# 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.

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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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