Believe those who are seeking the truth. Doubt those who find it. Andre Gide


Tuesday, March 19, 2013

Krugman on Taylor

I had five minutes to kill so I read this: Cogan, Taylor and the Confidence Fairy, by Paul Krugman.

Let's see, what do we have here? Ah, yes...I see Krugman accusing Taylor of being dishonest. Paulo, Paulo...tsk tsk.

To be more specific, Krugman accuses Cogan and Taylor of dishonesty concerning the current state of macroeconomic research. The claim they made was that expectations did not play and explicit role in "old style" Keynesian models. Of course, Keynes and most of the other great economists of the 19th and early 20th centuries assigned a critical role to expectations. But if by "old style" Keynesian models we mean Hicks' IS-LM representation of (a part of) Keynes' theory, then Cogan and Taylor are largely correct. For example, do you see expectations entering explicitly anywhere in this exposition?

By the way, I find it a bit of a hoot that it is Krugman complaining that others in the field are not keeping abreast with the literature. Steve Williamson has addressed this on more than one occasion; see here, for example. But anyway, this is getting rather tiresome.

In fact, it appears that Krugman did not even read the Cogan and Taylor paper. Fortunately, Noah Smith helps lift the lazyman's load: John Taylor's Austerity Model. (Oh gosh, it appears that their results have nothing to do with the "confidence fairy." Oh well, "confidence fairy" looks so good in the title of a NY Times Op-Ed piece.) Noah summarizes his assessment of their work as follows:
Upshot: If you have no Zero Lower Bound, and if the Fed partially counteracts the demand-side effects of fiscal policy, and if people have forward-looking expectations, and if you don't cut government purchases much, and if taxes are very distortionary, then austerity works. This is not really a new result, but it rarely gets shown so explicitly, so it's good that John Taylor and his co-authors went ahead and did it.
Now there's something that economists can debate.

Unfortunately, Noah stumbles a bit on the partisan divide with this concluding statement:
So John Taylor is not committing some major fallacy. He's just using a standard mainstream New Keynesian DSGE model to stump for the Republicans.
I may very well be wrong but I do not ever recall Noah saying something like (say, in regard to the Eggertsson and Krugman model):
So Paul Krugman is not committing some major fallacy. He's just using a standard mainstream New Keynesian DSGE model to stump for the Democrats.
I mean, come on ... let's all stop this nonsense. Debate the substance of the argument and the evidence supporting it. Doing anything else distracts from the task at hand.

Wonkish (and important) note: Those"powerful fiscal effects at the zero lower bound" that Noah alludes to are quite possibly an artifact of the manner in which the NK DSGE model is linearized around steady state (linearization not taking into account the zero lower bound, with zero lower bound imposed afterward). Please refer to: Some Unpleasant Properties of Log-Linearized Solutions When the Nominal Rate is Zero.

 

22 comments:

  1. In what way did Krugman misrepresent his own work with Eggertsson in order to "stump for the democrats"?

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    1. Nemi, please be more careful. Noah never claimed that Taylor misrepresented his work to stump for Republicans. And I am not saying that Krugman misrepresented his work either. They are both stumping for their favorite policies, and I think they both sincerely believe in what their models are telling them.

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    2. Noah implies that Taylor's model was written to reach certain policies he favors, such has Taylor's omission of ZLB

      Reading his post is seems to me he proved his case.

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  2. Regarding your "wonkish note": be warned that Braun, Korber, Waki is a really, really weird paper.

    By their own admission, the dramatic results are coming from the Rotemberg costs of price adjustment, which (in the parameter range they consider) can go up to nearly 100% of output (!!!) once you get to 20% deflation or inflation.

    Surely this should be viewed an argument for why we *should* log-linearize: if we take the nonlinear properties of a modeling hack like Rotemberg pricing too seriously, we get completely absurd results. Did the costs of price adjustment take up 20-30% of output during the Great Depression? What does that even mean?

    In other cases they have the same silly "reverse comparative statics" as in the Mertens and Ravn paper. Basically the story is this: people in other fields have long understood that when an equilibrium is unstable in a certain sense, all the comparative statics are reversed, in a way that doesn't really make any sense if you tell it as a causal story. Occasionally you see this fact inadvertently rediscovered, and misleading inferences drawn from it. This is one of those times.

    In the Mertens and Ravn paper (and implicitly in the Braun one too, though there's less of a focus on this), the government spending multiplier is less than one during a liquidity trap for the following reason. The expectations-driven liquidity trap is indexed by the Poisson exit rate of the sunspot process. For this to be a liquidity trap (in their parameter range), deflation has to be high enough that it substantially depresses demand and is self-fulfilling. So if you do anything at all to increase demand, including a government spending increase, the only way you can stay in a liquidity trap with this particular exit rate is that deflation becomes even worse. Inversely, if you do anything at all to decrease demand, a liquidity trap with that particular exit rate is only possible if deflation becomes less negative.

    But, of course, under these assumptions, literally anything you do that increases demand will actually result in lower output and more deflation. All the comparative statics are reversed. If the government offers a special consumption subsidy, we'll get less consumption. If a preference shock causes consumers to want to spend more, in equilibrium they'll spend less. Inversely, if the Fed raises interest rates, consumption will increase and deflation will shrink in magnitude. (Imagine that FOMC meeting: "Hey everyone, we've figured out that raising interest rates will actually increase demand, because everyone knows that we are stuck in a stochastic deflationary liquidity trap indexed by a certain Poisson exit parameter, and holding that parameter constant the only way for us to stay in equilibrium after interest rates are raised is for the trap to become less severe!")

    Honestly, this result is the "artifact", not the Keynesian one.

    Since I'm tired and cranky, let me blunt. I think that many macroeconomists have seized upon the Braun, Korber, Waki paper because its headline results are consistent with their general uneasiness about log-linearization. Unfortunately, neither these macroeconomists nor (apparently) the authors themselves really understand the channels through which these "unpleasant properties" are operating, and why they are mainly spurious. It's too bad, because we really could use an insightful examination of how log-linearization distorts our results. As it stands, BKW is just a distraction.

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  3. David,

    I could be wrong, but I suspect that the anti-liquidity trap features found by Braun et al are largely an effect of assuming a Rotemberg rather than Calvo generalization of the linearized dynamics. They say that this choice is motivated by the fact that it's "easier." OK, but it might worth mentioning that the general dynamics are conventionally thought of as Calvo rather than Rotemberg and the empirical evidence (IMO) is more consistent with Calvo. The title of the paper, at any rate, seems like a bit of a reach, and the abstract borders on deception: "Using the loglinearized equilibrium conditions the answer to the above question is yes. However, for the true nonlinear model the answer is no." There is no "true" nonlinear model. There are an infinity of possible generalizations of the linearized dynamics and of course there are some that could be used to argue for basically anything. The abstract doesn't even mention the word "Rotemberg." It seems the paper could just as well have been titled "On the Perverse Effects of Rotemberg Pricing."

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  4. More thoughts...

    I agree with you that both sides choose model features that tend to support their personal biases. E.g. one side will emphasize tax distortions and the other liquidity constraints. Fair enough. A great model would feature empirically reasonable estimates of both. But there is a big difference between a) ignoring complicating factors and b) choosing convenient, but senseless values for variables that actually exist in your model. I.e. why set the natural rate so high that your nominal rate never hits the ZLB, when a) it clearly hit the ZLB in the real world and b) it probably makes a huge difference in your model?

    Eggertsson and Krugman showed that optimal policy requires a mix of monetary and fiscal when at the ZLB if some agents are liquidity constrained, even with forward looking agents and full commitment by the CB. I would be fairly confident that this result would not be reversed by tax distortions. I am highly skeptical, OTOH, that Taylor's result wouldn't be reversed by imposing a bigger negative shock to the natural rate and a ZLB. Why else would he not have considered that scenario?

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  5. David has asked me to reply to these late night/early morning comments.

    The only situation where the resource costs of price adjustment approach the level of output is when one considers large Great Depression shocks that produce a 30\% decline in output and a 10\% deflation and one then ignores these costs by solving the model using the log-linearized equilibrium conditions.

    Both posters express concerns about the distinction between nonlinear Calvo versus nonlinear Rotemberg price adjustment. Braun and Waki have done such a comparison for much smaller shocks and under the assumption of perfect foresight. The biggest shock they consider produces a 10% decline in output (about 1/3 of the size needed to reproduce the Great Depression decline in output). They find that a 10% decline in output is associated with resource costs of price adjustment amounting to 5.5% of gross production under Rotemberg and resource costs of price dispersion of 3.5% of output under Calvo. Yes, Calvo is a bit smaller. But the principal takeaway is that for shocks of this size and larger the resource costs of price adjustment/dispersion are very large under either Calvo or Rotemberg price adjustment. These properties of the New Keynesian model pose an obstacle to anybody who would wish to use that model to analyze the Great Depression. We are hard pressed to understand how solving the model using a misspecified solution technique that abstracts from these costs is the resolution to this problem.

    The first poster is also confused about the types of equilibria that occur and when they occur in nonlinear economies of the zero bound. Braun, Koerber and Waki show that when one recognizes the resource costs of price adjustment new types of equilibria arise that are impossible when one abstracts from these costs. For instance, the AD and AS schedules can have their conventional slopes when the interest rate is zero (See Table 3 of Braun, Waki and Koerber (2012)). This occurs for moderate sized shocks that reduce output by 3.2%. Using the log-linearized equilibrium conditions one would conclude that the AD is upward sloping and steeper than AS for the same parameterization of the model. In fact, we show that a conventional configuration of the AD and AS schedules at the zero bound is a theoretical impossibility using the log-linearized equilibrium conditions.

    I think that we are far away from understanding what, if any, refutable properties that the New Keynesian model has for fiscal policy at the zero bound. But there is growing evidence that the results that emerge using log-linearized solutions can be highly misleading. Carlstrom, Fuerst and Paustian (2012) have an interesting analysis of the perfect foresight of properties of the Calvo model at the zero bound that I encourage you to read as well.



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    1. DeLong has laid out the case that 2007 forward has been as paid as the Great Depression, but with a different shape, so why are we talking about shocks smaller than those we know took place, by a factor of 3?

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  6. Since K has added some good commentary, I should clarify my points above.

    Basically, Braun et al are getting "unpleasant" results from two mostly distinct channels.

    First, they use Rotemberg pricing rather than Calvo, which dramatically attenuates deflation in a ZLB recession. The reason is that the quadratic costs of price adjustment are taken out of output. In general equilibrium, this pushes up hours (and therefore marginal cost, which is directly related to inflation) conditional on any level of consumption. The trick is that this effect can be extremely large when price changes are large, because the quadratic Rotemberg costs become huge. So when the model is calibrated to try and replicate a Great Depression level of deflation, it gets very different numerical results than the model would otherwise deliver, because the act of changing prices is literally taking up a huge fraction of national resources and cutting into slack, moderating deflation.

    (I asked a friend from Brazil whether 30% annual inflation takes up most of the resources of the economy in the form of price adjustment costs. He said something like "are you kidding? 30% inflation isn't bad at all. The real problems come later.")

    They claim that we'd get the same results from Calvo rather than Rotemberg, and that this is just a convenient modeling approximation, but this is mostly a misapprehension on their part. It is true that in the Calvo model, price changes lead to aggregate inefficiency that also creates a wedge between consumption and hours, just like in Rotemberg. The difference is that in the Calvo model, this inefficiency depends on the "stock" of accumulated price dispersion rather than the "flow" of instantaneous price change. This can make a big difference, because the price dispersion is still there when the trap ends. If the central bank targets inflation, for instance, then after the trap is over it will hold down consumption so that the wedge caused by price dispersion is noninflationary. This means that at levels of price dispersion similar to those at the end of the trap, the "moderating" effect of the price dispersion wedge on deflation is cancelled out by the endogenous decision of the (discretionary optimizer) central bank to target final consumption lower. Since the trajectory of price dispersion during the trap is nonmonotonic, the overall effect of the nonlinearity on deflation here is not clear, but the direct decrease in final consumption probably makes the output gap more severe under the nonlinearities, not less. This is in stark contrast to the Rotemberg-driven result in Braun et al.

    I feel a little silly going into detail about these aspects of the model, though, because the truth is that both the Rotemberg and Calvo models break down so thoroughly when price change is rapid that we should not stress ourselves thinking about the weird nonlinearities of either of them. It's worse for Rotemberg pricing (since rapid price change means that most of the economy may be devoted to price adjustment costs, whatever those are), but it's also bad for Calvo pricing (the i.i.d. assumption may be a nice and not too-unrealistic modeling hack for low rates of price change, but during rapid inflation or deflation it implies that some firms fail to change prices even though their prices are way off from the optimal ones; and quantitatively these extreme cases actually drive most of the inefficiency).

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  7. The other results in Braun et al., which are pretty much completely unrelated, come from their classification of equilibria into "Type 1" and "Type 2". The "Type 1" equilibria are the normal ones, while the "Type 2" are perverse equilibria similar to those in Mertens and Ravn, though a little more general. In "Type 2", the parameters are such that at the margin, each incremental bit of deflation during the trap lowers output so much, and in turn causes enough deflation, that deflation can be completely self-fulfilling. (The primary purpose of the Markov state variable is then not its direct effect on the discount rate, but rather its role as a "sunspot" to trigger the self-fulfilling trap.)

    More formally, Type 2 equilibria are unstable in the sense of E-stability; I believe that Christiano, Eichenbaum, and Rebelo criticized this feature in Mertens and Ravn. They criticized this on the grounds of realism ("if it's not E-stable, how will we ever get there?"), but I believe the stronger criticism is simply that all comparative statics are reversed, and that authors like Braun et al. are simply picking and choosing a few that will appeal to readers while failing to list all the other bizarre results implied by the same logic. The comparative statics they mention -- the absence of a paradox of toil, and a government spending multiplier below 1 -- are perfectly pitched toward macroeconomists skeptical of Keynesianism, but what about everything else? Their model implies that a massive, temporary consumption tax would increase output. I don't see them trumpeting that!

    (To be clear, I don't think they're being actively dishonest here; I just don't think they understand their results well enough. They probably plugged through the algebra to see whether high-profile Keynesian results were overturned, never thinking to check what other kinds of more intuitive features would also be "overturned".)

    Some lessons can be learned here, though. I think that the difficulties with "Type II equilibria" reflect two issues that happen in economics: (1) whenever equilibria are "unstable" in a certain sense, all comparative statics will be reversed, in a way that probably doesn't correspond to any real-world phenomenon, and (2) in an environment with multiple equilibria, the equilibrium selection criterion has the potential to completely drive your results.

    (2) is perhaps the most important here. Since the more important role played by the Markov state in the Type II equilibrium is essentially that of a coordinating device or "sunspot" for the self-fulfilling deflation, there is nothing particularly natural about assuming that the exit rate for this sunspot will stay fixed. The imposition of this particular stochastic structure on the problem -- and the assumption that it holds as the parameters shift -- is driving all the results on Type II equilibrium.

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  8. Unfortunately, it looks like I posted the last two comments right after Braun posted his (without noticing), so I'm afraid this conversation will be a little disjointed. I addressed many of the points in much more detail in the last two comments.

    First I'll discuss the Rotemberg issue, which (in my view) is actually the less important one -- so if this bores you, please skip ahead to the next comment.

    They find that a 10% decline in output is associated with resource costs of price adjustment amounting to 5.5% of gross production under Rotemberg and resource costs of price dispersion of 3.5% of output under Calvo.

    The resource costs of price dispersion are not the only issue; in my mind, the much bigger issue is the implications of these resource costs for the levels of output and inflation during trap. I recognize that there will also be resource costs of price dispersion under Calvo, perhaps not much smaller than the costs of adjustment under Rotemberg -- but as I mentioned, since these costs depend on the "stock" of price dispersion rather than the "flow" of adjustment, the implications for the variables that we care about (output and inflation) can be very different, especially once you take the central bank reaction function into account.

    For the perfect foresight simulations, I think that the following exercise, closely related to the exercise in the paper, would be very revealing:

    (1) Calibrate the log-linear NK model so that the initial level of output and deflation matches the levels at the trough of the Great Depression. (Yes, this would mean that the trajectory looks nothing like the actual trajectory in the Great Depression… this is just a rough exercise.)

    (2) See what happens to the nonlinear Rotemberg model given this calibration.

    (3) See what happens to the nonlinear Calvo model given this calibration.

    If I am correct, (3) will be very different from (2), with significantly lower consumption and more deflation. In fact, it is likely that (3) will have lower consumption than (1) -- due to the response of an inflation-targeting central bank at the end of the trap, which will target the (lower) consumption level that is noninflationary given all the accumulated price dispersion. (If you use a Taylor rule with only a moderate weight on inflation, then this will not be as big a deal -- I don't know how it would shake out quantitatively.) This is, incidentally, an interesting case where the parameterization of the reaction function does matter in analyzing the liquidity trap, since price dispersion (unlike anything in the log-linearized NK model) is a state variable.

    But the principal takeaway is that for shocks of this size and larger the resource costs of price adjustment/dispersion are very large under either Calvo or Rotemberg price adjustment. These properties of the New Keynesian model pose an obstacle to anybody who would wish to use that model to analyze the Great Depression. We are hard pressed to understand how solving the model using a misspecified solution technique that abstracts from these costs is the resolution to this problem.

    I recognize that these costs exist in either case, and certainly to some extent "matter". In both cases they become absurdly high when prices are changing rapidly; Calvo may be more realistic under normal circumstances, but it still assumes that firms fail to change prices even when the losses from doing so are enormous, which is not plausible. I suppose this ultimately depends on your perspective on macro models: I think that these models have so many clumsy hacks in them, and break down in so many places, that I am honestly not very bothered by the fact that nonlinear Calvo pricing becomes ridiculous at very rapid rates of price change, or that we use the misspecified log-linear model to gloss over this. It's a problem, but it's maybe #20 or #30 on the agenda, and vastly complicating the model to get around it would make it harder to address #1-#10.

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  9. The first poster is also confused about the types of equilibria that occur and when they occur in nonlinear economies of the zero bound. Braun, Koerber and Waki show that when one recognizes the resource costs of price adjustment new types of equilibria arise that are impossible when one abstracts from these costs. For instance, the AD and AS schedules can have their conventional slopes when the interest rate is zero (See Table 3 of Braun, Waki and Koerber (2012))…. In fact, we show that a conventional configuration of the AD and AS schedules at the zero bound is a theoretical impossibility using the log-linearized equilibrium conditions.

    This is pretty mechanical, though there is also an issue of terminology. You have defined the AD-AS diagrams with hours rather than output on the horizontal axis, and the wedge created between hours and output in the nonlinear version (necessarily absent in the log-linear version) means that both AD and AS can be downward sloping in the trap. In my view, the conventional choice of output rather than hours on the horizontal axis would be far simpler: in this case AD doesn't move at all (it's just the upward-sloping Euler equation), while AS is always upward-sloping but becomes less steep (and indeed asymptotes) as we get to extreme deflation.

    Since this more conventional rendering has one moving piece rather than two and is much easier to analyze -- there are only two fundamental configurations, depending on the relative slopes of AS and AD -- I will focus on it. Suffice to say I don't think there is any deep economic meaning in defining AD and AS your way and then observing that the slopes change. But to each his own, I suppose…

    In this rendering, the distinction between type I and type II equilibria remains clear: type I equilibria have higher slopes for AD than AS, while type II equilibria have higher slopes for AS than AD. Both equilibria are equally possible in the log-linear model. In fact, the Rotemberg nonlinearity makes type II equilibria less likely to occur, since it decreases the slope of AS. This is why I say that the two points made in your paper are essentially unrelated, as the latter point about comparative statics in Type II equilibria is not dependent on the "nonlinearity" that is supposedly the focus of the paper. As Mertens and Ravn and others have showed, a "self-fulfilling deflation" like your type II equilibrium is completely possible with the right parameterization of the log-linear model, and by making inflation less responsive to output the Rotemberg costs actually decrease the chances of this happening a little.

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  10. And let's be honest: of all the results in the paper, the one about fiscal multipliers, essentially the same one as in Mertens and Ravn, is the result that most commentators have seized upon. This has led to a great deal of confusion, as everyone falsely attributes the disparity between this finding and the "usual" Keynesian one to the log-linearization. David just did that on this blog, Josh Hendrickson did the same a few days ago, Mark Thoma did (with a different, more left-wing spin) back in October, etc.

    And this result (which, to repeat for the umpteenth time, has nothing to do with nonlinearities) is fundamentally fairly silly anyway. As I said before, it is just a rediscovery of the fact (which regularly crops up in various subfields) that when equilibria are "unstable" in some sense, comparative statics are reversed. Here is Paul Samuelson making a similar point in 1941! Since all comparative statics are reversed, there is no justification for emphasizing the few reversals that happen to go against mainstream Keynesianism -- namely, on the paradox of toil and government spending multipliers. This misleads readers into thinking that there is something uniquely fragile about these results, when in fact all intuitive notions can be rejected in the same manner. Type II equilibria don't have the paradox of toil, for instance, but by the same token they do have an even weirder paradox, whereby anything that encourages consumption (say, a large consumption subsidy) actually decreases it.

    Now, maybe you accept all this and will say "look, this just reinforces that New Keynesian models are not robust". But you could just as easily say that basic supply and demand are not robust, because (as the Samuelson paper shows) unstable equilibria can arise there that reverse comparative statics as well. The NK model is no more worthy of dismissal on this score than Walrasian equilibrium.

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  11. Our particular choice of definitions of AD and AS was made because these definitions are very informative about the response of employment to fiscal policy- a variable that is of some importance right now. Our choice is highly informative about one of the key fiscal properties of the model: the paradox of toil. If AD is upward sloping and AD is downward sloping then (locally) there is no paradox of toil. Similarly, if the AD schedule is upward sloping and cuts the upward sloping AS from below there is a paradox of toil. Similar results can be found in the paper for the other configurations of AD and AS as well.

    Determining the sign of the g-multiplier is easier when one graphs them the way that anonymous proposes. Our view though is that the central question here is not the sign of the g-multiplier but its magnitude and the response of employment to higher g. None of our calibrated results have negative g-multipliers or negative consumption and are thus all are a Type 1 equilibrium according to anonymous' definition. What is true though is that the sign of the response of response of employment and the size of the positive g-multiplier varies considerably with the size of the shocks and parameterization of the model. One way to understand why the sign of employment is changing to an increase in government purchases is to use our definitions of AD and AS.












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  12. Sorry the second reference to AD in my previous post should read AS.

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  13. I'm afraid I still don't understand why this choice of definitions is helpful. It seems like the simplest and more fruitful definition for these purposes takes the horizontal axis to be consumption. Then (1) the AD and AS curves are both always upward-sloping, with the Rotemberg adjustment costs tending to flatten the AS curve, (2) both stimulus and labor taxation shift the AS curve upward while leaving the AD curve (which is just the Euler equation) untouched, and therefore (3) the effects of stimulus and labor taxation on consumption will always have the same sign, which is positive when AD has a higher slope (type I) and negative when AS has a higher slope (type II).

    This approach handles both key comparative statics and reduces everything to only two configurations, which depend on the relative slopes of AS and AD. This feels very simple and intuitive -- I don't see the advantage in a definition that allows four configurations and causes both curves to move in response to stimulus. Am I missing something?

    Determining the sign of the g-multiplier is easier when one graphs them the way that anonymous proposes.

    It's rare that the sign of the g-multiplier is easily identified, because it's a combination of the direct spending effect and the effect on consumption. The typical question (directly corresponding to the AS/AD slopes in my plot) is whether the g-multiplier is greater or less than 1, which is equivalent to asking whether the effect on consumption is positive or negative. As the AS/AD plot implies, the sign here will always be the same as the sign of the response to a labor tax increase.

    By the same token, one can see that for the same reasons the Type II equilibrium lacks the usual Keynesian properties (positive consumption response to stimulus and paradox of toil), it has all kinds of other weird properties. In response to any intervention that moves the AD curve to the left -- basically, anything that discourages consumption, like a consumption tax increase or an increase in the fed funds rate -- consumption will actually decrease. This is another reason why I think the simple AS/AD diagram is better: it makes it trivial to see that the Keynesian conclusions are overturned only when every other comparative static is overturned as well.

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  14. Our view though is that the central question here is not the sign of the g-multiplier but its magnitude and the response of employment to higher g. None of our calibrated results have negative g-multipliers or negative consumption and are thus all are a Type 1 equilibrium according to anonymous' definition. What is true though is that the sign of the response of response of employment and the size of the positive g-multiplier varies considerably with the size of the shocks and parameterization of the model.

    Perhaps the fundamental problem here is that there's a disconnect between your vision of the paper and what most people are taking from it. If you're just trying to quantitatively explore how the g-multiplier responds to the model parameterization, I'm on board. (In fact, I think that the notion of a significant positive consumption response to stimulus through inflation's effect on real interest rates, or a positive consumption response to labor taxation through the same mechanism, is silly and irrelevant in practical terms. It might have mattered in the Great Depression, but quantitatively there's no way inflation responds that much now. This doesn't mean that I think the neoclassical model is operative either -- the substitution response to a labor tax hike is weakly positive, not negative.)

    Of course, your last sentence would also apply to a paper that exclusively focuses on the log-linearized model -- the policy elasticities there vary a lot with the parameterization as well! And for reasons already stated, I don't think that the quantitative disparities you've identified will hold up in a model with Calvo rather than Rotemberg pricing. But I'm not entirely opposed to the exercise.

    The issue, though, is that most people reading your paper are not treating it as just an exploratory quantitative exercise -- rather, they are focusing on the sensationalist claims in the paper about the "unpleasant properties" of log-linearized models. Most of the focus (like the mention on this blog post that prompted my cranky retort), indeed, has been on the claim that Keynesian policy results are overturned by a nonlinear analysis -- that they are not just quantitatively, but also qualitatively suspect. But in fact this reversal has nothing to do with log-linearization or the lack of it -- it's attributable to the instability of type II equilibria, which is possible both with and without log-linearization. Yet now there are a lot of very confused people who are attributing all this to the model's nonlinearities!

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    1. Anonymous,

      I love your contribution here, but maybe it's time to turn down the crank-o-meter. I never claimed here that Keynesian policy results *are* overturned for reason X. I said that the powerful effects of fiscal policy at the ZLB *are quite possibly an artifact* of X. Maybe the results are overturned for reasons other than X. Whatever. The reason for that reference was to serve more as a warning to anyone putting too much stock in the results stemming from *any* given model.

      I suspect that you and many other readers may believe that I may be motivated by some weird dogmatic opposition to "expansionary" fiscal policies. Such a notion is easily dispelled by the evidence (I have past posts supporting infrastructure investment and greater levels of US Treasury debt, for example.)

      I am enjoying your correspondence with Tony. I have yet to sort out exactly what is going on here, but thanks very much for motivating me to find out.

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  15. Perhaps this was not your intention, but effectively you are playing to a large constituency of macroeconomists that never really believed the Keynesian stories about a paradox of toil, and have always been a little worried about log-linearization. These people are understandably attracted to a claim that (1) the Keynesian stories are potentially fallacious, and (2) this is because Keynesian models rely on log-linearization. Thus all the coverage of your paper. But, of course, there is no connection between (1) and (2), and the logic underlying (1) would just as easily reject conventional supply-and-demand analysis in micro. Most of the high-level conclusions your audience is drawing from your paper are simply false.

    And even if you say that the paper is mainly quantitative, most readers seem to be misunderstanding it. After all, if the Rotemberg economy has positive inflation, the nonlinearities amplify the effects of Keynesian intervention -- the direct effect of government purchases on inflation is supplemented by a feedback loop arising from the costs of price adjustment. Yet almost all mentions of your paper have been in the context of skepticism about stimulus and the paradox of toil. The quantitative results about large-scale deflation as in the Great Depression are interesting but not directly relevant to the current environment, where (A) the departure from the model's steady state is small enough that the nonlinearities are mostly irrelevant, and (B) since inflation is currently positive, to the extent these nonlinearities are relevant they actually reinforce Keynesian conclusions rather than weaken them.

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  16. A couple things:

    1. Of course Taylor is stumping for the Republicans. Taylor always stumps for the Republicans. It's just one of those things. Massive bodies fall toward each other, lions hunt antelopes, and John Taylor stumps for the Republicans.

    2. Krugman, I think, is not stumping for the Democrats. He's stumping for stimulus to the Democrats, who traditionally are very reluctant to embrace the idea of stimulus except in extreme crises (even going back to FDR).

    3. DSGE frequently gets used to stump for stuff. As I see it, this isn't a problem with stumping for stuff, - stump for whatever you want! - it's a problem with the academic culture that says that you better have a DSGE model if you're going to stump for anything...see recent post:

    http://noahpinionblog.blogspot.com/2013/03/the-swamp-of-dsge-despair.html

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    1. Of course, nobody cares what Noah thinks.

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  17. Krugman, I think, is not stumping for the Democrats.

    Of course Krugman is stumping for the democrats. Krugman always stumps for the democrats. (Dude, where have you been for the last 10 years?) Its just one of those things.

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