A class of parametric for heteroscedasticity in linear models is discussed. For models with nonstochastic regressors, new exact within this class are suggested which utilize existing tables of the distribution of the von Neumann ratio and of the Durbin-Watson bounding ratios. Bound tests for heteroscedasticity in least squares regression are proposed. A rigorous treatment of within this class for heteroscedasticity in the errors of structural relations in dynamic simultaneous equations models is provided.
Charles Blackorby, Richard Boyce, R. Robert Russell, Estimation of Demand Systems Generated by the Gorman Polar Form; A Generalization of the S-Branch Utility Tree, Econometrica, Vol. 46, No. 2 (Mar., 1978), pp. 345-363
[This paper gives a constructive existence proof of a general equilibrium for a local public goods economy in which consumers are free to move among regions. The proof is based upon the Scarf algorithm for the computation of fixed points.]
[This paper describes a decentralized planning process which is a formalization of an iterative method proposed by Taylor [12] for the construction of an optimal plan in a socialist state. Further, it shows that this process is computationally and informationally more efficient than an alternative process proposed by Malinvaud [10] also as a formalization of Taylor's method.]
[This paper surveys some recent developments in equilibrium analysis based on a differential viewpoint. They deal with the structure of the set of equilibria, with the study of regular and singular economies, with the determinateness of the number of equilibria, and with an application to characterizing economies having a unique equilibrium. Equilibrium analysis from the differential viewpoint turns out to be formally similar to models encountered in Thom's catastrophe theory understood as a general theory of bifurcation phenomena.]
Is one distribution (of income, consumption, or some other economic variable) among families or individuals more or less equal in relative terms than another? Despite the seeming straightforwardness of this question, there has been and continues to be considerable debate over how to go about finding the answer. There are two points of contention. One is the issue of cardinality vs. ordinality. Practitioners of the cardinal approach compare distributions by means of summary measures such as a Gini coefficient, variance of logarithms, and the like. For purposes of ranking the relative inequality of two distributions, the cardinality of the usual measures is not only a source of controversy, but it is also redundant. Accordingly, some researchers prefer an ordinal approach, adopting Lorenz domination as their criterion. The difficulty with the Lorenz criterion is its incompleteness, affording rankings of only some pairs of distributions but not others. Current practice in choosing between a cardinal or an ordinal approach is now roughly as follows: Check for Lorenz domination in the hope of making an unambiguous comparison; if Lorenz domination fails, calculate one or more cardinal measures. This raises the second contentious issue: which of the many cardinal measures in existence should one adopt? The properties of existing measures have been discussed extensively in several recent papers. Typically, these studies have started with the measures and then examined their properties. In this paper, we reverse the direction of inquiry. Our approach is to start by specifying as axioms a relatively small number of properties which we believe a ?good? index of inequality should have and then examining whether the Lorenz criterion and the various cardinal measures now in use satisfy those properties. The key issue is the reasonableness of the postulated properties. Work to date has shown the barrenness of the Pareto criterion. Only recently have researchers begun to develop an alternative axiomatic structure. The purpose of this paper is to contribute to such a development.