SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 
69 
foreign trade statistics. We hope to undertake this work before 
long. 
c) Intermediate demand. 
The last element needed in calculating total output is inter- 
mediate demand. With the help of a projected current input- 
output matrix we can then bring all the estimates together as 
in (IV. 27). 
The methods we have used to bring up to date and project 
the input-output coefficients are described in detail in [0]. 
Apart from complications arising from changes in classification, 
the distinction between products and industries and similar 
practical problems, our procedure can be outlined as follows. 
First, we bring the coefficient matrix estimated directly for 
1954 [47] up to 1960 by adjusting the rows and columns of the 
corresponding transaction table to agree with marginal totals 
of intermediate outputs and inputs. These adjustments are 
based on the assumption that changes in coefficients are due 
to three factors: 1) price changes; 2) substitution effects which 
influence all the elements in a given row; and 3) fabrication 
effects which influence all the elements in a given column. On 
the further assumption that the second factor operates uniformly 
along the rows of the matrix and that the third factor operates 
uniformly along its columns, the problem and its solution can 
be formulated as follows. 
Let A, denote a known, initial matrix of input-output coef- 
ficients, and let A denote the unknown matrix for period 1 
which we wish to estimate. Let p denote a price vector whose 
elements are ratios of prices in period 1 to prices in period o, 
and let » and s denote vectors of unknown constants. Then, 
on the assumptions made 
(IV. 50, 
1] Stone - pag. 6;