Federal Reserve Bank of Philadelphia Launches Improved U.S. GDP Growth Series

Exciting news for empirical macroeconomics and finance: The Federal Reserve Bank of Philadelphia today released a new and improved \(GDP\) growth series, \(GDPplus\). It's an optimal blend of the BEA's expenditure-side and income-side estimates (call them \(GDP_E\) and \(GDP_I\), respectively). The \(GDPplus\) web page contains extensive background information and will be updated whenever new or revised data for \(GDP_E\) and/or \(GDP_I\), and hence \(GDPplus\), are released.

\(GDPplus\) (developed in Aruoba, Diebold, Nalewaik, Schorfheide and Song, "Improving GDP Measurement: A Measurement-Error Perspective," NBER Working Paper 18954, 2013) is based on a dynamic-factor model,

$$
\begin{pmatrix}
GDP_{Et} \\
GDP_{It}
\end{pmatrix}
=
\begin{pmatrix}
1 \\
1
\end{pmatrix}
GDP_t
+
\begin{pmatrix}
\epsilon_{Et} \\
\epsilon_{It}
\end{pmatrix}
$$
$$
GDP_{t} = \mu (1- \rho) + \rho GDP_{t-1} + \epsilon_{Gt},
$$
where \(GDP_E\) and \(GDP_I\) are noisy indicators of latent true \( GDP\), \(\epsilon_{E}\) and \(\epsilon_{I}\) are expenditure- and income-side stochastic measurement errors, and \(\epsilon_{G}\) is a stochastic shock to true \(GDP\). The Kalman smoother provides an optimal estimate of \(GDP\) based on the noisy indicators \(GDP_{E}\) and \(GDP_{I}\). That optimal estimate is \(GDPplus\). Note that \(GDPplus\) is not just a period-by-period simple average, or even a weighted average, of \(GDP_E\) and \(GDP_I\), because optimal signal extraction averages not only across the \(GDP_E\) and \(GDP_I\) series, but also over time.

The historical perspective on \(GDP\) provided by \(GDPplus\) complements the real-time perspective on the overall business cycle provided by the Aruoba-Diebold-Scotti (ADS) Index, also published by the Federal Reserve Bank of Philadelphia.

Moving forward, \(GDPplus\) will be updated at 2 PM on every day that new and/or revised \(GDP_E\) and/or \(GDP_I\) data are released. The next update will be November 7, the day of BEA's NIPA release for Q3 (delayed due to the government shutdown).

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.

A Conjecture Regarding Extracted Dynamic Factors (and Hence GDPplus)

Here's a conjecture that I'd love to see explored. It's well-posed, simple, and really interesting.

Conjecture: GDPplus (obtained by Kalman smoothing) may be very well approximated by taking a simple convex combination of exponentially smoothed GDPe (expenditure side GDP) and exponentially smoothed GDPi (income side GDP). 

That is,

\( GDPplus = \lambda \cdot SMOOTH_{\alpha_e} (GDPe)  + (1 - \lambda) \cdot   SMOOTH_{\alpha_i} (GDPi) , \)

where \(\lambda\) is a combining weight, \(SMOOTH(GDPx)\) denotes an exponential smooth of \(GDPx \), and the \(\alpha_x\)'s are smoothing parameters.

Or even more simply, forget about GDPplus, whose underlying probability model is a bit complicated, and just examine a simpler canonical case, as follows.

Conjecture: In a stationary bivariate single-factor dynamic factor model with AR(1) factor and all shocks Gaussian and orthogonal to all other shocks, the MSE-optimal factor extraction (obtained by Kalman smoothing) may be very well approximated by taking a simple convex combination of exponentially smoothed observed variables.

There are of course many variations and extensions:  N variables, richer dynamics, richer error correlation structures, different smoothers, etc.

Theoretically:

What, precisely, is the relationship between the optimal extraction and the approximation? The answer must be contained in the structure of the Kalman gain derived in ADNSS2.   

Empirically:

-- Check it out in simulated environments for various choices of \(  \lambda\), \(  \alpha_e\) and \(  \alpha_i\).

-- Again in simulated environments, minimize the average squared divergence between the exact and approximate extractions w.r.t. \( \lambda\), \(  \alpha_e\) and \(  \alpha_i\).  How close is it to zero?

-- Now do a serious application: GDPplus vs. a weighted combination of smoothed GDPe and GDPi.  Again minimize w.r.t. \(  \lambda\), \(  \alpha_e\) and \(  \alpha_i\). How close is it to zero? How much closer is it to zero than the divergence between GDPplus and GDPavg (the simple average of GDPe and GDPi now published by BEA -- see this No Hesitations post.)?

-- Based on ADNSS1 and ADNSS2, My guess is that the optimal \(\lambda\) will be around .4, and that the optimal \(\alpha_e\) will be much bigger than the optimal \(  \alpha_i\) (where bigger \(  \alpha\) corresponds to more smoothing).

[Note: In the two or three weeks since the draft of this post was written, we have explored things a bit, and it's looking good. The optimized parameters are \(  \lambda=.14\), \(  \alpha_e =.94 \) and \(  \alpha_i = .18\), and they deliver a predictive \( R^2\) for GDPplus of .94.]

The First Quarter GDP Contraction was Less Severe than you Think

As discussed in an earlier post, my co-authors and I believe that our "GDPplus," obtained by optimally blending the noisy expenditure- and income-side GDP estimates, provides a superior U.S. GDP measure. (Check it out online; the Federal Reserve Bank of Philadelphia now calculates and reports it.) A few days ago we revised and re-posted the working paper on which it's based (Aruoba, Diebold, Nalewaik, Schorfheide, and Song, "Improving GDP Measurement: A Measurement Error Perspective," Manuscript, University of Maryland, Federal Reserve Board and University of Pennsylvania, Revised June 2014).

It's important to note that GDPplus is not simply a convex combination of the expenditure- and income-side estimates; rather, it is produced via the Kalman filter, which averages optimally over both space and time. Hence, although GDPplus is usually between the expenditure- and income-side estimates, it need not be. Presently we're in just such a situation, as shown in the graph below. 2014Q1 real growth as measured by GDPplus (in red) is well above both of the corresponding expenditure- and income-side GDP growth estimates (in black), which are almost identical. 

Source:  FRB Philadelphia

New CEA Overview of GDO

The U.S. Council of Economic Advisors has a nice new review of "Gross Domestic Output" (GDO), a simple average of expenditure- and income-side GDP estimates now published by the BEA.

In an earlier post I wrote rather negatively about GDO as compared to GDPplus, which is an optimally-weighted blend rather than a simple average. (See the FRB Philadelphia GDPplus site and the corresponding Aruba et al. paper available there.) My view has not changed.

But I want to be very clear about one thing: Quite apart from whether GDO is as accurate as GDPplus, GDO is surely much, much more accurate than standard expenditure-side GDP alone, or income-side GDP alone. Just look at Figure 2 and the surrounding discussion here. (in X. Chen and N. Swanson, eds., Causality, Prediction, and Specification Analysis: Recent Advances and Future Directions, Essays in Honor of Halbert L. White Jr., Springer, 2013, 1-26).

As I said in the above-mentioned earlier post (but alas, burried at the end):

I applaud the BEA's new averaged GDP. If it's not at the cutting edge, it's nevertheless much superior to the standard approach of doing nothing ... and it's an official acknowledgment of the wastefulness of doing so. Hence it's a significant step in the right direction. Hopefully its publication by BEA will nudge people away from uncritical and exclusive reliance on expenditure-side GDP. 

So here's to GDO.

[By the way, speaking of the Hal White volume, the introductory chapter is marvelous, filled with wonderful memories of Hal's career and insights into his research. You must read his description of his career path leading to UCSD, pp. vii-xi in the gray box.]

ADS Perspective on the First-Quarter Contraction

Following on my last post about the first-quarter GDP contraction, now look at the FRB Philadelphia's Aruoba-Diebold-Scotti (ADS) Index. 2014Q1 is the rightmost downward blip. It's due mostly to the huge drop in expenditure-side GDP (GDP_E), which is one of the indicators in the ADS index. But it's just a blip, nothing to be too worried about. [Perhaps one of these days we'll get around to working with FRB Philadelphia to replace GDP_E with GDPplus in the ADS Index, or simply to include income-side GDP (GDP_I) directly as an additional indicator in the ADS Index.]

Source: FRB Philadelphia

One might wonder why the huge drop in measured GDP_E didn't cause a bigger drop in the ADS Index. The reason is that all real activity indicators are noisy (GDP_E is just one), and by averaging across them, as in ADS, we can eliminate much of the noise, and most of the other ADS component indicators fared much better. (See the component indicator plots.)

Note well the important lesson: both the ADS Index (designed for real-time analysis of broad real activity) and GDPplus (designed mostly for historical analysis of real GDP, an important part of real activity) reduce, if not eliminate, measurement error by "averaging it out."

All told, ADS paints a clear picture: conditional on the underlying indicator data available now, real growth appears to be typical (ADS is constructed so that 0 corresponds to average growth) -- not especially strong, but simultaneously, not especially weak.

New GDP Series From BEA

BEA's "new product" (see below) -- a U.S. GDP estimate that's a simple average of expenditure- and income-side GDP estimates -- is not yet at the cutting-edge of historical GDP estimation.

On the benefits of blending the expenditure- and income-side historical GDP estimates, see ADNSS1 for a forecast-combination perspective and ADNSS2 for a Kalman-filtering signal-extraction perspective.  The ADNSS1 "combined" GDP estimate is a convex combination of expenditure- and income-side GDP estimates, but the BEA equal-weight case is very special and generally sub-optimal. Moreover, ADNSS2's Kalman-filter approach is likely superior to ADNSS1's convex-combination approach for reasons detailed by ADNSS2, and for some years now it has been implemented and published to the web by FRB Philadelphia as "GDPplus".

Neverthess, I applaud the BEA's new averaged GDP. If it's not at the cutting edge, it's nevertheless much superior to the standard approach of doing nothing -- that is, using expenditure-side GDP alone -- and it's an official acknowledgment of the wastefulness of doing so. Hence it's a significant step in the right direction. Hopefully its publication by BEA will nudge people away from uncritical and exclusive reliance on expenditure-side GDP.    







May 14, 2015
Twitter: @BEA_News
www.bea.gov

Coming in July: 
BEA to Launch New Tools for Analyzing Economic Growth

WASHINGTON – The Bureau of Economic Analysis plans to launch two new statistics that will serve as tools to help businesses, economists, policymakers and the American public better analyze the performance of the U.S. economy. These tools will be available on July 30 and emerge from an annual BEA process where improvements and revisions to GDP data are implemented. BEA created these two new tools in response to demand from our customers.

Average of Gross Domestic Product (GDP) and Gross Domestic Income (GDI)

-- BEA will launch a new series that is an average of GDP and GDI, giving users another way to track U.S. economic growth.

-- BEA will present a nominal (or current-dollar) measure of the series and an inflation-adjusted (or chained-dollar) measure of the series.

-- For current dollars, the new measure will be a simple, equally weighted average of GDP and GDI for any given quarter or year.

-- For chained dollars, the new measure will be the current-dollar value deflated by the GDP price index.

-- The new series will be available back to 1929 on an annual basis and to 1947 on a quarterly basis.

-- The new series will not only provide users with another barometer on the U.S. economy but also make available series that several independent experts have recommended using in their analysis of the nation’s economic growth.

-- The new series could help account for known measurement inconsistencies between the two statistics. Those may include timing differences, gaps in underlying source data, and survey measurement errors.

-- The new statistics will be available in BEA’s interactive database as well as in the GDP news release tables.

FRB St. Louis is Far Ahead of the Data Pack

The email below arrived recently from the Federal Reserve Bank of St. Louis. It reminds me of something that's hardly a secret, but that nevertheless merits applause, namely that FRBSL's Research Department is a wonderful source of economic and financial data provision (FRED and much more...), and related information provision broadly defined (RePEc and much more...).

FRED, ALFRED, GeoFRED, RePEc, FRASER, etc. -- wow!  FRBSL supplies not only the data, but also intuitive and seamless delivery interfaces. They're very much on the cutting edge, constantly innovating and leading.

Other Feds of course supply some great data as well. To take just one example close to home, the Real-Time Data Research Center within FRB Philadelphia's Research Department maintains a widely-respected Real-Time Dataset and Survey of Professional Forecasters (and of course my favorites, the ADS Index and GDPplus).

But FRBSL is in a league of its own. Maybe there's been an implicit decision within the System that FRBSL will be the de facto data guru? Or maybe it's just me, not looking around thoroughly enough? I suspect it's a bit of both.

In any event I applaud FRBSL for a job marvelously well done.

Subject: Come visit the St. Louis Fed at the 2014 AEA Conference in Philadelphia

E-mail not displaying correctly? View it in your browser. Please join the Federal Reserve Bank of St. Louis at the American Economic Association meeting in Philadelphia Jan. 3-5, 2014 Philadelphia Marriott Downtown | Franklin Hall Stop by our booths, B322 and B321, to talk to St. Louis Fed experts and learn more about our free data toolkit available to researchers, teachers, journalists and bloggers. The toolkit includes: RePEc Representatives of the popular bibliographic database will be available to discuss the various websites, answer questions and take suggestions. FRED® (Federal Reserve Economic Data), our signature database with 150,000 data series from 59 regional, national and international sources; ALFRED® (Archival Federal Reserve Economic Data) Retrieve versions of economic data that were available on specific dates in history. Test economic forecasting models and analyze the decisions made by policymakers; GeoFRED® Map U.S. economic data at a state, county or metropolitan statistical area (MSA) level; FRASER® (Federal Reserve Archival System for Economic Research), a digital library for economic, financial and banking materials covering the economic and financial history of the United States and the Federal Reserve System; FRED add-in for Microsoft Excel, mobile apps for iPad, iPhone and Android devices; Also, take the opportunity to learn more about EconLowdown, our award-winning, FREE classroom resources for K-16 educators and consumers. Learn about money and banking, economics, personal finance, and the Federal Reserve. See you there. Federal Reserve Bank of St. Louis | www.stlouisfed.org To stop receiving these emails, click here to unsubscribe. Federal Reserve Bank of St. Louis | P.O. Box 442 | St. Louis, MO 63166

Congratulations to Loretta Mester, New President of The Federal Reserve Bank of Cleveland

Loretta is presently the Director of Research at the Philadelphia Fed, and she will replace Cleveland's Sandra Pianalto effective June 1. She has been a stunningly effective research director in Philadelphia; indeed her loss is a terrible blow to FRB Philadelphia and a massive gain for FRB Cleveland.  Not least I'm personally grateful for her enthusiastic support of FRB Philadelphia's ADS index and GDPplus series.  I will miss her, and I wish her every success in her new role.  

For additional information, see the Reuters article.