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