PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA ~ 
cerns time-horizons. Any discussion of how best to operate 
the economy so as to achieve certain ends involves comparisons 
over time and leads to a variational problem. In theory there 
is no reason to stop at any particular point in the future and 
so we are led to a consideration of an infinite time-horizon. 
Valuable insights can be gained by this method, as in RAMSEY’s 
theory of saving [34], but the weakness of the method from a 
practical point of view is that it calls for knowledge that we 
cannot possibly possess. This suggests that we should refor- 
mulate the problem with a finite, indeed fairly short time- 
horizon, a practice that is in fact adopted in all centrally plan- 
ned economies. 
c) Estimation. Having decided on the variables that are 
to enter into the model and on the forms of the relationships 
by which they are connected, the next thing to do is to estimate 
the parameters in these relationships. This may be a matter 
of simple arithmetic, as when an input-output coefficient is 
estimated by dividing the input of product j into product & 
by the output of product 2. So simple a method, however, is 
only resorted to when there is an extreme shortage of informa- 
tion; more generally statistical methods, and in particular re- 
gression analysis, are involved. In any case the estimation 
procedure that must inevitably be followed at the outset can 
be described as the econometric analysis of past observations. 
The methods of estimation available to econometricians have 
improved very considerably over the last generation. In par- 
ticular it has come to be realised from HAAVELMO’s original 
paper on the subject [16] that the fact that an economy is a 
system in which different influences may operate simultaneously 
has a bearing on the appropriate method of estimating economic 
relationships. This is called the problem of identification: in 
relating the price of a commodity to the quantity of it sold, how 
can we identify the parameter as a demand parameter, a sup- 
ply parameter or some mixture of the two; alternatively, how 
can we arrange our estimation procedure so that the estimate 
1] Stone - pag. 12