Introduction to Standard Indices

This chapter introduces standard indices used by statistical agencies and in academic research. It covers widely used price indices like the Laspeyres and Paasche indices, which rely on price and quantity data of various commodities over time. The construction of price indices typically involves a two-stage aggregation process: lower level (elementary) and upper level aggregates. Widely used index number formulas for elementary price indices include the Carli, Dutot, and Jevons indices. The chapter discusses their mathematical properties and practical applications, noting that the choice of formula significantly impacts the final index value. The Laspeyres and Paasche indices are introduced for upper level aggregation, where the Laspeyres index uses base-period weights and the Paasche index uses comparison-period weights. The chapter also covers quantity indices and their calculation methods, emphasizing the importance of the factor reversal test. The chapter concludes with a discussion on alternative index formulas like the Fisher, Walsh, Marshall–Edgeworth, Törnqvist, Sato–Vartia, Theil, and Young indices, highlighting their theoretical properties and practical implications. The Fisher index, in particular, is noted for its theoretical advantages but is less commonly used due to data collection difficulties.