Knowledge that Transforms

Simultaneity as a LimitA well-known and highly convincing position on the nature of simultaneity in econometric models is that such models are only approximations to the true state of affairs.In fact, causation takes time, and the reactions given by the equations of the model truly occur not instantaneously but with a very small time lag.Unfortunately, however, data do not come to us sufficiently finely divided in time to allow us to observe such fastmoving reactions, so we take simultaneous instantaneously-holding relations as approximations, valid between the observations which nature allows us.Time lags are thus considered negligible provided they are sufficiently small.The consequences of this position for parameter estimation when observations occur at discrete points of time separated by an interval much larger than that in which the true reactions take place have been discussed 2 in the literature.In fact, however, this particular variant of the above view does not seem a very realistic one, We very seldom have observations on the value of a particular variable at precise discrete moments in time, 3 and, if we do, we seldom use the observations in that form.Much more common is the case in which the observations either by necessity or by choice are in the form of averages or sums over a non-zero time interval.Simultaneous This view has been discussed at length by Bentzel and Hansen [2].The basic position on causation has been vigorously maintained by H. Wold in several works, e.g., Wold and Jureen [11]. 2 Strotz [10]; but see also Gorman [6].

A method is shown for finding all solutions to the generalized von Neumann model formulated by Kemeny, Morgenstern, and Thompson. The method uses results from decomposing economic production systems to extend the algorithm of Hamburger, Thompson, and Weil. THIS ARTICLE shows how the results derived by Weil [5, 6] for decomposable production systems can be used to extend the results of Hamburger, Thompson, and Weil [1] for performing calculations on the generalized von Neumann model of an expanding economy formulated by Kemeny, Morgenstern, and Thompson [2]. A method is shown for finding all solutions to a generalized von Neumann model. The model represents an economy of m goods and n fixed-coefficient, constantreturns-to-scale processes for producing those goods. The set of processes form an m by n input matrix A and an m by n output matrix B. When the jth process is operated at unit intensity the amount ai of the ith good must be supplied at the beginning of the production period and the amount bij of the jth good is produced at the end of the period. The element xj, xj > 0, Ixj = 1, of the stochastic column vector x is the level at which the jth activity is operated. The element yi of the stochastic row vector y is the price of the ith good. Von Neumann required that

[This paper extends the traditional analysis concerning the impact of factor accumulation on a country's terms of trade expounded in a two-by-two model to a world that consists of three countries, each producing three commodities with the help of three factors. It is shown that an "export-biased" factor growth must globally deteriorate the terms of trade of the expanding country--a result similar to that derived in the two-by-two model. An "import-biased" factor growth (of one factor only), however, will improve the growing country's terms of trade with respect to one country but worsen them with respect to the other. Consequently, the conventional view that an "import-biased" factor growth must raise the growing country's real income more than the rise in its output may not hold in a realistic world where trade is multilateral rather than bilateral.]

[This paper presents a considerably abbreviated deformation method for the minimization of a quadratic function subject to linear constraints. In Section 1 the method is explained for a positive definite function. In Section 2 it is extended to singular forms.]