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Index Numbers

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.

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Index Numbers

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  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

  2. 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

  3. 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

  4. 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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