Transcript Slide 1

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
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