Saturday, August 22, 2015

A great critique of Rational Expectations


How did I miss this great critique of Rational Expectations? Charles Manski, an econometrician at Northwestern University, published a paper in 2004 in Econometrica looking at the way economists measure expectations. Here is the final working-paper version. Manski spends a lot of his time discussing the possibility of measuring expectations through surveys. But in one section he critiques the idea of Rational Expectations, which is assumed in most economic models. Manski writes:
Suppose that the true state of nature actually is the realization of a random variable distributed P. A decision maker attempting to learn P faces the same inferential problems – identification and induction from finite samples – that empirical economists confront in their research. Whoever one is, decision maker or empirical economist, the inferences that one can logically draw are determined by the available data and the assumptions that one brings to bear. Empirical economists seldom are able to completely learn objective probability distributions of interest, and they often cannot learn much at all. It therefore seems hopelessly optimistic to suppose that, as a rule, expectations are either literally or approximately rational.
Rational Expectations basically say that economic agents behave as if the true model of the economy is the same as the model the economist is currently writing down. But that model includes stochastic processes. And in most situations, it's impossible to pin down the stochastic processes governing the economy - you have to make some guesses. Rational Expectations forces you to assume that economic agents are making all the same guesses you are. That goes way beyond rationality. It is also highly implausible, when you think about it, especially since econometricians themselves will almost always disagree on which guesses are appropriate.

Manski continues:
I would particularly stress that decision makers and empirical economists alike must contend with the logical unobservability of counterfactual outcomes. Much as economists attempt to infer the returns to schooling from data on schooling choices and outcomes, youth may attempt to learn through observation of the outcomes experienced by family, friends, and others who have made their own past schooling decisions. However, youth cannot observe the outcomes that these people would have experienced had they made other decisions. The possibilities for inference, and the implications for decision making, depend fundamentally on the assumptions that youth maintain about these counterfactual outcomes. 
In other words, economic agents just have no physical way of learning about all of the possible outcomes in an economy that never end up happening. 

Here's a simple example. Suppose I think that if I use pachinko machine A, I'll win with a 51% chance and lose with a 49% chance. And suppose that I think that if I use pachinko machine B, I'll win with a 40% chance and lose with a 60% chance. What do I do? I use pachinko machine A every time. Now suppose that I'm right about the odds of machine A (which I confirm by multiple uses), but wrong about machine B. Suppose that machine B actually has odds of 55% win, 45% lose. I should be using machine B, but I never do, so I never find out that I'm wrong, and I keep making the wrong decision! 

Now, if there are lots of people playing on lots of machines and we can all observe each other, it's clear that we'll figure out the odds of all the machines. But many economic models are macro models. The macroeconomy can only make one decision at a time. What would have happened if we had stayed on the gold standard in the Great Depression? We can make guesses, but we'll never really know. So this kind of limited knowledge makes Rational Expectations especially difficult to swallow in the context of macro.

Note that a lot of people think that Rational Expectations becomes a better and better assumption as the economy settles down into a long-term steady state. But the pachinko example above shows how this may not be the case, since in the steady state, the decision maker never learns the truth.

So why does everyone and their dog use Rational Expectations? Manski says that, basically, it's because A) it's easy, and B) there's no obviously better alternative:
Why do economists so often assume that they and the decision makers they study share rational expectations? Part of the reason may be the elegant manner in which these assumptions close an economic model. A researcher specifies his own vision of how the economy works, and he assumes that the persons who populate the economy share this vision. This is tidy and self-gratifying. 
Another part of the reason must be the data used in empirical research. As illustrated in Section 2, choice data do not necessarily enable one to infer the expectations that decision makers hold. Hence, researchers who are uncomfortable with rational expectations assumptions can do no better than invoke some other unsubstantiated assumption. Rather than speculate on how expectations actually are formed, they follow convention and assume rational expectations.
I'd add a third, more cynical reason: Rational Expectations can't be challenged on data grounds. If you measure expectations with surveys, people can poke holes not just in your theoretical model, but in the expectations data that you gathered and the econometric methods that you used to extract a signal from it. But if you assume Rational Expectations, they can only poke holes in the model itself. Basically, substituting theoretical assumptions for empirical results makes a model a more hardened target. If it makes the model less able to fit the data at the end of the day, well..."all models are wrong", right?

Anyway, everyone should go read Manzi's entire paper. Very interesting stuff, even if a decade old.

70 comments:

  1. I'm sure I'm being terribly naive, but why is rational expectations any easier to put into your model than some-other-expectations? We've got a bunch of theories about how economies behave, so why is it easier to plug theories into their own "expectations" slots than into other theories' slots? I see why this kind of self-reflexive theory might be more difficult to make, but not why it'd be easier to make. It's more elegant, of course, as Manski says. But I can't see why it's easier. (Please tell me why it's easier.)

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    1. It's easier than doing the econometrics to try to measure actual expectations, is what he means.

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    2. You could try finding out people's expectations indirectly, by measuring the accuracy of the predictions of models which say that people have such and such expectations. And if you're not interested in finding out what people's expectations are, you could follow convention and say they expect what you expect, or equally easily you could be a maverick and say they expect what one of your colleagues expects instead. I suppose it's hard in a way to be unfashionable, but non-reflexive models shouldn't be any harder to work with.

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    3. Anonymous6:36 PM

      Loosely speaking, in the model mathematically you already know what the true 'future distribution' is (it is a fundamental part of the model). So rational expectations means that the 'expectations' variable is just the same variable as the 'future distribution' variable. For any other kind of expectations the 'expectations' variable will be an extra variable in the model, and one that you will need an extra equation to explain how 'expectations' behave.

      As always, models with less variables and equations are easier to solve.

      There is a little bit more to it than this, but that should give you the general idea.

      [this explanation slightly abuses the meaning of 'variable' and 'equation', but the general idea is there]

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    4. Anonymous6:39 PM

      If you ever solved the Solow model, it is similar to how it is easy enough to solve the steady-state (or even balanced growth path), but much more difficult to say things about what happens out of steady-state.

      [again, the precise maths is much more complex, but the intuition is similar]

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  2. It is obvious from a subjectivist probability interpretation though. And if you look at some of the original RE papers it is never clear what probability space each expectation is taken over

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    1. That's interesting. Which early papers are you thinking of? In Muth's it's clear, IIRC.

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    2. The latter fact kind of assumes the conclusion

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    3. I think I might have been conflating it with this paper I read recently ( https://www.richmondfed.org/publications/research/economic_quarterly/2008/fall/pdf/nason_smith.pdf - This old blog post http://olethrosdc.blogspot.jp/2014/07/inflation-expectations-whose.html discusses my confusion)

      OTOH, reading the Muth paper quickly, I don't really see what states of the world and probabilities that the expectations are taken over. There seems to be a lot of handwaving about aggregation, or maybe that's just my own take on it as I am no economist.

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  3. Somebody, I forget who, said that rational expectations is the assumption that everyone understands how the economy works - except for economists.

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  4. If I understand this: (1) rational expectations says that economic agents have an expectation of the probability distribution of possible future outcomes that would result from decisions they might make now and as time passes and future possibilities become current realities; and (2) at every moment in time, the man in the street seeks to maximize the present value of some objective function by solving the resulting non-linear optimization problem in his head.

    Have I got that right?

    I once used a computer to solve a thirty year optimization problem to find the optimal strategy between investing in an IRA vs. using the money to pay down my mortgage. I had to make lots of assumptions even to be able to solve that small problem.

    How is the man in the street supposed to implement "rational expectations".

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    1. Rational Expectations requires a belief that while individuals may not obey it, the economy as a whole does. Which means you need some basically magic assumptions about aggregation.

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    2. Noah, you might enjoy another nearly-decade old paper in a similar vein. A fully Bayesian approach to estimating the equity premium. Sort of a "Bayesian Expectations" instead of "Rational Expectations" technique.

      http://www.statslab.cam.ac.uk/~chris/papers/EPP070306.pdf

      Jobert, Platania, and Rogers at the Cambridge Statistical Labootory.

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    3. "magic assumptions about aggregation"

      It may be that the man in the street is trying to "implement" rational expectations (knowing that he is working with incomplete and unreliable information) and a lot of interesting stuff results from him getting it wrong because of delayed or incomplete information.

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    4. Yep, Bayesian expectations = the main alternative people have considered. Or similar but slightly different learning-based models.

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  5. IMO issue is not whether expectations are rational or irrational. The real issue is that banking and the exogenous nature of the monetary base may prevent expectations, be they rational or irrational, from accurately aggregating into macro interest rates. In other words, interest rates in money markets do not accurately measure agents' expectations of future incomes and prices. Such imperfect aggregation results in ex-ante imbalance between desired savings and borrowings, which gives rise to the business cycle.

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  6. Grandmont's model (here is his Econometrica paper http://www.jstor.org/stable/2999573?seq=1#page_scan_tab_contents 1998 "Expectations Formation and Stability of Large Socioeconomic Systems") shows that learning can be chaotic if people's expectations can affect the outcome -- which, duh!, happens a lot in markets! If your choice of pachinko machine A forces B to change its odds, then boom.

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  7. Will somebody please explain how anyone can believe in "rational expectations" in a world in which gambling is rife?

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    1. I should have made clear, gambling in lotteries, roulette, etc, where the odds are published, and are against the person placing the bet.

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    2. This comment has been removed by the author.

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    3. the market price reflects the accumulation of all these guesses and is the correct price. that's RE in a nutshell

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    4. Because the objective function being maximized is not just about money. I am a rational, mathematically and commercially sophisticated millionaire. Once or twice a year I buy a lottery ticket.

      Quantify that.

      A better question might be: Why in a rational world does Amazon have a bigger market cap than WalMart? (A ten dollar lottery ticket is one thing. A two hundred billion dollar market cap is entirely different.)

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  8. Rational expectations has its limitations, but it's the least awful model . It's the one that most agrees with the empirical data of how markets react to news and policy .The market tends to be right even if individuals are clueless

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    1. Anonymous1:11 PM

      "The market tends to be right ...." Do you remember the 2007 bubble? The tech bubble a decade earlier? I think the key word in your statement is "tends:"

      The market tends to be right until it's wrong. And it just so happens that those who are periodically wrong-footed tend to be the 99% -- and that wrong-footedness enriches the 1%. So, restated:

      The market TENDS to be rational but it ALWAYS enriches TPTB.

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    2. Anonymous5:15 PM

      Saying the market "tends" to be right is like saying the earth tends to revolve around the sun. Just as the earth revolves around the sun, the market is always right.

      Henry

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  9. Will somebody please explain how anyone can believe in "rational expectations" in a world in which gambling is rife?

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  10. Will somebody please explain how anyone can believe in "rational expectations" in a world in which gambling is rife?

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    1. Anonymous7:56 AM

      I think prospect theory gave a pretty good answer to that question.

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  11. Well, the fact that we use RE rests on internal consistency:
    1) Assume you build a model which does not make use of RE. Your model works very well to fit the data.
    2) But as agents (firms, investors , central banks) learn your model, they'll revise the way they form their expectations.
    3) You adapt your model to include the new process of expectation formation.
    4) Iterate from step 1.

    I guess in the end, you'll converge to RE as a unique fixed point. No?

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  12. Cliffs: RE is pretty good and can be improved, in some cases, by incorporating elicited expectations.

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  13. As Karl Popper would ask "can we find situations/conditions where it is possible to test/challenge the model?" I believe this paper by Chiappori and Ekeland (2006) brings some interesting answers.
    http://www.columbia.edu/~pc2167/Identificationrevds.pdf
    Indeed the paper analyzes when, to what extent and under which conditions it is possible to recover the underlying structure - individual preferences and the decision process - from the group’s aggregate behavior.

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  14. "So why does everyone and their dog use Rational Expectations? Manski says that, basically, it's because A) it's easy, and B) there's no obviously better alternative..."

    I don't get it. Why is this a critique? I think most people who use rational expectations would say the same thing.

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    1. Why is this a critique?

      Because it is an example of the street light effect: https://en.wikipedia.org/wiki/Streetlight_effect

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    2. The critique is that there are good reasons to believe that in many cases, Rational Expectations doesn't well describe what's going on.

      So Manski is calling for an active search for alternatives, instead of contentment with what we've got.

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    3. RE fails? That's irrelevant. Robustness and parsimony beats fit in noisy samples. The question is what fails less.

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    4. (heard in a discussion amongst European physicians of the 13th century CE):

      Barber #1: "So why does everyone and their dog use blood letting? Hildegard says that, basically, it's because A) it's easy, and B) there's no obviously better alternative..."

      Barber #2: "I don't get it. Why is this a critique? I think most people who use blood letting would say the same thing."

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    5. Noah, are you similarly sympathetic to Robinson's critique of aggregate production functions? And if not, why not? ?

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    6. "...there are good reasons to believe that in many cases, Rational Expectations doesn't well describe what's going on."

      You mean that you believe this. I haven't seen any good reasons yet.

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    7. Anonymous9:06 PM

      "I haven't seen any good reasons yet."


      What about the Baring Crisis 0f 1890s?

      What about the Great Depression?

      What about the Great Recession?

      What about every recession you can think of?


      Henry

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  15. "If it makes the model less able to fit the data at the end of the day, well..."all models are wrong", right?"

    I really don't see why the economics profession doesn't insist on all theoretical framework derived claims about reality being falsifiable. Since this seems to be a problem (getting them to specify falsifying conditions), perhaps authors of theoretical frameworks and the models derived from them should be expected (as a matter of common operating procedure) to justify and identify clearly what conceivable states of a macro economy (past, present or future) would convince them that their model is false. And then they should be held to what they identified as a falsifying condition should it be found.

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  16. The general confusion here is that complex, multi dimensional dgp requires equally complex representation and optimization rules. That however is screaminglying false. It's well known that simple heuristics preform very well in complex environments - experienced option trader beats the best quant (unless the dimensionality of the underlying problem is low, which requires infinite liquidity).
    The quest for realism will only find noise.

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  17. This is spot on and jibes with what I've written here earlier. The reason so-called "rational expectations" models don't match real-world outcomes isn't that people aren't rational enough. The problem is that such models define "rational" in a totally arbitrary, unscientific manner.

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    1. As you can see in the comments here, because so-called "rational expectations" modeling was the first popular way of taking into account that people look forward, there's a tendency in economics forums to treat "rational expectations" and "forward-looking" as synonymous, and to worry that critiques of "rational expectations" modeling will throw out accounting for looking forward.

      So, likewise: the reason the models miss isn't that people aren't forward-looking. The models miss because they arbitrarily choose one singular particular view of the future to be the "rational" one and assume that all others are random aberrations whose differences from the chosen norm average to zero.

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  18. The ratex economist goes hunting. He sees a deer. He fires once and misses it by ten feet to the right. He fires again and misses it by ten feet to the left, whereupon he jumps and shouts, "I got it!"

    Barkley Rosser

    (I know, oldie, but still goodie... )

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    1. Anonymous4:25 AM

      The ratex economist goes hunting. He sees a deer. He fires a shot. The bullet explodes in the chamber and blows his nose away. "An exogenous event", he exclaims, "the rifle will work next time".


      Henry

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    2. Anonymous3:27 PM

      Henry goes hunting and hopefully shoots himself and Rosser.

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    3. It is well known in certain ciricles that I deserve to be shot, but who the heck is Henry?

      JBR

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    4. Anonymous4:56 PM

      This must be a Butch Cassidy and the Sundance Kid moment - "who are those guys?"


      Henry

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    5. Anonymous5:10 PM

      "Henry goes hunting and hopefully shoots himself and Rosser."


      A'mous,

      Depending on our prior's, this may take some time.


      Henry

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    6. Anonymous5:34 PM

      "Henry goes hunting and hopefully shoots himself and Rosser.


      `A'mous,

      Hate to point this out, but you can't even get the order of proceedings correct. I suppose in a stochastic world anything is possible.

      Henry.

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    7. Ratex guy reloads and fires again, and this time he gets a hit. "A technology shock!", he says. "Clearly this rifle is becoming more accurate."

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  19. Noah: Now I really cannot believe what I say now, but given recent articles you really passed an opportunity to throw another bone to Austrian economists, at least the sane ones. There is a great deal of literature where Austrians object to general practice to equalize choice with preferences.

    Or to be more precise, the main point of critique is to select an attribute and say that since agents have chosen a particular good that has this attribute it then means that they prefer things with that attribute as opposed to something else. So for instance one may assume that if people buy some particular brand of youghurt in the supermarket and our model only contains certain parameters (e.g. price and quality) then we may assume that since the "preferred" youghurt is more expensive than the other alternative, it probably has higher quality (it tastes better, it lasts longer etc.). However what if people pick the youghurt because it is on the eye level? What if they pick it because everybody else is picking it and noone wants to try the other brand that is in fact more tasty (the example you use in the article)?

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  20. Noah, in your opinion, what percentage of macro (by any measure: # of papers, # of practitioners, etc) is anti-science or pseudo-science? Basically mimicking the look of science (Much as an "intelligent design" "scientist" tries to mimic actual science and skepticism in his "work"), but in reality just "politics by other means," essentially only a rhetorical device, to be used for buttressing already held political arguments of the faithful and completely uninterested in discovery, belief revision, apportioning realistic confidence to the empirical evidence, and finding out what's actually true about economic reality?

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    1. Anonymous3:29 PM

      All of Austrian/Post-Keynesian "macro" is like that. The rest, not at all.

      And it is hilarious you ask Noah about macroeconomics. Maybe he should publish something before pretending to be an expert.

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  21. Anonymous8:21 PM

    Edmund Phelps had a 1983 book that made many of the same arguments as Manski. It was called "Individual Forecasting and Aggregate Outcomes". This was in an era when REH had even more of a stronghold. One of the co-authors of that book had a recent "pop" book on the subject as well "Beyond Mechanical Markets". Might be of interest to you.

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  22. So, I finally found time to go through Muth's paper. And indeed, while in the introduction his assumptions seem very mild, later on he makes an implicit strong assumption about the agents knowledge: that they have an internal view of the process. Is it sleight of hand?

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  23. Anonymous10:26 AM

    In the Pachenko machine example shouldn't you sample both machines with relative rates e^[best estimate of expected return] to balance information gain with immediate pay-off? In your example you would begin with sampling rates 1/(1+e^11) for A and e^1/(1+e^11) for b.

    That's what the physical world does to minimize energy and maximize entropy.

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    1. See "Two Handed Bandit Problem". Noah, you too.

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    2. Anonymous4:44 PM

      Yes! Thank you for providing the correct name for this problem.

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  24. What I find difficult to get with this, is the assumption that everyone has the same expectations (or the same method of forming expectations). Surely, the one thing we know for sure is that "views of the world differ" - hell, even journalists know that. If people were all alike, we wouldn't even have markets.

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  25. P.S. And as for "aggregate expectations" being on average correct, can this be meaningful. Let us imagine expectations are different, so that some people have expectations that are too low, some people too high and some people about right, and people act on those expectations. If those expectations matter then the people with wrong expectations will suffer in some way relative to those with more correct expectations. So do we really want to say it DOESN'T MATTER in aggregate how many people are wrong, and how wrong they are? (Are we assuming everybody is fully hedged?)

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    1. Anonymous3:47 PM

      Since you obviously are ignorant of anything in macro from the past 30 years, I suggest you look at the work by Marios Angeletos, Kristoffer Nimark, Todd Walker, and many others on heterogeneous expectations.

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  26. This all very much reminds me of one famous quip allegedly made by JMK, about making what economists do as useless as possible.

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  27. Anonymous3:25 PM

    'Very interesting stuff, even if a decade old': now what does that say about economics as a science, that it is deemed remarkable that a one decade old article could still be interesting?

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    1. Anonymous3:46 PM

      Interesting =/= relevant.

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    2. Anonymous5:31 PM

      The question should be, how was it received 10 years ago in pre-GFC times? Given its heterodox perspective, probably not very well. Post GFC, it could have a new audience.


      Henry

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    3. Anonymous4:07 PM

      'Interesting =/= relevant': what would you consider interesting but irrelevant research? Anything interesting is relevant to me.

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  28. If the agents in the economy can't in principle figure out the model, how did the economist do so?

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  29. O/T: Noah, philosophy Harry Frankfurt discusses bullshit, and says that society is remarkably tolerant of it (in contrast to their disapproval of lying). Do you think that factors into macro as well? Are macro professionals overly tolerant of bullshit?

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  30. I think the point you brought up about how we should be suspect of rational expectations when we move from certain kinds of micro questions is exactly the sort of thing economists should be doing more of.

    However, I think one of the major reasons RE is so resistant to such concerns is the long history of unjustified opposition to RE. Because RE deals with human behavior, unlike the equally incorrect assumptions of Newtonian physics, RE has been subject to a long line of misguided simplistic criticism. Realizing that actual people aren't rational isn't enough to make RE a bad assumption. You need to engage in the kind of reasoning you offered above.

    Sadly, after hearing people bitch about RE for so long I fear people have become numb to valid criticisms.

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