Knowledge that Transforms

The purpose of this paper is to analyze the accuracy of the Simon-Ando approximation for stochastic nearly-completely decomposable systems. Relations are established defining this accuracy as a function of the maximum degree of coupling (e) between aggregates, the conditioning and the indecomposability of these aggregates. A procedure is derived by which estimates in c2 may be computed from aggregate eigencharacteristics. Finally, the Simon-Ando approximation is shown to be optimal in block-stochastic matrices, and the accuracy achievable by higher-order aggregation is examined.

Direct or indirect additivity of production or utility functions implies dependence of substitution effects on income effects. This dependence is eliminated by implicit additivity, or strong separability along isoquants or indifference surfaces. The present study proposes and analyzes two models, with direct and indirect implicit additivity, respectively, which are generally non-homothetic, non-CES, and include less than 3n parameters for n goods. They give rise to log-linear systems of estimable demand relations. Many other models, such as Cobb-Douglas, CES, Direct and Indirect Addilog, CRESH, CDE, and Non-homothetic CES, are simple, testable special cases of either or both of these models.

It is shown that in markets with a continuum of traders, the allocations associated with the Shapley value are the same as the competitive allocations.

[Assuming each assignment of strong preference orderings to individuals is equally likely, we examine how the probability of social intransitivity (under asimple majority vote decision rule) changes with changes in the number of alternatives and the number of voters. A similar study is made of violation of quasi-transitivity and failure of existence of a maximal alternative.]

problems of a particular equation in the model. Examples are given. Further generalizations are also considered but only conditional results are given. Further work is suggested.

[This paper deals with the characterization and properties of "information improvement" which Theil has applied in Economics. A functional equation in three variables is formed. The solutions of this functional equation under suitable boundary conditions are defined as information-improvement functions. The "information improvement" is then defined in terms of information-improvement functions.]

Phoebus J. Dhrymes, R. Berner, D. Cummins, A Comparison of Some Limited Information Estimators for Dynamic Simultaneous Equations Models with Autocorrelated Errors, Econometrica, Vol. 42, No. 2 (Mar., 1974), pp. 311-332

This paper develops an economic theory of replacement investment that can provide a basis for specifying an econometric model of investment behavior. The long-run and short-run effects of changes in the interest rate and in tax laws are examined. The paper also investigates several reasons why the common assumption of a technologically constant rate of replacement is incorrect even as an asymptotic limit. LARGE VARIATIONS in capital spending continue to motivate econometric studies of investment behavior. The past decade has seen the development of attempts to model net investment as the adjustment of the capital stock to a desirable level. Building on earlier work by Lutz [35], Haavelmo [21], and others, Jorgenson and his collaborators (e.g. [24, 28, 31, and 33]) have provided an operational model of net capital accumulation that relates desired capital to the cost of capital services. Although serious objections have been raised about the specification of the optimal capital stock (including [5, 9, 13, and 15]) and about the arbitrary nature of the adjustment dynamics [37], it is likely that some form of this general model will continue to provide a framework for future investment studies. In contrast to these developments of a theory of capital expansion, replacement investment continues to be analyzed in terms of a non-economic model of technical necessity. Jorgenson and others have adopted the simplifying assumption that replacement investment is a constant proportion of the capital stock.2 This assumption has been challenged and contrary evidence has been offered by Feldstein and Foot [14] and Eisner [10]. The purpose of the current paper is to examine several aspects of a theory of replacement investment. We hope not only to show that a model with a constant replacement rate is implausible and unsatisfactory but also to provide a basis for better empirical work in the future. The magnitude of replacement investment (the annual rate of replacement investment generally exceeds expansion investment) makes this issue a matter of substantial importance.