Different definitions of noncausality (according to Granger, Sims, Haugh and Pierce,...) are analyzed in terms of orthogonality in the Hilbert space of square integrable variables. Conditions, when necessary, are given for their respective equivalence. Some problems of testability are mentioned. Finally noncausality is also analyzed in terms of rational expectations, extending previous results of Sims. (Author)

[We propose a new criterion for equilibria of extensive games, in the spirit of Selten's perfectness criteria. This criterion requires that players' strategies be sequentially rational: Every decision must be part of an optimal strategy for the remainder of the game. This entails specification of players' beliefs concerning how the game has evolved for each information set, including informaiton sets off the equilibrium path. The properties of sequential equilibria are developed; in particular, we study the topological structure of the set of sequential equilibria. The connections with Selten's trembling-hand perfect equilibria are given.]

In this note the relationship between alternative concepts of noncausality is analyzed using the tool of conditional independence among a-fields. (For the reader who is unfamiliar with this technique, the Appendix sketches the proofs and the basic technical apparatus, along with some basic motivations.) Furthermore, the relationship between the concepts of noncausality and transitivity is made explicit in order to facilitate, in econometric modelling, the use of results already obtained in sequential analysis.

T. A. Yancey, G. G. Judge, M. E. Bock, Wallace's Weak Mean Square Error Criterion for Testing Linear Restrictions in Regression: A Tighter Bound, Econometrica, Vol. 41, No. 6 (Nov., 1973), pp. 1203-1206

Treatment for depression is complex, requiring decisions that may involve trade-offs between exploiting treatments with the highest expected value and experimenting with treatments with higher possible payoffs. Using patient claims data, we show that among skilled doctors, using a broader portfolio of drugs predicts better patient outcomes, except in cases where doctors' decisions violate loose professional guidelines. We introduce a behavioral model of decision making guided by our empirical observations. The model's novel feature is that the trade-off between exploitation and experimentation depends on the doctor's diagnostic skill. The model predicts that higher diagnostic skill leads to greater diversity in drug choice and better matching of drugs to patients even among doctors with the same initial beliefs regarding drug effectiveness. Consistent with the finding that guideline violations predict poorer patient outcomes, simulations of the model suggest that increasing the number of possible drug choices can lower performance.