Index Numbers Notes

Chain Base Index Numbers

  • Base changes as time passes, adapting to new or removed items.
  • Compares current conditions effectively when fixed bases become obsolete.

Construction Steps:

  1. Link Relatives: Express each year's figure as a percentage of the preceding year using the formula: Link \ relative = \frac{Current \ year \ value}{Preceding \ year \ value} \times 100
  2. Chain Index: Multiply the link relative of the current year by the chain index of the previous year and divide by 100. The formula is: Chain \ index \ of \ current \ year = \frac{Link \ Relative \ of \ current \ year \times Chain \ Index \ of \ previous \ year}{100}
    • Note: If there is only one series, the chain base index figure is the same as the fixed base index figure.

Base Shifting

  • Involves changing the reference base of an index number series from one period to another without recomputing from original data.
  • A simple method divides all index numbers on the old base by the index number of the new base period, expressed as percentages.

Splicing

  • Converting two or more index number series with different bases into a continuous series with a common base.

  • Condition: All series must be constructed with the same items.

  • Forward Splicing: Splicing index number A to index number B

  • Backward Splicing: Splicing index number B to index number A

Deflating

  • Adjusting for the effects of changing price levels to reflect real values.

  • Purchasing power of money is the reciprocal of the price index: Purchasing \ Power \ of \ Money = \frac{1}{Price \ Index}

  • Real Wages Formula: Real \ wages = \frac{Money \ wage}{Price \ Index} \times 100