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Nowcasting Manufacturing Value Added for Cross-
Country Comparison
Kris Boudta Valentin Todorovb Shyam Upadhyayab
aK.U.Leuven and Lessius University College, Naamsestraat 69, 3000 Leuven, Belgium.
Email: kris.boudt@econ.kuleuven.be Tel: +32 16 326728 Fax: +32 16 326624
bResearch and Statistics Branch, UNIDO, P.O. Box 300, A-1400 Vienna, Austria.
Abstract
Manufacturing Value Added (MVA) is the key indicator of a country’s industrial production. In
order to facilitate international comparisons it is published in UNIDO’s International Yearbook of
Industrial Statistics for a large set of countries. Because of a time-gap of at least one year between
the latest year for which data are available and the year for which MVA data must be reported in
the Yearbook, nowcasting methods are used to fill in the missing data up to the current year. We
propose a parsimonious methodology that exploits the relationship between MVA and GDP to
produce reliable nowcasts of MVA.
Keywords: Manufacturing Value Added, Nowcasting, Robustness, UNIDO.
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1 Introduction
The Research and Statistics Branch of the United Nations Industrial Development Organization
(UNIDO) is responsible for implementing the international mandate of the Organization in the
field of industrial statistics. It maintains a unique industrial statistics database and updates it
regularly with data collected from the national statistical offices. A separate database at macro
level is also maintained primarily for compilation of statistics related to manufacturing value
added (MVA) such as its growth rate and share in gross domestic product (GDP) for various
countries and regions. These figures are published in the International Yearbook of Industrial
Statistics and posted on the statistical pages of the UNIDO web site. For current economic analysis
it is crucial that the Yearbook presents MVA data for the most recent years. This paper considers
the problem of providing an estimate of the missing values of the current-year MVA. Such an
estimate is called a “nowcast”, rather than a pure forecast.
Previous research has mainly focused on nowcasting current-quarter GDP growth. Small ([2,9]) or
large ([4,6,12]) models are then used to “bridge” the information contained in monthly data with
the quarterly growth rate of GDP. One exception is the research of [3,5] who describe how short
term interest rates and business survey data can be used to produce nowcasts of the monthly
industrial production index for the aggregated euro area. Their analysis (based on different data
sets) leads to different conclusions. [3] finds that models with indicators generally do worse than
simple autoregressive models. The empirical results of [5] indicate however that the nowcasting
method that exploits the information in the survey results outperforms the simple autoregressive
models.
Regarding the practical application of nowcasting methods in statistical offices, [4] mentions that
the Office for National Statistics (ONS) of the United Kingdom takes a conservative approach to
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using external data sources such as business surveys and financial market variables in compiling
its statistics. He notes that: “As a National Statistics institution, ONS has an obligation to meet
international standards on the formulation of National Accounts, and produce estimates in a
transparent way so that users can be confident that quality benchmarks are being maintained.
Combining official estimators with indicators would certainly compromise this.” ONS therefore
uses their nowcast of GDP based on external data only as an informal guide and check for the
internal GDP estimate based on timely but incomplete information of the GDP components.
For the research and statistics branch of UNIDO, the only way to obtain the nowcast of MVA is to
use external data. To comply with the high quality and transparency requirements for official
statistics, it is therefore necessary that the proposed method uses an indicator of high quality and
that the method linking the external indicator to the nowcast is simple to understand.
In this paper we propose a nowcasting method for yearly MVA which exploits the economic
relationship between MVA and GDP, together with the availability of reliable estimates of GDP
growth rates from external sources. The proposed method is based on a parsimonious model of
MVA as a function of contemporaneous GDP and past values of MVA. We consider different
model specifications. Because the nowcasts of MVA are published by UNIDO in the International
Yearbook of Industrial Statistics, a good nowcasting method is not only a method with a low mean
absolute error, but it also needs to satisfy the following three requirements:
R1. The nowcasts produced by the method are little influenced by revisions of single observations
in the data.
R2. The nowcasts should be plausible given the past values of MVA.
R3. The nowcasting method should not only be accurate on average, but also accurate for all
countries.
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R1 is needed because UNIDO receives new MVA data every year from its different sources. This
data contains not only the values of MVA that were missing before, but also revisions of the MVA
data delivered the year before. R2 follows from the fact that UNIDO compares the past values of
MVA with the nowcast published in the Yearbook. Finally, R3 is of major importance since the
MVA nowcasts are used for economic policy making and international comparison between
countries.
The remainder of the paper is organized as follows. In Section 2 we describe the data and
methodology. In Section 3 we compare the nowcasting accuracy for the different models
considered. Section 4 presents our conclusions.
2 Data and methodology
The database maintained by UNIDO for nowcasting MVA consists of yearly values of MVA
(from 1960 to T-2, where T is the current year) and GDP (1960 to the current year) at constant
2000 prices for around 200 countries. For many countries, observations are missing at the starting
points of the series (see [13,14] for more details). The GDP series equals the actual GDP for the
earlier years, while for the most recent one or two years they are derived from the nowcasts of
GDP growth rates reported in the World Economic Outlook of the IMF (see e.g. [1] for a study on
the accuracy of these nowcasts). In contrast with MVA, the GDP data are thus available up to the
current year. Note that the MVA is strongly connected to GDP, since on the one hand MVA is a
part of the total value added of the country and thus of GDP and on the other hand the production
of value added by the manufacturing industry is driven by the demand for its products and thus by
GDP. This suggests to nowcast MVA on the basis of the estimated relationship between the
contemporaneous values of MVA and GDP. Next we consider different modeling approaches and,
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because of outliers in the data, we propose to consider not only the OLS estimator, but also a
highly robust estimation method called the MM estimator.
Model. Denote by i,t
MVA and i,t
GDP the MVA and GDP of country i in year
t
. Up to recently,
UNIDO used a nowcasting model in which the log of MVA is modeled as either a linear or a
quadratic function of the contemporaneous value of the log of GDP:
i,ti,tiii,t e GDP b a og MVA
+
+
=
logl (1)
i,ti,tii,tiii,t e GDP c GDP b a MVA +++= 2
)(logloglog , (2)
where ti
e, is white noise. The nowcast of MVA is then computed as the exponential of the fit of
this regression.
The main advantage of this model is the ease of interpretation of its parameters. The parameters
give an answer to “what if” questions. Suppose i
c is zero. Then i
b equals the elasticity of MVA
in function of GDP. If ) (ci00 <> , the elasticity of MVA to GDP tends to be larger (smaller)
for larger values of GDP than for smaller values of GDP. For 0
=
i
c, the elasticity of MVA to
GDP is constant in function of the level of MVA. For our purpose of nowcasting the level of
MVA, the interpretability of the parameters is a nice by-product, but it is not a requirement.
The disadvantage of the nowcast method based on this model is that it does not satisfy any of the
three requirements enumerated in the Introduction. The first requirement that revisions of single
observations have a small influence on the nowcasts, is violated because the nowcast is completely
determined by the estimated parameters and the contemporaneous values of GDP. The latter are
the GDP nowcasts published by the IMF in its World Economic Outlook. Small changes in their
outlook can have a large impact on the MVA nowcasts. Also R2 is not fulfilled, since under this
model the nowcast of MVA does not depend on past values of MVA and therefore the nowcast of
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MVA can be very different from the most recently observed value of MVA. The third requirement
that the nowcast of MVA should be accurate for all countries, is violated because for many
countries (i) the share of MVA in GDP is not stable and hence the parameters in (1)-(2) are likely
to be time-varying and/or (ii) the log MVA and log GDP are non-stationary series that are not co-
integrated. A final disadvantage of models (1)-(2) is that the forecast based on taking the
exponential of the fit for i,t
MVAlog is downward biased if the error term is normally distributed
[7]. In practice we observed that (without the bias correction) the MVA nowcasts have already an
upward bias and hence imposing the bias correction will only amplify this upward bias. For our
application, the bias correction is thus not useful.
As an alternative for the econometric models in (1)-(2) we consider models based on the following
general representation of MVA:
)1( ,1 tii,ti,t gMVAMVAMVA
+
=
−, (3)
where the MVA growth rate 1,1,,, /)( −−
−
=
titititi MVAMVAMVAgMVA is a time series for
which we consider next four possible specifications. The advantage of modeling the growth rate
rather than the log of MVA is that the growth rate is stationary. Moreover, by construction and
provided the GDP growth rate is not extreme, the nowcast of the present values of MVA will not
deviate much from the most recently observed value of MVA. Requirement R2 is thus satisfied.
We only consider simple linear time series models for the MVA growth rate. This choice is
motivated by the objective of having a parsimonious nowcasting model. Moreover the extensive
comparison in [10] of sophisticated nonlinear time series models for GDP growth and inflation
with simple linear time series models has shown that in general simple linear time series models
can be hardly beaten if they are carefully specified.
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We first of all consider the possibility that the growth of MVA is stationary around its mean ai,
which we allow to be different for each country:
tiiti eagMVA ,,
+
=
, (4)
where ti
e, is white noise. In the second, third and fourth model, we incorporate the relationship
between MVA and GDP growth and/or the observed persistence in MVA growth.
titiiiti egGDPbagMVA ,,,
+
+
=
(5)
titiiiti egMVAbagMVA ,1,,
+
+
=
− (6)
titiitiiiti egMVAcgGDPbagMVA ,1,,,
+
+
+
=−, (7)
where 1,1,,, /)( −−
−= titititi GDPGDPGDPgGDP and ti
e, is white noise. Note that the models
(4)-(6) are all special cases of model (7).
Estimation. The standard OLS estimator may be biased because of a violation of the assumption
of exogeneity of the regressors ti
GDP,
log and ti
gGDP, with respect to the error term and
because of the presence of outliers in the data.
Indeed, as pointed out by the referees, an endogeneity problem arises because in the regression
models the contemporaneous value of the log (growth rate) of GDP is supposed to affect the log
(growth rate) of MVA, but the value of GDP depends itself on the value of MVA. Because of this
circularity, the OLS parameter estimates can be biased. If one is interested in the behavioural
interpretation of the parameter estimates, then an instrumental variable estimator should be used.
However, for our purpose of nowcasting MVA, the OLS estimator is still preferable (even if it is
biased) since it minimizes the mean squared error of prediction and is therefore the best linear
predictor (see e.g. Proposition 2.8 in [8]).
The scatter plots of ti
gMVA, versus ti
gGDP, indicate the presence of outliers for some
countries. Fig. 1 illustrates this for the 1991–2007 data for Poland. In the transition years 1991 and
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1992 the MVA and GDP growth rates are extreme. In 1991 and 1992 the MVA (GDP) growth
rates equal -16.3% (-7.0%) and 80.2% (2.6%), respectively. For all other years the MVA (GDP)
growth rates are between -0.6% (1.2%) and 13.8% (7.1%). The 1991 and 1992 MVA growth rates
are clearly univariate outliers, but from a bivariate perspective only the 1992 observation is an
outlier with respect to the general correlation pattern observed in the data. The estimation of the
regression models using Ordinary Least Squares (OLS) is known to be problematic in the presence
of outliers. As can be seen in Fig. 1, the 1992 observation tilts the OLS slope estimate to its
position and yields a distorted estimate of the regression line fitting the bulk of the data. The OLS
estimator thus does not satisfy the requirement that the influence of single observations on the
nowcast should be small. For this reason, we also consider a robust alternative to the OLS
estimator, namely the MM estimator.
The robust MM estimator is a two-step estimator. First, it estimates the parameter vector that
minimizes the sum of the 50% smallest squared residuals. This 50% Least Trimmed Squares
(LTS) estimate then serves as the starting value for the M-estimation, where a loss function is
minimized that downweights outliers. The MM estimator has a high efficiency under the linear
regression model with normally distributed errors. Because it is initialized at the LTS estimates, it
is also highly robust to outliers (see e.g. Chapter 5 in [11]). In Fig. 1 the OLS and robust MM
regression estimates are compared. We see that, in contrast with the OLS estimator, the robust
MM estimate is rather insensitive to the outlying observations and produces an accurate fit of the
bulk of the data.
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3 Results: nowcast accuracy comparison
In Section 2 we have presented 6 econometric models and 2 choices of the estimator. This yields
thus a total of 12 possible methods for nowcasting MVA. As an additional benchmark strategy, we
also consider the nowcast based on a random walk, i.e. the strategy of setting the nowcast of MVA
equal to the observed (or predicted, if not available) value of MVA of the previous year. Table 1
presents the results of a pseudo out-of-sample nowcast accuracy comparison between the methods
for the years 2004-2007. For each of these years and for every country, we do as if the MVA data
were missing and construct the one step ahead nowcast. For each nowcasting method, we then
compute the Mean Absolute Percentage Error (MAPE) and the proportion of observations for
which the Absolute Percentage Error (APE) exceeds 10% and 20%. The MAPE measures the
average accuracy of the estimator while the proportion of observations for which the APE exceeds
10% and 20% indicate in how many cases we get a very bad estimate (cfr. requirement R3).
The analysis is based on the 200 countries in the dataset used to produce the nowcasts published in
the 2009 edition of the International Yearbook of Industrial Statistics. We present the performance
measures not only as an aggregate over all countries, but also after splitting up the sample into the
countries for which the share of MVA in GDP in 2003 was below (resp. above) its median value
of 12.6%. This allows us to check whether the choice of nowcasting method should depend on the
country’s share of MVA in GDP.
Let us first focus on the criteria evaluated on all countries. We have the following results.
1. According to all three criteria, the choice of dependent variable in the econometric model is the
most important decision when designing the nowcasting method. The MAPE of the nowcast based
on the regression of the growth rate of MVA is 3 to 4 times smaller than the nowcast based on the
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regression of the log of MVA. The proportion of observations for which the APE exceeds 10%
(20%) is approximately 5 (10) times smaller.
2. For both the OLS and MM estimator, the nowcast based on the regression model for the MVA
growth rate with intercept and contemporaneous GDP growth has the lowest MAPE.
3. According to all criteria the most accurate MVA nowcasting procedure is the one that uses the
model for ti
gMVA, with an intercept and contemporaneous GDP growth and with parameters
estimated by the robust MM estimator. Its MAPE equals 4.1% and in only 2.7% of all cases, its
APE is above 20%. This is our preferred method.
The separate evaluation of the performance criteria for the countries with share of MVA in GDP
below and above the median shows that the performance of all nowcasting methods deteriorates
(improves) for countries with a low (high) share of MVA in GDP. For both groups of countries,
our preferred nowcasting approach based on a robust estimate of the regression model for
ti
gMVA, with an intercept and contemporaneous GDP growth has the lowest MAPE. For this
method, the countries for which the APE exceeds 20% are not key economies. Moreover the
extreme prediction errors are almost all isolated in time, indicating that these errors are not due to
model misspecification but rather to large shocks in the MVA of that country.
In practice, countries for which the APE has once exceeded 10% are put on an “intensive care
list”. For the countries on that list, the research and statistics branch of UNIDO evaluates case by
case the plausibility of the nowcast produced by the regression method and, if not, expert
knowledge is used to adjust the nowcast.
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4 Conclusion
To allow cross-country comparison of the current industrial economic situation, nowcasts of
manufacturing value added are published in the International Yearbook of Industrial Statistics. We
consider nowcast methods that exploit the relationship between MVA and GDP and the fact that
accurate nowcasts of current GDP are available from external sources. The nowcast accuracy
comparison made in this paper shows that the approach using (i) the econometric model that
specifies the conditional expectation of the yearly MVA growth rate as a linear function of the
contemporaneous GDP growth rate and (ii) a robust estimation method has the best performance
of all considered methods.
Acknowledgements
We thank Christophe Croux, Markus Froehlich, two anonymous referees and the editor for helpful
comments and suggestions.
References
[1] Artis, M.J. (1996) How accurate are the IMF's short-term forecasts? Another examination of
the world economic outlook. IMF working paper 96/89.
[2] Baffigi, A., Golinelli, R. and Parigi, G. (2004) Bridge models to forecast the euro area GDP.
International Journal of Forecasting, 20, 447-460.
[3] Blake, A., Kapetanios, G. and Weale, M.R. (2002) Nowcasting EU industrial production and
manufacturing output. National Institute of Economic and Social Research.
[4] Chamberlin, G. (2007) Forecasting GDP using external data sources. Economic & Labour
Market Review, 1, 18-23.
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[5] Ferrara, L. (2007) Point and interval nowcasts of the Euro area IPI. Applied Economics Letters,
14, 115-120.
[6] Giannone, D., Reichlin, L. and Small, D. (2008) Nowcasting: The real-time informational
content of macroeconomic data. Journal of Monetary Economics, 55, 665-676.
[7] Granger, C.W.J. and Newbold, P. (1976) Forecasting transformed series. Journal of the Royal
Statistical Society B, 38, 189-203.
[8] Hayashi, F. (2000) Econometrics. Princeton University Press, Princeton.
[9] Kitchen, J. and Monaco, R.M. (2003) Real-time forecasting in practice: the U.S. treasury
staff’s real-time GDP forecast system. Business Economics, 38, 10-19.
[10] Marcellino, M. (2009) A comparison of time series models for forecasting GDP growth and
inflation. Journal of Forecasting, forthcoming.
[11] Maronna, R.A., Martin, R.D. and Yohai, V.J. (2006). Robust Statistics: Theory and Methods.
Wiley, New York.
[12] Schumacher, C. and Breitung, J. (2008) Real-time forecasting of German GDP based on a
large factor model with monthly and quarterly data. International Journal of Forecasting, 24, 386-
398.
[13] UNIDO (1996) Industrial Statistics Database: Methodological notes. UNIDO, Vienna.
[14] Upadhyaya, S. and Todorov, V. (2008) UNIDO Data Quality. UNIDO, Vienna.
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Table 1. Nowcast accuracy over the years 2004-2007 and 200 countries for six regression
specifications and the OLS and MM estimation methods. The results are presented once for
all 200 countries together, and once distinguishing between the countries with share of MVA
in GDP in 2003 below (above) its median value of 12.6%.
Dependent variable i,t
MVAlog ti
MVA,
log ti
gMVA, ti
gMVA, ti
gMVA, ti
gMVA,
ti
GDP,
log ti
GDP,
log ti
gGDP, 1, −ti
gMVA ti
gGDP,
Regressors
(besides intercept) 2
,)(log ti
GDP 1, −ti
gMVA
Estimator Mean absolute percentage error
OLS (all countries) 16.8 17.3 5.1 4.4 4.7 4.4
(MVA/GDP≤12.6%) 21.6 21.8 5.9 5.8 5.9 5.9
(MVA/GDP>12.6%) 12.2 11.7 4.4 3.3 3.6 3.3
MM (all countries) 16.2 18.7 4.7 4.1 4.4 4.7
(MVA/GDP≤12.6%) 21.1 25.0 5.8 5.5 5.9 6.3
(MVA/GDP>12.6%) 11.2 11.0 3.9 2.9 3.5 3.2
Proportion of observations for which the absolute percentage error exceeds 10%
OLS (all countries) 54.5 40.9 13.9 12.1 10.4 11.8
(MVA/GDP≤12.6%) 65.3 48.6 18.5 19.4 13.9 18.2
(MVA/GDP>12.6%) 43.2 32.9 9.1 4.5 6.6 5.1
MM (all countries) 52.1 38.7 11.7 10.5 10.8 13.3
(MVA/GDP≤12.6%) 64.5 46.2 17.1 16.8 15.0 19.9
(MVA/GDP>12.6%) 39.3 30.8 6.0 3.9 6.0 5.4
Proportion of observations for which the absolute percentage error exceeds 20%
OLS (all countries) 29.5 18.3 3.2 3.1 2.8 3.5
(MVA/GDP≤12.6%) 40.2 23.4 5.5 5.2 4.6 6.4
(MVA/GDP>12.6%) 18.4 13.0 0.9 0.9 0.9 0.6
MM (all countries) 26.6 19.1 2.7 2.7 2.7 3.2
(MVA/GDP≤12.6%) 39.0 25.7 4.9 5.2 4.3 6.1
(MVA/GDP>12.6%) 13.6 12.1 0.3 0 0.9 0.6
Note: the benchmark strategy of setting the MVA nowcast equal to the value of the MVA of the
previous year yields a MAPE equal to 6.0% and 16.5% (2.8%) of observations for which the APE
exceeds 10% (20%).
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Fig. 1 Scatter plots of the 1991-2007 yearly GDP and MVA growth rates for Poland, together
with the OLS and robust MM regression fit