Index Numbers Summary measures of change over time

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 1

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 2

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 3

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 4