Index Theory and Price Statistics

Proposition of a General Formula for Price Indices

“…(8)). Commensurability is a very powerful property but this is an important test-when it is satisfied, the index function can be expressed in price relatives and then it is a function of 3N (instead of 4N ) variables (see von der Lippe, 2007). Certainly the set of functions satisfying (5) is not empty, for example we could assume f j X Y = c j X + Y for j = 1 2 m and some c j ∈ R + .…”

“…I P Q s Q t P s kP t = kI P Q s Q t P s P t (11) Downloaded by [New York University] at 12:50 07 December 2014 is said to be linear homogeneous 4 (homogeneity of degree +1) in prices at time t. There is a relationship between linear homogeneity, proportionality and mean value property, as monotonicity is related to all of these properties (see von der Lippe, 2007).…”

“…Białek theoreticians- Eichorn and Voeller (1976)-introduced a more generally acceptable system (EV) of five, and later also of four axioms: strict monotonicity, price dimensionality, commensurability, identity, and (optionally) linear homogeneity (see also Białek, 2005;von der Lippe, 2007). These five axioms imply other tests like proportionality (identity plus linear homogeneity) or quantity dimensionality (price dimensionality plus commensurability)-see von der Lippe (2007).…”

“…Depending on the type of an economic problem we may also use one of the following indices: the Fisher ideal index (see Fisher, 1992), the Törnqvist index (Törnqvist, 1936), the Marhall-Edgeworth index, and a number of other indices (see Shell, 1998;von der Lippe, 2007). Statistical indices are very useful in economy (see Moutlon et al, 1999).…”

“…Balk (1995) wrote about the axiomatic price index theory and Diewert (1978) showed that the Törnqvist index and the Fisher ideal index approximate each other. But it is really hard to choose the best one from the statistical indices (Dumagan, 2002;von der Lippe, 2007)). The choice of an index depends on the information we want to obtain.…”