SEMAINE D'ÉTUDE SUR LE ROLE DE L ANALYSE ECONOMETRIOUE ETC. 
Go. 
The final judgment on the performance of the process must 
be based on the criterion function. If we confine ourselves tc 
the first fi'ly years, the function can be written in the form: 
6.1) 
the expectation of which we try to minimize. The values whic 
the function (6.1) takes in the 50 x 3 cases are subject to a 
distribution and will therefore differ from case to case. How- 
aver, the distribution of the performance measures (6.1) is not 
very exciting. A more useful measure, particularly in the con- 
text of the present paper, is a relative performance measure 
describing how well the policy has done compared with two 
alternative approaches: the « perfect » approach, which fore- 
casts correctly all future values which the chance mechanism 
will produce, and the « naive » approach, which does not use 
the information which is available to the decision maker at 
the moment when he has to make his decision. The former 
approach is based on equation (5.1), its v’s being generated 
by the ¢’s of (5.7) as these were actually generated by the 
normal chance mechanism. [Strictly speaking, (5.1) and (5.7) 
require that we use an infinite number of ¢’s, which is somewhat 
anpractical, but the 25 which have been generated beyond the 
50 years of the experiment are sufficient for our purpose]. 
The second, naive approach is based on (5.10) except that the 
last term (in v, - v) is deleted. That is, the decision maker 
just acts as if the rate of increase of the population has been 
and will remain constant at the level v. The savings ratio of 
the last policy is not affected by any random element and can 
therefore be computed for any year ¢ at the beginning of the 
Theil - pag. 21