72 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28
with
0
E(y,lz,
RP -
We note the following general features of vector regression
systems:
1) The system contains one (and only one) explanatory relation
for each of the current endogenous variables;
2) In each relation, all of the explanatory variables are pre-
determined;
3) Each relation is an eo ipso predictor subject to random
disturbance.
[.2. Causal chain (CC-) systems.
The general formula for causal chain (also known as recur-
sive) systems is in the linear case given by
(10)
Vir=Li(y14 Vars +, Vici Nieto Vio» ++"5 Xp Xi_ 1» …)+U;,
where ¢=1, ..., n; the functions L; are linear; and L; is as-
sumed to be an eo ipso predictor of y., for all 7 and ¢,
(IT) Elyse Yatr wor Victts Verts Vr-ns +05 Xp Xp_45 ++)
Lyi Var oes Vi-1,e5 Veste Ve-2 +03 Xt oon)
To give the system (10)-(11) in matrix form we write
à" +B 3
12)
with
E(yly", 2)=A y, -B Z,
2] Wold - pag. 8