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\begin{document}

\title{2011 Update on the Income- and Expenditure-Side Estimates of
  U.S. Output Growth}\author{Jeremy J.  Nalewaik\thanks{Economist,
    Federal Reserve Board, 20th Street and Constitution Avenue,
    Washington, DC 20551 (e-mail: jeremy.j.nalewaik@frb.gov).  Thanks
    to Steve Braun, David Lebow, David Romer, Justin Wolfers, and
    participants at the September 2011 Brookings Panel on Economic
    Activity.  The views expressed in this paper are solely those of
    the authors and are not necessarily those of the Federal Reserve
    Board.}
  \\
  \\
%  First Draft - please do not distribute.  
}
\maketitle

\doublespacing

\begin{abstract}

  In light of recent large revisions to the official measures of US
  output, this update reviews the evidence in Nalewaik (2010) showing
  that the income-side estimate of output (currently called GDI)
  likely captures business cycle fluctuations in true output better
  than its more well-known expenditure-side counterpart (called GDP).
  Most notable, over the 2007-2009 downturn, the revisions moved the
  expenditure-side estimates closer to the income-side estimates,
  which showed the downturn was considerably worse than was reported
  initially by the expenditure-side estimates.  The tendency for the
  expenditure-side estimates to revise towards the income-side
  estimates is clearer now, as is a tendency for the smoothed
  income-side estimates to revise {\it away from} the smoothed
  expenditure-side estimates.

{\it JEL classification}: C1, C82.

{\it Keywords}: GDP, statistical discrepancy, measurement error,
business cycles

\end{abstract}

%\newpage
\section{Introduction}

Since Nalewaik (2010), the two official measures of US output, GDP(E)
and GDP(I), have passed through two annual revisions.\footnote{%
  Recall that in the Brookings papers, to make clear that GDP and GDI
  measure the same thing, we call the income-side estimate (called GDI
  by the official statistical agencies) GDP(I), and the
  expenditure-side estimate (called GDP by the official statistical
  agencies) GDP(E).}  The revisions took down GDP(E) by a sizable
amount: GDP(E) in 2009Q3 revised down about two percentage points
relative to its level in early 2006.  In light of these revisions, I
update the evidence in Nalewaik (2010) showing that GDP(I) likely
provides a more accurate estimate of output growth than GDP(E).
Broadly speaking, three things have changed due to the revisions.

First, some of the countercyclicality of the statistical discrepancy
(GDP(E) minus GDP(I)), a striking finding in Nalewaik (2010), was
revised away over the last few years.  The countercyclicality from the
mid-1980s to the mid-2000s remains.

Second, the tendency for the initial GDP(E) estimates to revise
towards the initial GDP(I) estimates has become clearer, strengthening
the evidence that initial GDP(I) growth is more accurate than initial
GDP(E) growth.
%At a minimum, it is now even more clear that
%the initial GDP(I) growth estimates contain a substantial amount of
%information missed by the initial GDP(E) growth estimates.  
In particular, GDP(I) picked up the onset and the severity of the
2007-2009 downturn better and sooner than GDP(E), adding to the long
list of cases where GDP(I) has recognized important economic phenomena
before GDP(E).  That list includes the productivity acceleration in
the mid- to late-1990s and the sluggishness of the recovery following
the 2001 recession.

Third, when smoothing the growth rates into year-over-year changes, a
tendency for the initial GDP(I) growth estimates to revise {\it away
  from} the initial GDP(E) growth estimates has become clear as well.
Indeed, the revisions to GDP(E) and GDP(I) growth tend to go in the
same direction: if initial GDP(I) growth is above initial GDP(E)
growth, both estimates tend to revise up, and if initial GDP(I) growth
is below initial GDP(E) growth, both estimates tend to revise down.
The paper discusses a potential explanation for this pattern in
the revisions, related to differences in how well the estimates pick up
output fluctuations from firm births and deaths.

Section 2 of the paper discusses the changes to the estimates over the
2007-9 cyclical downturn since Nalewaik (2010).  Section 3 discusses
the implications of these changes for our understanding of the
relative reliability of the latest available output growth rates.
Section 4 discusses changes to the cyclicality of the statistical
discrepancy.  Section 5 discusses the implications of the changes for
our understanding of the relative reliability of the initial output
growth rates (those available in real time about three months after
the close of each quarter).  Section 6 concludes with a brief
discussion of progress on the recommendations of Nalewaik (2010) to
improve GDP measurement.  An online appendix interprets the variance
of the estimates and the size of the revisions to the estimates,
providing a response to the assertions made in Fixler,
Greenaway-McGrevy, and Grimm (2011).

\section{The Estimates over the 2007-2009 Cyclical Downturn}

The table below shows revisions to the Q4-over-Q4 growth rates in
GDP(E) and GDP(I) in 2007 and 2008 since Nalewaik (2010):
%\begin{landscape}

\singlespacing
%\vskip 0.8cm
\centerline {\bf Changes to $\Delta GDP(E)$ and $\Delta GDP(I)$ since Nalewaik (2010):}
{\small
\begin{longtable}{c c c c c c c}
 & \multicolumn{3}{c}{2007Q4/2006Q4} & \multicolumn{3}{c}{2008Q4/2007Q4} \\
 & Spring 2010 & Latest & Revision &  Spring 2010 & Latest & Revision \\
\hline \hline
$\Delta$ GDP(E) & 2.5 & 2.2 & {\it -0.3} & -1.9 & -3.3 & {\it -1.5} \\
\hline \hline
$\Delta$ GDP(I) & 0.1 & -0.5 & {\it -0.5} & -2.2 & -2.9 & {\it -0.7} \\
\hline \hline
\end{longtable}}
%\end{landscape}
\doublespacing

Since that time, we have also received the initial (3rd) estimates of
the Q4-over-Q4 growth rates in 2009 and 2010, and these have passed through
two and one annual revisions, respectively:
%\begin{landscape}
%\newpage

\singlespacing
\centerline {\bf Changes to $\Delta GDP(E)$ and $\Delta GDP(I)$ since
  Nalewaik (2010):}
{\small
\begin{longtable}{c c c c c c c}
 & \multicolumn{3}{c}{2009Q4/2008Q4}  & \multicolumn{3}{c}{2010Q4/2009Q4} \\
 & Initial & Latest & Revision & Initial & Latest & Revision \\
\hline \hline
$\Delta$ GDP(E) & 0.1 & -0.5 & {\it -0.6} & 2.8 & 3.1 & {\it 0.4} \\
\hline \hline
$\Delta$ GDP(I) & -0.6 & -0.9 & {\it -0.2} & 3.1 & 3.5 & {\it 0.4} \\
\hline \hline
\end{longtable}}
%\end{landscape}
\doublespacing

One remarkable feature of these recent revisions, discussed further in
section 5, is the frequency with which they move $\Delta GDP(E)$ and
$\Delta GDP(I)$ in the same direction.  In particular, the downward
revisions to the output growth estimates in 2007, 2008, and 2009 have
continued, and were particularly large for $\Delta GDP(E)$ in 2008.
As can be seen in the update of Figure 6 from Nalewaik (2010), the
peak in GDP(E) at that time was still two quarters late, in 2008Q2,
but the current data now show the peak in GDP(E) was 2007Q4,
consistent with the NBER Business Cycle Dating Committee's call.
These latest GDP(E) estimates show just how badly the initial GDP(E)
estimates missed the onset and severity of the recession.

%Relative to the start of 2006, the post-BPEA revisions did little to
%alter the level of GDP(I) in the middle of 2008, as downward revisions
%in the middle of 2007 offset upward revisions in late 2007 and early
%2008.  In contrast, GDP(E) continued its string of downward revisions
%in the second half of 2007 and the first half of 2008.  In the second
%half of 2008, both GDP(E) and GDP(I) revised down considerably.

Based on the behavior of GDP(I), Nalewaik (2010) said output from
2007-9 likely decelerated sooner and more sharply ahead of the
recession, fell faster at the height of the recession, and recovered
less quickly than was shown by GDP(E) at the time.  The revisions have
largely validated these observations, with $\Delta GDP(E)$ revising
down towards $\Delta GDP(I)$ slightly in 2007 and more substantially
in late 2008 at the height of the downturn.\footnote{%
  At the time of Nalewaik (2010), average annualized $\Delta GDP(E)$
  was minus $6$ percent in 2008Q4 and 2009Q1, with $\Delta GDP(I)$
  about minus $7\frac{1}{2}$ percent.  Since then, average $\Delta
  GDP(E)$ revised down to about minus $7\frac{3}{4}$ percent, while
  $\Delta GDP(I)$ revised down further as well, to about minus
  $8\frac{1}{2}$ percent.}  And although 2009Q3 $\Delta GDP(I)$
revised from negative to positive, $\Delta GDP(E)$ revised down in the
second half of 2009, recovering less quickly than was initially
estimated.  These revisions to $\Delta GDP(E)$, both in the recession
itself and in the early stages of the recovery, make the rise in the
unemployment rate in 2009 less surprising than it seemed in early
2010.

Regarding the recovery, the news on output growth since Nalewaik
(2010) has not been all bad.  Initial $\Delta GDP(I)$ was above
initial $\Delta GDP(E)$ in 2010, typically a good sign, as discussed
in see section 5.  And we have finally seen some upward revisions to
output growth.
%, with the first annual revision to 2010 (although two
%more annual revisions remain, so the results for 2010 are somewhat
%tenuous).  Initial $\Delta GDP(I)$ remains above initial $\Delta
%GDP(E)$ in 2010, and in 2011Q1 as well, a quarter where $\Delta
%GDP(I)$ looks considerably less bleak than $\Delta GDP(E)$.  
An update of Figure 3 shows the latest year-over-year growth rates,
where we see the income-side measure moving above the expenditure-side
measure starting in 2010Q1 and continuing through 2011Q2.

\section{Information Content of the Latest Growth Rates}

%The original BPEA paper studied the latest estimates using a sample
%ending in 2006Q4, ensuring that these estimates incorporated all the
%major annual source data.  Using the same rule, we extend tables
%forward so they end in 2008Q4.  

The recent revisions have not altered the fact that GDP(E) and GDP(I)
paint a widely divergent picture of the behavior of the economy in
2007, and the sources of this discrepancy remain unclear.  Perhaps
capital gains are not being stripped out of GDP(I) properly.\footnote{%
%The original BPEA suggested that some
%capital gains may have leaked into GDP(I), accounting for part of its
%relatively larger deceleration in 2007, but that such leakage was
%probably not the bulk of the change in the statistical discrepancy in
%2007.  
  Taking capital gains out of the tax data used to compute corporate
  profits and proprietors' income seems like a relatively
  straightforward task, since tax forms have lines for capital gains,
  but the BEA has suggested the removal of capital gains might not be
  so straightforward.  Note that companies typically would have little
  incentive to misclassify capital gains as ordinary income, since tax
  treatments typically favor capital gains.  And since capital gains
  are likely procyclical, over-reporting of capital gains would reduce
  the cyclicality of GDP(I) relative to the cyclicality of true output
  (since measured capital gains are subtracted from outpu), not
  explaining why GDP(I) is more cyclical than GDP(E).}  Nalewaik
(2010) pointed out problems with some particular components of GDP(E),
suggesting the estimates were too high, and while these estimates
revised down, the revisions were not very large.\footnote{%
% in explaining the 2007 annual change in the statistical
%discrepancy of about 150 billion dollars.
  In particular, residential improvements and financial services PCE
  revised down only 4 billion and 9 billion dollars, respectively, not
  enough to be meaningful in explaining the 2007 annual change in the
  statistical discrepancy of about 150 billion dollars.  However, the
  BEA likely agreed that there were problems in their methodology for
  estimating residential improvements, because they changed that
  methodology soon after Nalewaik (2010).  The BEA has also started
  folding in newly available Census data on financial services PCE,
  from the Service Annual Surveys (SAS) and Quarterly Services Surveys
  (QSS).  However, since these new data begin in 2009, they are not
  helpful for determining what happened in 2007.}  Those components,
however, may remain badly mismeasured in 2007, as may much of services
PCE.
%\footnote{%
%  Somewhat perversely, another potential problem with 2007 GDP(E) is
%  related to the fact that 2007 is an Economic Census year.  The
%  Census Bureau, and in particular the Annual Survey of Manufacturers
%  (used by the BEA to compute equipment and software investment and
%  manufacturers' inventories), computes 2007 growth rates using the
%  ratio of the level computed from the more reliable Economic Census
%  data in 2007 over the level computed from the less reliable data in
%  2006.  The Economic Census may correct measurement errors in the
%  2003, 2004, 2005, and 2006 surveys cumulating to an incorrect level
%  in 2006, potentially moving growth that should have appeared in
%  those years into 2007.  For example, say output growth as measured
%  by the annual source data was too low in 2006.  The 2007 Economic
%  Census catches this error by getting the level right in 2007, but
%  the correction appears in the 2007 growth rate, biasing up 2007
%  output growth and biasing down 2006 output growth.  GDP(I) does not
%  suffer from any of these complications since its annual source data
%  (mainly tax data) is consistent across all years.}

Generalizing beyond 2007, Aruoba, Diebold, Nalewaik, Schorfheide, and
Song (2011) discuss optimal combination of the latest GDP(E) and
GDP(I) estimates.  Nalewaik (2010) discussed how variances and
revisions could be used to provide information on the relative
reliability of the {\it latest} estimates (not the initial estimates,
but the latest estimates).  This analysis is little changed by the
recent revisions; the update to table 1 provides the new summary
statistics, which are similar to those in Nalewaik (2010).  An article
printed recently in the BEA's monthly publication, Fixler,
Greenaway-McGrevy, and Grimm (2011), makes a different set of
assumptions about variances and revisions, and the online Appendix
analyzes the validity of those assumptions.

\section{The Cyclicality of the Statistical Discrepancy}

The update to Figure 4 shows that the clear systematic relation of the
statistical discrepancy to the unemployment rate in Nalewaik (2010)
was subsequently largely revised away in 2008 and 2009.  Whether the
cyclicality of the discrepancy will appear again in the future may
hinge on whether the lack of official annual surveys on much of the
enormous service-producing sector of GDP(E) was the source of the
cyclicality problem from the mid-1980s to the mid-2000s, and whether
the availability of new annual services surveys starting in 2009
solves the problem.  If that is not the case, the deviation from the
pattern could be temporary, and from 2009Q4 to 2011Q2, we have already
seen the pattern emerge again with a level shift, as the statistical
discrepancy and the unemployment rate have both drifted down.  In any
event, there remains a very large cyclicality problem from the
mid-1980s to the mid-2000s that is not addressed by the availability
of new annual services data; this problem remains and may plague
econometric analyses until it is fixed.

\section{The Information Content of the Initial Growth Rates}

\subsection{Quarterly Growth Rates}

The update to Table 2 extends the sample for most the regressions out
to 2011Q2, with little change to most of the results showing initial
GDP(I) growth is the better predictor of a wide variety of business
cycle indicators, including the change in the unemployment rate in the
current period and subsequent periods, employment growth (measured
using the CPS household survey) in current and subsequent periods
(recall that there is no reason to suspect these labor market measures
to be spuriously correlated with $\Delta GDP(I)$ since data from the
CPS household survey is not used in the construction of $\Delta
GDP(I)$), the manufacturing purchasing managers index in current and
subsequent periods, changes in stock prices over previous periods, the
slope of the treasury yield curve in previous periods, and SPF
forecasts of GDP(E) growth itself from previous periods.  Initial
GDP(I) growth is also a better predictor of initial GDP(E) growth over
the next quarter or two than is initial GDP(E) growth.

%\footnote{%
%  This result carries over to the latest estimates as well, and can be
%  seen clearly even without regression analysis.  For example,
%  consider predicting whether $\Delta GDP(E)$ will be negative next
%  quarter using $\Delta GDP(E)$ and $\Delta GDP(I)$ this quarter.  The
%  unconditional probability of negative $\Delta GDP(E)$ is 16 percent,
%  using a 1947-2009 sample.  The probability of negative $\Delta
%  GDP(E)$ next quarter rises to 35 percent when $\Delta GDP(E)$ is
%  negative in the current quarter (14 out of 40 cases), but that
%  probability rises to 50 percent when $\Delta GDP(I)$ is negative in
%  the current quarter (20 out of 40 cases).  In other words, negative
%  $\Delta GDP(E)$ is more likely to be preceded by negative $\Delta
%  GDP(I)$ than negative $\Delta GDP(E)$, making $\Delta GDP(I)$ the
%  better predictor.}

The results that have changed the most are the revision results using
the short sample at the end of the table.  Nalewaik (2010) used a
sample ending in 2006Q4, ensuring that the revised estimates on the
left-hand-side of the regression incorporated all their major annual
source data.  Using the same rule, we roll the sample forward to end
in 2008Q4.  Using these 60 quarterly observations from 1994Q1 to
2008Q4, we see the statistically significant tendency for $\Delta
GDP(E)$ to revise towards initial $\Delta GDP(I)$.  Indeed, when
predicting latest quarterly $\Delta GDP(E)$ using initial $\Delta
GDP(E)$ and initial $\Delta GDP(I)$, it has been optimal over this
time period to place almost 50 percent weight on GDP(I), up from about
30 to 40 percent in the sample employed in Nalewaik (2010).

\subsection{Q4-over-Q4 Growth Rates}

Smoothing into Q4-over-Q4 growth rates, the evidence is even more
favorable to GDP(I), as can be seen in the update to Figure 2.  The
top panel shows that, since the mid-1990s, when predicting latest
Q4-over-Q4 $\Delta GDP(E)$ it has been optimal to place 84 percent
weight on initial Q4-over-Q4 $\Delta GDP(I)$ and only 16 percent
weight on initial Q4-over-Q4 $\Delta GDP(E)$.  The regression slope is
highly significant (adjusting for limited degrees of freedom using a
t-distribution); 12 out 17 data points are in the correct quadrants
(northeast and southwest); and the adjusted $R^2$ is 0.37, up from
0.25 in Nalewaik (2010).

Interestingly, the bottom panel now shows a statistically significant
tendency for $\Delta GDP(I)$ to revise {\it away from} initial $\Delta
GDP(E)$, with 11 out 17 data points in northwest and southeast
quadrants, and an adjusted $R^2$ of 0.26.  If initial $\Delta GDP(I)$
is higher than initial $\Delta GDP(E)$, $\Delta GDP(I)$ tends to
revise up; with initial $\Delta GDP(E)$ tending to revise towards
initial $\Delta GDP(I)$, both estimates then tend to revise up if
initial $\Delta GDP(I)$ is higher than initial $\Delta GDP(E)$.
Similarly, both estimates tend to revise down if initial $\Delta
GDP(I)$ is lower than initial $\Delta GDP(E)$.  These results show
that the gap between initial $\Delta GDP(I)$ and initial $\Delta
GDP(E)$, averaged over several quarters, has been highly informative
in recent years.  A possible explanation is discussed
below.\footnote{%
  These results counsel that if the BEA has in place any procedures
  for shrinking the initial $\Delta GDP(I)$ estimates towards the
  initial $\Delta GDP(E)$ estimates, those procedures should probably
  be discarded, or at least minimized so they have less of an effect
  on average growth rates over several quarters.  That assumes the BEA
  wants their initial $\Delta GDP(I)$ estimates to be optimal
  predictors of their latest, revised $\Delta GDP(I)$ estimates.  If,
  in contrast, the BEA wants their initial $\Delta GDP(I)$ estimates
  to be optimal predictors of their latest, revised $\Delta GDP(E)$
  estimates, the initial $\Delta GDP(I)$ estimates are fine the way
  they are.}

Naturally, the revisions to the two estimates have a positive
correlation, over 0.6, and, a rather-striking 15 out of 17
revisions have been in the same direction for both estimates.
1999 and 2005 are the only exceptions.  But while the revisions to
$\Delta GDP(I)$ and $\Delta GDP(E)$ tend to go in the same direction,
the magnitudes can differ.  Sometimes the estimates converge, as in
2008, when initial $\Delta GDP(E)$ and $\Delta GDP(I)$ started at
around -1 percent and -2 percent, respectively, with both converging
to around -3 percent, but typically the estimates do not converge and
actually become more dissimilar, as in 2007.

\subsection{On the Gains to Placing some Weight on $\Delta GDP(I)$}

The root-mean-square (RMS) of the $\Delta GDP(E)$ revisions plotted in
Figure 2 is around 0.9, and could be reduced to 0.7 using the
regression results illustrated in Figure 2.\footnote{%
  Similarly, the root-mean-square (RMS) of the $\Delta GDP(I)$
  revisions is around 0.7, which could have been reduced to 0.6 by
  moving initial $\Delta GDP(I)$ away from initial $\Delta GDP(E)$.
  Note that while the variance of the revisions to quarterly $\Delta
  GDP(I)$ is higher than the variance of the revisions to quarterly
  $\Delta GDP(E)$ in table 1 (also true using a sample starting in
  1994), the reverse is true using the Q4-over-Q4 growth rates.}  Is
such a gain in the accuracy of the initial estimates worth the costs
associated with changing current procedures?  Couching the issue in
terms of root-mean-square errors does not do adequate justice to the
issue, in my opinion, because initial $\Delta GDP(I)$ picked up some
very important economic developments over the past couple of decades
much better than initial $\Delta GDP(E)$.  Given the BEA's historic
emphasis on $\Delta GDP(E)$, modifying the initial $\Delta GDP(E)$
estimates would have allowed the economics profession and the broader
public to recognize and reach consensus on these important
developments sooner than they did in real time, which could have been
quite valuable.  The list of important economic developments, which
can all be seen in the updated Figure 2, includes:
\begin{enumerate}
\item The onset and extent of the productivity acceleration in the mid-
  to late-1990s.  In Anderson and Kliesen's (2010) characterization:
  ``The increasingly rapid productivity growth that began in the 1990s
  was the defining economic event of the decade ...'' [p. 129].  While
  this may be debatable, it was clearly a very important development.
  While some analysts did use GDP(I) to analyze productivity in real time (see the Economic Report of the President, 1997),
  the issue was obscured by measurement error in $\Delta GDP(E)$.
  From 1994 to 1999, the initial Q4-over-Q4 GDP(E) growth rates were,
  on average, $\frac{1}{2}$ percentage point below the initial
  Q4-over-Q4 GDP(I) growth rates, and the Q4-over-Q4 GDP(E) growth
  rates ended up revising up a little more than $\frac{1}{2}$
  percentage point, on average, over this time period.

\item The sluggishness of output growth in the ``jobless recovery''
  following the 2001 recession in late 2002 and early 2003.  While
  this was apparent in the jobs data themselves in real time, it was
  less evident in initial $\Delta GDP(E)$ than in initial $\Delta
  GDP(I)$.  Ultimately, much of the discordance between the output
  data and the jobs data (the subject of much discussion and analysis
  in real time, to be sure) went away after subsequent downward
  revision to both $\Delta GDP(E)$ and $\Delta GDP(I)$.  In 2002 and
  2003, both estimates revised down an average of between
  $\frac{1}{2}$ and $\frac{3}{4}$ percentage points per year.

\item The weakening of the economy ahead of the 2007-9 recession.  As
  discussed earlier, $\Delta GDP(E)$ revised down towards $\Delta
  GDP(I)$ in 2007.  Although the downward revisions are not
  particularly large, a best guess is that at least part of the large
  remaining discrepancy between $\Delta GDP(E)$ and $\Delta GDP(I)$ in
  2007 is due to unresolved measurement errors in $\Delta GDP(E)$.

\item The fact that the economy was in recession in the first half of
  2008, and the severity of the downturn in late 2008, as discussed
  earlier.
\end{enumerate}
It would seem worth considerable cost to have official output data
that pick up very important events such as these.

\subsection{A Closer Look at 2008}

Before concluding, the enormous downward revisions to the initial 2008
$\Delta GDP(E)$ estimates are worthy of some additional attention.
The table below breaks down the revision to 2008 Q4-over-Q4 $\Delta
GDP(E)$:\footnote{%
  The contributions are averages over the four quarters of 2008 of the
  quarterly contributions reported by the BEA.  }
%\newpage


\singlespacing
\begin{longtable}{c c}
GDP(E) Components & 2008Q4/2007Q4 Revision Contribution\\
                  & (from Initial (3rd) to Latest)     \\
                  & Percentage Points     \\
\hline \hline
GDP(E)                        & -2.5 \\ \hline
PCE, durable goods            & -0.2 \\
PCE, nondurable goods         &  0.2 \\
PCE, services                 & -0.7 \\
Nonresidential stuctures      & -0.3 \\
Equipment and Software        & -0.3 \\
Residential Structures        & -0.2 \\
Change in Private Inventories & -0.6 \\
Exports                       & -0.1 \\
Imports                       & -0.3 \\
Government                    & -0.1 \\
\hline \hline
\end{longtable}
\doublespacing The striking thing in the table is the widespread
nature of the downward revisions, with all major components revising
down except nondurable goods PCE.  What could have caused such large
widespread downward revisions?  The potential problems with the
initial estimates of $\Delta GDP(E)$ and $\Delta GDP(I)$ include
missing data for some components, sampling errors, and non-sampling
errors such as survey non-response.  Sampling errors are random and
should be uncorrelated across the range of surveys used for compute
the different components, so this is an unlikely explanation.  Missing
data were likely part of the problem for services PCE, but as Steve
Landefeld noted in his comments on Nalewaik (2010), the other
components of GDP(E) are based on ``some form of direct monthly or
quaterly source data.''  So the widespread downward revisions are
probably due to non-sampling errors correlated across components.

\subsection{One Potential Explanation:  Firm Births and Deaths}

While this is speculative, incomplete corrections for firm births and
deaths, particularly of small businesses, have all the ingredients
required to cook up the correlated non-sampling errors that appeared
in 2008.  First, output fluctuations due to firm births and deaths are
likely highly correlated with the aggregate business cycle, and
through that channel, across components of GDP(E).  Second, output
fluctuations from births and deaths do not appear to be picked up by
the monthly and quarterly surveys used to produce GDP(E).  New firms
are added with too long of a lag.  And when a firm drops out of the
sampling frame, the survey administrator will not always know whether
the firm has shut down (making an imputed growth of minus 100 percent
applicable for that firm) or whether it has simply chosen to stop
responding to the survey (which would require a different imputation),
since the monthly and quarterly surveys used to produce GDP(E) are
voluntary.  The fraction of non-respondents that are firm deaths
likely varies with the business cycle, and while a birth-death model
may pick up some of this, I know of no such model being applied to the
expenditure surveys, so misclassification of non-respondents is
probably correlated with the business cycle.  And third, output
fluctuations from firm births and deaths appear much more likely to be
picked up by the annual surveys the BEA folds into GDP(E) after the
initial estimates.  These annual surveys fold in new firms, and are
mandatory (although some non-response continues), allowing a better
parsing of the fraction of firm non-respondents that have shut down.

While this is somewhat speculative as well, initial $\Delta GDP(I)$
may pick up firm births and deaths better then initial $\Delta
GDP(E)$, for several reasons.  First, in contrast to the major surveys
used to compute GDP(E), the current Employment Statistics (CES) survey
actually has a birth-death model, facilitated by the availability of
quarterly benchmarks from the Quarterly Census of Employment and Wages
(QCEW), which should pick up firm births and deaths because it is a
universe count of wage and salary payments derived from tax
records.\footnote{%
  The CES is the source data for the initial estimates of wages and
  salaries and also some components of initial GDP(E), but the CES
  comprises a larger share of initial GDP(I), at least 40 percent.}
Second, the Appendix of Nalewaik (2010) shows that response rates to
the CES are generally higher than response rates to the major surveys
used to compute GDP(E), suggesting misclassification of
non-respondents is less of a problem for the CES.  And third, since
2002, the initial Q4-over-Q4 growth rates of GDP(I) incorporate QCEW
data into the first three quarters of the four quarter change,
probably picking up a substantial amount of output variation due to
firm births and deaths.

Finally, and most speculative of all, these conjectures may help
explain patterns in the revisions to $\Delta GDP(I)$ and $\Delta
GDP(E)$.  While initial $\Delta GDP(I)$ likely picks up some of the
cyclical variation from firm births and deaths, more than initial
$\Delta GDP(E)$, which may pick up close to none, initial $\Delta
GDP(I)$ probably does not pick up all of that cyclical variation.
Then the tendency of $\Delta GDP(I)$ and $\Delta GDP(E)$ to revise in
the same direction could be due to both of them incorporating cyclical
variation from firm births and deaths.  The revisions would tend to go
in the direction of initial $\Delta GDP(I)$ minus $\Delta GDP(E)$, if
part of that initial gap reflects cyclical variation from firm births
and deaths picked up by $\Delta GDP(I)$ and missed by $\Delta GDP(E)$,
variation that is likely positively correlated with the remaining
cyclical variation from firm births and deaths that will appear later
through revisions.

Of course, some other constellation of facts might explain the
patterns in the revisions described in this paper.  Some additional
analysis from the statistical agencies explaining these patterns would
certainly be helpful.

%This relation broke down 
%somewhat recently, especially in 2006 and 2007, but snapped back to
%form with the latest revision to 2008.\footnote{%
%  Note that subsequent annual revision may change these results for
%  2007 and 2008, and the next benchmark revision may change the
%  post-2002 results.}


\section{Concluding Thoughts}

%and that taking a weighted average of $\Delta
%GDP(E)$ and $\Delta GDP(I)$ over these past couple of years would
%probably balance the risks and produce the best possible estimate of
%true output growth over this period. 

Nalewaik (2010) concluded with some recommendations for improved GDP
measurement, and we conclude with an update on how those
recommendations have progressed since then.  The first suggestion was
that the BEA report $\Delta GDP(I)$ in its press releases, preferably
in table 1 along with $\Delta GDP(E)$, and provide some discussion of
$\Delta GDP(I)$.  While the BEA has added real GDI growth (as they
call it) to its press release, it is currently in the very last table
of the release, Appendix Table A, and the press release does not
discuss it.  More could be done on this front.  A second
recommendation was that the BEA feature as its headline output measure
a 50-50 averge of GDP(E) and GDP(I).  The BEA has made it clear that
they will not consider reporting such an average without a methodology
for balancing the accounts, so that the components of GDP(E) and
GDP(I) add up to the average.\footnote{%
  Nalewaik (2010) argues that this is not essential, because while
  $C+I+G+NX=GDP(E)$ now, the evidence strongly suggests that GDP(E)
  does not equal true GDP, so $C+I+G+NX \neq GDP$ now.  Averaging
  without balancing would simply make that explicit.  It is certainly
  understandable that the BEA would be concerned about non-additivity,
  although they accepted non-additivity in their real estimates when
  moving to chain weighting in the mid-1990s.  } This is a difficult
task, but the BEA has said they have begun researching the issue, and
have suggested they might consider producing and publishing a set of
averaged and balanced accounts as satellite accounts.  A project like
that would not be particularly costly, probably be a lot less costly
than some other projects the BEA is pursuing, and the evidence here
and in Nalewaik (2010) suggests that it would be well worth the
effort.

\vskip 0.6cm
\begin{thebibliography}{99}
%\centerline{\bf References}
\vskip 0.6cm

\singlespacing


\bibitem {bcm} Anderson, R., and Kliesen, K. (2010), ``FOMC Learning
  and Productivity Growth (1985-2003): A Reading of the Record.''  {\it Federal Reserve
    Bank of St. Louis Review} March/April 2010: 129-153.

\bibitem {ms} Aruoba, B., Diebold, F., Nalewaik, J., Schorfheide, F.,
  and Song, D.  (2011) ``Improving GDP Measurement: A Forecast Combination
  Perspective'' National Burea of Economic Research working paper
  17421.

\bibitem {cea} Council of Economic Advisers (1997), {\it Economic
    Report of the President,} Washington, D.C.: United States
  Government Printing Office.

\bibitem {ms} Fixler, D., Greenaway-McGrevy, R. and Grimm, B. (2011)
  ``Revisions to GDP, GDI, and their Major Components'' {\it Survey of
    Current Business}, July 2011, pp. 9-31.

\bibitem {ss}  Nalewaik, J., (2010), ``On the Income- and
  Expenditure-Side Measures of Output''  {\it Brookings Papers on Economic
    Activity} 2010(1): 71-106.

\end{thebibliography}

\newpage

\singlespacing



\centerline {\bf Update of Table 1: Variances and Correlations,}
\centerline {\bf Initial (3rd) and Latest Estimates of $\Delta$ GDP(E) and $\Delta$ GDP(I)} 
\vskip 0.5cm
\centerline {\bf Correlation Matrix, 1978Q3 to 2011Q2:}
\begin{longtable}{c c c c c}
& \multicolumn{2}{c}{Initial (3rd) Estimates} & \multicolumn{2}{c}{Latest Estimates} \\
& $\Delta$ GDP(E) & $\Delta$ GDP(I) & $\Delta$ GDP(E) & $\Delta$ GDP(I) \\
\hline \hline
\input{table_corr2.txt}
\hline \hline
\end{longtable}

\vskip 0.5cm
\centerline {\bf Correlation Matrix, 1984Q3 to 2008Q4:}
\begin{longtable}{c c c c c}
& \multicolumn{2}{c}{Initial (3rd) Estimates} & \multicolumn{2}{c}{Latest Estimates} \\
& $\Delta$ GDP(E) & $\Delta$ GDP(I) & $\Delta$ GDP(E) & $\Delta$ GDP(I) \\
\hline \hline
\input{table_corr.txt}
\hline \hline
\end{longtable}

\vskip 0.5cm
\centerline {\bf Variances:}
\begin{longtable}{c c c c}
\multicolumn{2}{c}{1978Q3 to 2011Q2} & \multicolumn{2}{c}{1984Q3 to 2008Q4} \\
$\Delta$ GDP(E) & $\Delta$ GDP(I) & $\Delta$ GDP(E) & $\Delta$ GDP(I) \\
\multicolumn{4}{c}{Initial (3rd) Estimates}\\
\hline \hline
 8.16 & 8.61 & 4.73 & 5.30 \\
\hline \hline
\multicolumn{4}{c}{Latest Estimates} \\
\hline \hline
 9.73 & 10.54 & 6.11 & 7.39 \\
\hline \hline
\multicolumn{4}{c}{Revision: Latest-Initial (3rd)} \\
\hline \hline
 2.86 & 3.70 & 2.71 & 3.37 \\
\hline \hline
\end{longtable}

\newpage

\centerline {\bf Update of Table 2: Predictive Content of Initial Growth Rates, 1978Q3-2011Q2} 
\vskip 0.1cm
{\scriptsize
\begin{longtable}{c c c c c c c c c}
\hline \hline
 & \multicolumn{7}{c}{Explanatory Variables} & \\
 & \multicolumn{3}{c}{$\Delta GDP(E)$, initial (3rd)} & \multicolumn{3}{c}{$\Delta GDP(I)$, initial (3rd)} & Constant & Adj. $R^2$ \\
Dependent Variable & $t$ & $t-1$ & $t-2$ & $t$ & $t-1$ & $t-2$ & & \\
\hline \hline
\input{table_GDP_forecasts_2.txt}
\input{table_GDI_forecasts_2.txt}
\input{table_aux_forecasts.txt} \hline
\input{table_GDP_revisions_f.txt} \hline
\input{table_GDI_revisions_f.txt}
\hline \hline
\end{longtable}}

\end{document}
