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Real Modelling of Expectations

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Noah Smith snarks at Robert Lucas:

The power and the terror of Irrational Expectations: In September 2011, in an interview with the Wall Street Journal, Robert Lucas gave the following justification for the use of Rational Expectations:

If you're going to write down a mathematical model, you have to address that issue. Where are you supposed to get these expectations? If you just make them up, then you can get any result you want.

So, are Rational Expectations not "just made up"? Does the evidence tell us that this is how people form expectations? I don't think so. It seems to me that Lucas is saying that we should pick Rational Expectations because they are appealing in some a priori way. I'm not sure what that is, though.

Note that Lucas does not say that one should impose rational expectations on one's model because that is in fact how people form their expectations. I think it tends to lead to the conclusions that he wants, and that is why he picks it--just as he abandoned econometric estimation for calibration because estimation was producing results he did not want.

Noah Smith then goes on to talk about reality:

[F]iguring out how people actually form expectations… is devilishly hard… Bayesian learning… "belief function[s]"… models in which people don't always update their beliefs… rational inattention… older, simpler ideas of expectation formation that were pushed out by the Lucas revolution, but which may have received a bad rap. One of these is Milton Friedman's theory of "adaptive expectations", which in its simplest form doesn't seem to explain the data, but may actually be going on….

That is the conclusion of a recent paper by Ulrike Malmendier…. [I]nflation expectations are strongly affected by recency bias….

How do individuals form expectations about future inflation? We propose that past inflation experiences are an important determinant absent from existing models. Individuals overweigh inflation rates experienced during their life-times so far, relative to other historical data on inflation. Differently from adaptive-learning models, experience-based learning implies that young individuals place more weight on recently experienced inflation than older individuals since recent experiences make up a larger part of their life-times so far. Averaged across cohorts, expectations resemble those obtained from constant-gain learning algorithms common in macroeconomics, but the speed of learning differs between cohorts.

This comes via Carola Binder, a grad student blogger at Berkeley (whom you should follow, by the way)….

In most theories of non-rational expectations, like Bayesian learning or rational inattention, expectations evolve in a smooth, stable way. And so these models, as Chris Sims writes, look reassuringly like rational-expectations models. But there is no guarantee that real-world expectations must behave according to a stable, tractable model. I see no a priori reason to reject the possibility that expectations react in highly unstable, nonlinear ways… "information cascades"…. [E]xpectations might just make themselves up… and we might get any result that we don't want…

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