By Dr. Shinichiro Nakamura (auth.)
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Extra resources for An Inter-Industry Translog Model of Prices and Technical Change for the West German Economy
Finally, AES in Group 8 refer to AES between capital services and labor services. The number of AES in Group 8 is one. 2. 1. Now we are ready to state the implications of the separability assumption in terms of the number of free AES. The assumption of separability of the production f~nc tion fo' 0 EI,with respect to the partition Nand N imposes equality restrictions on AES belonging to the groups 2, 3, 4, 5, 6 and 7 defined above. That is, the separability assumption reduces the number of free AES in the groups 2, 3, 4, 5, 6 and 7.
27), Z. , are used as J nJ parameters in the third stage optimization problem. For the formulation of the three stage procedure itself weak separability of f. with respect to Nand N is necessary J and sufficient (Blackorby et al. 2). 26). 25) are necessary and sufficient for the consistency of the three stage optimization procedure. 2. 31c) XX sj = (xXm+e+1j, ... 32) i,jE I, , , where Vj = (Pmj'Pej,Psj,Pkj,Plj) (PPm+1 j , .. 29). One remarkable feature of this three stage optimization procedure is that with the advance of stages (from the first to the second, and from the second to the third stage) the degree of decentralization and the number of parameters used in solving the optimization procedure increases 1 ).
H . (X . 8), 'Ij E I. Hej is the quantity aggregator function of energy inputs used in sector j, and gives the aggregate quantity of energy inputs used in sector j, say x . 8), 'Ij E I. H . 11) x sj Hsj (hm+e + 1 j (Xm+e + 1 j ,t) , •.. 8), 'Ij E I. Finally, F. is the production function in terms of five ] aggregates. , capital services: (K), labor services (L), energy (E), material (M), and service (S). We refer to F j as the KLEMS production function. 1. 1 aggregator functions are indicated below the lines connecting aggregates and variables to be aggregated.
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