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It might be worth adding a reminder at the end that the New Keynesian sine waves you are describing are in the absence of the Zero Lower Bound and aimed at preventing the interest rate from hitting that ZLB (I think?). I got quite tripped up because I thought you were trying to describe the New Keynesian countercyclical solution in some case where you hit the ZLB during a recession. But, if I understand correctly, this is a model for how NK fiscal policy would look when working "properly", that is, when the ZLB does not obtain and monetary policy is doing the heavy lifting of stabilizing output. I had to read it a couple times to see it clearly.

Under the condition the CB successfully targets a nominal price?

How do expectations figure here?

What's the smoothing window?

Dan: I've added a sentence: "***Suppose we want a countercyclical fiscal policy to help smooth out those fluctuations in the natural rate, to help prevent us hitting the ZLB.*** What would countercyclical fiscal policy look like, in the same picture?"

Does that make it clearer? (I really want to make this post as clear as possible, so thanks for your help.)

Jon: I was assuming the CB targets inflation, which is standard in NK models. But I think the point here would apply more generally.

I was implicitly assuming rational expectations, again standard in NK models, but again I think my point would apply a bit more generally.

Infinite horizon model where people try to smooth consumption with no lags. Again standard simple NK model.

dumb question alert: so does this mean in NK models there is no simple role for fiscal policy in the sense that an increase in the level of government spending raises contemporary demand hence output and employment? I ask because I dimly remember being TA in an intermediate macro course that included a simplified three-equation NK model, and the NK-IS curve included shock term 'g', variously described as either a demand shock or government demand shock, positive values of which shifted the curve up. Is the model you have in mind excluding such a thing?

Luis Enrique: if we interpret "g" as government spending, then what would cause an upward shift in the NK IS curve (raising the natural rate), would not be g, but g(t)-E[g(t+1)]. In a continuous time model, this becomes minus dg/dt.

thanks v much Nick.

If I'd taken the trouble to check my notes before commenting, I would have seen the IS curve in output form including exactly that expression.

Interestingly though, if you think that NK macro isn't always taught in a fashion that emphasizes what you do here, the accompanying text says "[the IS curve] would shift rightward/upward with an increase in Et[y(t+1)] or g(t)" - i.e a change in the level of g(t) not -dg/dt.

Presumably the author had in mind E[g(t+1)] held constant.

so to answer my dumb question, the NK model does say an increase in the level of government spending raises contemporary demand hence output and employment, so long as that increase is accompanied by an expected future downward sloping path for g?

Luis Enrique: Yep. In the standard NK model, a permanent change in G does not shift the IS upwards, but a temporary increase in G does shift the IS upwards. People know that. But what that really means is that a decline in the expected growth rate of G is what shifts the IS curve upwards. In a discrete time model, with iid shocks to G, you won't see the distinction, because E[G(t+1)] is always constant.

In other words, an announced cut in future G is exactly as expansionary (for given current r) as an immediate increase in G that is announced to be temporary.

Nick: did you mean this old post of yours: http://worthwhile.typepad.com/worthwhile_canadian_initi/2013/03/fiscal-policy-with-old-and-new-keynesian-is-curves.html?cid=6a00d83451688169e2017c37f2df91970b

I also remember one important critique of fiscal stimulus (I think it was by you) based on the fact that using fiscal policy instead of monetary policy to create inflation (aggregate demand) it would require ever increasing deficits. So to have 2% inflation driven solely by fiscal stimulus (monetary policy is impotent, remember?) we would have to have increases in level of government spending also by 2%. I reckon that I saw that critique very simple but also very powerful as I did not think about it that way then.

Thanks JV! That's the one. I have updated the post to add the link.

I made a similar but different critique in comments once of using fiscal policy to drive the natural rate of interest down to 0% (some MMTers want something like this).

gah! of course you are right - the author "had in mind E[g(t+1)] held constant" because g is iid.

(ok, more accurately, stochastic process has some persistence, so E[g(t+1)] isn't exactly constant but still g expected to revert to mean)

So for us dim non-economists, what is the lesson here?

Is it that when we are not at the ZLB it is reasonable and even maybe optimal (if your main goal is to keep natural rate over zero) to let politicians follow their austerian instincts?

What would be the optimal phase of monetary stimulus in this sine graph?

Benoit: good questions.

The lessons:

1. It's not enough just to look at the math. We need to get our intuitions around what the model says and see what the math is really trying to tell us.

2. We should be very careful forcing new wine into old bottles, where it might not fit.

3. We need to be very careful about framing what our models say to fit our political desires. People use NK models to justify temporary increases in G in a recession. They could just as easily be used to justify announcing future cuts in G in a recession.

4. "Is it that when we are not at the ZLB it is reasonable and even maybe optimal (if your main goal is to keep natural rate over zero) to let politicians follow their austerian instincts?" Well, my tongue was in cheek when I said that, though I am a bit annoyed (for many reasons) at both sides who talk about "Austerity". That would probably be scary, because God only knows what they would do, if they are doing it for all the wrong reasons. And there are very good micro reasons (that I don't explore here) for running deficits in a recession.

If you think of monetary policy as setting a rate of interest (which is sort of how New Keynesians think, though not totally how they think) then the central bank should try to make the actual rate of interest go up and down to follow the natural rate of interest as closely as possible. Exact same sine wave as the original. The only problem is that if the natural rate of interest gets very low, the central bank hits the ZLB, and it can't do that.


I'm not sure you'd agree but what I take from this is that a model driven solely by the inter-temporal optimisation of an infinitely forward-looking household might not have that much to teach us about what happens in a recession.

Eh, the consumption Euler equation says that about expected values, and the reasonable presumption here seems to be that supply shocks (and the ensuing contingent fiscal response) are unexpected things. ZLB NK fiscal policy has a space where it simply validates the previously-expected rate of interest.

Luis: I'm not sure I would agree that that is the take-away from this post (though one might agree with that for other reasons). I am assuming that the government can see those fluctuations in the natural rate coming, but that seems to be an assumption that favours the use of countercyclical fiscal policy. If the shocks to the natural rate were unforecastable, and had a unit root, that would make countercyclical fiscal policy very hard, I think.

david: I'm not sure I follow you. But the sort of shocks I am talking about here are any shocks that cause the natural rate of interest to fluctuate over time. Those could be AS shocks, but they could also be IS shocks, like changes in technology that shift investment demand, or changes in time preference that shift saving. Or changes in expectations of those things.

All right, to elaborate. Your argument, if I interpret it right, is that the NK intertemporal-consumption model basically hinges on the Euler equation, and the link between G and the Euler equation is actually pretty ambiguous, because the only actual mathematical relationship that can be drawn is between consumption levels in each period and G is via the expected rate of change of G. That's fair. That leaves enough free variables for the relationship between actual G and C itself to be completely arbitrary, dependant on how you handwave how people form E[Pi(t+1)] under the ZLB, and that's even without any newfangled liquidity constraints or financial frictions. I dimly recall Cochrane making a similar point back in February.

But I think that picks on the wrong element of NK here. The core intuition should be that private-sector adjustment to unanticipated shocks is really freaking expensive, so we should try to have less adjustment, where possible. Intertemporal optimization is entirely the wrong way to start modelling, because it presumes away the point of interest. New Keynesian modelling is all about throwing enough obstructions at intertemporal shifts to make an RBC model behave obediently Keynesian. Nitpicking at models of these obstructions to say that there's actually some loophole so that it doesn't obstruct as universally as might be hoped misses the point. If an engineer goes "... and let's assume a point mass here" you don't go "I've caught you, mass concentrated at a point would actually cause a nuclear explosion!"

(incidentally: why is policy here smoothing the natural rate just to give the ZLB traction, instead of smoothing Y directly?)

Er, did I lose a reply to 12:40PM to the spam filter, or did my browser eat it.

I just looked through the spam bin and I didn't see it there.

It showed up immediately after I posted my 1:48 remark, even after I hard-refreshed a few times before that. I dunno. :|

david: I'm not sure if I don't understand you or if I don't agree. Let me fire off some random remarks, to see if any hit.
Suppose, to keep it simple, there are no supply shocks to the LRAS/LRPC or SRAS/SRPC, so Y* stays constant over time, and we want to keep Y constant over time too. But there are shocks that shift the IS curve up and down, so the height of the IS curve at Y*, which is r*, is also going up and down. And the job of the central bank is to try to move r up and down, so r always equals r*, so Y always equals Y*. But the ZLB may be binding, so maybe the CB can't always do that, so the job of the fiscal authority is to try to prevent r* moving up and down so much,

This is an excellent post. I totally agree this holds for traditional new keynesian models and thus for Wicksell too. It should be noted that in Krugman's latest work the natural rate of interest is endogenous and is a function of the level of private debt (assuming there is an exogenous borrowing limit). other recent papers have financial market "frictions" that generate negative natural rates of interest. Thus in this type of model government deficits targeted at the "impatient" agents would raise the natural rate of interest and thus output not only through purchasing output but also by reducing their debts.

A challenge for advocates of monetary policy:

Monetary policy makes no sense because it channels stimulus into the economy exclusively via borrowing and investment, and there is no reason to suppose the optimum mix of investment and consumption spending changes as between when an economy is in recession and when it ins’t. You might as well channel stimulus into the economy exclusively via car production, restaurants and massage parlours.

Ralph Musgrave,

"it channels stimulus into the economy exclusively via borrowing"


Also, how do you have a symmetric contractionary policy based on car production? Or restaurants or massage parlours? The mind boggles.

The opposite of buying bonds, on the other hand, is fairly obvious.

Nathan: Thanks!

Another way of thinking about what you are saying: the "impatient" agents are borrowing-constrained, and their consumption depends on current income, like in Old Keynesian models, rather than being consumption smoothers, like in New Keynesian models.

Suppose there were fluctuations in the relative demand or supply of apples vs bananas. We would want the relative price of apples to bananas to be allowed to fluctuate. A central bank that prevented that relative price from fluctuating would mess with price signals and the allocation of resources.

Suppose there were fluctuations in the relative demand or supply of current apples vs future apples. We would want the relative price of current apples to future apples to be allowed to fluctuate. A central bank that prevented that relative price from fluctuating would mess with price signals and the allocation of resources. We call that relative price "the real interest rate".

And, as W Peden says, monetary policy does not work via "lower interest rates mean that people borrow more to spend more". That is true for one individual, but it is not true in aggregate, because income=expenditure. The extra spending creates the extra income to finance that extra spending; it is not financed by borrowing.

And, as I said right at the beginning of the post, letting monetary policy hit the macro target frees up fiscal policy to try to hit its many micro targets. There are always more targets than instruments for fiscal policy (i.e. there are trade-offs between those micro targets), so adding one extra macro target for fiscal policy only makes things worse for its other targets.

"...and there is no reason to suppose the optimum mix of investment and consumption spending changes as between when an economy is in recession and when it ins’t."

Yes there is. Because (unless the central bank adjusts the real rate of interest correctly in response) booms and recessions happen precisely *because* (in these NK models) there has been a change in desired consumption/saving or investment.

Keynes said something good on this point. Suppose you were central planner, and you learned that people wanted to consume less today and consume more in future. What would you do? You would send a signal to firms to invest more, and send another signal back to people saying that there's no point in them cutting their consumption unless firms invest more to offset that. In a market economy, that signal is a reduction in the real interest rate. It needs to go down.

If booms and recessions happened because there was a change in the desired mix of private spending vs public spending, ("I want more roads and fewer cars") then there would be a case for countercyclical fiscal policy. But they don't. Booms and recessions happen precisely because there is a change in the desired mix of private consumption and private investment.

"The nutters think that booms are a good time to be increasing government spending, because we can afford it; and recessions would be a good time to be decreasing government spending, because we can't afford it."

The nutters believe that terms like "we can afford it" and "we can't afford it" apply to sovereign governments.


Thanks for your detailed response. Re Keynes’s point and to keep it simple, let’s assume constant GDP (in the long term). GDP has actually DECLINED in the UK and elsewhere since the crunch, so that’s not an unrealistic assumption.

Given constant GDP, employers won’t produce more in the future, so there is no point in cutting interest rates so as to get them to invest more.

As to individual households, a distinction needs to be made between two phenomena:

1. A desire to consume less now and more in the future with a view to building up cash savings.

2. A simple desire to consume less now and more in the future.

I suggest that changes in the latter are pretty much random: i.e. one household’s decision to consume more now and less in future will be matched by another households desire to do the opposite.

In contrast, it’s blindingly obvious that there are substantial shifts over time in households’ aggregate tendency to go into irrational exuberance mode and spend their cash savings, and then two years later, go into “cash savings” mode (which is where we are now).

So the solution to recessions is to have government net spend (which I call “fiscal boost” - though you could say there is a bit of "monetary" mixed in there, if the government / central bank machine is printing and spending new money into the economy). I.e. the solution is to feed the cash that households want into their bank accounts. In contrast, interest rate adjustments (i.e. inducing households to borrow more, lend less or whatever) are not relevant to the problem. And that’s all very much compliant with MMT thinking, particularly MMT ideas on "private sector net financial assets" – for what that’s worth.

Thanks for making me think this thru – even if I’ve got it all wrong!

@Nick Rowe: I'm not sure I'd fully agree with that characterization. the agents are still consumption smoothers- just subject to debt constraints. Anyway, this is the problem with models without default and thus money...

Nick, Ralph Musgrave is stuck in spam.


"But if a big drop in demand causes the natural rate of interest to fall too low, relative to the inflation target, the ZLB maybe be a binding constraint on monetary policy in New Keynesian models, because the central bank cannot drop the actual real rate of interest down to the natural rate. So you might want a countercyclical fiscal policy, that raises the natural rate when private demand is low and the natural rate is low, and lowers the natural rate when private demand is high and the natural rate is high, to keep the economy away from the ZLB."

Or you drop the after tax cost interest rate down to the reduced natural rate of interest. And on an after tax basis, the interest rate can be negative.

"but it is not true in aggregate, because income=expenditure. The extra spending creates the extra income to finance that extra spending; it is not financed by borrowing."

This is an appeal to an accounting accounting identity, not a mechanism. Never reason from an accounting identity. It is impossible to design an economy, no matter how ridiculous where this isn't true under NIPA rules. Aggregation is no more necessary than it is for assets = liabilities.

Credit created by fractional reserve bank lending and shadow bank financial operations enters the economy as investment. There may be a reasonable mechanistic argument that shows this additional credit has no effect on the real economy, but income = expenditure isn't one.

Under NIPA rules invested borrowing is instantaneously and automatically expenditure and income, since GDP = GDI = GDE always. It's defined to. It took me a while to figure it out, but there are no loopholes or counterexamples. Results needn't be reasonable, just well defined.

It also only applies to transactions that are involved in GDP, not all economic transactions. The government is in the process of a major flow of funds accounting redesign which will subsume GDP. It can't happen too soon.

Nick, perhaps a dumb question here, but what's the difference (if there is one) between "neo-Keynesian" and "new-Keynesian?" neo = new in my book, but I've seem some people write as if these are two different things. Specifically (if I recall correctly) I remember seeing in a single post somewhere Paul Krugman being called "neo-Keynesian" while Greg Mankiw was referred to as "new-Keynesian" in a deliberate way: as if there's a difference. Anything to that, or are they really pretty much the same?

@Tom Brown: New Keynesians are people who (generally) use DSGE models and have agents who "smooth" their consumption through out their lifetime but get effects supposedly similar to what one would expect from a "keynesian" perspective by assuming prices are sticky for some reason or some other imperfection is driving the outcomes of the model. Neo-Keynesians are from a generation before that who used the "neoclassical" perspective (utility maximizing, rational agents, supply and demand etc) for microeconomics but didn't explicitly model the behavior of individuals in their macroeconomic models (most commonly, the IS-LM model).

Krugman is an interesting case in that he both builds DSGE models but argues for the usefulness of the IS-LM model in specific cases such as the one we're in now. In short: yes there is a major difference but no, it doesn't necessarily trickle down to the policy level (of course many new-keynesians are anti-keynesians in the traditional sense. see John Taylor and Greg Mankiw).

Nathan Tankus,

I think that's a good summary. I'd add that the New Keynesian Phillips Curve is the same as the monetarist Phillips Curve (short-run tradeoff, long-run neutrality) and all good New Keynesian models have an output gap which allows for non-cyclical shifts in potential output, unlike Neo-Keynesian and monetarist models. Finally, there's no place for uncontrollable cost-push inflation in New Keynesian models.

It gets complicated with the UK, where pre-Neo-Keynesianism ("palaeo-Keynesianism") never really went away and a very cost-push based model seems to have dominated until 1979. The shift of the British economics profession in the 1980s and 1990s would be interesting to study, because it followed rather than led policy and monetarism & RBC & New Classical macroeconomics were never big here, so the jump to New Keynesianism must have been more or less direct from palaeo-Keynesianism.

Interesting fact: Mervyn King was one of the economists who signed a letter predicting deepening depression in 1981, shortly before the recovery began. How he got from there to his career at the Bank of England will be an interesting project for his official biographer...

Frances Woolley,

That's not a very articulate response to my points. But if it's the best you can do, I'm much encouraged.

Ralph: "Frances Woolley,

That's not a very articulate response to my points. But if it's the best you can do, I'm much encouraged."

Frances was saying that your comment had got stuck in the spam filter (she can see what's in spam), so this was her way of letting me know about the problem, so I fished it out of spam. (Or did I miss the joke?)

Just to be clear you're talking about:

c = E{c(t+1)} - 1/σ(i-E{π(t+1)} - ρ )

(where I've suppressed all the t subscripts, E is the expectation operator for time t and all lower case letters are natural logarithms except i right?

i isn't a log since it comes from (log 1 + i). ln(1 + 0.05) = 0.0488.

Peter N@ 12.47: Yes, I think that's right.

@ 3.27: OK, NIA identities don't tell you about the world, but they do prevent us from saying contradictory things. And to say that there is a big difference between the individual experiment and the economy-wide experiment regarding the relation between income and expenditure is an important insight about the world.

Nathan @11.01: OK, but a consumption smoother who is constrained in his borrowing (or lending?) will act very much like an agent in an Old Keynesian model.

Ralph @10.06: You have lost me a little there, but I think you are making an important distinction between an increased desire to save and an increased desire to save in the form of money. It's hard to see that distinction in simple NK models, since money isn't in the model explicitly. (BTW, I'm slowly working on another post, that is sort of in response.)

Tom: I think Nathan and W Peden gave good answers. It's probably not useful to try to give overly precise answers anyway, since there are rarely any hard and fast dividing lines where all economists in group A believe one set of things, and all economists in group B believe another set of things. You can sort of see clusters, across economists and across time, but it's always fuzzy. Crudest distinction: "New Keynesian" is newer than "Neo-Keynesian"!

I found this interesting paper on NK models, the zero lower bound, and the effects of log-linearization on the models' range of applicability:


"In this paper we have documented that it can be very misleading to rely on the loglinearization economy to make inferences about existence of an equilibrium, uniqueness of equilibrium or to characterize the local dynamics of equilibrium. We have illustrated that these problems arise in empirically relevant parameterizations of the model that have been chosen to match observations from the Great Depression and Great Recession."

It should be right up your alley, it explains its results in terms of the relationship between the AD and AS curves. It looks like it would be good course material for an advanced course.

@Nick: exactly. this follows Krugman's long history of mimicking older insights in newer models.

Peter N,

That paper makes some highly dubious assumptions. For an extensive discussion (including comments by Braun) see here http://andolfatto.blogspot.ca/2013/03/krugman-on-taylor.html

How is capital extracting its share? This chart doesn't seem to correlate very well:

Apologies, the chart is for the wrong article.

Nathan Tankus,

I'll not try to referee this food fight. I was mostly interested in the way they used the AD and AS curves, and you'd certainly expect odd things if the slope of AS exceeded that of AD. Certainly the attempt the critic made to equate a +30% shock with a -30% shock is bogus. This won't be settled until somebody reruns the model with the critics' suggestions, if then.

I'm quite willing to believe price adjustment costs are large in a deflationary situation. You can get this effect with a contract model or other model with memory, and I've found other authors who believe price adjustment costs were very large in the great depression, though you, of course, need to clearly define what costs you're talking about.

In other news, Japanese bond yields seem to have fallen back down to pre-Abenomic enthusiasm levels. I am commenting here as the original post is closed, but as we made references to predictions, there should be some place here where we can monitor the ongoing developments in Japan.

rsj: yep. I find the more recent news out of Japan very disappointing, even depressing. Not just the bond yields, but the stock market too. I normally discount special interest conspiracy theories, but in this case...here's how it looks to me: Abenomics was starting to work. People were starting to expect that the BoJ was actually serious about hitting its 2% inflation target, figured out the consequences for future short interest rates, and so long bond yields started to rise. Then Koo suddenly changed his tune from "monetary policy can't do anything" to "monetary policy can raise expected inflation, which is causing bond yields to rise, and that is a very bad thing, especially for Japanese banks that hold a lot of government bonds, and for Nomura, my employer". So the BoJ changed its tune, and people saw that Koo was winning that debate politically, so bond yields fell again. (Abe's communications strategy takes part of the blame, but Koo and his friends take most.) So unless things change direction soon (and I haven't got any reason except hope to think they will), things now look bad again for Japan. Worst case scenario: Japan won't recover until the debt/GDP gets big enough that fears of default (via inflation, presumably) start to bite. And that may take some time. Very depressing.

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