Knowledge that Transforms

A model is presented for the derivation and implementation of optimal linear decision rule for a firm producing and dealing in a number of interacting products, and possessing partial influence on their prices. The behavior of a multi-item production-inventory complex is represented as the dynamics of suitably defined state variables under the influence of decision rules that are stable and linear in the state variables, but otherwise unspecified. The dynamical equations are stochastic owing to the presence of stochastic processes in the forcing terms. The statistical properties of these processes, together with the decision rules, determine the statistics of the outcome or the criterion functional. The optimum inventory decision is then derived as the "best" linear transformation on the past of the state variables such that the mean value of the criterion functional is optimized subject to the system constraints. [Likely published between 1961-1966.]

Economists and other users of statistical methodology often posit a probabilistic model of some real world phenomenon which has more unknown parameters than there are sample observations. In such cases it is usually impossible to estimate jointly all parameters from the sample data. Even in those instances where there are well established estimation procedures when the number of sample observations, n, is than the number of parameters, r, these methods are generally inadequate when n < r, as the necessary calculations cannot be carried out. Furthermore, when n is only slightly larger than r, such estimates often prove to be unreliable in more than one sense. One particular example of such a problem that frequently occurs in analysis of psychological and economic data can be paraphrased as follows: the researcher posits a linear regression model as defined in equation (1) below with r 1 independent variables, but only n < r observations are available. Since the standard least squares procedure cannot be applied, he may ask the following seemingly reasonable question: What subset of the r 1 independent variables should I select for inclusion in a new model to which I can apply the standard least squares procedure? Our purpose here is to demonstrate that one frequently used ad hoc method for determining such a subset by ordering simple sample correlation coefficients can be highly misleading. Any procedure which uses a given set of sample data both to determine the structure of the model to be estimated and to estimate parameters of this model is intuitively unsettling. Here we present tables which quantitatively demonstrate how dangerous such ad hoc methods can be. II Ad Hoc Use of Simple Correlation Coefficients to Determine Model Structure

International Relations/Trade, Research Methods/Statistical Methods

THE balance-of-payments statistics of the United States have received a thorough examination at the hands of a distinguished committee chaired by Edward MI. Bernstein in a report submitted to the United States government in the spring of 1965.1 The committee was asked to review "basic conceptual problems, problems of presentation and analysis, and technical statistical problems" pertaining to the balance of payments. The committee produced an excellent document, useful not only to government officials but also to all users of balance-of-payments statistics. Its Report follows several other valuable reports on U.S. government statistics that bear on measuring economic developments and interpreting them for the formulation of economic policy. The National Bureau of Economic Research submitted a report on the national accounts in 1957 (NBER, 1957), the Stigler report on price statistics appeared in 1961 (NBER, 1961), and the Gordon report on unemployment statistics was released in 1962 (President's Committee To Appraise Employment and Unemployment, 1962). These excellent reports not only aid in pursuit of the tenet of American economics,

I. Introduction, 526. — II. Alternative discrete capital models, 528. — III. Reswitching in two-good technologies, 531. — IV. Reswitching in a general capital model, 538. — V. Some additional implications for economic theory, 546.

Charles F. Walker, Allan H. Meltzer, Edgar Peske, Bion B. Howard, John P. Shelton, Ragnar D. Naess, Developments in the Curriculum and Teaching of Finance: Discussion, The Journal of Finance, Vol. 21, No. 2, Papers and Proceedings of the Twenty-Fourth Annual Meeting of the American Finance Association, New York, New York, December 28-30, 1965 (May, 1966), pp. 423-434