Monday, October 24, 2016

A Behavioral new-Keynesian Model

Here are comments on Xavier Gabaix' "A Behavioral new-Keynesian model." Xavier presented at the October 21 NBER Economic Fluctuations and growth meeting, and I was the discussant. Slides here

Short summary: It's a really important paper. I think it's too important to be true.

Gabaix' irrationality fixes the pathologies of the standard model by making a stable model unstable, and hence locally determinate. Gabaix' irrationality parameter M in [0,1] can thus substitute for the usual Taylor principle that interest rates move more than one for one with inflation.


Gabaix imagines -- after three papers worth of careful math -- that people pay less attention to future income when deciding on consumption than they should.  Making today's consumption less sensitive to future income, means expectations of future income are larger for any amount of today's consumption. Thus, it makes model dynamics unstable.

But just a little irrationality won't do. If you move a stable eigenvalue, say 0.8, by a bit, say 0.85, it's still stable. You have to move it all the way past 1 before it does any good at all.

Thus, Gabaix puts irrationality right in the  middle of monetary policy. If Gabaix is right, you simply cannot explain monetary policy in simple terms with money supply and money demand, or interest rate rises lower investment and inflation via a Phillips curve, as simple approximations that more complex models, perhaps involving some irrationality, improve on. Monetary policy is centrally about the Fed exploiting irrationality, full stop, and cannot be explained or understood at all without that feature.

More in the comments. There are too many equations and figures to mirror it here, so you have to get the pdf if you're interested. This is for academics anyway.

20 comments:

  1. I very much like reading your comments, and I agree that this does seem like it could be potentially a very important innovation in NK models.

    I particularly like that the innovation of the model, how much agents misunderstand the future, is a fairly intuitive addition (even if the maths seem daunting) and it is a aspect of 'human nature' that seems like it could play a significant role in determinacy in NK/business cycle models... without it being clear, a priori, exactly how the addition would alter the equilibrium.

    That is to say, this doesn't seem to be one of those additions to a model where it's fairly obvious how the equilibrium results will change (except, of course, for the forward guidance puzzle). On the contrary, it isn't at all obvious, at least to me, and, given how it could potentially play a big role, as seems to be the case, it's very interesting to see the results play out.

    (Not, to be clear, that it's a worthless exercise to make additions where the outcome is fairly obvious, we need the rigors of modelling after all, but it's a risky endeavour to try to make such changes, which makes any attempt, failed or successful, praiseworthy in itself.)

    I'll have to go through the maths of the paper myself sometime in the future, but I agree with you that this could be a very significant paper. Thank you for sharing the comments!

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  2. "Explosive Equilibria" ??!!??

    Tell us again this is a paper to be taken seriously.

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  3. Although I need more rigorous training in New Keynesian framework to understand this paper thoroughly, I am able to get the big picture based on this thoughtful comment. All the models are wrong, but some are useful. Standard model fails to explain quiet inflation when interest rate hits the zero lower bound. A new framework or model that incorporates all the empirical facts would substantially expand our knowledge in monetary economics and fiscal theories. Uncovering the unknown, that's the most exciting part of academic research.

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  4. Confession up front - I did not read Gabaix's paper, just quickly looked at it. But, Cochrane says "Gabaix imagines - after three papers worth of careful math - ..." So, we need more complicated math in econ, to deal with the behavioral component? Isn't one criticism that we have too much math in econ? Like too much "mathiness", to quote an economic luminary out there in New York somewhere (but soon to be in Washington, DC as chief economist of the World Bank)?
    Since we are at it, wasn't one criticism of economics that "people do not walk around in a supermarket maximizing utility functions and calculating Lagrangians"? And now in Gabaix's paper, people are supposed to walk around in a supermarket or wherever, doing "three papers worth of careful math"?
    I am definitely not against math. But I have to say that I am confused.

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  5. Thanks Prof Cochrane,
    bit confused - why do you need more math? Prove, what? You’ve got very robust equity markets. The U.S. market’s at all-time highs. You have people wondering what’s going to happen with interest rates towards the end of this year and going into next year.So policy is regime-dependent and it’s unpredictable. You can switch out of these regimes to something else, but it’s unpredictable when that will happen. Once you’re in a regime, you just predict that you’re going to stay there for the forecast horizon, which is about two to two-and-a-half years for the Fed. The regime is characterized—the current regime is characterized by low growth, low productivity, and especially by very low real rates of return on government debt, what we’re calling r-dagger. etc..
    I shell stick with Taylor..brgds

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  6. If we're truly facing irrationality and fundamental unpredictability then all of the models we use are crap and so is our discipline.
    Worse, why would the Fed try to "exploit" irrationality? The Fed shouldn't be "exploiting" anything.
    Geez, where's Friedman when you need him.
    Why not just say that all speculative goods markets are funky, thus trying to stabilize inflation is not easy.

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    1. The market for lemons affects only price discovery, not robustness of the supply-demand concept. And as to the Fed, all banking relies on TRUST, and trust can be exploited and abused.

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  7. on page 17 "....There are two kinds of economic policies: policies that rely fundamentally on basic supply
    and demand economics, but whose dynamics and real-world application may be
    influenced by behavioral and other frictions, and policies that fundamentally are based
    entirely on exploiting people’s irrational behavior, using mechanisms that would be entirely
    absent in a supply-demand world. The analysis of taxes and tariffs are examples of
    the former. Keynesian multipliers are examples of the latter...." Thank you, prof. Cochrane - it's worth struggling through your impulse functions (really unnecessary here) to get to this obvious truth!

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  8. Prof. Cochrane, can we cut to the chase? Is the model capable of explaining what happened in Japan in the last 25 years? Lots of fiscal expansion and still no inflation at all?

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  9. Hi John.
    Can you comment on another potential contender in this debate, the incomplete info without common knowledge model of Angeletos and co?
    http://economics.mit.edu/files/12277
    I still have trouble understanding the forward guidance puzzle that this model in part and other New Keynesian modelers are trying to address. The typical experiment is to see what happens when the central bank commits to shifting the real interest rate by x in the future. But if the central bank just shifts the nominal rate, why does that translate directly into real rate shifts? You'd expect agents to also expect a potentially compensating change in future expected inflation. How is the forward guidance studied in recent papers different from the anticipated interest rate moves you analyse here but reversing signs,
    https://faculty.chicagobooth.edu/john.cochrane/research/papers/fisher.pdf
    ? In which case, forward guidance has a small initial impact, rising as the time of the interest rate cut approaches. The only resolution I see here is that you and others such as Angeletos or Werning or Gabaix seem to be systematically selecting different values for the expectational shock (delta in your notation) as their default IRF.
    We can argue that if delta is really indeterminate, then if many financial market participants really do think that in the short term interest rate cuts raise inflation, then we should just select that as our equilibrium, without contradicting RE (at any rate, I think that's what Roger Farmer would suggest).
    As for the difficulty in deriving Gabaix's Math: I think the basic idea of this model as expressed in the earlier papers on the micro applications and on sparse dynamic programming is quite intuitive and plausible from a microfoundations perspective: the brain essentially follows a 2 stage decision process in which the optimisation is first simplified by reducing attention to elements of the environment which are less costly to ignore based on a simpler value function approximation (used to solve the infinite regress problem of bounded rationality). But maybe there's some lattitude in deciding which terms to ignore and declare as "small" in the approximation you take. Maybe algebra disagreements are possible in deciding which terms are O([X^2]) and hence ignorable for producing nice expressions?

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  10. Thanks for pointing to the paper. I haven't read it yet (Oct. 30 paper). It took me 3 weeks to read Gabaix! These papers aren't easy. In part that's what drives me to the fiscal theory -- when something so easy and transparent is available, going back to Deep Theory about higher order beliefs and equilibrium formation is even more daunting.

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  11. This is wonderful. I’ve reported some typos below so that you can make it more wonderful.

    In the future post, could you please summarize many “adjectives” used in NK paradigm (i.e. “(un)stable” E, “unique” E, “(in)determinate”, etc.)? That must be very useful to graduate students like me. I can’t understand the difference in meaning between “unique E” and “determinate”.

    Here are typos:
    (page 6) “passve phi<1” => ”passive phi<1”
    (page 11) “gives a gives a nearly 2%” => “gives a nearly 2%”
    (page 15) “[01]” => “[0, 1]”
    (page 19) “I gave up in the time a even a masochistic…” (?)
    (References) In the text, you write like “Cochrane (2016a)” or “Gabaix (2016b)”. But in References, you don’t put “a” or “b”. So, it takes a little time to figure out which paper you are talking about.

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    1. Thanks much for pointing out the typos. The adjectives are not standardized alas. I'm trying to use a consistent language, but different people use the same word to mean very different things. "Stable" often means "low variance" for example. The biggest confusion of all, I think: In old keynesian models the taylor rule takes a model which is unstable -- tends to explode on its own -- and makes it stable -- tends to return to where it was after a shock. In new keynesian models, the taylor rule takes a model which is stable but has multiple equilibria, and turns it into a model that is unstable so only one equilibrium doesn't explode -- it induces instability to obtain local determinacy, i.e. only one nonexplosive equilibrium. These are totally different ideas, and often confused. There was an agenda that NK models were really just holy water sprinkled on ISLM, which is what drove a lot of confusion. It took a long time to figure out that the actual equations of the NK model are a lot different -- and that its taylor rule produces determinacy, not stability.

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    2. Many thanks for your explanation. Can I ask one more?

      You have long been suggesting that "NK plus FTPL" ==> "determinate" and "stable".

      In the comments, you point out that Gabaix produced determinacy by making the model "unstable". So, do you mean "determinate" is "better" than "unstable"? That is, is there any "ranking" like (determinate, stable) > (determinate, unstable) > (indeterminate, stable) > (indeterminate, unstable)?

      If I'm correct, Werning (2012) belong to (determinate, stable), though he just assumes determinacy.

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  12. There's no better or worse in models, just understanding how they work. Werning is stable during the liquidity trap, but yes, he just picks one equilibrium and in a footnote says there is some off equilibrium threat or FTPL that can be invoked. See "the new keynesian liquidity trap." I'm almost done a new paper that will have a big section on this.

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    1. Again, thank you very much for your informative response. I've learned a lot from your replies.

      I'm also enjoying your on-line course, Asset Pricing. I especially liked the videos of stochastic continuous time math.

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  13. If you have time, can you help me understand one more mystery about New Keynesian? (Since you are the rare one who really understands "Old" vs "New" Keynesian models, please allow me to ask you many times...)

    When one professor read my thesis on New Keynesian models (simple - which include only sticky wage), he said, "Why is unemployment absent in your model? Because labor market is imperfect due to nominal wage rigidity, there must be unemployment. Your model is not closed." - my response: "'Demand-Supply' world doesn't exist in NK models. Even though the model has sticky wage, the labor market clears." - but he was not convinced.

    What did he (or I?) misunderstand?

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    1. I haven't really done NK models with detailed labor markets, but I'll hazard a guess. Just like neoclassical models (kydland and prescott, king plosser rebelo), you can start with a very simple model where the labor market clears, and fluctuations in employment have supply = demand. Yes, there is no unemployment there, but if you get the variation in employment right, the distinction between leisure and job search is not a huge issue. If you really want, tack on a good model of search in labor markets, and likely you get "unemployment" but not much difference to other aggregates dynamics. As to your question about sticky wages, my first guess is that it works like product markets in these models. In those markets, prices are sticky, but set by producers under monopolistic competition. So there isn't a market that doesn't clear like classic supply and demand with a price that can't move. Response from those doing detailed labor markets with wage stickiness in NK models welcome!

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    2. Wow, many thanks from the bottom of my heart! A very thoughtful response! Based on your advice, I'll think harder again. I feel I'm coming closer to the "solution" to this problem.

      Warm Regards,
      Mizuki Tsuboi

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