Univariate autoregressive moving average models for the endogenous variables of a dynamic simultaneous equations system can be interpreted as a form of solution of that system. This paper considers the interrelationships between the various representations of the system, and develops joint estimation and model selection procedures for the multiple time series model which arises as a multivariate representation of the individual autoregressive moving average models. A test of the restriction of common autoregressive parameters is incorporated. Two empirical examples are presented, the first concerned with a model of the hog cycle and the second with a model of the United States economy previously considered by Zellner and Palm.
This study introduces ordinally additive, ordinally linear, and ordinally Cobb-Douglas utility functions for the analysis of risky decisions when the uncertainty affects several attributes. Practical algorithms for the determination of utility functions with these forms are provided. Further, the study offers several risk invariance axioms on choice behavior under multidimensional risk. These axioms, for the first time, extend to the multidimensional context the heuristic correspondence between risk aversion and subjective wealth, heretofore familiar in only one dimension. In addition, the consequences of these new risk invariance axioms for utility functional forms in the multi-dimensional context are investigated. The result is a sequence of theorems which show that ordinally linear, ordinally Cobb-Douglas, and ordinally additive von Neumann-Morgenstern utility functions are characterized by the risk invariance axioms. IN THE STUDY OF DECISION MAKING under uncertainty, it is well known that plausible sets of axioms imply that the decision maker acts as if he maximizes his expected von Neumann-Morgenstern utility. (See [1], for example.) If the uncertain outcomes are multidimensional, then the appropriate utility concept is a function of many variables. This is the case, for example, for a firm choosing marketing policies which will affect sales and profits, for an individual faced with investment choices which will affect consumption during several years, and for a government deciding among projects which differ in their costs, outputs, and environmental impacts. In grappling with such problems, decision analysts have found it impossibly difficult to proceed with utility measured by a general function of the outcome variables. Instead, they have used multi-attribute utility functions with special forms, and found that their conclusions are sensitive to the particular form utilized. (See [13], for example.) Thus, it falls to theorists to develop testable hypotheses about risky choice which are equivalent to special (and, hopefully, convenient) functional forms for multiattribute utility. Fishburn [2, 3, and 4], Keeney [5 and 6], and Pollak [9, 10, and 11] have made contributions in this vein. This study introduces ordinally additive von Neumann-Morgenstern utility functions (i.e., those which are a monotonic transformation of a sum of functions, each of one variable) to the literature. I show that they should be well suited to practical decision analysis by presenting algorithms for their use. I propose several risk invariance axioms which plausibly extend to the multidimensional context the intuitive link between risk aversion and wealth in one dimension. These axioms are shown to characterize (in the presence of some other assumptions) ordinally additive, ordinally linear, and ordinally Cobb-Douglas von NeumannMorgenstern utility functions.
[We develop a demand model from a utility tree possessing interactions at all levels. The model is both highly flexible and globally integrable. We use an approach to recursive subaggregation permitting convenient estimation with an unlimited number of goods, and we apply the approach to the construction of a food price forecasting model.]
[This paper develops a theory of the firm's demand for labor when workers, at the time they are hired, know that they may later be laid off. The derived behavior shows how the firm, in response to price falls of increasing severity, will first reduce hours of work. After a minimum work week has been reached layoffs start. The point at which this occurs depends upon the income workers expect to receive if they are laid off. Since unemployment insurance (UI) benefits are an important determinant of this income level, they influence the number of layoffs. Given the absence of an effective incentive tax in practice, we would predict that the present UI system encourages layoffs. An effective, incentive tax could stop this encouragement. Two possible wage strategies are explored, both of which are consistent with the basic layoff and hours model. The flexible wage policy has the advantage of giving no incentive to the firm to default on the (privately) efficient layoff rules derived earlier, but seems to be inconsistent with observed short-run wage policy. The fixed wage policy has its strength and weakness the other way around.]
[This paper presents a general proof of a fundamental proposition of rationing theory and demonstrates that it applies to some basic postulates of macroeconomic theory, including the consumption function. The approach used is to study individual consumer behavior under conditions of quantity constraints. In so doing, the choice-theoretic foundations of the household sector's excess demand functions, as well as the functions themselves, in a general disequilibrium model are developed. These functions include quantities as well as prices as arguments. The response to a change in an effective quantity constraint is shown to depend on the substitutability between the goods involved. Responses to price changes are also determined. The results are then related to the literature on macroeconomic disequilibrium.]
L'6tude de C. Fourgeaud et A. Nataf visant a degager toutes les classes de fonctions de consommation en prix et revenu reels compatibles avec la th6orie des choix, contient une erreur; l'indice de prix associe a une de ces classes s'avere plus general que celui degage par ces auteurs. Dans cette note, apres avoir corrige cette erreur, on examine l'utilite 6conomique et empirique de ces classes qui sont apparues jusqu'ici depourvues d'interet, en y introduisant des quantit6s oblig6es. Il en resulte une generalisation interessante du celebre systeme lineaire de depenses dont on explicite la forme de l'indicateur d'utilit6 indirecte.
THE ALGORITHM DESCRIBED here is used to generate all simultaneous submodels of an econometric model. F. M. Fisher's correspondence principle [1] for simultaneous equation models requires that all simultaneous submodels of the full model be solvable by a particular form of simple iteration, and suggests that the smallest simultaneous submodels be tested first. This algorithm does that by using the primitive v cycle (hereafter called seed) description of a simultaneous equation model [2]. Using the seed description of a model, the algorithm generates every simultaneous submodel only once and its execution time is linear in the number of simultaneous submodels. That number may be very large, however, and for this reason the algorithm proceeds step-by-step, generating simultaneous submodels using previously generated submodels. In this way, only successful submodels (those which pass Fisher's iteration test) need to be used to generate more simultaneous submodels. This feature makes the application of Fisher's test practical even for very large models. The algorithm, called SIFT, is written in 360/370 assembly language. It is available on the National CSS time-sharing network which operates in the USA and Europe or from the author at National CSS, 485 Summer Street, Stamford, Connecticut 06901.