Online Learning vs. TVP Forecast Combination

[This post is based on the first slide (below) of a discussion of Helene Rey et al., which I gave a few days ago at a fine NBER IFM meeting (program and clickable papers here). The paper is fascinating and impressive, and I'll blog on it separately next time. But the slide below is more of a side rant on general issues, and I skipped it in the discussion of Rey et al. to be sure to have time to address their particular issues.]

Quite a while ago I blogged here on the ex ante expected loss minimization that underlies traditional econometric/statistical forecast combination, vs. the ex post regret minimization that underlies "online learning" and related "machine learning" methods. Nothing has changed. That is, as regards ex post regret minimization, I'm still intrigued, but I'm still not persuaded.

And there's another thing that bothers me. As implemented, ML-style online learning and traditional econometric-style forecast combination with time-varying parameters (TVPs) are almost identical: just projection (regression) of realizations on forecasts, reading off the combining weights as the regression coefficients.  OF COURSE we can generalize to allow for time-varying combining weights, non-linear combinations, regularization in high dimensions, etc., and hundreds of econometrics papers have addressed and explored those issues. Yet the ML types seem to think they invented everything, and too many economists are buying it. Rey et al., for example, don't so much as mention the econometric forecast combination literature, which by now occupies large chapters of  leading textbooks, like Elliott and Timmermann at the bottom of the slide below.

Big Data and Economic Nowcasting

Check out this informative paper from the Federal Reserve Bank of New York: "Macroeconomic Nowcasting and Forecasting with Big Data", by Brandyn Bok, Daniele Caratelli, Domenico Giannone, Argia Sbordone, and Andrea Tambalotti.

Key methods for confronting big data include (1) imposition of restrictions (for example, (a) zero restrictions correspond to "sparsity", (b) reduced-rank restrictions correspond to factor structure, etc.), and (2) shrinkage (whether by formal Bayesian approaches or otherwise).

Bok et al. provide historical perspective on use of (1)(b) for macroeconomic nowcasting; that is, for real-time analysis and interpretation of hundreds of business-cycle indicators using dynamic factor models. They also provide a useful description of FRBNY's implementation and use of such models in policy deliberations.

It is important to note that the Bok et al. approach nowcasts current-quarter GDP, which is different from nowcasting "the business cycle" (as done using dynamic factor models at FRB Philadelphia, for example), because GDP alone is not the business cycle. Hence the two approaches are complements, not substitutes, and both are useful.

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.]

Coolest Paper at 2015 Jackson Hole

The Faust-Leeper paper is wild and wonderful.  The friend who emailed it said, "Be prepared, it’s very different but a great picture of real-time forecasting..." He got it right.

Actually his full email was, "Be prepared, it’s very different but a great picture of real-time forecasting, and they quote Zarnowitz." (He and I always liked and admired Victor Zarnowitz. But that's another post.)

The paper shines its light all over the place, and different people will read it differently. I did some spot checks with colleagues. My interpretation below resonated with some, while others wondered if we had read the same paper. Perhaps, as with Keynes, we'll never know exactly what Faust-Leeper really, really, really meant.

I read Faust-Leeper as speaking to factor analysis in macroeconomics and finance, arguing that dimensionality reduction via factor structure, at least as typically implemented and interpreted, is of limited value to policymakers, although the paper never uses wording like "dimensionality reduction" or "factor structure".

If Faust-Leeper are doubting factor structure itself, then I think they're way off base. It's no accident that factor structure is at the center of both modern empirical/theoretical macro and modern empirical/theoretical finance. It's really there and it really works.

Alternatively, if they're implicitly saying something like this, then I'm interested:

Small-scale factor models involving just a few variables and a single common factor (or even two factors like "real activity" and "inflation") are likely missing important things, and are therefore incomplete guides for policy analysis. 

Or, closely related and more constructively: 

We should cast a wide net in terms of the universe of observables from which we extract common factors, and the number of factors that we extract. Moreover we should examine and interpret not only common factors, but also allegedly "idiosyncratic" factors, which may actually be contemporaneously correlated, time dependent, or even trending, due to mis-specification.

Enough.  Read it for yourself.

[General note: My use of terms like "factor modeling" throughout this post should be broadly interpreted to include not only explicit reduced-form statistical/econometric dynamic factor modeling, but also structural DSGE modeling.]