RDP 2018-08: Econometric Perspectives on Economic Measurement Appendix E: The Dutot Index Has an Unexpected Interpretation

Aside from the combination listed in Table 1, the Dutot price index corresponds to the choices f (x) = ln(x), quality_tv = z_v ∈ℝ₊₊, and Here l(·,·) is the logarithmic mean, defined as

The result draws on Balk (2008, p 193), and the proof from personal correspondence with Bert Balk (pers comm 16 March 2018).

Start with the identity

It follows that

Applying linear homogeneity of the logarithmic mean,

From here the rest is clear.