"Temporary" increases in G at the ZLB in an NK model

Paul Krugman says: "Monetary policy at the ZLB requires a perceived regime change to be effective, fiscal policy doesn’t — in fact, fiscal policy works better if people believe that it’s temporary, and will end when the economy recovers."

In a New Keynesian model temporarily stuck at the Zero Lower Bound with less than potential output, a "temporary" increase in Government spending will increase output, but a "permanent" increase in G will have no effect. But "temporary" has a very precise meaning here. It does not mean what a normal person might think it means. If people expect any delay, however short, in cutting G after the economy escapes the ZLB and returns to potential output, the increase in G might as well be permanent. It will have no effect on output at the ZLB.

Take a simple example where the economy is at the ZLB in period zero, and will have escaped the ZLB and be at potential output Y* in period one and thereafter. Assume C+G=Y, and that the Consumption-Euler equation tells us that C(0)=C(1) if the (real) interest rate is 0%. Suppose initially that G(t) is fixed at G* for all t. That's the base case.

If the government increases G by one unit in period zero, keeps it there in period one, and cuts G by one unit in period two (one period too late), what happens? In period one, C(1)+G(1)=Y*. So a one unit rise in G(1) means that C(1) falls by one unit, relative to the base case. Consumption-smoothing means that C(0) therefore also falls by one unit relative to the base case. Since Y(0)=C(0)+G(0) < Y*, the one unit rise in G(0) and the one unit fall in C(0) exactly cancel out, leaving no effect on Y(0).

Now ask yourself this question: if the government increases G when the economy is at the ZLB, will people expect it to cut G immediately when the economy escapes the ZLB and returns to potential output? Or might they expect some lag? Because if they expect any lag, however short, it won't work. Because the "period" is only a modelling device, and can be arbitrarily short.

Now ask yourself a second question: which would be easier: getting people to expect there will be zero lag in cutting G; or getting people to expect a permanent increase in M? (Where "permanent" means "lasting longer than the ZLB".)

Now I really must get back to marking exams. I totally blame Kevin Donoghue for distracting me.

Comments

[Kevin Donoghue]

I strenuously object, but in fairness to your students I'll shut up until you've done your marking.

[Majromax]

This is perhaps a silly question, but isn't your base-case inconsistent? If the real interest rate is 0% implying that Y(0) = Y(1), then how are we below potential output Y* in period 0 with government spending G*?

[Nick Rowe]

Sorry Kevin ;-)

Majro: yes. I wondered if anyone would notice that. I was trying to make my example as simple as possible, and slightly overcooked it.

The quick and dirty way to fix it would be to assume that Y* is higher in period 0 than in period 1 and 2.

A better way to fix it would be to have a time-varying rate of time preference. Or I.

Doesn't affect the principle though.

[dwb]

Actually, alot of people expect increases to G to be permanent. Even worse, the way alot of funding formulas at the state level work (e.g. on education), is that funding can never be cut, by law. So if we spend a windfall, it becomes permanent, and takes a special act of the legislature to re-base spending.

In reality, look at how hard it is to reduce "emergency" SNAP (food stamps) spending after the recession. Nearly impossible! You are taking food from babes (and other tropes)!

[Jacques René Giguère]

dwb: SNAP was reduced in the last farm bill. Rethuglicans don't have problem cutting any G, provided it had benefited the poor.

[Noah Smith]

Nick, you don't allow G to push output above potential, but for some monetary reaction function it will be able to do that in a New Keynesian model. So this post is wrong.

[Nick Rowe]

Noah: you are right. If people expected the central bank to push Y(1) above potential, then fiscal policy would work even if they expected G to be cut too late. But if people expected the central bank to push Y(1) above potential, that would work even without any fiscal policy at all.

dwb and Jacques Rene: so if people expect a small government party to win the election and cut G immediately the economy recovers, everything will work out fine.

[Jacques René Giguère]

Provided the CB can provide food to unemployable proles...
Maybe I am too much of a micro guy to rejoice in success in the aggregate.

[Tom Powers]

Nick, I think fixing the real rate at 0% rules out the main channel for fiscal policy. In standard NK models, government demand causes firms to reset their prices higher. Raising inflation pushes the real rate down despite the ZLB.

See here:

http://johnhcochrane.blogspot.com/2013/11/new-vs-old-keynesian-stimulus.html

[Ray Lopez]

So this is what modern economics has become: a bunch of 'fudge factors': Confidence Fairy, Rational Expectations Fairy, Zombie Confidence Fairy (Krugman), Crony Fairy (Id), Inflation Expectations Fairy. Why not replace these fudge factors with Keynes' Animal Spirits, or just admit that economics is non-linear and cannot be explained with linear models?

[Derivs]

" I think fixing the real rate at 0%"

How would one do that? Isn't r (Nominal - ? in time). The bond market tells you it doesn't know ? within a confidence of 6 percent volatility, so why should someone else?

Which raises a question. When you purchase a bond instead of one of the hundreds of other assets you could be investing in, what do you believe you are trying to achieve with that investment???

Are you under the assumption this is a risk free investment? If yes, then why should risk free not be reward free? X and Y axis both start at 0.

Shouldn't r really be (Nominal - (Nominal * Tax rate)). It appears that r increasing as rates are increasing might in part be a function of demanding back your tax payments in order to be kept whole??

[Nick Rowe]

Jacques Rene: Yep. There are lots of things monetary policy cannot do, and only fiscal policy can do. Which is why I think monetary policy should take sole responsibility for doing the one thing it can do (control AD), giving fiscal policy as much freedom as possible to concentrate on the other (micro) things.

Tom: " In standard NK models, government demand causes firms to reset their prices higher."

Yes, but that only works if increased government demand does in fact increase aggregate demand. And that's what's at issue here. So I have ignored that secondary effect for simplicity.

Ray: it was ever thus. It's just that nowadays we are discovering what those expectational fudge factors are, and being explicit about them.

And economics is, and always has been, "non-linear", in the Artsie sense of that word. A simple ECON 1000 supply and demand model is Artsie non-linear. (Plus, if you draw curved supply and demand *curves* it's non-linear in the other sense, as well.

[Majromax]

@Derivs:

> How would one do that? Isn't r (Nominal - ? in time).

One could fix r at 0% by having a hardtack economy: goods produced are good only for consumption, but they store indefinitely at negligible cost. Investment in this model is only in the form of inventory, and the trivial storage cost means that the real return is exogenously fixed at 0%.

[Jacques René Giguère]

Nick: which is exactly what we were taught when we were young and beautiful. Tinbergen principle and all that. Now that we are mature and magnificient, our friendship is growing better by the day...

[dwb]

Jacques Rene:: "Rethuglicans don't have problem cutting any G, provided it had benefited the poor."

Proving my point!

Nick: "so if people expect a small government party to win the election and cut G immediately the economy recovers, everything will work out fine."

Well, aren't elections endogenous? Doesn't the fact that we have to wait for elections mean there is a lag built into the process? Maybe there is some dynamic inconsistency introducing elections.

More importantly, do the results of said elections tell us anything about the revealed preferences of voters when it comes to the cost of unemployment, vs big govt?

[Min]

"dwb: "In reality, look at how hard it is to reduce "emergency" SNAP (food stamps) spending after the recession."

The recession is not the reason for food stamps. Why should its end (in 2009 !!!) mean a reduction in food stamps?

[Min]

Nick Rowe: "so if people expect a small government party to win the election and cut G immediately the economy recovers, everything will work out fine."

Except that small gov't parties gut G regardless of whether the economy recovers or not. In the US, Republicans, who claim to be a small gov't party, spend like crazy when the economy is good, and only cut spending when it is bad. (Although the "cut anyway" faction has gained power lately.)

[Min]

Nick Rowe: "I think monetary policy should take sole responsibility for doing the one thing it can do (control AD)"

Control AD? Really? I thought that the evidence of the past generation -- not so long, really -- was that monetary policy could restrain inflation. Showing that it can control AD is a long row to hoe, isn't it?

[Nick Rowe]

Min: Jeez! Central banks control inflation by controlling AD!

[Min]

Nick: Then why isn't inflation higher?

[Tom Powers]

Nick, hmm.

If households have a low elasticity of intertemporal substitution, then period 1 government spending would not crowd out consumption. People would just work harder to keep consumption smooth with periods 2, 3, 4, etc in which G=0. The [higher goods demand] -> [expected inflation] -> [lower real rate] channel would stimulate consumption in period 0.

Thus, it seems like a key assumption in the argument is that EIS is large. Yet, a large EIS will make fiscal policy more powerful "per unit." Look at the Euler equation in logs:

c(0) = c(1) - EIS * r

where r is the real rate.

A large EIS means fiscal policy only needs to lower r by a tiny bit to counteract any fall in c(1) resulting from excess government spending at time 1.

So it seems like fiscal policy would work here, right?

[Min]

Question: If the way to control inflation is through AD, what is the problem with fiscal policy. Gov't spending is, after all, part of AD. Direct effect.

[Min]

On a more philosophical level, it is a priori unlikely that, in a complex adaptive system, such as a national economy, one factor should control another, instead of one factor being affected by a number of others, with (presumably) negative feedback loops.

It may happen that, under usual circumstances, one factor has a strong and predictable effect upon another. Under different circumstances, if the evidence is that that effect is weak, then we have the opportunity to discover other factors that also affect the second factor. If that is the case, it is unproductive to double down on the single "controlling" factor hypothesis.

[Nick Rowe]

Tom: you mean that an increase in G(1) would raise P(1), which would increase expected inflation at time 0, and this would reduce the real rate of interest at time 0?

Sure, that would work, if the central bank is expected to let P(1) increase.

But if the central bank can promise to increase P(1), and if that promise is believed, you don't need fiscal policy at all.

[Nick Rowe]

Min: "Gov't spending is, after all, part of AD. Direct effect."

Direct effect BS. You are reasoning from an identity:

"Y=C+I+G, therefore if G increases Y must increase!"

"Y=MV/P, therefore if M increases Y must increase!"

"number of animals on the island = number of sheep + number of wolves. Therefore if we introduce more wolves the number of animals will increase!"

[W. Peden]

Nick Rowe,

Ain't drawing a general equilibrium result from a partial equilibrium relation great fun? It reminds me a bit of the old claim that bank lending to the private sector necessarily expands the money supply, since it results in new deposits.

[Min]

Moi: "Gov't spending is, after all, part of AD. Direct effect."

Nick Rowe: "Direct effect BS. You are reasoning from an identity:"

Just like Isaac Newton.

Nick Rowe: "Y=C+I+G, therefore if G increases Y must increase!"

That is not my reasoning.

Oh! I don't know when I'll get back to this discussion. Happy New Year!

[Nick Rowe]

Happy New Year Min!

Must get back to marking. Because my New Year will be miserable until it's done.

[Min]

Nick, don't look at this until next year. ;)

Here is my reasoning about that equation in this context:

Y(t) = C(t) + I(t) + G(t)

=> ∆Y(t) = ∆C(t) + ∆I(t) + ∆G(t)

and

∂Y(t)/∂G(t) = 1

[Tom Powers]

Hi Nick, my point was that even if fiscal policy ends "too late," it will still work, unless you pick certain parameter values (like EIS = infinity). I'm not taking a stance on whether fiscal policy is better than monetary policy, although it would be theoretically useful for the reasons Krugman mentions.

I get a different conclusion from the model above because it kneecaps fiscal policy in a couple ways: 1) assumption that parameter values make G crowd out C one-for-one (there is no classical multiplier); 2) assumption that the ZLB stops binding immediately (there are no ZLB Keynesian multipliers). Of course, if G can't increase Y, then it can't increase P, and thus can't affect real rates. This seems like a general principle, rather than something about ending stimulus too late.

It would be interesting to think about what happens when you end stimulus too late in a model with both of those channels available.

[Nick Rowe]

Min: Too late! Try that same math of my sheep and wolves example. See what it tells you.

Tom. Again, if you increase Y(1) and/or P(1), then of course you will increase Y(0). But you don't need fiscal policy to do that. Monetary policy works in period 1, by assumption, since we have escaped the ZLB. And if monetary policy offsets fiscal policy in period 1, then fiscal policy won't work.

[Philippe]

W. Peden,

I get what you are saying, but you added the word 'necessarily' there, which is not what the people you criticise actually claim..

[Min]

Nick Rowe: "Try that same math of my sheep and wolves example. See what it tells you."

You mean this?

A(t) = S(t) + W(t)

=> ∆A(t) = ∆S(t) + ∆W(t)

and ∂A(t)/∂W(t) = 1

also ∂S(t)/∂W(t) = -1

Impeccable. :)

OC, there are other considerations. ;)

For Y = C + I + G we also have

∂C(t)/∂G(t) = -1

∂I(t)/∂G(t) = -1

which are suggestive of crowding out. :)

OC, other considerations apply. But that fact does not invalidate reasoning from identities.

Now, suppose that we wish to increase Y, but both C and I are resistant to increase. What to do?

[W. Peden]

Philippe,

Put another way: that bank lending to the private sector increases the money supply with a constant monetary base and no change in banks' demand for base money.

[Min]

Moi: "Now, suppose that we wish to increase Y, but both C and I are resistant to increase. What to do?"

What I had in mind was conditions during and after a combination recession and financial crisis, or in a depression. Of some interest then, is this post about ∆G and ∆Y in the US in recent times. :)

angrybearblog.com/2014/12/g-and-gdp-during-the-current-recovery.html