Expansions Don't Die of Old Age

As the expansion ages, there's progressively more discussion of whether its advanced age makes it more likely to end. The answer is no. More formally, postwar U.S. expansion hazards are basically flat, in contrast to contraction hazards, which are sharply increasing. Of course the present expansion will eventually end, and it may even end soon, but its age it unrelated to its probability of ending.

All of this is very clear in Diebold, Rudebusch and Sichel (1992). See Figure 6.2 on p. 271. (Sorry for the poor photocopy quality.) The flat expansion hazard result has held up well (e.g., Rudebusch (2016)), and moreover it would only be strengthened by the current long expansion.

[I blogged on flat expansion hazards before, but the message bears repeating as the expansion continues to age.]

Exogenous vs. Endogenous Volatility Dynamics

I always thought putting exogenous volatility dynamics in macro-model shocks was a cop-out.  Somehow it seemed more satisfying for volatility to be determined endogenously, in equilibrium.  Then I came around:  We allow for shocks with exogenous conditional-mean dynamics (e.g., AR(1)), so why shouldn't we allow for shocks with exogenous conditional-volatility dynamics?  Now I might shift back, at least in part, thanks to new work by Sydney Ludvigson, Sai Ma, and Serena Ng, "Uncertainty and Business Cycles: Exogenous Impulse or Endogenous Response?", which attempts to sort things out. The October 2016 version is here.  It turns out that real (macro) volatility appears largely endogenous, whereas nominal (financial market) volatility appears largely exogenous. 

Econometric Analysis of Recurrent Events

Don Harding and Adrian Pagan have a fascinating new book (HP) that just arrived in the snail mail.  Partly HP has a retro feel (think: Bry-Boshan (BB)) and partly it has a futurist feel (think: taking BB to wildly new places).  Notwithstanding the assertion in the conclusion of HP's first chapter (here), I remain of the Diebold-Rudebusch view that Hamilton-style Markov switching remains the most compelling way to think about nonlinear business-cycle events like "expansions" and "recessions" and "peaks" and "troughs".  At the very least, however, HP has significantly heightened my awareness and appreciation of alternative approaches.  Definitely worth a very serious read.

More on Nonlinear Forecasting Over the Cycle

Related to my last post, here's a new paper that just arrived from Rachidi Kotchoni and Dalibor Stevanovic, "Forecasting U.S. Recessions and Economic Activity". It's not non-parametric, but it is non-linear. As Dalibor put it, "The method is very simple: predict turning points and recession probabilities in the first step, and then augment a direct AR model with the forecasted probability." Kotchoni-Stevanovic and Guerron-Quintana-Zhong are usefully read together.

Nearest-Neighbor Forecasting in Times of Crisis

Nonparametric K-nearest-neighbor forecasting remains natural and obvious and potentially very useful, as it has been since its inception long ago.

[Most crudely: Find the K-history closest to the present K-history, see what followed it, and use that as a forecast. Slightly less crudely: Find the N K-histories closest to the present K-history, see what followed each of them, and take an average. There are many obvious additional refinements.]

Overall, nearest-neighbor forecasting remains curiously under-utilized in dynamic econometrics. Maybe that will change. In an interesting recent development, for example, new Federal Reserve System research by Pablo Guerron-Quintana and Molin Zhong puts nearest-neighbor methods to good use for forecasting in times of crisis.

Hazard Functions for U.S. Expansions

Glenn Rudebusch has a very nice 2016 FRBSF Letter, "Will the Economic Recovery Die of Old Age?".  He draws on perspective and results from our joint work of 25 years ago (including a paper we did with Dan Sichel -- see below), and he applies them to the present expansion.  He correctly emphasizes that U.S. expansion hazard functions are basically flat, so "old" expansions are no more likely to end than "young" ones. That's of some comfort, since the present expansion, which started in mid-2009, is getting long in the tooth!

Actually, the flat expansion hazard is only for post-WWII expansions; the prewar expansion hazard is sharply increasing. Here's how they compare (copied from Glenn's FRBSFLetter):

Probability of an Expansion ending within a month

Perhaps the massive difference is due to "good policy", that is, post-war policy success in "keeping expansions alive".  Or perhaps it's just "good luck" -- but it's so big and systematic that luck alone seems an unlikely explanation.

For more on all this, and to see the equally-fascinating and very different results for recession hazards, see Diebold, Rudebusch and Sichel (1992), which I consider to be the best statement of our work in the area.

[Footnote:  I wrote this post about three days ago, intending to release it next week. I just learned that The Economist (May 21st issue) also reports on the Rudebusch FRBSF Letter (see http://www.economist.com/news/finance-and-economics/21699124-when-periods-economic-growth-come-end-old-age-rarely-blame-murder), so I'm releasing it early.  Interesting that both The Economist and I are not only slow -- Glenn sent me his Letter in February, when it was published! -- but also identically slow.]

Three Reasons to Prefer GDPplus to Simple GDP Averages

Let's start with some notation. GDPe is expenditure-side GDP from BEA. GDPi is income-side GDP from BEA. GDPavg is the average of GDPe and GDPi recently introduced by BEA. GDPplus is the Kalman-smoother extraction of GDP from GDPe and GDPi, produced and published to the web by FRB Philadelphia.

The key insight is that the optimal Kalman-smoother extraction that underlies GDPplus involves averaging not only over series (i.e., GDPe and GDPi), but also over time. Hence:

(1) GDPplus can be calculated for the most recent quarter for which GDPe data are available, even if GDPi data are not yet available for that quarter, because the Kalman smoother optimally interpolates the missing GDPi data and includes that prediction in its assessment. In contrast, GDPavg simply cannot be calculated if GDPi is unavailable.

(2) Desirably, GDPplus is not constrained to be between the expenditure- and income-side estimates, let alone exactly midway between, as with as with GDPavg.  Look, for example, at 2014Q1 in the FRB Philadelphia plot here.

(3) Related, GDPplus is robust to the problem of spuriously low Q1 GDP reported a nice recent NYT piece by Justin Wolfers. For example, the much-discussed mysterious apparent GDP collapse of 2014Q1, based on GDPe, is largely absent from GDPplus, or at least much less pronounced. (Again see the FRB Philadelphia plot here, as well Tom Stark's fascinating recent FRB Philadelphia "Research Rap".) Evidently GDPplus doesn't suffer as much from the Q1 anomaly for two reasons. You guessed it: (a) it blends GDPe with GDPi, which is not as influenced by the Q1 distortion, and (b) it smooths over time.