By Dr. Shinichiro Nakamura (auth.)
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Additional info for An Inter-Industry Translog Model of Prices and Technical Change for the West German Economy
2 . 1 7), ( 2 • 2. 19), and (2. 2 . 21 ), j E I. , that is, from F. we can derive Q. ,t) J J J = J r . T Z. -1 'm~nLV, J Z. x j VjTZ j ], ] j E I. 1. 4. 4 price aggregator functions are indicated below the lines connecting aggregates and variables to be aggregated. 8] has shown that homothetic weak separability of fj with respect to Nand N is necessary and sufficient for the price aggregates, PP1j,···,PPnj' Pmj' Pej' Psj' and the quantity aggregates, xx 1 ]" ••• ,xxn]" xmj ' x ej ' x sj ' derived above to satisfy the condition of additive price aggregation (APA).
We can write the equality restrictions on AES in the above six groups imposed by the separability assumption as follows: 1 ) 1) We use Theorem 3 of Berndt and Christensen [1973a]. We note that f. 13) hold if and only if f. , p. 2). 2 Partition of AES (cr .. J The numbers in the first column and row refer to the numbers identifying 2n+2 inputs and the numbers inside the squares refer to the numbers identifying groups. 2. 13f) C5 o ,ik C5 o 0,1 = C5 = C5 'v'i,j EN r' 'v'k EN s' r " s, jk' 'v'i,j EN r' 'v'k ENs' r E Ie, s E IS, ,jk' 'v'i,j E Nr , 'v'k ENs' r " s, 0, C5 o r , s E Ie, ,jk' 0, jk' 'v'i, j E NO, 'v'k E Nk U NI , r , s E IS, o E 1.
J -,:;--:;-_']_0 dInG. 0 CllnQ. 36d) v .. 36d) gives value shares of capital services and labor services. 36) we obtain the following expressions of B .. 37a) Bij CllnQ. Cl 2lnG. Cllng k . m]. ]_o Cl 2lnQJ' dlnG. dIng k . ·x. 38e) v lj = Psj °Xsj pjOX j PkjOXkj pjOX j PljOX lj p. ox. J J CllnQ. = Clln J P sj , CllnQ. = Clln J Pkj , alnQ. = Clln J P lj , j E I. 39) B1ij - ~ , iEJ, jEI. We refer to B1 .. as the bias of technical change for ~J input i at the first stage. If B1 .. > 0, the value share ~J of aggregate input i increases at constant prices of five aggregates: technical change at the first stage is input i-using.
An Inter-Industry Translog Model of Prices and Technical Change for the West German Economy by Dr. Shinichiro Nakamura (auth.)