State the chief characteristics of Index Numbers.

Chief Characteristics of Index Numbers

Index numbers possess several key characteristics that determine their reliability and usefulness. These can be broadly categorized into characteristics related to their formula, base year selection, weighting methods, and other important properties.

1. Formula-Based Characteristics

• Time Reversal Test: This test states that if we multiply two index numbers – one calculated for the forward period and another for the backward period – the product should equal 100. Mathematically, P₀₁ x P₁₀ = 100, where P₀₁ is the price index from period 0 to 1 and P₁₀ is the price index from period 1 to 0.
• Factor Reversal Test: This test asserts that if we multiply a price index and a quantity index, the result should equal the value index. This ensures consistency between price and quantity changes and their impact on overall value.
• Circular Test: This test involves calculating index numbers for three consecutive time periods. The product of these three index numbers should equal 100. This ensures consistency across multiple periods.

2. Base Year Selection Characteristics

• Choice of Base Year: The selection of the base year is crucial. Ideally, the base year should be a normal year, free from significant economic disruptions like wars, famines, or major policy changes.
• Representativeness: The base year should be representative of the overall economic conditions and the items included in the index.
• Fixed Base vs. Shifting Base: Index numbers can be calculated using a fixed base year (e.g., 1990-91) or a shifting base year (chain-linked indices, where the base year changes periodically). Shifting base indices are useful for long-term comparisons as they mitigate the effects of outdated base year structures.

3. Weighting Method Characteristics

• Weighting Schemes: Items included in the index are assigned weights based on their relative importance. Common weighting methods include:
  • Laspeyres Index: Uses base year quantities as weights. Formula: Σ(P₁/P₀)Q₀ / ΣQ₀. Tends to overstate inflation.
  • Paasche Index: Uses current year quantities as weights. Formula: Σ(P₁/P₀)Q₁ / ΣQ₁. Tends to understate inflation.
  • Fisher’s Ideal Index: The geometric mean of Laspeyres and Paasche indices. Considered the most accurate but computationally intensive. Formula: √[(Laspeyres Index * Paasche Index)].
• Impact of Weights: The choice of weights significantly impacts the index value. Different weighting schemes can lead to different conclusions about price or quantity changes.

4. Other Important Characteristics

• Purpose of the Index: The purpose for which the index is constructed influences its characteristics. For example, a Consumer Price Index (CPI) focuses on goods and services consumed by households, while a Wholesale Price Index (WPI) focuses on goods traded at the wholesale level.
• Scope and Coverage: The scope of the index (e.g., geographical area, items included) determines its applicability and relevance.
• Data Quality: The accuracy and reliability of the data used to construct the index are paramount.

Example: The Consumer Price Index (CPI) in India, released by the National Statistical Office (NSO), uses 2012 as the base year for CPI-Rural and CPI-Urban. It employs a weighted average of prices for a basket of goods and services, with weights determined by the household consumption expenditure survey. The CPI is a crucial indicator for measuring inflation and adjusting wages and allowances.