SEMAINE D’ETUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 
row and column conditions satisfied. Thus, after » + 1 iter- 
ations. we shall obtain 
Sadly —1 451 A xR+L, =1 991 
(IV. 57) ("Huet out Axo tly = oe =u, 
For a sufficiently large #, the term in brackets in (IV. 57) 
can be taken as an estimate of A. This we call the RAS method. 
The Belgian tests described in [9] show that the RAS 
method works well, provided that it is possible to estimate 
the controlling totals # and v, accurately and that certain coef- 
ficients, whose determination is different from that expressed 
by the theory, can be detected and estimated directly. For 
example, there has been a general tendency for coal input-coef- 
ficients to fall as a result of the competition of electricity and 
oil; but this tendency is at work only where coal is used as a 
fuel and not where it is a raw material, as in coke ovens. Since 
the theory is incapable of handling such exceptional cases and 
since coke ovens use a lot of coal, it is important to estimate the 
input of coal into coke ovens independently, remove this 
amount of coal from the transaction table and the controlling 
totals, and add it back after the remaining items in the matrix 
have been calculated. 
An up to date matrix obtained in this way can only be 
approximate, and the next thing to do is to discuss the entries 
with experts in the different industries. In many cases signifi- 
cant improvements can be made in this way, but there will 
always remain a number of industries for which little or no 
up to date information can be obtained and which will still 
have to be handled in a theoretical way. 
For purposes of projection, the theory can only offer the 
simple method of extrapolating the coefficients along exponen- 
tial trends. Thus if A, denotes the estimated coefficient matrix 
for year 1, and if A,, denotes the coefficient matrix for a future 
year, 2, expressed at the prices of year 1, then 
(IV. 50, 
1] Stone - pag. 69