1 index numbers summary measures of change over time or differences in levels in set of related...
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Index Numbers
• Summary measures of change over time or differences in levels in set of related variables– Price index numbers – output and input price index and terms of trade effects– Output and input index numbers
• Laspeyres, Paasche, Fisher and Tornqvist are commonly used.
• Fisher and Tornqvist index have desirable properties– Economic: Exact and Superlative– Axiomatic: Satisfy most of the properties, not circularity test– There does not exist an index number formula which satisfies all the desirable
properties
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Index Numbers
• Comparisons involving several periods– Use chained index numbers with Fisher or Tornqvist
• Multilateral spatial comparisons– Need transitivity – Fisher and Tornqvist do not satisfy this
property
– Use EKS method to compute transitive indexes• Note that EKS can be used on binary comparisons based on Fisher
or Tornqvist indexes
• Use of index numbers for productivity comparisons– TFP index = Output index/Input index
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Index Numbers
• Log of Tornqvist index has simple interpretation– Growth rate in output less growth rate in input
– Similar to the Solow residual
• Index numbers play a major role in reducing the dimensionality of data– In the case of multiple outputs and inputs, there is a
problem of degrees of freedom
– Need to aggregate data into a small number of aggregates• Crops and livestock aggregates in agriculture formed from 180
primary commodities
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Index Numbers
• Choices for quantity index numbers– Direct measurement of quantity index numbers
• Use the standard formulae
• Use Malmquist approach – here Fisher and Tornqvist indexes are appropriate
– Quantity measures are obtained as deflated value aggregates – value aggregates at constant prices
– Direct or indirect measures – which one to use?• Decision needs to depend upon the availability of data
– Many times only value aggregates are available along with information on price level differences
– Reliability of the index numbers – if price relatives show more variability then direct quantity indexes are preferred and vice versa