indexnumber

An index number is a statistical measure that describes how the value of a variable changes relative to a reference point, usually a base period or base year. Index numbers are commonly expressed as a percentage and are used to summarize trends in prices, quantities, or other economic magnitudes. They provide a simple way to compare values over time.

Construction involves selecting weights and a basket of items, setting a base period, and calculating the ratio of current values to base values. A typical price index compares the total cost of a fixed basket in the current period with the cost in the base period and multiplies by 100. Chain linking updates the basket periodically to reflect new conditions, reducing distortion from a fixed base.

Two standard families of index numbers are Laspeyres and Paasche. The Laspeyres index uses base-period quantities as weights, tending to overstate price increases when buyers substitute toward cheaper goods. The Paasche index uses current-period quantities, which can understate inflation when substitution occurs. The Fisher index, the geometric mean of Laspeyres and Paasche, is often viewed as a compromise. In practice, many statistical agencies also publish chain-linked indices that aggregate year-by-year changes.

Index numbers are widely used to monitor inflation (price indices), real output (quantity indices), wages, and financial markets (stock and bond indices). While useful, index numbers have limitations, including substitution bias, quality changes in goods, and the introduction of new products, which can distort comparisons across periods. Proper interpretation requires understanding the construction method and the context of the data.