Knowledge that Transforms

[The paper is partitioned into two parts. The first contains a description of an "economic system" which allocates resources in exchange environments when consumer preferences are not selfish. This section also contains the conditions under which this economic system allocates resources optimally. The second part utilizes the allocation process described above, as well as four variants, to examine the concepts, and formal definitions, of informational decentralization and efficiency found in Hurwicz [8]. It is shown that various types of trade-offs exist between optimality in resource allocation and informational decentralization.]

[A linear programming model is used to estimate the cost of achieving certain air quality goals for the St. Louis airshed. The choice set of control methods is based on engineering data compiled by the author. The model is used to generate a set of alternative air quality levels for sulfur dioxide and particulates which can be attained at the same total cost as the goals initially considered. This frontier of trade-off possibilities is compared to a particular social indifference curve which is based on medical considerations. It is found that both curves are concave in the same direction.]

[This paper describes empirical laws (formulated abstractly, as axioms) that lead to simultaneous measurement of utility and subjective probability under circumstances where decisions delimit which states of nature may occur.]

[The paper defines and analyzes a functional form for a one-output, many-factórs production function, which is homothetic (or homogeneous), and exhibits CRES; that is, its ES (Allen-Uzawa elasticities of substitution) vary along isoquants and differ as between pairs of factors, but the ES stand in fixed ratios everywhere. Given data on factor prices, quantities, and output, and assuming competitive costminimization, the parameters of CRESH are estimable from a system of log-linear equations, each containing at most three independent variables. The CES function, as well as its limiting forms (the Cobb-Douglas (σ = 1), Leontief (σ = 0), and linear (σ = ∞) functions) are special cases of CRESH. The Mukerji CRES function has an identical unit-isoquant surface, but it is not homothetic. Appendix A analyzes the Mukerji function. Appendix B derives the (implicit) CRESH cost function.]

[Availability of data on a large number of individuals, but on each individual only over a very short period of time, has become increasingly common in a number of different fields in economics. Very often we would like to use such data to study behavioral relationships that are dynamic in character, i.e., that contain a distributed lag or other form of autogressive relationship. Since only a few observations are available over time, but a great many observations are available for different individuals at a point in time, it is exceptionally important to make the most efficient use of the data across individuals to estimate that part of the behavioral relationship containing variables that differ substantially from one individual to another, in order that the lesser amount of information over time can be used to best advantage in the estimation of the dynamic part of the relationship studied. As it turns out, the problem is far from simple: obvious devices such as the pooling of all observations and estimation by ordinary least squares, or the introduction of dummy variables for individuals, produce estimates having serious small sample bias. In earlier papers, the author and others have formulated a simple variance components model for the disturbance term in a relationship to be estimated from cross section data over time. This paper presents a series of Monte Carlo studies designed to explore the small sample properties of various types of estimates within this context. Not only is the bias of the obvious methods of estimation mentioned above confirmed, but certain serious deficiencies of the maximum likelihood approach which had been suspected earlier are also confirmed. A two-round estimation procedure is proposed which appears to work well for a wide variety of parameter values.]

In an earlier paper on "Interdependence as a Specification Error," Strotz has considered a recursive model with endogenous variables lagged by θ; letting θ go to 0, he argued that the likelihood function of the limit form of the model differed from the limit form of the likelihood function of the model. We show here that the two limits are obtained under different underlying assumptions; these alternative assumptions are brought out explicitly; under fixed assumptions, the two methods are shown to yield identical results.