By Dr. Shinichiro Nakamura (auth.)
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Extra info for An Inter-Industry Translog Model of Prices and Technical Change for the West German Economy
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. 2. 31c) XX sj = (xXm+e+1j, ... 32) i,jE I, , , where Vj = (Pmj'Pej,Psj,Pkj,Plj) (PPm+1 j , ..
1 ) excludes such a case in which for a given sector an input is used as material and as energy as well. 3) is a stronger condition and states that in the n producing sectors of the economy an output is used for one technological function 1)only. That is, if a particular output is used, for example, as material in sector j, then the output is used as material in all other sectors, too. : 1, and m + e + s = n. 1) Recall that we have divided intermediate inputs into three groups (material, energy and services) according to their technological function in the production process (seep.
N+mJ ,/ xm+ 1j "'-xn+m+1j h m+ 1j x. ] F. J x ej Hej < x h . m+eJ . I , f - - - SJ H . sJ ~--------------~---------------------Xlj 28 As is well known the separability assumption implies equality restrictions of AES among certain groups of inputs. Without the separability assumption the number of unknown AES between input i and input j (ifj) is (2n+2) (2n+1) /2 = 2n 2+3n+1 for each of the n sectors. Since the separability assumption imposes equality restrictions of AES among certain groups of inputs, it results in the reduction of unknown or free AES.
An Inter-Industry Translog Model of Prices and Technical Change for the West German Economy by Dr. Shinichiro Nakamura (auth.)