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TLS 
the terms in the expansion for W(1) to be negligible for : 
greater than some value, perhaps for 6>1. 
All this, however, has leaned a bilt heavily on the stability 
of DB. If that matrix has a latent root greater than unity in 
absolute value, then part of the reason for assuming that the 
right-hand side of (5.25) is negligible even for high values of 9 
has disappeared. Of course, it is the case that the diagonal 
elements of A are known to be less than unity in absolute 
value, so that the infinite sum involved in W(1) may still con- 
verge. However, such convergence is likely to be slow in an 
unstable case and may not occur at all, so that the effects of 
serial correlation are even more serious than in the stable 
case. Clearly, the stability assumption requires additional 
discussion at this point. 
The usual reason for assuming stability of the dynamic 
model being estimated is one of convenience or of lack of 
knowledge of other cases. Since the unstable case tends to lead 
to unbounded moment matrices, the usual proofs of consistency 
of the limited-information estimators tend to break down in 
that circumstance. Indeed, maximum-likelihood estimators are 
presently known to be consistent only in the stable case and 
in rather special unstable cases (*). It is therefore customary 
to assume stability in discussions of this sort. For present pur- 
poses, even if limited-information estimators are consistent in 
unstable cases and even if the Generalized Proximity Theorems 
which guarantee small inconsistencies for sufficiently good 
approximations also hold (¥), the approximations which we 
are now discussing are relatively unlikely to be good ones in 
such cases. Even if the existence of W(1) is secured by as- 
suming that the dynamic process (2.1) begins with non-stoch- 
astic initial conditions at some finite time in the past (and even 
(*) For example, if all latent roots are greater than unity in absolute 
value. See ANDERSON [1]. J. D. SarGaN has privately informed me that 
he has constructed a proof of consistency for the general case. The classic 
paper in this area is that of MANN and Warp [21] 
(47) See FrisHeEr [8 
v| Fisher - pag. 36