indexnummer

Indexnummer, or index number, is a relative measure used in statistics and economics to compare changes in a variable over time with respect to a base period. Typically the base period is assigned a value of 100, and subsequent values indicate percentage changes from that base. The standard formula is I_t = (X_t / X_0) × 100, where X_t is the value in period t and X_0 is the base value.

Indices can be classified by the type of variable they track. Price indices measure changes in prices for a fixed basket of goods and services; quantity indices reflect changes in the volume of goods produced or sold; value or monetary indices combine price and quantity movements to track overall value changes. Weighted indices use weights to reflect the relative importance of different components.

Two classical methods for price indices are the Laspeyres index and the Paasche index. The Laspeyres index uses base-period quantities as weights, while the Paasche index uses current-period quantities. A Fisher index, which is the geometric mean of the Laspeyres and Paasche indices, is often used to reduce bias. Chain indices link period-to-period indices, updating weights regularly to accommodate changes in the composition of the basket or market.

Applications include measuring inflation, supporting cost-of-living adjustments, and evaluating economic performance. In finance, stock and other market indices serve as benchmarks for investment performance. Limitations of index numbers include sensitivity to the base period, choice of items, substitution effects, and quality changes in goods or services. Data revisions and methodological differences can also affect comparability over time.

Example: the consumer price index (CPI) tracks changes in the average price level of a fixed basket of consumer goods and services.