The New Keynesian confidence fairy multiplier

The graphs from the University of Michigan's Survey of Consumers (HT Mark Thoma) show something that isn't supposed to happen in New Keynesian macroeconomics. It's not that New Keynesian macroeconomics says it can't happen; it just assumes it doesn't happen. So if the empirical evidence says that it did just happen, we need to re-think New Keynesian macroeconomics. In particular, we need to start thinking about the confidence fairy multiplier in New Keynesian macroeconomics.

Lets start with the graphs.

The second graph shows a big quick drop in US expected income growth in 2008. Prior to 2008, people had been expecting around 2.5% income growth over the next 12 months. That dropped to barely above 0% from 2009 onwards. Expected income growth fell by over 2.0% in 2008.

Was this real or nominal income? Presumably the survey participants interpreted the question to mean nominal income. But the first graph shows survey data on expected inflation over the next 12 months. Expected inflation jumps around a lot (less so for a 5 to 10-year horizon) but does not show consistently lower expected inflation after 2008 compared to before 2008. I conclude that expected real income growth also fell in 2008, by around the same 2.0%.

OK, so the stylised facts say there was a 2% drop in expected real income growth in 2008, which persists to the present. And we also know there was a drop in the level of actual real income, relative to trend, which also persists to the present. A recession. How do those stylised facts fit with the New Keynesian narrative of recessions?

Nothing in New Keynesian models rules out the possibility that real shocks to the aggregate supply side of the economy could cause a reduction in the actual and expected growth rate of real income. New Keynesian macroeconomists admit that real business cycles can happen, and occasionally even do happen. But they say this particular recession doesn't look like a real business cycle. It looks like a recession caused by a drop in Aggregate Demand. I agree, and don't want to argue that here in any case, so let's just accept that.

So what's the problem? Couldn't a drop in aggregate demand in 2008 have caused the recession, and also caused people to become more pessimistic about their future incomes, which reduced Aggregate Demand still further, and worsened the recession, as in a standard multiplier analysis? Sure it could. Indeed, it probably did.

But that multiplier analysis is not part of the standard New Keynesian model. It's something that disappeared along with the Old Keynesians. It doesn't belong at a New Keynesian party. It's all got to do with the distinction between levels and expected rates of change.

Take the simplest possible New Keynesian macro model:

1. Y(t) = E(t)[Y(t+1)] - B(R(t)-N(t))

2. R(t) = E(t-1)[N(t)] + M(t)

Equation 1 is the new IS curve. Y(t) is the deviation of real income from (an assumed constant) supply-side trend at time t. E(t)[Y(t+1)] is today's expectation of next period's deviation of income from trend. R(t) is the interest rate, and N(t) (the "natural" or "neutral" rate of interest) is what the interest rate would need to be to keep income at trend, provided expected future income were also at trend.  That italicised bit is important. B is just some (positive) parameter.

Equation 2 is the monetary policy reaction function. The central bank tries to set R(t) equal to N(t), to keep prevent the economy deviating from trend. But I have assumed that the central bank has a one-period lag in getting information on N(t). So it makes random mistakes M(t) in monetary policy. And those mistakes cause booms and recessions. As shown in the standard solution to this model:

3. Y(t) = -BM(t)

What would a recession look like in this model?

The level of income is lower than trend because the central bank has set the rate of interest too high. But people expect the central bank to (on average) get it right next period, so that E(t)[Y(t+1)]=0 and the economy reverts to trend. This means that, in a recession, when the level of income is below trend, people expect their incomes to grow faster than trend. Which is exactly the opposite of what is happening now in the US.

The inuition is straightforward. Recessions are temporary, and caused by temporary mistakes in monetary policy, because central banks get information with a lag, or rect to that information with a lag, or because there's a lag between the central bank reacting to information and the economy responding. Whatever. Central banks don't have a crystal ball, and can't get monetary policy perfectly right. So we get booms and busts. But those booms and busts are temporary, and people will know this, and so when they are in a recession they will expect to come out of it eventually, and so will expect their future income to be high relative to their current income in the recession. Which means they expect above-normal income growth.

Which is not what is happening now, in the US.

In Old Keynesian models, an initial shock (for example the central bank setting the interest rate too high) causes an initial  decline in demand and income. That initial decline in income causes people then revise downwards their expectations of current and future income, which causes a subsequent decline in demand and income, and so on. That is the Old Keynesian multiplier process. It's a deviation-amplifying positive feedback mechanism. But in a New Keynesian model, the expectation in a recession that future income will be higher than current income makes current demand and current income higher than it would otherwise be. The belief that the economy will revert to trend acts as a deviation-reducing negative feedback mechanism. Old and New Keynesianism are very different.

Now, why should people, rationally, expect their income to revert to trend? What's the fundamental re-equilibrating force that ends recessions in a New Keynesian model? The short answer is that there isn't one. Mathematicians will recognise that my solution 3 is just one of many possible solutions. Y(t) = A - BM(t), where A is any positive or negative number, also works. We just assume that people trust the central bank will do whatever it takes to bring income back to trend eventually, and work backwards from there. We assume there's a confidence fairy, in other words.

And now we have empirical evidence that the New Keynesian confidence fairy isn't working. We might even say that the failure of the New keynesian confidence fairy is sufficient, all by itself, to explain the recession. A permanent(?) 2% drop (OK, 2 percentage point drop, for the picky) in real income growth is a fairly big drop, historically. Previous drops, in previous recessions, were not that big and lasting, and were presumably matched in part by drops in expected inflation.

The failure of the New Keynesian confidence fairy is a pity, because she has a very big multiplier. Look again at equation 1. Suppose initially that E(t)[Y(t+1)]=Y(t)=0, and R(t)=N(t), so the economy is at trend and expected to remain at trend . Or maybe it's currently 10% below trend and expected to remain 10% below trend. Now assume the confidence fairy waves her wand and people expect 1% growth, relative to trend growth. 1% higher expected future income, holding R(t) and N(t) constant, causes 1% higher current income, which causes an additional 1% higher expected future income, which causes an additional 1% higher current income, and so on forever, until real capacity constraints eventually prevent the fairy magic working any more. It's a (potentially) infinite multiplier. Much better than that Old Keynesian 1/(1-mpc).

Comments

[Joe]

Does this support Sumner's theory of plunging NGDP expectations causing the '08 crash?

[Joe]

Sorry for the double comment. The reason I said that was because of you'r line... "

So what's the problem? Couldn't a drop in aggregate demand in 2008 have caused the recession, and also caused people to become more pessimistic about their future incomes, which reduced Aggregate Demand still further, and worsened the recession, as in a standard multiplier analysis? Sure it could. Indeed, it probably did. "

That's exactly his story for summer of 2008. Tight money -> AD fell -> NGDP expectations fell -> AD fell again.Its like two tight money sequences in a row.

[Frances Woolley]

Nick: "Now, why should people, rationally, expect their income to revert to trend?"

Imagine that the economy is made up of a bunch of different types of people
1. people whose income comes from capital, e.g. people living off private pensions, business owners or other capitalists.
2. people whose income comes from labour, some of whom who keep jobs throughout, some who lose jobs and don't regain them, some who lose jobs and regain them, and some who enter the labour market as the economy is pulling out of re cession.
3. people who live off government pensions, etc.

The question is, when the recession ends, which of these groups experience an increase in incomes? I'd imagine that those who keep their jobs through out don't experience that much of an income increase. But I'd expect capitalists, and people who gain jobs as the economy picks up, to enjoy the greatest income increase.

Would this explain some of the discrepancy between people's expectations about the future trend of their own personal income and what we would expect to be true at the macro level?

[Determinant]

"The New Keynesian Confidence Fairy" - I recommend we call her "Tinkerconomist" for short. Instead of Fairy Dust which you have to really, really believe to make it work, you know Tinkerconomist's Economic Fairy Dust works when you truly, honestly believe good times are just around the corner...

[Nick Rowe]

Joe: yes, let's say it is consistent with Scott Sumner's story.

Frances: good point. I just re-read the Cleveland Fed link, and it does say that the graph shows *median*, not *mean* expected income growth. The macro model would say that mean expected income growth should be higher, in a recession. Can't see how that difference would explain the data though. If (say) 51% (or more) of the population were unaffected by the recession, there should be no change.

Determinant: We've called her Tinkerbell in the past. I forgot to mention her name this time.

[Frances Woolley]

Nick: "I just re-read the Cleveland Fed link, and it does say that the graph shows *median*, not *mean* expected income growth."

People's incomes typically increase fairly rapidly throughout their 20s and 30s (with women having a dip around the time that they have kids, though that's now disappearing from the US data). Then incomes typically flatten off and start plateauing or decreasing 50, 60-ish. Not always but often.

Population aging means that the median person is probably now in their 40s, especially if having a phone and answering it is positively correlated with age.

So perhaps Tinkerbell only comes and waves her magic wand if you're young enough to still believe in fairies?

(or I might be totally missing your point).

[Kent Peacock]

Aren't we just in a situation where N(t) < 0?

[Andy Harless]

The mean/median distinction may be pretty critical here. I would guess that the median is typically someone who is employed (or rather, a household in which no member is unemployed) and perceives their income as coming almost entirely in the form of wages. In that case, the median expected income change may be just an expectation about changes in wages. But changes in wages are not where most of the aggregate variation of income comes from at the one-year horizon. If my interpretation is correct, then these charts may be consistent with an expectation of rising capital income (and therefore rising aggregate income).

[Ralph Musgrave]

Nick, You say “What's the fundamental re-equilibrating force that ends recessions in a New Keynesian model? The short answer is that there isn't one.” That’s a question that has bugged me for some time. Put another way, recessions prior to the days when governments artificially tweeked AD seem to me to have ended more quickly than would be expected from Keynes’s “economies can get stuck in recessions for ever” proposition. So the $64k question is: why? My answer (based on hunch) is thus.

You say, recessions are caused by monetary policy mistakes. Certainly central banks and base money have a big influence. On the other hand if central banks closed down altogether and the monetary base shrank to zero, the economy would not collapse. People, firms, banks, etc would simply fill the gap with commercial bank created money, bills of exchange and so on (or in the case of California: issuing IOUs!). The latter forms of money require a better knowledge of the creditworthiness of those one does business with than is the case with base money. And acquiring that knowledge takes time. But it does not take for ever: a few years perhaps.

[Kevin Donoghue]

"We just assume that people trust the central bank will do whatever it takes to bring income back to trend eventually, and work backwards from there."

Even in a liquidity trap?

[Adam P]

I'm not sure what to make of this post. It seems to me to rely heavily on the statement

E(t)[Y(t+1)]=0

being true in the model.

Yet not one NK model in existence says this. In fact, for a shock arriving at time t (monetary or real) every single NK model would specifically say that E(t)[Y(t+1)] does *not* equal zero.

So, while the post is interesting, why Nick seems to think he's saying anything at all about New Keynsian modelling is quite mystifying.

[Nick Rowe]

Frances: there might be reasons why e.g. changing demographics change median or mean expectations of future income growth. But that chart shows such a sudden big drop in 2008, coincident with the recession, that I can't believe that anything smooth and slow-moving like demographics could explain the data.

Kent: Maybe. But if the central bank *can't* set R=N, then the New Keynesian assumption that people have faith that the central bank will eventually bring future Y back to trend looks even more suspect.

Andy: OK. But why the sudden persistent drop in wage income expectations in 2008?

Ralph: that exact same question has been really bugging me too. Except I don't think recessions ended more quickly in the olden days, and that's not really the question. The puzzle is why they ended at all. I did some old posts on this a couple of years back.

http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/12/why-dont-we-observe-macroeconomic-black-holes.html

http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/09/pre-darwinian-macroeconomics.html

No real answers there. Just me bashing my head against the question.

Kevin: agreed. See my response to Kent.

[Nick Rowe]

Adam: I disagree. Admittedly, I have taken a very simple version of the NK model, where there are no adjustment costs or stocks etc. that could serve as impulse-propagation mechanisms. But NK models do assume a return to the natural rate of output Y*. Could you expand?

[Nick Rowe]

Adam again: maybe what you have in mind is that, with Calvo pricing, it will take more than one period for everything to go back to trend. OK. But I think my basic point still stands. People in a recession expect above-trend income growth as the economy (both output and inflation) recovers.

[Adam P]

Well yes, it could take many, many periods for everything to return to trend if the shock is large. So even on the face of it there is nothing inconsistent with the model and the survey data.

However, my deeper point was that the models do *NOT* assume that income reverts to a trend growth rate.

TFP growth reverts to trend.

There is no reason why TFP growth can't revert quickly to trend but, perhaps because the labour dependency ratio is falling (a higher percentage of the population will be retired), per capita consumption and income are still rationally expected to stay permenantly below trend.

[Nick Rowe]

Adam: but I did assume away real shocks to aggregate supply. And there wasn't a sudden demographic change in 2008.

[Frances Woolley]

Nick "And there wasn't a sudden demographic change in 2008."

If you're 17 and you break a bone you figure you'll quickly recover.

If you're 50 and you break a bone you figure there's a good possibility that this injury will be slowing you down for the rest of your life.

There's a parallel with the labour market - realistically, if you're a 55-year old guy who loses your job, your chances of.... - actually, this line of thought is just going to depress you so I'll stop.

What Adam P said.

[Alex Carr]

As others have said, I think the fact that the Fed IS NOT doing everything in its power to bring output back up is where the fault lies. However, this does not preclude that people have confidence in bringing Y back up. After all, the central bank does a good job in normal times.

Instead, people see that the central bank is not going to do anything else and that the economy is not going toward the output trend any time soon, so they expect lower incomes. Once the economy actually gets back on track you should see above trend income growth.

Or in terms of your model, since N(t)!=R(t) then it takes more than t+1 time for output to recover.

[David Pearson]

One explanation is that total income gains outstripped wage gains during two successive bubbles. Americans now realize that future real income gains will come predominantly from wage gains. Unfortunately, the trend on real wage gains does not inspire much confidence. Along with this comes the discovery by the 45-65 cohort that lower future returns require higher levels of retirement savings. Talk of reforming entitlements -- the only way to solve the long-term budget problem -- only contributes to their perceived need to increase savings.

The Fed could attempt to conjure up expectations of higher returns to capital. QE2 was essentially an attempt to summon Tinkerbell by doing just this. It succeeded in driving the stock market higher. Unfortunately, it failed to arrest the decline in house prices, and it arguably (through portfolio re-balancing) amplified the spike in food and energy prices. Moreover, it appears to have failed to deliver a sustained increase in business investment, credit growth, or equity issuance (desired Tobin Q effects).

[Determinant]

I've been turning this over for a while. My best response is that the reliance on the Central Bank and the use of interest rates is misguided and unnecessarily limited. The problem is the paradigm shifted. It shifted in 2008 in a way it hadn't in North America since 1929. Part of our problem is that we can't recognize that we're back in the 1930's. Nick's New Keynesian description shows why we have trouble addressing the problem.

According to my home-cooked macro model, the economy is limited by one of two boundary conditions: the Production Possibility Frontier (determined by investment, supply constraints and other real, physical factors) and the Money Supply. It looks like two bubbles next to each other.

Most of the time it is the Production Possibility Frontier, the physical capabilities of the economy that is the limiting case. The money supply isn't limiting. This is the "Classical" world where there is a "natural" or equilibrium interest rate that can be achieved in the market and tinkered with by the Central Bank. In this world we are supply-constrained and investment works by expanding the PPF.

The other world is a money-limited world. The money supply contracts due to a confidence shock, in this case home defaults, and the "natural" rate of interest now lies beyond the area of rates achievable with the current money supply. The economy gets strangled by the money supply contracting. An output gap opens up and we get a Depression.

A key to understanding where I'm coming from is that there is more than one type of recession: there are supply-shock recessions and demand shock recessions. The last demand-shock recession in North America was in 1929; we didn't have another one until 2008. In that time we forgot what such demand recession felt like, what its causes were and what to do about it. This is especially true at the micro level. I have a feeling we might be in for a lost decade.

Let me break this down a little bit more. The natural rate of interest which an economy can actually realize is determined by both the money supply and the PPF. If the money supply contracts and becomes the limiting case, both businesses and will have financing taken out at the previous, higher rate. Naturally they will want to pay this off. It's a perfectly natural micro behaviour. But it kills aggregate demand.

Furthermore, in the case of a contracted money supply, fiddling with the interest rate, in particular cutting it won't do much. If money is already a limiting case and everyone fears default, lowering the rate of interest is tangential to their concerns. What is really needed is balance sheet repair. We don't need cheaper dollars, we need more total dollars.

If we need more total dollars then in a fiat-money world that source is the government, not the central bank. Hello, Functional Finance.

Determinant's recommendation for the economy: print money until we get back to full capacity utilization. Use that money to deleverage. Interest rate changes are irrelevant with a contracted money supply and an output gap. Once we are back to full capacity and the economy is able to interact with the money supply at the natural rate of interest again (determined by the PPF), then we can resume our regular interest-rate adjusting central bank program.

[reason]

I would be suspicious that people don't answer these surveys very accurately. Many probably compare their "expected" income to their "normal" income, not their actual income.

[David Pearson]

This news item from Investor's Business Daily helps explain the shift in expectations:

"The increase in total private-sector wages, adjusted for inflation, from the start of 2001 has fallen far short of any 10-year period since World War II, according to Commerce Department data. In fact, if the data are to be believed, economywide wage gains have even lagged those in the decade of the Great Depression (adjusted for deflation)."

[Determinant]

That really is the key macro and micro question of the decade: "What went wrong with wages?"

[Adam P]

China.

[Determinant]

Godwin's Rule of Economics: If you blame China, you have to say exactly what went wrong, and how to correct it.

[Adam P]

my take:

http://canucksanonymous.blogspot.com/2010/07/why-we-keep-having-bubbles.html

http://canucksanonymous.blogspot.com/2010/07/so-why-are-profits-high-if-demand-is.html

http://canucksanonymous.blogspot.com/2010/07/cant-we-just-stop-buying-chinese-stuff.html

http://canucksanonymous.blogspot.com/2011/01/purchasing-power-parity-real-business.html

http://canucksanonymous.blogspot.com/2011/01/it-takes-two-to-tango.html

http://canucksanonymous.blogspot.com/2011/02/is-china-being-bad.html

[Tom Powers]

I wonder if people are just irrationally pessimistic about income growth during recessions. They don't have anything at stake when answering a survey — they may just be sounding off.

Either that or they believe the Fed will continue making mistakes (believable).

Can people even tell the difference between levels and rates of change? They may have simply meant that income would be lower by 2.5% in levels, rather than as a growth rate, even if the question were posed that way.

[Determinant]

In which case I agree with Adam P: China wants to pump out goods and not take anything in return. This is unbalanced. The West should be exporting high-value capital goods in China and China should be using its own savings to pay for them, but it isn't.

Instead they buy bonds and have to dig down and go past the Good Investment List and use the Stupid Investment List in order to use all that investment money. That creates bubbles.

[K]

Determinant: "China wants to pump out goods and not take anything in return. This is unbalanced"

It's certainly unbalanced but it's not unfair to *us*. (As Adam points out, though, it is extremely unfair to China's non-exporting sector workers).  If China wants to give us goods with unlimited credit, then it's up to us to decide if we want to borrow to consume those goods and *how we want to distribute them between ourselves*.  It is our choice to let median incomes, rather than just wages, decline, and it's our choice to destroy productive capacity rather than to put the unemployed to work creating useful public services and infrastructure. Of course, its also up to future generations of Americans whether they feel they want to pay off all the debt that bought flat screen TVs for their ancestors, but built no productive infrastructure whatsoever.  If not, that's going to suck for China.

[RSJ]

K,

What do you mean by "us"? China is selling intermediate inputs to U.S. firms, who then turn around and sell them to U.S. consumers. U.S. consumers do not have a choice as to buying a good made in China or not. How many Chinese brands do you buy? You buy the domestic brands you were always buying, except that the goods are now many elsewhere.

The firms rationally choose to outsource because it increases their profits. The consumers don't have any say in the matter one way or another.

[K]

RSJ: the choice is not "which brand?". The choice is to buy, or not to buy. They want to finance us buying discounted goods. That gives us a choice we wouldn't have in an equilibrium market. Choice is good. Worst case, say "no thanks"? Our lot has been improved by their behaviour. If we have turned that against ourselves, that's not their fault.

[RSJ]

Right. We won't buy any good then in a type of mass protest.

Look, this is reminiscent of the reaction to Lucas's post. Aggregate consumption, aggregate income distribution, and the national trade deficit are not choice variables. They are determined by the optimizing choices of individuals and firms.

The firms are the ones who buy from China, not consumers. The consumers buy from firms because they want goods. Consumers don't care where the goods are made. Firms don't care where consumers get the income to buy their output.

But in aggregate, we need firms to pay consumers enough in wages to maintain the optimum level of demand. But there is no one to ensure -- other than Government via income adjustments -- that all the individual choices result in aggregate consumption, wage, and income distribution patterns that are sustainable. You cannot say the "private sector" has a "choice" as to how much to consume, import, pay and produce. There is no such beast.

[Determinant]

RSJ:

I will now quote from the Dark Side:

Imagine a Hayekian Triangle. The height represents consumption, the base is time divided into stages of production. The middle of the triangle is the intermediate manufacturing stages. Consumption is on the right. We have scooped out the middle of the triangle and replaced it with imports from China. We don't have counterbalancing exports to make up for this gaping crater in the triangle.

You might say the Hayekian Triangle is ugly and unbalanced. It is, and without a stable middle it leads to an unstable economy.

If we picture an island economy which exported one raw material (coconuts) and imported all other consumption goods, we would say that the island would naturally have an unstable economy, since its imports are dependent on one export.

The modern North American economy is not far from the coconut island model with decent primary resource extraction activities, an undersized manufacturing middle and a large consumptive and service sector.

[K]

RSJ: There are a lot of ways you can take advantage of the present from China. Buying nothing is clearly not one of them. A simple way is to impose a tariff that makes Chinese goods cost what they would have cost under free market conditions. Now you get all the benefits of free market trades *and* your trading partner hands over a share of their own gains from trading. Pretty sweet! There are endless other good solutions, all of which involve distribution of the surplus to those whose livelihoods are most affected by Chinese imports. The point is, the US is a powerful country, who is not forced into doing anything. If they *choose* to take advantage of this in a way that is detrimental to a large portion of their own citizens, that is because, like China, the US is run for the benefit of minority group of special interests.

[RSJ]

K,

We agree on much. But note that all of your proposals have the following two attributes:

1) They are *government interventions* to coordinate private sector behavior. It is not something that can or will be done by individuals.
2) Trade tariffs are *opposed* by the majority economists because they are government interventions, supposedly interfering with our pareto-optimal paradise. You cannot be a serious person until you get the little triangle of dead-weight losses engraved on your right hand and forehead.

In terms of the political ramifications, the U.S. *is* a powerful country, but not particularly responsive to the welfare demands of its population. As long as trade improves the profits of each individual firm re-selling the foreign made good, then government is going to be squarely on the side of the firm.

It might be useful to note the difference in the U.S. political reaction to our trade deficit with Japan vis-a-vis with China. In the case of Japan, Japanese firms were directly competing with U.S. firms, seizing market share and offering consumers a better/cheaper product. There were howls of outrage, the plaza accord, etc. In the case of China, Chinese firms are subsidizing U.S. firms by directly competing with U.S. labor, improving the profitability of domestic business rather than competing with domestic business. They are supplying supplying domestic businesses with cheaper inputs. No Plaza accord, no outrage among the elites -- a completely different political response.

[Jacques René Giguère]

RSJ:
"Consumers don't care where the goods are made. Firms don't care where consumers get the income to buy their output."

Consumers care but they don't and mostly can't know. Firms don't care whether you buy from income, dissaving or borrowing.

[K]

RSJ: I think you've hit the nail on the head regarding the contrast with Japan. Couldn't agree more on all points.