Index Numbers

• Meaning and Definition

  • Definition of Index Number
  • Statistical device measuring relative changes over time/space
  • Often called the barometer of economic activity
  • Expressed in percentages (usually drop the % sign)

• Characteristics and Features

  • Specialized averages
  • Expressed in percentages
  • Measures relative changes (not absolute)
  • Compares changes over time or between places

• Types of Index Numbers

  • Wholesale Price Index (WPI)
  • Consumer Price Index (CPI) / Cost of Living Index
  • Index of Industrial Production (IIP)
  • Agricultural Production Index
  • Import-Export Index (Terms of Trade)

• Methods of Constructing Index Numbers

  • Simple (Unweighted) Index
    • Simple Aggregative Method
    • Simple Average of Price Relatives Method
  • Weighted Index
    • Weighted Aggregative Method
    • Weighted Average of Price Relatives Method

• Important Formulas (Weighted Aggregative)

  • Laspeyres's Method (Uses Base Year Quantities, $q_0$)
  • Paasche's Method (Uses Current Year Quantities, $q_1$)
  • Fisher's Ideal Method (Geometric mean of Laspeyres and Paasche, Golden Rule)

• Tests of Adequacy of Index Numbers

  • Unit Test
  • Time Reversal Test ($P_{01} \times P_{10} = 1$)
  • Factor Reversal Test ($P_{01} \times Q_{01} = V_{01}$)
  • Circular Test ($P_{01} \times P_{12} \times P_{20} = 1$)

• Consumer Price Index (CPI) Construction

  • Selection of consumers/class
  • Family Budget Enquiry
  • Obtaining price quotations
  • Calculation using weighted average of price relatives: $CPI = \frac{\sum (R \times W)}{\sum W}$

• Problems in Construction

  • Selection of base year (must be normal)
  • Choice of formula
  • Selection of items/commodities
  • Collection of accurate prices

• Uses and Significance

  • Measuring purchasing power of money
  • Formulating policies (wage, taxation, DA)
  • Studying trends in economic activities
  • Deflating nominal values to real values