The unit-root zombie: Dead, but still wreaking havoc

If there's one thing that is guaranteed to drive the still-too-small community of Bayesian macroeconometricians up the wall, it's the debate about whether or not GDP - or any other variable - has a unit root. If you don't know what a unit root is or why it has anything to do with GDP, then you might want to give the rest of this post a miss: the stuff after the fold is pretty darn wonkish.

Firstly, let's dispense with classical attempts to deal with the question. As Chris Sims and Harald Uhlig showed in their seminal paper, the frequentist obsession with focusing attention on the distribution of an observable statistic conditional on an unobservable parameter is fundamentally wrong-headed: the real distribution of interest is that of the distribution of the unobservable parameter conditional on the observed statistic.

Secondly, the way in which the trend and the cyclical components of the series are modeled matters very much. At this point, I am forced to draw attention to an unjustly-overlooked paper of mine (ungated version here):

The purpose of this study is to examine the role of the auxiliary hypotheses that are commonly used in time series models for output:

1. Using linear time series models to represent the stationary component of output in studies of the trend in output.

2. Using a stochastic trend to represent the non-stationary component of output in studies of the business cycle features of output.

It is found that neither assumption is innocuous. Conclusions about the nature of the trend in US GDP are reversed if non-linear business cycle specifications are taken into consideration, and conclusions about the most appropriate model for the business cycle are altered if a deterministic trend is not ruled out...

Although the stochastic trends model is favoured if either the linear or the TAR (Threshold Autoregressive) models are used to describe the stationary component of output data, the marginal probabilities associated with these models is small: 0.037 and 0.083, respectively. Of the six models considered, the Markov-switching specification with a deterministic trend receives enough support such that the marginal probabilities for both the DT and MSW hypotheses are higher than the marginal probabilities for the alternative hypotheses...

It is generally the case that the data points observed at the onset of a recession produce strong upward revisions in favour of the ST (stochastic trend) hypothesis, while the data points observed at the beginning of an expansion generate important downward revisions in the cumulative probability for the stochastic trends hypothesis...

[T]he information contained in the data is not uniformly distributed across the sample; information about the appropriate model for both the stationary and non-stationary component of US GDP appears to be concentrated at data points that are generally associated with business cycle turning points. Since turning points are relatively rare - the NBER identifies 16 over the period 1952-1994 - it is perhaps unsurprising that it has proven to be difficult to make definitive conclusions about the nature of the trend in output.

So here's my take on the DeLong-Krugman-Mankiw-Chinn debate:

• There's little evidence that we should be operating under the unit-root hypothesis during recessions. Or during expansions, come to that.
• The world would be a better place if we could all agree that that the whole unit root literature never existed.

Comments

[Nick Rowe]

Leigh Caldwell has a very nice and simple post about some of the theory on whether or not we should expect a unit root: http://www.knowingandmaking.com/2009/03/recession-and-recovery-krugman-and.html

Some dumb questions:
1. "There is a unit root" means that *at least part* of the recession is permanent. Yes? (It doesn't mean *all* of the recession is permanent, no?)
2. If only a very small part were permanent, it would be almost impossible to find it econometrically, unless you had a very large sample (which we don't). Yes?
3. Would it make sense to run a horse race between two hypotheses: "It's all permanent" vs. "It's all temporary"?

[Stephen Gordon]

1. Having a unit root means that that one component of the series is a random walk, where all innovation are permanent.
2. That's another way of looking at the results. The unit root really only matters in the very long run, and we (usually) don't have that kind of data.
3. That 'horse race' is what Figure 1 is graphing.

[Brad DeLong]

Bravo!

[David Beckworth]

A couple of questions:

(1) So in a world without unit roots, as your research indicates is the case, the big policy implication is that business cycles are largely about countercyclical management of aggregate demand, right? Similarly, a trend stationary world also means there are no cases where the natural rate of unemployment has changed due to some permanent innovation/structural shock, correct? If so, these are huge policy implications. Everyone taking a stand either way on the stimulus packages is implicitly assuming a trend-stationary or difference stationary world, correct?

(2) Menzie Chinn's long run graph of log GDP from the 1860s to the present is amazing. He reports formal tests showing trend stationarity, but the eyeball test itself is fascinating as you see this persistent trend for 150 years. If indeed the US GDP is on this trend stationary process what explains it? It is remarkable to me that the US so closely follows the trend all these years. But is the US really bound to it? Are there reasons why we would expect this relationship to hold up?

[Jacob]

Stephen, you said: "Having a unit root means that that one component of the series is a random walk, where all innovation are permanent." Doesn't any causal model still have a white noise component? I assume you mean that having a unit root means that THE ONLY (important) component is the random walk, right?

I think it's just silly to suggest that economic growth is independent from year to year.