Knowledge that Transforms

An axiomatization is presented for a Savage-type conditional subjective expected utility model. The axioms consist of extensions of the Herstein-Milnor [11] axioms for measurable utility, a generalization of an averaging condition in Bolker [4], and several structural conditions. The structural conditions are examined in some detail, and examples are given to show what happens to the numerical model when they do not hold. The numerical model expresses the utility of an act (or mixed act), given an event, as a weighted sum of the utilities of the act given events that partition the initial event, the weights being personal probabilities for the partition events conditioned on the initial event. The theory is compared to Savage's theory [18] and to a version of the theory of Luce and Krantz [14] for conditional expected utility. 1. DECISION UNDER UNCERTAINTY THE PREDICAMENT BETWEEN mathematical tractability and situational reality that is characteristic of mathematical models in the behavioral sciences is epitomized in the axiomatizations of subjective expected utility models. These axiomatizations include structural conditions that facilitate the derivation of the desired numerical representations for preference. Unfortunately, actual situations of decision making under uncertainty often fail to exhibit the structural properties that occur in the axiomatizations. Thus there is real concern about the applicability of such models to realistic decision situations. As might be expected, decision theorists have attempted to alleviate this predicament by weakening the structural conditions while maintaining the ability to derive the desired model from the axioms. An early move in this direction was made by Suppes [21] in his alternative to Savage's axiomatization [18]. The more recent axiomatizations of Bolker [3 and 4], based on Jeffrey's decision model [12], and of Pfanzagl [15 and 16] and Luce and Krantz [14], continue this line of research. The present paper is a further effort in this direction. To understand its approach we shall first review briefly some other theories. The formulation of the paper is set in the context of Savage's states-of-the-world approach to decision under uncertainty, and I shall therefore focus the discussion within this context. We suppose that the decision maker is to select an alternative, or act, from a set of acts. The consequence of his decision will depend not only on the selected act but also on which state in a set of exclusive and exhaustive states of the world obtains. The state that obtains is not known beforehand by the decision maker and does not depend on the selected act.3

[Given n observations on a system of linear stochastic difference equations with appropriate initial conditions, and given a prior density (possibly diffuse) of its parameters, this paper obtains the predictor of the time series k periods into the future with minimum mean squared error. Completely analytical solution is given for predictions from the first-order univariate system, and, in the general higher-order multivariate case, for k up to 5.]

where y(t) represents the vector of endogenous variables, x(t) the vector of exogenous variables, u(t) the vector of stochastic disturbances, and t the tth period of observation. The matrices A, (T = 0, 1, . . . , m) of the structural coefficients are square matrices of order G. It is assumed that the conditions justifying the theorems in [3, Ch. 10] are satisfied, and that there are no nonlinear restrictions on the elements of A.. The stability of the system is determined by reference to the dominant root of the polynomial equation (2) det E Atmt) =0. t=O

[The purposes of this paper are to establish propositions about the behavior of the supply curve of labor to the individual firm and to estimate the distribution of the elasticities of this supply curve by firm. The main statistical problem faced is the possibility that labor quality increases with firm size so that one does not know how to interpret the relationship of firm size and measured wages. My solution to that problem is to look at the relationship of wages to firm size relative to population density, since I expect the "quality" and the labor supply effects to differ markedly in this respect.]

[In this paper we generalize the family of single equation k-class estimators to systems of equations. The systems k-class estimator with k = 1 is the 3SLS estimator. After developing the asymptotic properties we introduce a further member of the systems k-class, the systems LVR estimator. A systems version of Basmann's identifiability test statistic is also considered.]

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

[Dans un article déjà ancien, les Professeurs C. Fourgeaud et A. Nataf [7] s'étaient attachés à définir la forme la plus générale prise par un système complet de fonctions de demande lorsque ces fonctions ne dépendent que du revenu réel et du prix réel du bien considéré. Ce papier retrace un essai d'interprétation et une expérience d'estimation numérique de ces fonctions. On sait que le système de Fourgeaud et Nataf constitue une généralisation intéressante du bien connu système linéaire de dépenses de R. Stone. Il permet en effet d'introduire un peu plus de flexibilité dans les effets de substitution permis par le modèle mais surtout il accroît fortement la richesse des effets revenu. Dans cette étude cette possibilité est appliquée à la prise en compte d'effets revenus de courte et de longue période, le but étant de pouvoir disposer d'un modèle de cheminement applicable aux études de planification à moyen terme.]

[The limited information maximum likelihood and two-stage least squares estimates have the same asymptotic normal distribution; the ordinary least squares estimate has another asymptotic normal distribution. This paper considers more accurate approximations to the distributions of the so-called "k-class" estimates. An asymptotic expansion of the distribution of such an estimate is given in terms of an Edgeworth or Gram-Charlier series (of which the leading term is the normal distribution). The development also permits expression of the exact distribution in several forms. The distributions of the two-stage least squares and ordinary least squares estimates are transformed to doubly-noncentral F distributions. Numerical comparisons are made between the approximate distributions and exact distributions calculated by the second author.]

SEVERAL ECONOMISTS2 have argued that if individuals correctly perceive the rate of inflation so that their expectations are rational, then deterministic models of money and economic growth are unstable. In this view, points on the steady state equilibrium paths examined by Tobin [9] and others are saddlepoints, there being a tendency to diverge more and more from such a path as time elapses if the system is not initially on the path. The source of instability is understood most easily in the context of a model in which money is neutral, with real growth and capital accumulation both being exogenous with respect to the money supply and price level and, moreover, with both equaling zero. Time is continuous. The price level P and money supply M are assumed at each moment to satisfy the demand function for real balances