The parting of the ways between causal chain (recursive) and interdependent (nonrecursive) systems is reviewed from the point of view of explanatory relations specified in terms of conditional expectations. On the customary assumptions, a causal chain system is designed so that its relations both in the original form and in the reduced form can be specified in terms of conditional expectations, whereas the relations of interdependent systems allow such specification only in the reduced form. A third type of model is discussed, called conditional causal chains, which formally is similar to interdependent systems, with the important difference that the behavioural relations of the original system are specified in terms of conditional expectations.
This is applicable to the flow of any kind of quantifiable transactions, and to matrices from three to more than one hundred actors, utilizing a 650 IBM electronic computer or similar equipment. The method develops a matrix of expected or baseline data from assumptions of complete indifference among the actors, and measures the plus or minus differences between this baseline value and the actual amount of transactions in each direction for every pair of actors. It thus removes gross size effects and permits tentative inferences about the distribution of preferences among pairs of larger groups of actors; about degrees of clustering or integration among actors; and about changes over time, if several matrices are used. It thus locates interesting pairs or groups for further study. Import-export data are used as an example to show the detailed application of the method. For a given year and a group of countries, the importexport data can be arranged like a contingency table, except the diagonal cells are zero and the other entries are quantities of money, a continuous variable instead of a discrete variable. A describing the data and techniques for the statistical analysis are presented. This is a null model in the sense that the departures from it are of primary interest. The North Atlantic Area (1928) is used as an illustration.
This paper, which in part serves as a common introduction to the two papers following in this issue, attempts to define the meaning of the interpretability of a parameter in a system of simultaneous linear relationships. It attempts, moreover, to expound a basis for interpreting the parameters of a nonrecursive or interdependent system causally. This is done in terms of an underlying causal chain system to which the interdependent system is either an approximation or a description of the equilibrium state. OVER THE PAST fifteen years there has been an extended discussion of the meaning and applicability of nonrecursive as distinct from recursive systems in econometrics, and throughout this discussion there has been a marked divergence of views as to the merits of the two types of models. It is not the purpose of this note to extend that controversy further, but rather to attempt a constructive statement of the relationship betweenthe two approaches and the circumstances under which each is applicable. We assume that the reader is generally familiar with the past discussion' and that it will suffice here simply to recall that a recursive, or causalchain, system has the formal property that the coefficient matrix of the non-lagged endogenous variables is triangular (upon suitable ordering of rows and columns) whereas a nonrecursive, or interdependent, system is one for which this is not the case. While the triangularity of the coefficient matrix is a formal property of recursive models, the essential property is that each relation is provided a causal interpretation in the sense of a stimulus-response relationship. The question of whether and in what sense nonrecursive systems allow a causal interpretation is the main theme of this paper.
A computational procedure is given for finding the minimum of a quadratic function of variables subject to linear inequality constraints.The procedure is analogous to the Simplex Method for linear programming, being based on the Barankin-Dorfman procedure for this problem.
I n the classical linear programming problem the behaviour of continuous, nonnegative variables subject to a system of linear inequalities is investigated.One possible generalization of this problem is to relax the continuity condition on the variables.This paper presents a simple numerical algorithm for the solution of programming problems in which some or all of the variables can take only discrete values.The algorithm requires no special techniques beyond those used in ordinary linear programming, and lends itself to automatic computing.Its use is illustrated on two ~lumerical examples.
What is the exact nature of the consumption function? Can this term be defined so that it will be consistent with empirical evidence and a valid instrument in the hands of future economic researchers and policy makers? In this volume a distinguished American economist presents a new theory of the consumption function, tests it against extensive statistical J material and suggests some of its significant implications.Central to the new theory is its sharp distinction between two concepts of income, measured income, or that which is recorded for a particular period, and permanent income, a longer-period concept in terms of which consumers decide how much to spend and how much to save. Milton Friedman suggests that the total amount spent on consumption is on the average the same fraction of permanent income, regardless of the size of permanent income. The magnitude of the fraction depends on variables such as interest rate, degree of uncertainty relating to occupation, ratio of wealth to income, family size, and so on.The hypothesis is shown to be consistent with budget studies and time series data, and some of its far-reaching implications are explored in the final chapter.