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Extra info for An Inter-Industry Translog Model of Prices and Technical Change for the West German Economy
13d) refers to AES in Group 5, and reduces the number of free AES in the group from 4es to 1. 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.
TXX ej eJ XX . eJ eJ eJ T ( 2 • 2. 2 8 c) max [H . , t) I PP sj XX sj XX,. T maxl h .. ( X .. ,t) I p1 X .. 1J 1J X .. ·x sJ sj pp .. ·xx .. 1J 1J I ], ] I ], j EI I j E I, j EI I i,j E1. 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.
The use of separability assumption and the resulting imposition of equality restrictions of AES is the price we have to pay for using the trans log function or more generally flexible functional forms. In this study we follow the approach of Hudson and Jorgenson  and employ a flexible functional form in the specification of the sectoral price function gj. This implies the necessity of employing certain separability assumptions of technology to make the econometric 1) The translog function belongs to the family of flexible functional forms.