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If you are a dyed-in-the-wool New Keynesian, and you want an expansionary Aggregate Demand policy, to get the economy up off the ZLB, and if you don't agree with Scott Sumner and other "monetary policy optimists", and so you want to use fiscal policy, you will want to increase the natural rate of interest, and you do that by ensuring that G will be expected to be falling over time from now on. And there are two ways to do that: either raise current G holding expected future G constant; or else cut expected future G holding current G constant. Probably: Paul Krugman wants to do the first; John Taylor wants to do the second.

This is a first-year math problem, there are two solutions to an equation, but only one is valid in the model parameters due to an external constraint not used in the equation itself.

"or else cut expected future G holding current G constant." is not a valid answer because it implies that the economy is not in a liquidity trap. It assumes equilibrium conditions, which is contrary to the definition of a liquidity trap/depressed economy, so given that we are in a liquidity trap (want to lift ourselves off the ZLB), then John Taylor is wrong.

In a liquidity trap, as Krugman says, paying for G is free because of surplus resources, while Taylor's Policy lowers Y (see Europe, UK, Austerity, Failure of) and destroys it own multiplier.

Lower future government spending allows increased future consumption out of future income, less need to save now, higher natural interest rate.

Higher interest rate means less consumption now, more consumption later, higher growth rate of consumption.

Higher interest rate means less investment now....why is there more investment in the future?

Just cut government spending from current levels (or planned growth paths) is pretty straightforward.

Raise government spending now, would normally result in less consumption now and less saving now to reduce consumption in the future. But that only works if government spending is going back down in the future.

By the way, if the cuts in government spending is aid to the elderly (social security and medicare,) I don't think this will really work. If the cuts are in military spending, I think it might work.

Determinant:

What does this have to do with the zero bound? The argument is that lower future government spending raises the natural interest rate so that the zero nominal bound is less binding. Do it enough, and it is no longer binding.

Bill: You've got it for consumption. For investment: think of a 2-period Irving Fisher type model, for simplicity. Low interest rate means high investment today so you can disinvest tomorrow, which means investment is falling over time. Imagine a farmer holding back more seed from the market.

Yep, this really only works for government spending on goods which do not affect the marginal utility of private consumption. But that's the benchmark NK assumption. Transfer payments are different, but are just negative taxes, and don't matter in a Ricardian model, except insofar as they are non-lump-sum. (There are also distorting taxes in John Taylor's model, but my hunch is that's not the main driver of the results, though it would have some effect, and I've ignored that effect here for simplicity.)

http://krugman.blogs.nytimes.com/

Yes Bill, your reasoning is false because it tries to optimize C instead of Y. You are cutting G in the future, *assuming* the slack gets moved over to C (not at all a good assumption given the empirical results of Austerity in Europe) and therefore assuming that Y is in equilibrium and stays constant. You destroyed the multiplier effect (exponential growth) by assuming equilibrium. You assumed the pie didn't grow, you just changed the slice size.

Further, because you assumed the same size of Y (pie) and reduced G, the future population is in fact poorer because they have less consumption of government services.

Krugman assumes you are trying to grow the whole pie and maintain the present fraction of domestic consumption and government services.

Any time you try to solve a second-order Ordinary differential equation for two roots (r1, r2), by definition you can have a positive or negative root. A negative root leads to decaying growth, we want a positive root to exponentially grow the whole pie. r1, r2 !< 0, which is the external constraint which binds the interpretation. Taylor is not observing the constrain, and is therefore wrong.

http://noahpinionblog.blogspot.ca/

Noah Smith worked through John Taylor's model. John Taylor assumes that the ZLB doesn't exist, my critique that Taylor is excluding a binding constraint that throws out possible answers stands. He failed first-year modelling.

Notice that the fundamental logic of choice over time applied to production goods which is at the root of the the concept of the natural rate of interest as pioneered by Bohm-Bawek & Wicksell -- ie the fact of choice that no one will extend the length of a production process without the promise of superior output -- is completely missing from this 'Keynesian' modeling of the relation of government spending to 'natural' interest rates & "aggregate supply". This is the original sin of Keynes -- to take a profound fact of the logic of choice which structures all choice & resource allocations across time, and disappear it with smoke and mirror, pretending to reproduce Wicksell while gutting it of its only functional internal mechanism

Nick

A great post! A Ricardian drain on private I might further explain why John Taylor prefers the cut G later option.

Tobin had explored this question in his '78 paper Government Deficits & Capital Accumulation. He used the *stock* IS curve (he called it the WW' curve - also called the KI curve by Sargent) rather than either the old Keynesian or NK flow IS curve. He concluded that while any path of natural rates may be consistent with any level of G, raising G-T *now* raises the natural rate. His way of framing the conclusion was, IIRC :

1) Ricardian equivalence does not hold, so current decisions have impact even if they are not expected to be permanent.
2) G-T can stoke inflation or drain private investment but does not do both. Today, we would say that it depends on the monetary policy reaction function.

Determinant: Within the context of this sort of NK model, an announced time path in which government expenditure would be falling over time, relative to the previously expected time-path, would *raise* the natural rate of interest. So John Taylor's proposed policy would be *even more* expansionary in a model where the ZLB were currently a binding constraint.

Noah is a very smart young guy who is up on all the latest models and who could cream me at math-modelling. But sometimes us clapped-out old minor university administrators who only do macro part-time nowadays and who can only see curves can see things the young-uns miss.

Annoyingly, I've run out of monthly visits to the NYT, and can't see PK's latest. Does he just say "read Noah"? (I blew my last visit by reading PK on Steve Keen, where PK is totally right, of course.

Greg: I disagree. If you accused them of *over-simplifying* the time-structure of production you would have a point. But a positive MEI in Keynes does mean "superior output" by "lengthening the production process". (And by the way, whenever we store goods, which we do, if storage is costly we get inferior output by lengthening the production process, as you know.)

Ritwik: Thanks! I can't remember whether I once read that Tobin paper, or what was in it if I did read it, but it wouldn't totally surprise me if the basic idea was in Tobin a few decades ago.

Perhaps I should have given this post a much more inflammatory title: "Why (phased in) austerity works in New Keynesian models at the ZLB". That title would have been true, but misleading. But no more misleading than "Why (temporary) increases in government spending works in New Keynesian models at the ZLB".

There are two ways to increase (Gtoday minus Gtomorrow). Obviously.

I am a little annoyed at both left and right on this. Because they both frame it in ways to support what they want. But I am even more annoyed at the left for being so annoyed at the right for doing the same thing they are doing.

Maybe I should just be annoyed at math?

Here is the paper Nick. Also contains interesting discussions of the dynamic efficiency question wrt government debt.

http://cowles.econ.yale.edu/P/cd/d05a/d0502.pdf

By the way, off-topic, but I use your 'Borges problem' nomenclature for the right way of slicing and dicing things pretty often these days. Sometimes to argue against your positions. I trust you don't mind. :)

By the way, on PK vs Steve Keen on IS/LM, I always remember what Leijonhufvd had to say about liquidity preference and IS/LM. He argued that liquidity preference as in the interest elasticity of money demand is the sine qua non of Keynesian theory, but liquidity preference as in the argument that interest rates are determined solely by the interplay between money and non-money assets is a particularly Cambridge Keynesian formulation that IS/LM didn't ever handle head-on.

He attributed this to the Walrasian nature of IS/LM formulation where the sequence of changes implied by the different models was swept under the rug of joint determination. His own Marshallian re-formulation helped clarify the matter.

This is the paper, beginning page 22 is the discussion I'm referring to. Still the most clear exposition on the controversies around IS/LM that I've read.

http://www.econ.ucla.edu/workingpapers/wp186.pdf

Annoyingly, I've run out of monthly visits to the NYT, and can't see PK's latest. Does he just say "read Noah"?

A bit more than that. I just sent you an e-mail.

Kevin Donoghue

Nick,
Maybe I'm being unfair but I think you're making a mountain (or at least a mound) out of a molehill here. Consider a simple 2-period Old Keynesian model, where G1 is current-period government purchases and G2 is government purchases in the long-run (the rest of time). Since G2 is part of The State of Long Term Expectation, traditional OK modelling treats it as an exogenous constant. If G1 increases, it necessarily reduces Gdot = (G2-G1)/G1. So there isn't much difference between Old and New really, in that respect.

Nick, your logic of choice here is wrong -- if we are moving goods thru time via storage for a reason, this is a choice made because the consequences are chosen as preferred to the alternative, it is chosen as a superior outcome. The economics categories of inferior or superior are relative to human preferences, they are not defined in physical terms regardless of place or time or context or persons, etc. The apple we store for eating in March is superior to the apple we didn't eat in September in order to store. Menger, Menger, Menger.

Nick writes,

"by the way, whenever we store goods, which we do, if storage is costly we get inferior output by lengthening the production process, as you know."

On Keynes, the burden is on me to work through Keynes & the Keynesian on this so I confidently have what he & they are doing stored in my permanent memory. It has always seemed to me the 'simplified' Keynesian version of output gains via lengthened production does gut Bohm-Bawerk / Wicksell but I need lay this out clearly for myself and others. And I need to make sense of how this is consistent with Keynes' repeated attack on Bohm-Bawerk's logic of choice in production goods across time.

We don't expend the costs of storage and waiting unless the outcome later is preferred over what we could have done today, that is, unless the outcome later is considered superior to non-waiting / non-storage alternatives available right now.

Nick writes,

"by the way, whenever we store goods, which we do, if storage is costly we get inferior output by lengthening the production process, as you know."

Nick:

Delete your browser cookies that say New York Times on them. That should give you a reset and let you back in.

The math result isn't complicated, and Noah goes through them very thoroughly, but the problem is more basic than that.

First, what exactly are we trying to do in a Keynesian fiscal stimulus exercise is to kickstart exponential growth through the fiscal multiplier. The fiscal multiplier turns into an exponential expression at its limit. We are taking sidelined resources now and growing the whole economy, which requires a positive rate of return.

Looking through the math, ah, math error, right here:

either raise current G holding expected future G constant; or else cut expected future G holding current G constant.

Graph that in your head, or on paper. There are two lines: (G is high government, g is low government spending): (G, g) or (g,-G) The slope is the same but those are not the same functions and therefore won't have the same effect. Integrating a function (which you did to solve the rate of change expression for Y) produces multiple results because integration is not a linear function. So you have to constrain the results with an outside expression, which the ZLB does, which is part of the broader thesis that we want to kick-start exponential growth with unused resources.

Bad modelling plus sloppy math = errors.

Nick - if you go to the blog's front page (http://krugman.blogs.nytimes.com) it doesn't count as a "visit". Going to an individual post counts as a visit, but unlike some other Times bloggers, PK usually puts the full text on the front page. (The exceptions are some of the longer "wonkish" posts and the guest posts on Hungary).

To reiterate, Noah Smith pretty much destroys John Taylor. Specifically, using Taylor's own models and parameters, he shows that:

a) Taylor assumes that the ZLB is not a factor, when 2008 pretty much demolished that claim. Per Smith, Krugman et. al. fiscal policy gets much more traction at the ZLB. "Everyone is a Keynesian in a slit trench" (Foxhole for Americans)

b) In his Point 6, Smith demonstrates that cuts to government purchases of goods in Taylor's model will throw the economy into a significant recession. Taylor arm-waves away his cuts by saying that they are cuts to household income transfers (those nasty redistributional social programs). Now I will concede (and Smith concedes) that government spending on newly-produced goods is a more effective stimulus, but if expectations have any meaning imperilling household income security through transfer cuts in a recession is bad economics and bad policy.

So what we have here (aside from some sloppy modelling) is

plain right-wing spin on income transfers using a half-cooked model to justify it.

Determinant:

Are you assuming a zero nominal bound forever?

Suppose it goes away in 2015 and then, in 2018, when the nominal interest rate would be 5% with high government psending, government spending is cut, and the nominal interst rate is only 3%. All above the zero bound, and there is full employment.

Consumption is higher in 2018.

Expecting that to happen now, in 2013, there is less need to save now. Consumption rises now, and so production rises now.

It is the other side of the coin of the consumption smoothing argument as to why increased government spending now doesn't result in matchign decreases in consumption. If the increase in government is temporary, then there is only a small decrease in consumption now and slight decreases in consumption in the future, when the zero bound will no longer be a problem.

Rowe argues that these two arguments are really the same.

Ransom:

Why exactly is it impossible for people to prefer more consumption in the future than in the present and so are willing to shift production to the future?

Perhaps if you thought about the difference between short and long term interest rates.

Accumulating stocks of gold does not shift production to the future.

Greg: "The apple we store for eating in March is superior to the apple we didn't eat in September in order to store. Menger, Menger, Menger."

Of course. But we live in a world where relative prices coordinate the plans of those who store apples and those who produce and consume apples. If the real interest rate on apples (= nominal interest rate minus expected rate of inflation on apples) is negative, it will be profitable to store apples. Irving Fisher diagram. (Not that there is anything in that diagram an Austrian would object to, apart from its possible overs-simplification through having only 2 periods).

Determinant: as I said before, adding the ZLB as a binding constraint to John Taylor's model would only strengthen the results he is talking about. That's because: making Gdot negative raises the natural rate r*, and raising r* is expansionary unless the Fed raises actual r by an equal amount, and if the ZLB is a binding constraint the Fed would not raise actual r by an equal amount.

You need to actually understand the model, not fly blind by the math.

Kevin: but G2 (expected future G) either doesn't play any role in Old Keynesian models, or plays the opposite role to what we have here. A cut in G2, holding G1 constant, would be expansionary in a NK model, and equal increases in G1 and G2 would have no effect, while it would be expansionary in an OK model.

(Thanks for the info on PK's post.)

Thanks for the links Ritwik. Yep, I have mu own doubts about ISLM, that I think are sort of similar to Leijonhufvud's. I think we observe points off both the IS and LM.

Suppose it goes away in 2015 and then, in 2018, when the nominal interest rate would be 5% with high government psending, government spending is cut, and the nominal interst rate is only 3%. All above the zero bound, and there is full employment.

Consumption is higher in 2018.

Expecting that to happen now, in 2013, there is less need to save now. Consumption rises now, and so production rises now.

Suppose it doesn't? Which is the point, that is a conditional assertion. You have to deal with what is in front of you. If we are in a depressed economy (see Statscan findings re Beveridge Curve, 5.7 job seekers per vacancy, that is involuntary unemployment). Further, relying too much on expectations (a derivative expression) carries the risk of engaging in a base-rate fallacy, in which ignores prior probability. I am adding in prior probability.

What you are positing Bill is a shift from a demand-limited to a supply-limited economy. Per the above Beveridge Curve, we (and the US) live in a demand-limited economy. Therefore we should engage in demand-enhancing activities.

When you argue from a model that isn't linear, you have a strong risk of having a fallacy because converses are by definition insufficiently descriptive with non-linear expressions.

Nick:

Well, I side with Noah Smith and Paul Krugman, aside from the various math error and fallacies.

You cannot have a clear conclusion without clear math. If you have a complicated model, you need to clearly state and justify your assumptions and parameters. Noah's excellent example shows where Taylor comes up short on this.

Nick,

Taylor is not really talking about G though, is he? Taylor's result only works for transfer payments, not government consumption. But transfers have no impact on the representative household *except* through tax incentives. The way I read your argument, a planned declining government consumption, even if it's funded via 100% efficient taxation, would be stimulative. In Taylor's model, though, declining government consumption is not stimulative by his own admission.

Nick: but G2 (expected future G) either doesn't play any role in Old Keynesian models, or plays the opposite role to what we have here. A cut in G2, holding G1 constant, would be expansionary in a NK model, and equal increases in G1 and G2 would have no effect, while it would be expansionary in an OK model.

Maybe I’m nit-picking here. I do agree of course that there are differences. As I see the OK model, the second period is the Long Run, in which:

(1) we are all dead, but
(2) the next generation is alive and
(3) Classical rules apply.

Since the Long Run is Classical, higher G2 means lower C2, since Y2 cannot be boosted above the full-employment level. There is complete crowding-out. So dY1/dG1 > 0 and dY2/dG2 = 0.

As for the NK claim that dY1/dG2 < 0, Keynes did acknowledge that as a possibility (as Judge Posner noted some time ago). The prospect of a permanent increase in the role of government might well depress the animal spirits of entrepreneurs. But of course that’s not the NK consumption-smoothing mechanism.

At the end of the day, the big difference is that OK models allow for involuntary unemployment and NK models do not. Advantage OK, say I.

K: the mechanism I see for transfer payments, in Taylor's model, is that if transfers decline, that reduces long run distorting taxes, which increases future Y and C, which increases current C via consumption smoothing. I ignored that mechanism in this post, because I wanted to concentrate on the future G mechanism.

Admittedly, what I'm saying is just a (informed, I hope) *conjecture* about what's driving the results in his model. But at the end of PK's first post, he says something like he can't see what's driving JT's results. And what I'm doing is putting forward my explanation of what's driving his results, and trying to reconcile JT's results with PK's intuition (or vice versa). Like PK, whenever I see a math model I ask myself "OK, what's *really* going on here?". Like PK, I never trust a math model, unless I can *understand* where the results are coming from, because you never know what's been slipped in without anyone noticing (including the modeller, in many cases). (I'm the exact opposite of Determinant, in other words.)

Kevin: we are on the same page, except: "But of course that’s not the NK consumption-smoothing mechanism." Yep, and I think it's important to note that's what's driving the results. Because it's exactly the same mechanism that PK himself pointed to in some old posts of his about why a temporary increase in G works in NK models.

"At the end of the day, the big difference is that OK models allow for involuntary unemployment and NK models do not."

Yes and no. NK models can sorta have involuntary unemployment in Keynes' (strict peculiar) sense. Plus, if you add sticky wages to a NK model, you simply convert the voluntary unemployment into involuntary unemployment without otherwise (much) affecting the results. So I don't think that is a big difference.

Nick,

" I ignored that mechanism in this post, because I wanted to concentrate on the future G mechanism."

Right. My point is, I don't think cutting G works at all in Taylor. Some agents are liquidity constrained, if I understand correctly. The tax efficiency gains might not be affected by the liquidity constraints so long as you assume no correlation between being a transfer recipient, and being liquidity constrained, which is what I suspect is going on. If so, that is a really bad assumption because a) liquidity constraints have powerful multipliers and b) it's totally wrong. My feeling is that if transfers are strongly targeted at liquidity constrained consumers, the borrowing constraints will vastly outweigh the tax inefficiencies. Anyways, enough speculation because I haven't actually cranked through the model, and without that it's pretty well all idle speculation (that criticism applies equally to Noah as far as I can tell, and certainly to Krugman.)

This remains false:

"by the way, whenever we store goods, which we do, if storage is costly we get inferior output by lengthening the production process, as you know."

We do pure logic of choice first -- and we use it to understand things like the relations of time discount to alternative production outputs per alternative production times.

the language of inflation and interest rates doesn't help -- these are the concepts we are attempting to clarity, they are the product of the anaysis, and we don't want to beg the question, and go in a circle.

Bill writes,

"Why exactly is it impossible for people to prefer more consumption in the future than in the present and so are willing to shift production to the future?"

You must misunderstand the logic I presented -- I don't get how you inferred I made any such statement,

I'm baffled.

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