124 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
this does not suffice for the existence of the probability limit), 
the effects of serial correlation will not die out (or will die out 
only slowly) as we consider longer and longer lags. The con- 
clusion seems inescapable that if the model is thought to be 
unstable (and the more so, the more unstable it is), the use 
of lagged endogenous variables as instruments anywhere in an 
indecomposable dynamic system with serially correlated 
disturbances is likely to lead to large inconsistencies at least 
for all but very high lags. The lower is serial correlation and 
the closer the model to stability, the less dangerous is such use. 
Is the stability assumption a realistic one for economy-wide 
models, then? I think it is. Remember that what is at issue 
is not the ability of the economy to grow, but its ability to 
grow (or to have explosive cycles) with no help from the exogen- 
ous variables and no impulses from the random disturbances. 
Since the exogenous variables generally include population 
growth and since technological change is generally either treated 
as a disturbance or as an effect which is exogenous in some 
way, this is by no means a hard assumption to accept. While 
there are growth and cycle models in economic theory which 
involve explosive systems, such models generally bound the 
explosive oscillations or growth by ceilings or floors which 
would be constant if the exogenous sources of growth were 
constant (*). The system as a whole in such models is not 
unstable in the presence of constant exogenous variables and 
the absence of random shocks (#). We shall thus continue to 
make the stability assumption. 
Even when the stability assumption is made, however, it 
may not be the case, as we have seen, that one is willing to 
take the expression in (5.25) as negligible for all 8>>1. (In 
particular, this will be the case if serial correlation is thought 
to be very high so that the diagonal elements of A are close 
(*) See, for example, Hicks [13] and Harrop [12]. 
(*) Whether a linear model is a good approximation if such models are 
realistic is another matter 
61 Fisher - pag. 40