is right to ask: “What’s the empirical evidence here?”

Lars Syll takes Wren-Lewis to task here:

http://larspsyll.wordpress.com/2013/11/08/simon-wren-lewiss-attempt-at-rescuing-rational-expectations-an-unmitigatted-failure/

[Luis Enrique]

I like your ordinary/extraordinary times distinction. I wonder if models of costly information acquisition, or Sim's rational inattention models, imply that people use adaptive expectations during normal times, but during periods in which the newspapers etc. are loudly proclaiming "things are changing!" start to do something that could be reasonably modelled as Rat Ex.

I find these discussions often frustrating. One only has to be told what Rat Ex means to know that it is unrealistic, so, for example, Lars Syll's response to Simon - repeating at greater length that Rat Ex is unrealistic - gets us nowhere. The question is whether - or as you remind us, when - Rat Ex is one of those unrealistic things it makes sense to employ in a model, on a least-bad basis.

Robert Waldmann adds to your attention to the empirical evidence. Here.
http://angrybearblog.com/2013/11/rational-vs-adaptive-exectations.html#comments

I'm sure one could quibble, but let's say he's right. Does that mean that if we use adaptive expectations, in some form that accords with the empirical evidence, those models will be less wrong than Rat Ex models? My guess is that it depends on what the model if for, and if you put adaptive expectations in a model built to ask the question how should we conduct monetary policy, you will get an answer that essentially says we should exploit the fact people only have adaptive expectations and dupe them, which may turn out to be unrealistic if, as you suggest, just at the time you need monetary policy that turns out not to be how people behave.

[p.s. I also like Robert's defence of Rat Ex in the comments to his own blog. I think that carries a lot of weight in academia]