The Confidence Fairy Multiplier

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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).

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

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.

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?

"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...

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.

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).

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

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