We're going to imagine there exists a right-wing version of Paul Krugman, and we'll call him/her APK. APK has a good gig with the Wall Street Journal, or some other such right-wing rag, and is also pissed with the Obama administration. APK thinks that Obamacare is an abomination, and wants a smaller government. For some reason, dating perhaps to his time in graduate school at the University of Chicago, APK just cannot abide nerdy types, particularly the ones armed with functional equations, and would like to hoist those characters on their own petards, as it were. APK went to Chicago in 1976 expecting some kind of low-tech economics on the order of what Stigler and Friedman did, but got that idiot Lucas instead. Good God!
APK reasons that there is an army of people he/she can recruit for the cause - those who have seen only a smattering of undergraduate economics. If they have studied only principles of economics from books like Mankiw or Krugman and Wells, all the better. The game here is that he/she wants to tell an accessible story that should be convincing to this type of person - no more and no less.
The model APK is going to use is a straightforward AD/AS model with a liquidity trap. It's like Krugman's (second figure), except APK reasons that the effect of the debt overhang on the demand for goods is really large, so the AD curve should have a slope smaller than the slope of the AS curve. APK has been reading my blog too, for some reason that I can't figure out, and has come across this post and this one, and that's giving him/her some ideas.
The APK model is in the figure.
So, APK says, we're in a bad situation. In line with other Inflationistas - APK just had Ron Paul over for dinner - APK is worried about high inflation, as his/her model predicts that it should be well above PI*, which is the 2% anticipated rate of inflation that appears to be well-anchored by the Fed. But we don't have to suffer this high inflation for such a long time - possibly until we are all dead - as there is something we can do now now now. APK resons that we can reduce government spending, which will shift the aggregate demand curve left from AD1 to AD2, reduce the inflation rate (though of course the price level is actually higher at F than at B - but APK thinks that people are going to forget about the price level rise quickly), and get all those whiny unemployed people off our backs at point F. How does this happen? Lower government spending unleashes a torrent of private spending because of the rise in the price level that deflates private debts - there is a negative multiplier that can be very large in absolute value.
Hopefully you get the point now. I've used all the elements of Krugman's narrative, I think, and put these things into the model that he likes to argue is all we need to think about the serious macroeconomic problems of the day. And most everything goes the wrong way, in ways that some knee-jerk right-wing cretin would find very appealing. Conclusion? Though AD/AS analysis seems parked forever in undergraduate textbooks, researchers and policy analysts abandoned it long ago for good reasons. Once modern macroeconomists figured out how to incorporate all the standard tools of economic analysis - game theory, general equilibrium theory, contract theory, mechanism design, etc. - in what they were doing, the game was up. Doing it properly keeps everyone honest - we present models so that they can be taken apart and analyzed to see if they square with the preceding research in convincing ways. I don't see how we would want it any other way.
But if APK said that, someone like me would reply:ReplyDelete
"Hang on. That won't work. Because if you shift the AD curve left you will create an excess supply of output at the initial equilibrium price Pa, so the price level will not rise towards the new equilibrium at point F. Instead the price level will fall without limit, and the economy will slide down along AD2 to the left, making things even worse."
If you have an unstable equilibrium, the comparative statics give weird results, but they are useless results, because the economy won't go there.
You get exactly the same problem in Narayana Kocherlakota's recent model. If you draw the AD curve with the inflation rate (rather than the price level) on the vertical axis, you automatically get an upward-sloping AD curve if the nominal interest rate is held fixed. (Because higher inflation reduces the real interest rate for a given nominal interest rate.) A leftward shift in the AD curve seems to result in a higher equilibrium inflation rate. But that result doesn't make sense, because the equilibrium is unstable, so the economy won't go there. I blogged about it here: http://worthwhile.typepad.com/worthwhile_canadian_initi/2013/06/the-usefulness-of-as-ad-an-example.html
Nice try, Nick. Again, you're just making up dynamics, for a model that's static. It's a crappy model to start with, but given what it is, all it has anything to say about are equilibria. We define what an equilibrium is, then do comparative statics. Who taught you this stuff anyway? You're doing an excellent job of showing why we work with dynamic models where you can do this properly.Delete
Who taught me this stuff? I think, ultimately, Samuelson. "How often have you seen an egg standing on its end?"Delete
If an egg were standing on its end, and we added a small weight to the North side of the egg, the new equilibrium has the egg leaning South. But we know the egg will start leaning more and more North. To solve for the exact rate at which it would start leaning more and more North (to solve for the dynamic path) would require a lot more knowledge about the exact shape of the egg, and the force of gravity, and the relative masses of the egg and the weight, etc. But we do know the egg will lean more and more North.
Or, put it this way: individual agents might be able to recognise an (e.g. Nash) equilibrium time-path if they were in it, but if the equilibrium time-path changed, it is unlikely that all agents would immediately know where that new equilibrium was. And if they don't know where that new equilibrium is, it is unlikely they will all immediately jump to that new equilibrium. In which case, it seems a reasonable question to ask: if individual agents were learning where that new equilibrium is by some sort of trial-and-error process, would that process converge towards the new equilibrium? In some cases we can be fairly confident it won't converge. We call those cases "unstable" equilibria.Delete
The egg is interesting. That's something like the monetary equilibria you get in some models. An OG model is the simplest. The steady state monetary equilibrium is like the egg standing on its end. The egg on its side is like the non-monetary steady state. And there exists a whole continuum of equilibria that converge to the non-monetary steady state. Except the analogy isn't quite right, as with the egg there's something that chooses the initial state. In the monetary economy, the initial state chooses itself, so all those equilibria are potential outcomes.Delete
But... the egg is a bad analogy to the problem you're addressing here as, again, its not a dynamic system we're dealing with here. It's static. I didn't know anyone thought like this any more. You need to take some time off and read Recursive Methods for Economic Dynamics.
"it seems a reasonable question to ask"Delete
No, it's not a reasonable question to ask. If you think learning and whatnot is important, then you put it in the dynamic model, and do it properly.
Nick, my understanding is also that the assumption that trial-and-error (what Walras called tatonnement) will lead to equilibrium is, exactly, just an assumption. This is why in static models we rely on Walrasian auctioneers to do the job.Delete
Of course in this case the Keynesian auctioneer is constrained in some ways concerning what he/she can say.Delete
Slightly of topic perhaps, but it might be worth noting that there was no "auctioneer" guiding Walras' tatonnement process in the original 4 versions of his Elements. The auctioneer appeared in William Jaffe's English translation. Interestingly, the question of dynamics behind the tatonement process was itself the source a fierce debate and misunderstanding between Walras and Edgeworth, and continues to attract the interest of scholars (e.g., http://www.tandfonline.com/doi/abs/10.1080/0967256021000024727#preview).Delete
Please, I think it is possible to actually have a civilised debate about this with arguments that are more up to date than Samuelson and old style discussions of convergence to competitive equilibrium(the new litterature on convergence to competitive equilibria is no longer in terms of things like tatonnement anyways- it's more about convergence of bargaining markets or directed search to perfect competition- Gale 1986, Kircher 2010 I think are good references) . For the current debate on stability of different zero lower bound equilibria, I'd start by going throughReplyDelete
, section 4 in
and further discussion by same authors in
. My intuition is that rational expectations equilibria are not really justifiable anyways based on the idea that simple backward looking learning dynamics would converge to them. It's more about the notion that they're a natural starting assumption for modeling expectations compared to maybe even more wrong versions of adaptive expectations based on the directly observable variables it's most convenient for statisticians to use, rather than the noisy perceptions of unobserved state variables that are behind people's expectations. But that's just my opinion.
Sorry, I was thinking of a paper by Kircher from 2009 about labour markets (but labour market models can be turned into product market models with some reasonably doable modifications),ReplyDelete
The last word on tatonnement style convergence may be this one:
And I meant to say rational expectations isn't really justified by adaptive learning anyways because of the time it would take to learn the RE equilibrium: by then you'd get a structural break anyways. It's more about the difficulty of having a convincing model of learning for more sophisticated issues than learning French. McCallum has a nice statement of this argument,
. Which isn't to say rational expectations is correct or should be the last word on anything, of course.
daniels: I was aware of Peter Howitt's paper, which is an important classic in this area (though if I were being petty I would say it just proved with a lot more math what anyone with an intuition knew anyway, except that Peter himself has a very strong intuition). That's basically where I'm coming from.Delete
I wasn't aware of the Christiano and Eichenbaum paper (it looks too hard for me anyway), but I was very amused to read this bit in their section 6 on E-stability:
"Take as an example a pencil and a table top. The pencil has two equilibria. It can lay on its side on the table or it can stand on its head. The second equilibrium, which no doubt exists, has never been observed (at least, by anyone we know!) because the slightest deviation from it causes the
pencilís position to diverge from the second equilibrium. For this reason, the second equilibrium is uninteresting and can (perhaps!) be ignored."
They have rediscovered the exact same parable as Samuelson, except that the egg has become a pencil!
But yes, I think this is a good literature, that is in keeping with the old. The way I see it, what they are doing is interpreting stability in terms of learnability, which is sensible.
Daniels: Different set of models of course. There is a whole literature on convergence to rational expectations equilibria (of various kinds) under various learning rules. Not sure what to make of it. Could be learning is very important in particular circumstances - another propagation mechanism perhaps.Delete
Nick: You deserve the bad analogy prize for this week. I know a good joke. An egg, a pencil, and a table top are alone on a desert island. They have a can of tuna fish, but no can opener ...
As I said. adaptive expectations based on purely observable aggregate variables may not be a good model for how people form expectations for large shocks. As Christiano et al themselves suggest, it may be too simple.Nick, you should read the response by Mertens and Ravn as well, to see why the egg analogy may not apply. And Stephen, it would be interesting to hear a more explicit discussion from you on the implications of learnability for equilibrium selection. Personally, I'm not sure a zero lower bound equilibrium in which raising payroll taxes on employers increases demand for workers or in which faster price adjustment increases the output gap (until of course the price level becomes flexible enough for the AS curve to become steeper than the AD curve) is learnable in finite time regardless of what some simple learning model says, given the highly counterintuitive nature of these properties for many people. What if people place certain prior bounds on parameter values when learning, excluding certain equilibria (funnny, that's just what estimation of macro model ended up doing given the lack of data, either via arbitrary zero restrictions or smoother bayesian estimations). Howitt's paper is interesting, but it may not generalise as much as you may want to believe. Meanwhile, it's not obvious the deviations from RE are easy to predict. In which case it's better to use RE as a baseline, adjsting perhaps in applied policy work with some ad hoc shock process to expectations from time to time (as John Cochrane said in a recent discussion of discount rates, there's an isomorphism between discount factor shocks and deviations from RE in behavioural models).ReplyDelete
"And Stephen, it would be interesting to hear a more explicit discussion from you on the implications of learnability for equilibrium selection."Delete
This is one of the things that I run across from time to time, and I know a little bit about it. This was a big interest of Jim Bullard's, for example. Work on optimal learning is scarce, so this research is mainly confined to thinking up a learning rule, putting it in a model, and seeing what happens. I think the conclusion is that a lot of stuff can happen.
I could add that perhaps the more interesting problem involves a policymaker who doesn't know how the world works. One approach to that problem is Hansen and Sargent's book:Delete