Friday, May 29, 2015

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.