[Conditions under which a single iteration approximation to the maximum likelihood estimator dominates ordinary least squares are approximated analytically for the class of linear models for which the eigenvectors of the error covariance matrix are known.]
This paper examines conditions for the uniqueness of an equilibrium price distribution in stochastic macroeconomic models with rational expectations. A model is developed in which many price distributions, each with a finite variance, satisfy the equilibrium requirements of rationality. Hence, the condition that the variance of the equilibrium price distribution be finite, or equivalently, that the conditionally expected price path be stable, does not guarantee uniqueness. In such cases it is shown that an arbitrary random quantity which is widely publicized can become a leading indicator of prices and, consequently, influence the behavior of actual prices. However, by extending the finite variance (stability) condition to a minimum variance condition, these nonuniqueness problems can be avoided. Such stability or minimum variance conditions suggest a kind of collective rationality which, although not unreasonable, has not yet been fully analyzed in rational expectations models. 1.
[Social decision mechanisms that admit dominant strategies and result in Pareto optima are characterized by the class of mechanisms proposed by Groves. The concept of decision mechanisms is generalized and the characterization is shown to extend to these cases.]
This paper surveys alternative testing criteria in the linear multivariate regression model, and investigates the possibility of conflict among them. We consider the asymptotic Wald, likelihood ratio (LR), and Lagrange multiplier (LM) tests. These three test statistics have identical limiting chi-square distributions; thus their critical regions coincide. A strong result we obtain is that a systematic numerical inequality relationship exists; specifically, Wald , LRa LM. Since the equality relationship holds only if the null hypothesis is exactly true in the sample, in practice there will always exist a significance level for which the asymptotic Wald, LR, and LM tests will yield conflicting inference. However, when the null hypothesis is true, the dispersion among the teststatistics will tend to decrease as the sample size increases. We illustrate relationships among the alternative testing criteria with an empirical example based on the three reduced form equations of Klein's Model I of the United States economy, 1921-1941.
Grayham E. Mizon, Inferential Procedures in Nonlinear Models: An Application in a UK Industrial Cross Section Study of Factor Substitution and Returns to Scale, Econometrica, Vol. 45, No. 5 (Jul., 1977), pp. 1221-1242
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.