Knowledge that Transforms

Decentralized decision making is consistent if it is executed without cost (i.e., without a loss of output or utility). Consistency requires that the objective function be appropriately structured. In this paper, a hierarchical decision making structure is rationalized by an objective function which combines some of the properties of homothetic separability and asymmetric separability. THIS PAPER EXAMINES consistent decentralized decision making in a hierarchical structure. The decision making process is rationalized by a class of objective functions which combines some of the properties of homothetic separability [1, 3] and recursive, or asymmetric, separability [5,8]. We refer to these functions as homothetically recursive. After introducing our basic notation and definitions, we prove a representation theorem for homothetically recursive functions in Section 1. In Section 2 we prove two duality theorems for homothetically recursive structures. A recursively decentralized decision making process, described in Section 3, is made manifest in the structure of the associated cost function. The analysis is carried out in the context of the theory of the firm but other applications are discussed briefly in Section 4.

James L. Kenkel, Some Small Sample Properties of Durbin's Tests for Serial Correlation in Regression Models Containing Lagged Dependent Variables, Econometrica, Vol. 42, No. 4 (Jul., 1974), pp. 763-769

The purpose of this paper is to give a systematic account of the significance that antagonism among opinions of individuals has on the theory of social choice. We define an intensity of antagonism among individuals and an index of possibility of constructing social welfare functions, and show that when there is less antagonism in a society, then there is more possibility of constructing social welfare functions. Since antagonism is an opposite concept to similarity, this relation can be viewed as a formal realization of Arrow's assertion [1, Ch. 7] that sets preference similarity as the basis of social welfare judgement.

[Cette note discute les conditions d'existence d'un noyau non vide dans une économie de propriété privée où des possibilités de production sont associées à chaque coalition en fonction de sa composition. On étudie les relations entre noyau et équilibre concurrentiel dans le cas particulier où il existe un ensemble d'entreprises et où l'ensemble de production d'une coalition est égal à la somme des ensembles de production des entreprises dont les membres de la coalition possèdent une majorité des parts.]

[Arrow's impossibility theorem can be viewed as requiring that each subset of two social alternatives be a potential feasible subset or environment, with transitive and complete social choices over these subsets for each profile of individual preference orders. The feasibility assumption for every two-alternative subset is relaxed with consequent changes in the social ordering condition. An Arrow-type impossibility result still obtains when the set of social alternatives is the union of two disjoint sets, each of which has two or more elements, and when \{x, y\} is feasible whenever x is from one set and y is from the other. Variants of the basic theorem are included, one of which requires that strict binary social choices be acyclic.]

[This paper extends the single equation regression model with the truncated dependent variable considered by Tobin [10] and Amemiya [1] to multivariate and simultaneous equation models and proposes a computationally simple consistent estimator.]

In applications of linear regression analysis, the unknown error covariance matrix has to be somehow estimated. This can lead to biased estimates of the covariance matrix of the regression coefficients. Since such bias is difficult to eliminate completely, its sensitivity to alternative estimates of error covariances is studied by Watson, Theil, Malinvaud, and others with the help of bounds on the bias derived under certain assumptions. This paper gives similar bounds under less restrictive assumptions, and illustrates them in the context of heteroscedasticity and autocorrelation problems. In particular, for the first order error autocorrelation coefficient of p the upper bound on proportionate bias is shown to be reasonably approximated by (1 + p)/(l - p) - 1.

[This paper proposes a method for measuring the numerical value of the conjectural variation which has been a key concept in oligopoly theories. The statistical property of the estimator for the conjectural variation is examined and two statistical tests are presented. One is a test for the hypothesis that the conjectural variation is a specified value. The other is designed for the hypothesis that there is a certain type of collusion among oligopoly firms. These are applied to the Japanese flat glass industry.]