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Extra info for An Inter-Industry Translog Model of Prices and Technical Change for the West German Economy
P 2n and xx 1 ,,··,xx, ). J nJ 1) For the concept of decentralization, see Blackorby et al. 177-179]. ), which are used as parameters at the J ~ • third stage, are endogenous variables at the second stage. We can state that as far as quantity variables are concerned the optimization problem at the first stage is the only problem whose parameters referring to quantities are exogenous variables. The parameters referring to quantities at the second- and third stage are all endogenous variables.
13f) refers to AES in Group 7, and reduces the number of free AES in the group from 4n to 6. As a whole the separability assumption reduces the number of 2 n + m2 + e 2 + s2 free AES from 2n +3n+1 to 2 + 10. We note that the separability assumption results in a remarkable reduction in the number of free AES in Group 3 (from 4m(n - m) to 2), in Group 5 (from 4es to 1), and in Group 7 (from 4n to 6). 1. 2. 3 Division of free AES Under the Separability Assumption int0 Eight Groups: 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 the groups.
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.
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