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