[A process which combines a planning procedure for the allocation of final products and a multilateral nonrecontracting trading process for allocating primary and intermediate goods is defined and shown to satisfy Malinvaud's criteria for evaluating planning procedures. Central processing costs are lower than in the Malinvaud procedure since the central planner only collects information on final products.]

[The parameters of dynamic simultaneous equation models are often estimated using methods which are appropriate only when the errors of the equations are serially independent. The purpose of this paper is to propose a large sample test for serial correlation to replace the invalid Durbin-Watson test. The test requires only simple calculations and can be easily added to standard two-stage least squares/instrumental variables programs. The treatment of serial correlation is discussed. An example is given to illustrate the test procedure.]

IN REGRESSION ANALYSIS most empirical economists use the well-known Durbin-Watson (DW) procedure [1] to test the hypothesis of no autocorrelation among the disturbances of a linear regression model against the hypothesis of a first-order autocorrelation. The use of this procedure is compromised by the fact that it is a bounds text and, hence, cannot discriminate between the two competing hypotheses for a range of intermediate values of the test statistic. This shortcoming can be eliminated by determining the distribution function [5] for the Durbin-Watson test statistic and enumerating it for a given level of significance and a particular regression matrix. The authors have written a FORTRAN IV program for finding the probability that the DW test statistic is less than the observed value if the null hypothesis of no autocorrelation were true. The program enables the investigator to perform the DW test for either positive or negative correlation by comparing the above probability to a specified level of significance. This procedure provides a conclusive test for first-order autocorrelation. The procedure begins with a transformation of the Durbin-Watson test statistic stated as

THE MEASUREMENT of economic inequality is a timely and important topic. Often the Gini index or the entire Lorenz curve is used; however, the relative mean deviation (or Pietra ratio) has been used by Schutz [9] and Budd [1] to study United States data. Eltet6 and Frigyes [2] developed new measures to aid in their analysis of Hungary's income distribution, and Kondor [6] has shown that these new indices are related to the relative mean deviation. In order to draw valid conclusions from actual samples, one needs to know the sampling distribution of the statistic used to estimate the measure of inequality. The purpose of the present paper is to adapt methods used by the author [3 and 4] in another context to obtain the large sample theory of the mean deviation, Pietra ratio, and the measures of Eltet6 and Frigyes. Since several of these measures estimate some parameters of the underlying income distribution function, the asymptotic theory of the estimators is more complicated than might appear at first glance.

ECONOMISTS OFTEN SUMMARIZE the income distribution by the Lorenz curve and Gini index. A variety of parametric methods (e.g., [1 and 8]) have been developed to estimate these measures from the grouped income data governments provide (e.g., [3 and 12]). Previously, one of the authors developed a distribution-free approach [5] which yielded accurate bounds on the Gini index. While analogous bounds on the Lorenz curve can be obtained [5 and 10], the resulting curve is not smooth so a method of interpolation is needed. The purpose of this paper is to adapt an old technique of numerical analysis, Hermite interpolation [7 and 13], to our problem and to show that it usually works in theory and in practice. Our paper was motivated by the work of Brittain [2] who also used numerical methods. Unfortunately, his procedure often resulted in estimates of the Gini index which were inconsistent with the above-mentioned bounds. Although the piecewise Hermite interpolation yielded accurate estimates of the Gini index, it is not always convex as the Lorenz curve must be. Section 5 states conditions for the interpolated curve to be convex or at least increasing over an interval. While these conditions are usually satisfied by real data, a theoretical example illustrates how an error may arise.