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Analysis of Divergence of quarterly and Annual Index of Industrial Production

Shyam Upadhyaya, Shohreh Mirzaei Yeganeh

United Nations Industrial DevelopmentOrganization (UNIDO), Vienna, Austria

unido.org/statisticsThe 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, andi: Number of industry sectors

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Divergence of sub-annual and annual index series

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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:

unido.org/statisticsEstimation of monthly value added using Pro Rata distribution (India)

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IIP and the Derived Benchmarked Monthly VA using Pro Rata Distribution (India)

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Benchmark-to-Indicator Ratio and the Step Problem (India)

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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

WhereVAt: 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/statisticsEstimation of monthly value added using Proportional Denton Method (India)

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unido.org/statisticsIIP and the Derived Benchmarked Monthly VA using Denton Method (India)

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Benchmark-to-Indicator ratios (India)

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

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Thank you for your attention!