Can GDP measurement be improved further? Jan P.A.M. Jacobs University of Groningen, University of Tasmania, CAMA and CIRANO Samad Sarferaz KOF Swiss Economic Institute, ETH Zurich, Switzerland Jan-Egbert Sturm KOF Swiss Economic Institute, ETH Zurich, Switzerland and CESifo, Germany Simon van Norden HEC Montr´ eal, CIRANO and CIREQ Work in progress, June 2017 Abstract Recently, Aruoba et al. (2016) provided several estimates of historical U.S. GDP growth (GDP plus), adopting a measurement-error perspective. By distinguishing news and noise measurements errors and allowing for data re- visions, we propose a new measure for U.S. GDP growth based on releases of expenditure-side estimates of GDP (GDE) and income-side estimates of GDP (GDI ). Our measure is more persistent than GDE and GDI and has smaller residual variance. It has a similar autoregressive coefficient but smal- ler residual variance than GDP plus. Historical decompositions of GDE and GDI measurement errors reveal a larger news share in GDE than in GDI . JEL classification: E01, E32 Keywords: output, income, expenditure, state space form, dynamic factor model, data revisions, news, noise
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Can GDP measurement be improved further?
Jan P.A.M. JacobsUniversity of Groningen, University of Tasmania, CAMA and CIRANO
Samad SarferazKOF Swiss Economic Institute, ETH Zurich, Switzerland
Jan-Egbert SturmKOF Swiss Economic Institute, ETH Zurich, Switzerland and CESifo, Germany
Simon van NordenHEC Montreal, CIRANO and CIREQ
Work in progress, June 2017
Abstract
Recently, Aruoba et al. (2016) provided several estimates of historical U.S.GDP growth (GDPplus), adopting a measurement-error perspective. Bydistinguishing news and noise measurements errors and allowing for data re-visions, we propose a new measure for U.S. GDP growth based on releasesof expenditure-side estimates of GDP (GDE) and income-side estimates ofGDP (GDI). Our measure is more persistent than GDE and GDI and hassmaller residual variance. It has a similar autoregressive coefficient but smal-ler residual variance than GDPplus. Historical decompositions of GDE andGDI measurement errors reveal a larger news share in GDE than in GDI.
JEL classification: E01, E32Keywords: output, income, expenditure, state space form, dynamic factormodel, data revisions, news, noise
1 Introduction
Unlike most developed nations, U.S. national accounts feature distinct estimates of
real output based on the expenditure approach (GDE) and the income approach
(GDI), see Figure 1. While these should be identical in theory, measurement errors
result in discrepancies between the two estimates, as is well-known from the data
reconciliation literature initiated by Stone, Champernowne and Meade (1942).1
Figure 1: U.S. GDP growth: Expenditure side vs. income side
2000 2002 2004 2006 2008 2010 2012 2014-10
-8
-6
-4
-2
0
2
4
6
8
10
GDPI
GDPE
A series of recent articles has examined the extent to which future revisions in
one series may be predicted by the other, as well as whether a weighted combin-
ation of the two series gives an improved estimate of real output. Key papers in
this literature include Fixler and Nalewaik (2009), Nalewaik (2010, 2011a, 2011b,
2012), Greenaway-McGrevy (2011), and Aruoba et al. (2012, 2016). Underlining
1The same applies to the production-based estimate of output. See e.g. the study of Rees,Lancaster and Finlay (2015) on Australian GDP.
1
the perceived importance of this issue for forecasting and current analysis, the Fed-
eral Reserve Bank of Philadelphia draws on the above work to show estimates of a
combined indicator (GDPplus), which they feature as an indicator of recent eco-
nomic performance.2 Yet, GDPplus is subject to important revision, as shown in
Figure 2.
Figure 2: GDPplus in real-time
2011 2012 2013 20140
1
2
3
4
5
6
GDPplusNov.2014
GDPplusMay2015
GDPplusJan.2016
GDPplusOct.2016
Various vintages of GDPplus according to the estimates of the Federal Reserve Bank of Phil-
adelphia.
In this paper we reconcile GDE and GDI in a real-time data environment using
a multivariate extension of Jacobs and van Norden (2011, henceforth JvN), to de-
compose measurement errors into news and noise. We discuss identification through
real-time data and news-noise assumptions. No additional variables or assumptions
are needed like in Aruoba et al. (2016). We compute a new GDP series, GDP++,
that takes data revisions into account, and compare the new GDP++ series to GDE,
GDI and GDPplus. In addition we provide a historical decomposition of GDE and
GDI into news and noise shocks.
Much of this work has been motivated by a desire to improve forecasts of GDP
growth or turning points.3 However, it also poses serious questions about the extent
to which fluctuations in output growth have been mis-measured. One approach to
assessing the severity of the measurement error has been to compare GDE growth
estimates with those from a dynamic factor model which also incorporates GDI
and perhaps other variables as well, see for example Aruoba et al. (2016). However,
standard factor models applied in this setting typically assume that measurements
are noise. This forces the estimated growth factor to be less volatile than the series
upon which it is based.4 In contrast, our framework allows for both news and noise
errors, where noise implies that measurement errors are uncorrelated with the unob-
served “true” value, and “news” implies that measurement errors are uncorrelated
with available information. This in turn allows the latent growth factor to be more
volatile or less volatile than the observed series.
The paper is structured as follows. In Section 2 we present our econometric
framework, including identification. We show that our system is identified using
real-time data and news-noise assumptions. In Section 3 we describe our data and
estimation method. Results are shown in Section 4. Section 5 concludes.
3See for example Nalewaik (2011b) or Diebold’s published discussion following Nalewaik (2010).4As an example, consider the special case where GDI perfectly measures “true” output and
GDP captures only some of this variation and is less variable than GDI. A simple factor modelbased only on GDI and GDP growth assumes that the additional volatility in GDI growth reflectsmeasurement error and will interpret the reduced variability of GDP growth estimate as a sign ofbetter accuracy. As a result, it will place more weight on GDP than GDI even though the optimalweights would be (0, 1).
3
2 Econometric Framework
Our point of departure is the dynamic-factor measurement error model of Aruoba
et al. (2016), in which GDE and GDI are measures of latent true GDP , GDP+.
Similar to Aruoba et al. we work with growth rates of GDE, GDI and GDP+ and
we assume that the true GDP growth rate follows AR(1) dynamics:
GDEtGDIt
=
1
1
GDP+t +
εEtεIt
(1)
GDP+t = µ(1− ρ) + ρGDP+
t−1 + εGt, (2)
where
[εEt, εIt, εGt, ]′ ∼ N(0,Σ).
Moving to a real-time data environment, we have l releases on GDEt and GDIt,
and for each release of GDEt and GDIt news and noise measurement errors, denoted