1. unido.org/statistics
Analysis of Divergence of quarterly and Annual
Index of Industrial Production
Shyam Upadhyaya, Shohreh Mirzaei Yeganeh
United Nations Industrial Development
Organization (UNIDO), Vienna, Austria
2. unido.org/statistics
The Index of industrial production
One of the important Short-term economic indicators in official statistics which
measures the changes in value added over a given period.
Computation of the IIP
The laspeyres volume index for period t
Where:
pi0: Prices for Industry sector i at the base period 0,
qi0: Quantity for industry sector i at the base period 0,
qit: Quantity for industry sector i at period t,
wi0: Relative weight of industry sector i in the base period 0, and
i: Number of industry sectors
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Reasons for divergence
• Difference in coverage and sample
• Difference in definition and variables
output replaces the value added
• Accounting period
Calendar year versus accounting year effect
• Estimation method, non-response treatment, imputation, etc.
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What is benchmarking?
• Statistical techniques which are aimed to ensure coherence
between time series data of the same target variable measured
at different frequencies, e.g., sub-annual and annual
• Underlying assumption: low frequency data tends to be more
comprehensive and accurate than high frequency data
• High frequency data (indicators) are aligned to low frequency
data (Benchmark)
• Inconsistency is detected by the movement of ratio between
Benchmark value (B) and Indicator value (I)
6. unido.org/statistics
Benchmarking methods
-Benchmarking techniques can be categorized into two approaches:
• Numerical approach:
Pro Rata Distribution, Proportional Denton Method
• Statistical modeling approach:
ARIMA-model based methods, GLS model, etc.
-Another aspect of benchmarking: Extrapolation
Linking of quarterly source data onto previous annual estimates, or
Constructing forward series by adjusting the last available benchmark level
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Pro Rata distribution
Splits the annual total based on the proportions indicated by the four (or
twelve) quarterly (monthly) observations
In mathematical phrase
Where
VAQt: estimated quarterly value added for quarter Q of year t;
IQt: indicator value in quarter Q of year t; and
AVAt: the annual value added for year t
Extrapolation:
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Advantages
• Easy to compute and interpret
• No special software is needed
• Sub-annual estimates can be derived each year independently
Disadvantages
• Smoothens sub-annual estimates only within a year
• Concentrates bias in one quarter (month) and causes the abrupt change
• As a result, it creates so called “step problem”, therefore it is not
recommended for longer time series
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The Proportional Denton Method
Allows to find VA estimates by minimizing it’s difference with indicator values
subject to the constraints provided by the annual benchmarks.
Under the restriction that
Where
VAt: derived value added estimate for quarter/ month t;
It: value of the indicator for quarter/ month t;
AVA: annual value added
T: last quarter/ month for which quarterly/ monthly source data is available
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Discussion
• Unlike Pro Rata distribution BI ratio in this method changes
gradually so there is no jump from one year to another
• Computation for estimation of quarterly/ monthly VA is more
complicated, thus requiring specialized software such as
GAMS and CPLEX
• The quarterly/ monthly estimated derive by solving a so-called
quadratic programming problem (QP)
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Discussion and Recommendations
• While seasonally adjusting the Pro Rata benchmarked series,
the significant changes in the first quarters (or first months) are
often recognized as outliers by seasonal adjustment software
• the significance of the step problem depends on the size of the
variations in the annual BI ratio
• The proportional Denton is most widely used benchmarking
method
• Denton method provides estimates which are closer to
preliminary index series than pro rating distribution on
preserves the short-term movements of the IIP time series
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• Running the QP problem for the whole series each
time a new benchmark is available
• The sub-annual data should be benchmarked to the
annual MVA as soon as it becomes available. The
benchmark time series must be revised based on the
revision policy
• Improving the estimates for the forward series and
reducing future revisions of benchmarked sub-annual
data by improving the extrapolation techniques
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• e.g., The enhanced version of proportional Denton
method introduced by IMF’s QNA manual
• UNIDO encourages developing countries to perform
the benchmarking exercise at country level
• Benchmarking the source data in earlier steps before
compiling the aggregations in highly recommended
