Download This PDF is a selection from a published volume from... Bureau of Economic Research Volume Title: NBER International Seminar on Macroeconomics

This PDF is a selection from a published volume from the National
Bureau of Economic Research
Volume Title: NBER International Seminar on Macroeconomics
2010
Volume Author/Editor: Richard Clarida and Francesco Giavazzi,
organizers
Volume Publisher: University of Chicago Press
Volume ISBN: 978-0-226-10736-3 (cloth); 0-226-10738-8 (paper)
Volume URL: http://www.nber.org/books/clar10-1
Conference Date: June 18-19, 2010
Publication Date: September 2011
Chapter Title: Comment on "Globalization, the Business Cycle, and
Macroeconomic Monitoring"
Chapter Authors: Lucrezia Reichlin
Chapter URL: http://www.nber.org/chapters/c12199
Chapter pages in book: (p. 287 - 298)
Comment
Lucrezia Reichlin, London Business School and CEPR
I.
Introduction
The objective of the paper by Aruoba et al. is to construct an index of
the global business cycle, more precisely, an index tracking the cycle
of Group of 7 countries. The index is computed using GDP data, which
are available at a quarterly frequency, and monthly business cycle indicators. The latter are included for capturing features of the business
cycle that are not summarized in the GDP series and to obtain an indicator that is available at a higher frequency than GDP.
The econometric model is based on the assumption that the observable series have a factor structure representing global and countryspecific comovements across series. The model is estimated in two
steps: first, for each country separately, the authors extract a common
(country) factor; second, they extract the global factor by estimating a
factor model on the country factors extracted in the previous step. Following standard practice, the model is written in its state space form,
and the Kalman filter is used to handle the mixed-frequency data problem. The global index is defined as the estimated common factor obtained in the second step.
Another exercise proposed by the paper is to use the same approach
for each single country in order to extract, for each model, the seven
national factors and then study the relation between the latter and
the global index.
Empirically, the results of the paper are not surprising. The factors are
generally highly correlated with GDP. The description of depth and
length of various recessions as well as the declining volatility of the cycle
are well-known facts that do not require more than eyeballing econometrics to be identified. However, there are also some puzzles. For example, what is the interpretation of the fact that the U.S. country factors
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Reichlin
comove more with industrial production and employment than with
GDP? Is this telling anything of economic significance on the nature of
the U.S. cycle?
In my discussion I will argue that a common factor extracted from
GDP and the monthly coincident, lagging, and leading indicators of
the business cycle used in this paper is not very informative as a business
cycle index and can be hard to interpret. In particular, in cases in which
the index is highly correlated with GDP, we wonder what we have
learned more than if looking just at GDP; when it is not, as in the case
of the United States, we wonder if the difference is due to the fact that
the index is attributing too much weight to series that are lagging the
cycle such as labor market data or to series that are measured with error
like many of the monthly indicators.
However, the paper is promising but incomplete. As a consequence,
the methodology is underexploited and the exercise lacks some motivation. As the authors suggest, the econometric approach described
in the paper could have been used to obtain a timely indicator of the
business cycle that could track it in real time. With that objective, the
motivation of including monthly variables in the model is clear: they
provide information on the state of the economy in a more timely
way than GDP, and this is important since GDP is typically available
after the close of the quarter (e.g., 1 month after in the United States,
6 weeks after in the euro area). Ideally one wants to update the view
of current business cycle conditions, global or national, in relation to
publication of data throughout the quarter and exploit any available statistic that is likely to provide a signal. However, in this paper,
the authors limit themselves to the construction of an index based on
complete data, including current-quarter GDP. In other words, this is
an index computed once all information is available rather than in real
time. In this case, the motivation of including monthly variables is
unclear.
In my comments I will discuss real-time analysis with some detail and
I will argue that, if the authors decided to push the paper in that direction, they should not consider computing updates of a factor as a proxy of
business cycle but rather use monthly data to obtain a sequence of early
estimates of current-quarter GDP. The update of estimates of currentquarter GDP in relation to the real-time data flow within the quarter is
called “nowcasting,” and it has been successfully implemented in many
institutions with a focus on national GDP.1
To illustrate my points I will present an empirical application of nowcasting on U.S. and euro area data.
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Comment
II.
289
How Should We Interpret a Global Factor?
The global index estimated by the model is an unobserved common factor that is identified by imposing a unit variance normalization. Given
the unit variance normalization, the factor estimated by maximum likelihood is roughly the weighted average of the variables included in the
model, where the weights are the inverse of the standard deviation. To
understand the implication of this observation, let us consider the panel
of GDP series for the G7 countries and disregard the monthly variables.
With this panel we can estimate the factor by maximum likelihood and
compare it with a weighted average of demeaned GDP using as weights
the inverse of standard deviation. As shown by figure 1, the two series
are almost identical.
But how does this weighting scheme compare with G7 aggregate
GDP? This series, computed by statistical agencies, is a weighted average
with weights depending on the countries’ size. As shown in figure 2, the
two series have similar dynamic profiles, but the estimated factor, having
zero mean and unit variance, does not convey information on the first
two moments. Clearly, aggregate GDP is more informative than the
factor as an index of the business cycle.
The authors, however, include in their model not only GDP series but
also other (monthly) business cycle indicators. What do we gain when
considering monthly variables as well as GDP series? In this case the
index is monthly and does not necessarily track GDP since all variables
are weighted with weights depending on relative volatility rather than
countries’ size. I am not sure this is a reasonable way to proceed. Take
the example of retail sales. This series is typically monitored because
it is an early indicator of current-quarter GDP. However, the series is
highly volatile (and has a large idiosyncratic component), and once
GDP is published, it does not carry extra information: including it in
the computation of the index, once GDP becomes available, just adds
noise. With employment the problem is different. Labor market variables
are lagging indicators of the business cycle. The common factor between GDP and employment aggregates the two series statically, but
averaging contemporaneously coincident and lagging variables leads
to a series that cannot be interpreted as a proxy for current business
cycle conditions.
Without the objective of real-time monitoring of the cycle, there is
no case for using monthly variables. But even in the case in which the
method had been used for the real-time computation of the index, it is
not clear to me why they focus on the factor rather than on the projection
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290
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Fig. 1. Panel of GDP series of G7 countries: the maximum likelihood estimate of the common factor and the weighted (inverse of standard deviation)
average of the demeaned GDP series.
291
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Fig. 2. Panel of GDP series of G7 countries: the maximum likelihood estimate of the common factor and the weighted (country size) average of the
GDP series; aggregate GDP as computed by the statistical agency.
292
Reichlin
of GDP on the factor. Such a projection recenters the factor around GDP
and can be interpreted as an early estimate of the current value of GDP
growth, that is, its nowcast. In the next section I explain in more details
the exercise of nowcasting and provide an illustration based on international data.
III.
Nowcasting
An alternative strategy to that proposed in Aruoba et al.’s paper is to
use the factor analysis framework to compute a sequence of timely estimates of current-quarter GDP (national or global), which corresponds
to a calendar of monthly data releases. In what follows I will illustrate
the basic modeling ideas.2
Let us denote by Ωv a vintage of data available at time v, where v refers
to the date of a particular data release. Further let us denote GDP growth
Q
at time t as yQ
t . I define the problem of nowcasting of yt as the orthogonal
Q
projection of yt on the available information set Ωv :
Q
P½yQ
t jΩv ¼ E½yt jΩv ;
ð1Þ
where E½jΩv refers to the conditional expectation. One of the elements
that distinguish nowcasting from other forecast applications is the structure of the information set Ωv . One particular feature is typically referred
to as its “ragged” or “jagged edge.” It means that, since data are released
in a nonsynchronous manner and with different degrees of delay, the
time of the last available observation differs from series to series. Another
feature is that it contains mixed frequency series, in our case monthly and
quarterly. Hence we will have
Ωv ¼ fxi;ti ; ti ¼ 1; 2; . . . ; Ti;v ; i ¼ 1; . . . ; n; yQ
3k ; 3k ¼ 3; 6; . . . ; TQ;v g;
where Ti;v corresponds to the last period for which in vintage v the series j
has been observed. Because of the nonsynchronicity of data releases, Ti;v
is not the same across variables, and therefore the data set exhibits the
above-mentioned jagged edge.
One important feature of the nowcasting process is that one rarely
performs a single projection for a quarter of interest but rather a sequence
of nowcasts, which are updated as new data arrive. The first nowcasts
are usually made with very little or no information on the reference
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Comment
293
quarter. With subsequent data releases they are revised, leading to
more precise projections as the information on the period of interest
accrues. In other words, we will, in general, perform a sequence of
Q
projections: E½yQ
t jΩv , E½yt jΩvþ1 , . . ., where v, v þ 1, . . . refer to dates
of consecutive data releases. Typically the intervals between two consecutive data releases are short (possibly a couple of days or less) and
change over time. Consequently, v has high frequency and is irregularly
spaced.
Let us first analyze the difference between the two information sets
Ωv and Ωvþ1 . At time v þ 1 we have a release of a certain group of variables, fxj;Tj;vþ1 ; j ∈ Jvþ1 g, and consequently the information set expands.3
The new information set differs from the preceding one for two reasons.
First, it contains new, more recent figures. Second, old data might get
revised. In what follows I will abstract from the problem of data revisions. Therefore, we have Ωv ⊆ Ωvþ1 and Ωvþ1nΩv ¼ fxj;Tj;vþ1 ; j ∈ Jvþ1 g.
Given the “expanding” character of the information and the properties of orthogonal projections, we can decompose the new forecast
as
Q
Q
E½yQ
t jΩvþ1 ¼ E½yt jΩv þ E½ yt jIvþ1 ;
|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}
|fflfflfflfflffl{zfflfflfflfflffl} |fflfflfflfflfflffl{zfflfflfflfflfflffl}
new forecast
old forecast
ð2Þ
revision
where Ivþ1 is the subset of the information set Ωvþ1 whose elements
are orthogonal to all the elements of Ωv . Given the difference between
Ωv and Ωvþ1 specified above, we have that
Ivþ1; j ¼ xj;Tj;vþ1 E½xj;Tj;vþ1 jΩv ;
and Ivþ1 ¼ ðIvþ1;1 Ivþ1; Jvþ1 Þ′, where Jvþ1 denotes the number of elements
in Jvþ1 . Hence, the only element that leads to a change in the nowcast is
the “unexpected” (with respect to the model) part of the data release,
Ivþ1 , which I label as the news. The concept of news is useful because
what matters in understanding the updating process of the nowcast
is not the release itself but the difference between that release and what
had been forecast before it. In particular, in an unlikely case in which the
released numbers are exactly as predicted by the model, the nowcast
will not be revised. However, we would intuitively expect that, for example, negative news in industrial production should revise the GDP
forecasts downward. Below I show how this can be quantified.
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Reichlin
From the properties of the conditional expectation, we can further develop (2) as
Q
1
E½yQ
t jIvþ1 ¼ E½yt I′vþ1 E½Ivþ1 I′vþ1 Ivþ1 :
ð3Þ
In order to expand (3) further and to extract a meaningful model-based
news component, one needs to have a model that can reliably account
for the joint dynamic relationships among the data. Given such a model
and assuming that the data are Gaussian, it turns out that we can find
coefficients bj;t;vþ1 such that
X
Q
E½ yQ
bj;t;vþ1 ðxj;Tj;vþ1 E½xj;Tj;vþ1 jΩv Þ :
t jΩvþ1 ¼ E½ yt jΩv þ
|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} |fflfflfflfflffl{zfflfflfflfflffl} j ∈ J
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
new forecast
vþ1
old forecast
news
In other words, we can express the forecast revision as a weighted sum
of news from the released variables:
X
Q
bj;t;vþ1 ðxj;Tj;vþ1 E½xj;Tj;vþ1 jΩv Þ :
E½ yQ
t jΩvþ1 E½yt jΩv ¼
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} j ∈ J
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
forecast revision
vþ1
ð4Þ
news
Hence, consistent with the intuition, the magnitude of the forecast revision depends, on the one hand, on the size of the news and, on the other
hand, on its relevance for the target variable as quantified by the associated weight bj;t;vþ1 .
Decomposition (4) enables us to trace the sources of forecast revisions
back to individual predictors. In the case of a simultaneous release of
several (groups of ) variables, it is possible to decompose the resulting
forecast revision into contributions from the news in individual (groups
of ) series, therefore allowing commenting on the revision of the target
in relation to unexpected developments of the inputs. This decomposition is also useful when the forecast is updated less frequently than at
each new release (I provide an illustration in the empirical section).
IV.
My Own Illustrative Exercise: The United States
and the Euro Area
Once the problem is described conceptually, we can choose a model
and an estimation method in order to perform the projection in practice.
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Comment
295
Here I will use a factor model estimated by maximum likelihood to stay
close to the method proposed by Aruoba et al. to construct the indicator (for a review of different estimation methods and a discussion of
the properties of the estimation method used here, see Bańbura et al.
[2011]).
I consider euro area and U.S. data for the sample 1990–2008. For the
euro area I include monthly total industrial production, industrial production in manufacturing, unemployment rate, retail sales, a euro area
economic sentiment indicator, purchasing manager index, and quarterly
employment and GDP. For the United States, I include monthly industrial production, Institute for Supply Management manufacturing production index, employment, and quarterly GDP.
The purpose of the exercise is to illustrate the concept of nowcasting
and its application to international data. I emphasize again that, rather
than constructing an index, I will produce a nowcast of euro area GDP
using U.S. and euro area data. A trivial extra step would be to construct
the U.S.–euro area aggregate nowcast.
My illustration here is meant to show that, since economies are interrelated, the nowcast for economy i benefits from inclusion of data from
economy j. The potential benefit is explained by the fact that economic
activities in countries i and j are correlated but also by the fact that data
releases in country i are more timely than in country j. In that case the use
of releases in country i for the nowcast of country j GDP should be particularly useful at the beginning of the quarter when important releases
of country j data are not yet available.
To illustrate these points I estimate two models: one with euro area
data only and one with both U.S. and euro area data. For each of the
two models I produce a sequence of forecast updates for GDP growth
rate in the fourth quarter of 2008. This is a particularly interesting quarter
because, ex post, we now know that it was the fourth of the U.S. and euro
area recession, but, ex ante, there was still much uncertainty. In particular, in the euro area it was not yet recognized that the recession was
well under way as shown by the fact that the European Central Bank
raised interest rates in July.
We consider bimonthly updates of current-quarter forecasts. Specifically, we produce a first forecast with data available in mid-July 2008
and we subsequently update it at 2-week intervals, each time incorporating new data releases. The resulting six updates performed from July
to September target the next-quarter GDP growth. With the update from
mid-October till the end of December we effectively project currentquarter GDP growth. The last two updates are performed in January
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Reichlin
2009, and they refer to the previous quarter (the flash estimate for 2008Q4
GDP was released in mid-February).
The evolution of the forecast for euro area GDP based on the two
models is depicted in figure 3. In the same graph, for the model including
both U.S. and euro area data, I report the contribution of the news component of the various data groups to the forecast revision.4 The difference
between two consecutive forecasts, that is, the forecast revision, is the
sum over all the released variables of the product of the news related
to a particular variable and the associated weight in the GDP estimate
(see eq. [4]). The contribution of the news from a block of variables is
the sum of contributions of the series belonging to this block.
I now comment on the evolution of the forecasts. For both models, at
the beginning of the forecasting period the forecasts remain rather flat,
confirming the well-known difficulties in forecasting beyond the current
quarter.
The forecast based on U.S. and euro data is more pessimistic than that
based on euro area data only and, from the beginning, closer to the final
estimate. The difference between the two models is particularly large
at the beginning of the quarter when hard data for the euro area are
not yet available and early U.S. releases contribute in a sizable way to
the revisions.
Fig. 3. Nowcast of euro area GDP 2008Q4 from model based on (a) U.S. and euro area
data and (b) only on euro area data and news from model a.
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Comment
297
This exercise shows that, indeed, considering multicountry data is important to improve the accuracy of early estimates of GDP and, therefore, of business cycle conditions. I think that the framework used in
this paper could be more fruitfully used to produce early estimates of
current-quarter GDP for each country, using international data and then
aggregating them to obtain an early estimate of G7 GDP.
Notice that, with nowcasting, not only do we obtain an early indication of the current status of national and global business cycles but we
also have a framework on the basis of which we can comment on the
revisions and their unexpected components in relation to new data
releases. We therefore not only obtain a more interpretable indicator of
the business cycle than an index based on the common factor but also
provide a way to describe the evolution of our view in relation to the
real-time data flow.
V.
Concluding Remarks
Tracking global business cycles is certainly relevant, but only if this is
done in real time, providing a valuable tool for policy making. Once
data are published, simple aggregate GDP is a more informative statistic than a global factor extracted from GDP and lagging, leading, and
coincident monthly indicators.
I encourage the authors to pursue their research in the direction of
real-time monitoring of the business cycle but to follow the nowcasting
literature in providing updates of current-quarter GDP growth rather
than updates of an unobserved factor since the former exercise provides
an output that is easier to interpret.
Endnotes
1. Giannone, Reichlin, and Small (2008) were the first to formalize the problem. The
model was first implemented at the Board of Governors of the Federal Reserve in a project
that started in 2003 and then at the European Central Bank (Angelini et al. 2008; Bańbura
and Rünstler 2011; Rünstler et al., forthcoming). The methodology has also been implemented in other central banks for other economies, including Ireland (D’Agostino,
McQuinn, and O’Brien 2008), New Zealand (Matheson 2010), and Norway (Aastveit and
Trovik 2008). Bańbura, Giannone, and Reichlin (2011) provide a review of the literature and
a discussion of econometric issues.
2. This discussion follows Bańbura et al. (2011).
3. Typically one “additional” observation is released, and we have Tj;vþ1 ¼ Tj;v þ 1 for
all j ∈ Jvþ1 . GDP could be also included in a release; I abstract from this case in order not
to complicate the notation.
4. In this exercise I abstract from the effect of parameter reestimation. For each forecast
sequence the parameters are estimated only once before the first forecast in the sequence
is made and kept constant for all the subsequent forecast updates.
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