Knowledge that Transforms

[Introduction] To a large extent the cooperative theory of games has an altogether different appearance from the noncooperative theory. The noncooperative theory generally deals with games in either extensive form or normal form, while the cooperative theory is usually described in characteristic function form. One of the central concepts in the cooperative theory is that of the core, which is the set of utility allocations which no coalition can improve upon. This notion of the core and of the characteristic function form of a game depends heavily on the existence of a utility representation for players' preferences. Recently Gale and Mas-Colell [3] and Shafer and Sonnenschein [6] have proven theorems on the existence of a Nash equilibrium for noncooperative games in normal form in which the players' preferences over strategy vectors are not necessarily complete or transitive and so may fail to have a utility representation. Thus it might appear that the noncooperative theory is applicable in environments where the cooperative theory is not. In order to formulate theorems in the cooperative theory of games which can be applied to environments in which players may have nonordered preferences, the characteristic function must be reformulated in terms of physical outcomes as opposed to utility outcomes. The players' preferences can then be expressed in terms of the physical outcomes without the use of a utility function.

[The model considered is a two-equations model consisting of a binary choice equation and a regression equation. Tests for the bivariate normal distribution are derived for the truncated samples case and the censored samples case. The tests are Lagrangean multiplier tests for testing the bivariate normal distribution within the bivariate Edgeworth series of distributions. Simple intuitive interpretations for the statistics are provided.For the truncated case, the test compares with the estimated differences between some sample moments of order (r,s) for which r + s extgreater 2 and the corresponding hypothesized moments of the disturbances. For the censored case, the test is equivalent to the testing of some sample semi-invariants for which r + s extgreater 2 are zeros.]

[A generalization of the Nash bargaining solution is defined for two-person bargaining problems with incomplete information. These solutions form the smallest set satisfying three axioms: a probability-invariance axiom, an extension (or independence of irrelevant alternatives) axiom, and a random-dictatorship axiom. A bargaining solution can also be characterized as an incentive-compatible mechanism that is both equitable and efficient in terms of some virtual utility scales for the two players.]

Develops a specification error test sensitive to negelected heterogeneity, which is viewed as causing parameter variation, by deriving a score test of the hypothesis that parameters have zero variance. The test turns out to be the Information Matrix test and is a useful diagnostic for researchers using cross-sectional or longitudinal data to estimate models of individual economic agents behavior. -from Author specification error neglected heterogeneity parameter variation Information Matrix test

This paper examines the implications of imposing a weak aggregation condition on inequality indices, so that the overall inequality value can be computed from information concerning the size, mean, and inequality value of each population subgroup. It is shown that such decomposable inequality measures must be monotonic transformations of additively decomposable indices. The general functional form of decomposable indices is derived without assuming that the measures are differentiable. The analysis is suitable for extension to the many other kinds of indices for which a similar relationship between the overall index value and subaggregates is desirable.

This paper investigates the performances of dynamic econometric models in relationship to their size. More precisely, the central issue addressed in this paper is whether there exists a procedure that systematically associates with every large-scale model a small-scale model that constitutes a reasonably good approximation of the large-scale model. Such a procedure is shown to exist for both endogenous and exogenous variables. This result is applied to show that a model with approximately twenty endogenous and four hundred exogenous variables can do almost as well as the current models with thousands of variables. This result also implies that a necessary condition for small models of twenty to thirty variables to perform satisfactorily is that only regular patterns of variations for the exogenous variables be considered. THE DEVELOPMENT OF HIGH-SPEED POWERFUL COMPUTERS has enabled econometricians and model makers to design operational large-scale models, the idea being that the complexity of reality is better described by models with the largest feasible number of unknowns and equations than by smaller size models. Nevertheless, the costs involved in operating large-scale models combined with their intrinsic complexity has led many econometricians to favor, when dealing with specific questions, the use of smaller size models which can be operated with comparatively less difficulties. This paper investigates the relationships that can be established between the size of a dynamic econometric model, i.e. the number of its endogenous and exogenous variables, and its accuracy through time. This paper also addresses another question related to the general theme of the size of econometric models, namely the existence of procedures that can systematically associate with every large-scale model a small-scale model that provides a reasonably good approximation of the large-scale model. An important feature of the analysis developed in this paper is the focus put on the local point of view and on the consequences that can be derived from the local approach. Local here means that only the behavior of the model in small neighborhoods of suitably chosen points belonging to some, possibly largedimensional, Euclidean space is considered. Though the validity of the local point of view might be questioned when dealing with the most general problems, it seems to be particularly well-suited to the current practice of econometric modelling. The strength and the main interest of the local point of view is that it enables one to define concepts of approximation up to arbitrary orders that apply to econometric models, approximations being taken here in a sense that is