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It seems you are mixing cause and effect or perhaps conflating static equations with the dynamics that animate them. All else being equal, lower interest rates increase growth, but more growth raises interest rates, which lowers growth, which lowers rates, etc.

foosion. I am being very careful to distinguish between levels and rates of change over time. Even though it's not easy to make that distinction in words. Check my math in the linked posts.

"lower interest rates increase growth"

That is not what the Old Keynesian ISLM model says. It says that the central bank setting a lower *level* of interest rates causes a higher *level* of output.

I think you are making the assumption of a balanced budget in the second equation Y = C + S + T, in which case increasing taxes increases government spending. That would probably increase Y in an AD recession.

The third equation is not an "accounting" identity and can be proven to have no information content -- if Y = gG then dY/dt = G dg/dt + g dG/dt. The total number of goats sacrificed in North America is likely low, so any individual sacrifice should make a large contribution to Y. Select a random sequence of goats to be sacrificed at a time (2, 4, 9, 1, ...). If G dg/dt = g dG/dt always and with the magnitudes in proportion to the change in the number of goats sacrificed in your random sequence, then you've shown that Y = gG has no information content.

Nick,

"...the only feasible policy to increase the natural rate of interest and prevent a recession is to announce that government spending will be falling from now on, until the threat of recession is past."

Where does taxation fall into government policy? If government taxation can fall without affecting the level of government spending or the nominal interest rate set by monetary policy, then haven't you achieved first best fiscal policy?

"If one passenger has the screwdriver, and another has the allen key and synthetic grease, solve for the game's equilibrium. We need to know their preferences. (If the synthetic grease is back home in the garage, the equilibrium is simpler, and the fiscal screwdriver will get used.)"

The assumption is that the screwdriver holder and the allen key / grease holder cannot operate simultaneously without getting in each other's way. What if they could? What if monetary policy and fiscal policy could operate completely independent of each other?

One way to do it would be central bank lends federal reserve notes and government taxes and spends some other currency. Of course this creates arbitrage opportunities between central bank currency and government currency.

Another way would be for the government to seek other (non-debt) financing means.

Jason: "I think you are making the assumption of a balanced budget in the second equation Y = C + S + T,..."

No I'm not. C+S+T=Y=C+I+G+NX. Therefore S+T=I+G+NX. Therefore T-G=I-S+NX is the budget surplus.

"The third equation is not an "accounting" identity and can be proven to have no information content..." ???

It *is* an accounting identity, because g is defined as Y/G, and *therefore* it has no information content. You can do calculus on the other two accounting identities as well, and come to the same conclusions.

Your mind has been warped by Y=C+I+G+NX. Compare it to: number of children=number of sons+number of daughters. What does that tell us about how to increase the birthrate?

Frank: "Where does taxation fall into government policy? If government taxation can fall without affecting the level of government spending or the nominal interest rate set by monetary policy, then haven't you achieved first best fiscal policy?"

No.

"The assumption is that the screwdriver holder and the allen key / grease holder cannot operate simultaneously without getting in each other's way. What if they could?"

OK. Assume they can. We don't need to do both.

Nick,

"OK. Assume they can. We don't need to do both."

"I did a fiscal bodge-job with a screwdriver to free it, and did a proper monetary repair with allen key and synthetic grease when I got back home."

You just said that you did both. Apparently, you weren't sure that the screwdriver fix was adequate, and so you did a "proper" repair job at home. I sense that you have the opinion that fiscal policy is always second best to "proper" monetary policy presumably because of the politics involved. But what economic principle does this rest on? Politics had to be overcome to establish a central bank in the first place. And if they can be overcome, why is fiscal policy a second best solution?

Frank: because I didn't have the synthetic grease with me in the car, and I didn't want to be stopping to use a screwdriver again.

Because we want to build the right number of schools for the kids regardless of aggregate demand. Because we want the right taxes over time to tax the right people the right amounts regardless of aggregate demand.

No more comments on this post.

Surely if everyone is hand-to-mouth, then you get the old Keynesian result that raising current G (assuming taxes held constant) is what stops a recession. I can't believe there's a discontinuity where a single permanent income consumer among many dramatically changes the result. Surely if your objective is to stop a recession using fiscal policy (assuming monetary won't offset it), the most effective way is to raise current G and keep future G constant, so you pick off both the hand-to-mouth consumers and the permanent income consumers. Of course if you want to talk about optimality it becomes more complicated. Your other post makes the odd assumption that the hand-to-mouth consumers are just being inexplicably irrational. The more standard, and more reasonable, assumption is that they are liquidity constrained -- which is to say that, even in the absence of a recession, they would prefer to borrow but can't. So there's a case for running deficits even in the absence of a recession threat. But if there is a recession threat, you might as well reduce Gdot by doing what was perhaps optimal anyhow, raising current G.

Nick writes:

"...and if we see output and employment then rise, that is empirical evidence in favour of the New Keynesian model."

Does somebody here know what the empirical evidence is on this? Thanks.

Andy: "Surely if everyone is hand-to-mouth, then you get the old Keynesian result that raising current G (assuming taxes held constant) is what stops a recession."

I think that is right. The discontinuity may kick in if the desired consumption of the Ricardian agents hits a non-negativity constraint? Or it may be there's a second-order effect from changing the weighted average (weighted by what?) of Ricardian to Hand-To-Mouth agents (I fudged that in my post, because I couldn't do the math). But that second-order effect would presumably be very small, and would require very big changes in the distribution of consumption to get any traction from level effects.

"Your other post makes the odd assumption that the hand-to-mouth consumers are just being inexplicably irrational. The more standard, and more reasonable, assumption is that they are liquidity constrained -- which is to say that, even in the absence of a recession, they would prefer to borrow but can't."

I don't think it would change my results (except it would mean we could do the welfare analysis properly). Unless we made the borrowing constraint endogenous to the model. But if we do make the borrowing constraint endogenous, I think the HTM agents would act more Ricardian, because a cut in their future taxes would mean they would be able to pay back more debt in future, so would be able to borrow more today.

"But if there is a recession threat, you might as well reduce Gdot by doing what was perhaps optimal anyhow, raising current G."

But then why was current G too low in the first place?

Nick,

"If you want to increase the natural rate of interest, you must announce a slower growth rate of government spending."

Seems very weird

Can you offer your intuition on their thinking (or your take on their intuition)

without the math?

and without the rage against accounting?

thanks

"The New Keynesian model says that announced increasing austerity will be expansionary."

How did that work out in Europe? How did it work out in the US? Obama: "People are tightening their belts and the gov't will, too."

As for the goat sacrifice stimulus, maybe we can call that the New Orleans plan. ;)

The natural rate of interest rises when, all else equal, agents in the economy desire to increase spending in the current period. Gold is discovered is California, and everyone rushes to extract it. A hot new idevice is released and consumers decide they would rather save less so they can buy one. A hurricane wipes out homes and infrastructure, and there is a rush to rebuild.
Intuitively, it's not clear why an increased desired by the government to spend more on infrastructure wouldn't do the trick. You'd need everyone else to make an offsetting decision to reduce their desired spending to neutralize the effect of the higher level. With "hand-to-mouth" agents, balance sheet effects, and procyclical investment cycles, that is hard to imagine. If the government announces a temporary countercyclical, spending boom (i.e. jump and negative delta) then you would agree that the offsetting effects will certainly be smaller than the initial effect. It is mathematical hacking of the model to suggest that simply decreasing the future path of government spending, without changing the current level, will induce an increased desire to spend by everyone else. It's sounds like an argument from a disequilibrium that you would normally decry. In a recession, something is wrong, and you can't expect some mathematical curiousity of a simplified model to hold true when it has little intuition behind it.

Min, isn't that "voodoo economics?" Or am I thinking of the "Santeria policy?" Actually I used to work with a guy that sacrificed at least one goat... I didn't think to take note of the change in total output though. Oh well... opportunity lost.

Nick, you said: "Compare it to: number of children=number of sons+number of daughters. What does that tell us about how to increase the birthrate?"

C = S + D, then increasing S increases C. Does increasing S cause D to go down? Or do they both go up at approximately equal rates? Maybe. But those hypotheses need a model. One model would say that if the government gave everyone $10k for every son that they had, that would increase both S and D. Another model would say that people only have a fixed number of children, so that increasing S means that D goes down and dC/dt remains roughly the same (e.g. China's one child policy). The impact is model dependent.

That is to say arguing Y = C + I + G + NX is a content-less accounting identity is implicit modeling. You seem to be assuming if G goes up, something else must go down. But if I add population to the economy, C goes up and Y goes up -- I don't think you would consider that "warped" :) ... now just trade the labels C and G.

Also, total momentum = sum of all momenta. Is that just an accounting identity? It is model dependent. If I increase the momentum of one particle, then is total momentum increased? Yes -- if you add momentum from outside the system. No -- if you try to do it from inside the system. In the former case, it is more of an accounting identity. In the latter, it is a conservation law.

JKH: the intuition (very crudely):

Assume C+G=Y (no investment or foreign trade). The natural rate of interest is defined as that interest rate compatible with Y always being at full employment. Assume full employment income is constant over time. If G is constant over time, that would require that C is constant over time. If G is falling over time, that would require that C be increasing over time.

Assume diminishing marginal utility of consumption. If consumption increases by 10%, assume marginal utility will fall by 10%. Particular numerical example to keep the math simple.

If real interest rate r=0%, people will equalise current MU with future MU. That requires that MU be constant over time, and so C be constant over time. That is an equilibrium at full employment if G is constant over time.

If r=10%, for every 100 fewer apples I consume today, I get to eat 110 extra apples next year. In equilibrium, I must get the same marginal utility from 100 extra apples this year as 110 extra apples next year. So MU must be falling at 10% per year, so C must be rising at 10% per year. That is an equilibrium at full employment if G is falling over time.

Nick - To follow up on your reply to JKH:
Where does a recession fit in? Let's assume its a mistake of monetary policy and as you set it up above, fiscal policy must for some reason remedy it.
Say the natural rate is 0%, and at full employment C and G are constant. The central bank sets r at 5%. People want to save on the margin, and so C falls. G is independent of r, and therefore Y falls below full employment.
Are you saying that if we promise to reduce future G, consumers today will expect higher future wealth and therefore consume more today for a given r?
This assumes people are confident that we will get back to full employment quickly (why?), that they are not liquidity constrained, that they can perfectly calculate what a change in future G means for their future wealth, and that they are true consumption smoothers. Seems like this rests on highly unrealistic assumptions.

louis: this is the simplest way to think about it: instead of seeing how changes in the gas pedal will affect my speed, so that I can figure out what I need to do to drive the speed limit; assume I am driving at the speed limit, and work out what that implies about where the gas pedal needs to be.

Yes, I am using the NK model, with all its strengths and weaknesses. But as I said in the post, I relaxed the assumption that nobody is borrowing-constrained.

Nick Rowe,

Brilliant post. Is the easiest NK response to say that NK was always just a means of proving the possibility of Keynesian-type results in a model with rational expectations, rather than as a descriptive model of how the economy really works, and therefore if we get weird results from the model that are independent of those Keynesian-type results, we can ignore them? Idealized model results that are a result of how you abstracted away from the world are precisely the idealized model results you can justifiably ignore.

Tom Brown,

"isn't that "voodoo economics?""

Best piece of wit I've heard in a while!

W Peden: Thanks!

Dunno. The New Keynesian model was more organic than that. It grew in stages. Nobody had a big picture of the finished product at the beginning. Hmmm. I ought to do a post on that.

Nick Rowe,

I'd be very interested to read it. One day, I'd love to write a book on the transition of academic economists away from Old Keynesianism in the UK, because the current histories focus almost entirely on policymakers and furthermore, unlike in some other countries, there was never a significant monetarist counterrevolution in the UK.

W. Peden,

Thanks! ...and for the record, whatever you call it, count me worried when talk turns to sacrificing jackasses to boost output. )c:

@Nick:
> Does that result survive if we include some hand-to-mouth agents in the model, who consume their current disposable income every period regardless of the future? I have done the math, and I think it does, but my math might be wrong. And it says that announced increasing taxes would work too.

That wasn't quite your conclusion. An unannounced increase in taxes will work to stabilize the economy only *after* the problem of HTM agents is addressed. From your post:

> T(t) should alone be used to offset shocks to A(t). If the Old Keynesian agents go on an irrational consumption binge, raise taxes enough to stop them, without changing G(t) or r(t).

However, a recession can also be seen in the OK framework as a declining A(t) due to insufficient goat sacrifice. I think that this can even happen endogenously: recession causes unemployment (sticky wages), which causes a massive reduction in current income, which causes OK agents to massively reduce spending. This seems especially sensible incorporating Andy's thoughts that OK agents are really just NK agents who can't get credit.

Thinking about it this way, I think your combined model reinforces the conventional intuition. Consider taxes as net of transfers, and your statement above means "agents should act like they're not liquidity constrained."

Consequently, the combined model suggests that in a consumer recession (A(t) or MPC decreasing: ultimately HTM agents spend less of their income), the immediate first step is to restore consumer spending via fiscal transfers. Then, the interest rate can be adjusted over longer time horizons by announcements of expected government budget balance, which affects behaviour of the NK agents.

Complicating matters, your fraction of OK agents is not fixed in reality. Unemployment means that formerly NK agents become credit constrained. I think this has a significant effect to play with regards to government-spending stimulus.

(Other random thought when thinking of the mixed OK/NK model: at the zero lower bound, couldn't the government also reduce the real rate r by threatening to blow random property up, regardless of the level of government spending?)

W Peden: Well, I have posted it now!

"...unlike in some other countries, there was never a significant monetarist counterrevolution in the UK."

Hmm. I wonder why. Maybe because the monetarists emigrated? (Laidler and Parkin, for example, went to Canada, and taught me macro.)

Majromax: Fair point. It depends on the nature of the shock. But in this post, all I need is the result that increasing Tdot would raise the natural rate.

I think that the level of A(t) would have no effect on the natural rate, but an increase in Adot (the borrowing constraints will get relaxed over time as the financial crisis gets resolved) would reduce the natural rate.

"Complicating matters, your fraction of OK agents is not fixed in reality. Unemployment means that formerly NK agents become credit constrained."

Good point. That won't affect the natural rate, since the natural rate of interest is that rate compatible with unemployment staying at the natural rate. But if we move away from the natural rates, it will matter.

Nick Rowe,

I have a number of speculations, but this is post-post doc research, and I should focus on the doc first.

I'd ask:

Does that result hold if:

1. We include portfolio preferences and financial-asset values in the model?

2. If consumption spending is a non-linear function not only of income, but of wealth? (With, irresistible aside, the nonlinearity meaning that aggregate consumption is also a function of wealth concentration/distribution?)

"We're going to lower government consumption and increase taxes over future years."

"Wow. I'm going to have less wealth in the future:

A. Less government spending coming to me.

B. Less government spending to firms in general, so equity values will decline. (I'm not at all certain that the increased private spending from reduced taxes will offset the government spending decline.)

C. This will push up interest rates, so my bond portfolio will lose value.

Ergo: I have less (foreseeable) wealth now.

I'd better cut spending."

Steve: in the New Keynesian model, current consumption *is* a function of wealth (and the expected time-path of real interest rates), and not a function of current income at all (except insofar as current income affects wealth).

And if we have lower G and higher T for the next 3 years (relative to what we had previously expected), that means we will expect to have higher G and/or lower T (relative to what we had previously expected) after those 3 years are up.

Nick Rowe: "this is the simplest way to think about it: instead of seeing how changes in the gas pedal will affect my speed, so that I can figure out what I need to do to drive the speed limit; assume I am driving at the speed limit, and work out what that implies about where the gas pedal needs to be."

But what if in order to figure out where the gas pedal needs to be in order to drive the speed limit, you have to assume that you are on a flat straightaway? And then, when you put the gas pedal in that position, you find that not only are you going below the speed limit, you are decelerating? If you do not know how changes in the gas pedal will affect your speed, you are, to switch metaphors, driving blind in the dark. Cruise control does a better job of adjusting speed, despite not being programed with a theoretical setting for the desired speed.

Min: true. But I don't need to assume a flat straightaway, except for simplicity of wording (my linked post on the hybrid model does not make that assumption). I do need to assume that the output gap is a decreasing monotonic function of the gap between the actual rate and the natural rate, and that setting the actual rate equal to the natural rate means zero output gap. (I think that assumption is problematic, but New Keynesians make it, and I am following New Keynesianism here).

Thanks, Nick! :)

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