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 V 1 /V 0 = P(p 1, q 1, p 0, q 0 ) × Q(p 1, q 1, p 0, q 0 ). When Q(p 1, q 1, p 0, q 0 ) = P(q 1, p 1, q 0, p 0 ) then the indices are called ideal.

4. Alternative problem Decompose the aggregate value difference into two parts V 1 - V 0 = P(p 1, q 1, p 0, q 0 ) + Q(p 1, q 1, p 0, q 0 ). When Q(p 1, q 1, p 0, q 0 ) = P(q 1, p 1, q 0, p 0 ) 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.