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Searching for the Holy Grail of Index Number Theory

Delve into the search for the elusive Holy Grail of index number theory, exploring classical and alternative approaches, ideal indices and indicators, and recent contributions to the field.

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Searching for the Holy Grail of Index Number Theory

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  1. Searching for the Holy Grail of Index Number Theory Bert M. Balk Statistics Netherlands and Rotterdam School of Management Erasmus University Washington DC, 14 May 2008

  2. The Holy Grail • … that is, • a symmetric pair of price and quantity indices that satisfy all known requirements, • … does not exist.

  3. Classical index number problem • Decompose the aggregate value ratio into two parts • V1/V0 = P(p1, q1, p0, q0) × Q(p1, q1, p0, q0). • When Q(p1, q1, p0, q0) = P(q1, p1, q0, p0) then the indices are called ideal.

  4. Alternative problem • Decompose the aggregate value difference into two parts • V1 - V0 = P(p1, q1, p0, q0) + Q(p1, q1, p0, q0). • When Q(p1, q1, p0, q0) = P(q1, p1, q0, p0) then the indicators are called ideal. • Go from additive to multiplicative decomposition and vice versa by logarithmic mean.

  5. Ideal indices and indicators • Fisher indices • Montgomery-Vartia indices (correspond to Montgomery indicators) • Sato-Vartia indices • Stuvel indices • Bennet indicators

  6. A recent contribution • Steve Casler, J. of Economic and Social Measurement 2006, developed a new decomposition. • Defects of these indices: • Not globally monotonic; • Not linearly homogeneous; • Fail time reversal test.

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