productivity growth to data based upon discrete time periods To allow consideration of more finely differentiated inputs, one can assume that aggregate capital and labour input are, in tun, constant returns to scale translog indices of sub-inputs: 5 (2.4)K=expla InK,+diNk,+.+o Ink (n}2+Bn)nk2)+…+B(n L= exp(afInE1+吃lnL2+…,+a Bi(nL,+Bi(nL,(nL BL, (nL] First differencing the logarithms of these translog indices provides a measure of the growth of aggregate capital and labour input as weighted averages of the growth rates of their sub-inputs (2.5) K, (T) Li T) K(T-1) KT-1) e(m)+6(T-1) nd where the 0,'s denote the share of each sub-input in total payments to its aggregate factor. In a manner analogous to the continuous time Divisia analysis, these indices adjust for improvements in the"quality"of aggregate capital and labour input by, to a first order approximation, weighting the growth of each sub-input by its average marginal product The appropriate measure of capital and labour input is the flow of services emanating from those inputs. For labour, one can reasonably assume that the flow of services is proportional to total hours of work, i. e L, (T)=mH,(T),with With similar restrictions on parameter values. 7