unido.org/statistics analysis of divergence of quarterly and annual index of industrial production...
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Analysis of Divergence of quarterly and Annual Index of Industrial Production
Shyam Upadhyaya, Shohreh Mirzaei Yeganeh
United Nations Industrial Development
Organization (UNIDO), Vienna, Austria
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The Index of industrial productionOne 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)
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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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IIP and the Derived Benchmarked Quarterly VA using Pro Rata Distribution (China)
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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 MethodAllows 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)
unido.org/statisticsDiscussion 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