170 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA
The discussion further reflects that the theory and application
of simultaneous equations is in rapid progress along several lines
of development. Hence the research situation was not quite the
same during the Study Week as now ten months later when the
replies are edited. In my replies I shall stick to the notes and
tape record from the round table discussion; when reference is made
to later developments, they will be made by way of footnotes (1).
With gratitude and satisfaction I note that the discussants of my
paper have to a large extent been concerned with my approach of
defining interdependent systems in terms of conditional expectations;
Refs. 12, 13, 30. The ensuing approach of bi-expectational inter-
dependent systems is in an early stage of development, and so
much the more I welcome a thorough scrutiny of its foundations and
implications. For easy reference in my replies, let an interdependent
system be written :
y=0By+T 2
when defined in accordance with the classic assumptions of the
approach, and
(B,)
y =
Ey*+T z+¢
hal val
+B (y—y#)=(i—8
() Reference will be made to the following two papers:
(a) L. R. KLEIN, Problems in the estimation of interdependent systems.
Forthcoming in the « Transactions des Entretiens de Monaco 1964 »;
Centre International d’Etudes des Problemes Humains, Monaco.
‘b) H. Worp, À fix-point theorem with econometric background. Forth-
coming in « Arkiv f. Matematik ».
2]
Wold - pag. 56