Knowledge that Transforms

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.]

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Axioms for an individual's preferences over time, taken from the present perspective, usually assume that the individual will live, or expects to live, throughout a given horizon span. This paper offers an axiomatization that explicitly recognizes the uncertainty of an individual's lifetime. It divides a horizon span into n periods and assumes that if death is not immediate then it will occur at the end of one of the periods. The theory is based on an unconditional preference relation over potential future consumption streams that accounts for uncertain lifetime, along with a conditional preference order that is based on the hypothesis that death will occur at the end of period i. There is a conditional order for each i from 1 to n. The utility representation involves an order-preserving utility function for each of the n conditional orders such that one potential consumption stream is unconditionally preferred to another if, and only if, the sum of the conditional utilities for the first stream exceeds the sum of the conditional utilities for the second. It is argued that the theory seems fairly reasonable only if probability of survival does not depend significantly on past consumption.

[A parametric procedure for linear programming is shown to solve the bilinear complementarity problem, of which a special case is the problem of computing a competitive equilibrium of a piecewise linear economic model.]