What is the difference between Laspeyres, Paasche, and Fisher’s Ideal Index?

Answer:

Index numbers are formulas used to measure relative changes in prices or quantities over time.

1. Laspeyres Index:

   • Uses base-year quantities as weights.​​

   • Advantage: Easy to compute (quantities fixed at base year).

   • Limitation: Tends to overstate inflation (does not account for substitution effect).

2. Paasche Index:

   • Uses current-year quantities as weights.

   • Advantage: Reflects current consumption pattern.

   • Limitation: Requires current-period quantities → data collection difficult. Also, tends to understate inflation.

3. Fisher’s Ideal Index:

   • Geometric mean of Laspeyres and Paasche.

   • Advantage: Balances the upward bias of Laspeyres and downward bias of Paasche.

   • Limitation: Computation heavy, requires both base and current data.

👉 In short:

• Laspeyres = Base year weights → upward bias.

• Paasche = Current year weights → downward bias.

• Fisher = Geometric mean → balanced.

Cross-question:

Why is Fisher’s index often called the “ideal” index?

• Reasons:

  1. It satisfies most test criteria (time reversal, factor reversal, circular test).

  2. It eliminates the biases of Laspeyres and Paasche.

  3. Considered theoretically superior, hence called “ideal”.

  4. Recommended by economists like Irving Fisher himself.

• Practical issue: Despite being “ideal,” Fisher is rarely used in official statistics due to data demands (needs both q₀ and q₁). Instead, countries often prefer Laspeyres-type indexes (like CPI).

👉 So, Fisher is “ideal” in theory, but Laspeyres is more practical for real-world policymaking.