By Dr. Arthur Vogt, Dipl. math. János Barta (auth.)
Arthur Vogt has committed loads of his medical efforts to either individual and paintings of Irving Fisher. This publication, written with J� nos Barta, offers a great influence of Fisher's nice contributions to the idea of the associated fee index at the one hand. nevertheless, it maintains Fisher's paintings in this topic alongside the traces which a number of authors drew with admire to cost index idea on account that Fisher's loss of life fifty years ago.
"This is a hugely instructive publication on either the heritage and thought of size in economics. it is very a wealthy resource of attention-grabbing houses of kind of renowned indices and recognized males, specifically Irving Fisher, than an exact mathematical textual content at the axiomatic foundations of indices." (From the Foreword by means of Wolfgang Eichhorn)
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Extra resources for The Making of Tests for Index Numbers: Mathematical Methods of Descriptive Statistics
P;0 . Pi1)2 -0 -0 ° k -0 -0 0 i=1 q . P Pi i=1 q . 22) and the standard deviation of the quantity relatives a(q) = n n ~ qi0 . PiO( qi1 _ ~ ~ -0 -0 i=1 q . P 0 qi qi0 . 1)2 -0 -0 0 i=1 q . P qi ~ (cf. 4). 23) 1. 20) shows directly that the discrepancy between Laspeyres' and Paasche's index disappears. One can see this also in the following way: If cr(p) =0 all commodities have the same price relative. 25) equal this price relative in this case. As both Laspeyres' and Paasche's index satisfy this axiom, their difference disappears.
58) + Ppaasche We owe the following six indices to Banerjee's factorial approach (Banerjee 1985: 11): (1) p. - PLaspeyres - QLaspeyreS + 2 p. (Laspeyres Banerjee II - -Q Laspeyres ) 2 +V . 18). _ V - PLaspeyres p. 9). 18) (and, contrary to case (2), to Edgeworth-Marshall's quantity index). (6) p. - PLaspeyres + QLaspeyres + ( PLaspeyres + QLaspeyres )2 V . Banerjee IV & V - 2 2 With the "+" we call the last formula Banerjee IV and with the "-" Banerjee V. 5 Sequences of Binary Indices versus Chain Indices If there are not just two situations but more, let us say time points, then there are three ways of solving the price index problem.
43) 6. Withdrawal or entry as to trade The correlative trade index should be unaffected by the withdrawal or entry of a quantity ratio agreeing with the index. Base situation independency The ratios between various price indices (and therefore also, as we shall see, the ratios between the correlative trade indices) should be unaffected by reversing or changing the base. Thus, if the index number for 1910 is twice that for 1900, when calculated on the basis of 1860, it should remain twice, when calculated on the basis of 1870.
The Making of Tests for Index Numbers: Mathematical Methods of Descriptive Statistics by Dr. Arthur Vogt, Dipl. math. János Barta (auth.)