Ben W. Bolch

On the Testing of Regression Disturbances for Normality

Abstract OLS and BLUS residuals in the classical linear regression model are compared with respect to testing the normality of regression disturbances. It is shown that in theory both types of residuals suffer from the common problem of lack of independence under the alternative hypothesis of nonnormal disturbances. Further, Monte Carlo experiments appear to show the superiority of OLS over BLUS residuals, as well as the superiority of the Shapiro-Wilk test over other tests studied, when one is testing for normality.

More on Unbiased Estimation of the Standard Deviation

In a recent issue of this journal, Edward E. Cureton [1] published a table of correction factors, k, which allow unbiased estimation of the standard deviation of a normal population using the sample standard deviation. Excerpts from the following table which I have recently calculated will appear in [2]. The table was calculated using double precision arithmetic and the table of logarithms of the gamma function given in [3]. The table is in a form preferred by many statisticians and is more complete than Curetons. If n is the sample size, x2 = (X X)2, and you are given lx2 S n n-I (1)

A Reappraisal of Some Factors Associated with Fluctuations in the United States in the Interwar Period

enriched by these efforts, but many of the hypotheses concerning the perverse economic behavior of this period have never been brought together in any formal way, nor have they been subjected to an analysis which seeks to assess their relative importance. This paper seeks to carry out such an analysis by use of an econometric model and a simulation technique which to a statistician might be called a dynamic analysis of variance, while to a historian it might be called a statistical excursion into counter-

The Depletion Allowance and Vertical Integration in the Petroleum Industry

The Hay Model of vertical integration is applied to the petroleum industry to test the conventional belief that additional cash flow from increased crude production will offset any losses from downstream operations. By contrast, the model results show that the combined effects of an income tax and depletion allowance are enough to motivate downstream integration. Even though fixed coefficients do not allow economies of factor substitution, vertical integration can be prompted by the fact that cash flow from income tax deductions may be increased by increasing the crude oil posted price. The model not only shows that downstream losses may be a rational reaction to a depletion allowance, but it also predicts that integration will be less viable without depletion. 11 references.

The Windfall Profit Tax and Vertical Integration in the Petroleum Industry

An analysis of the combined influence of the corporate income tax and a percentage depletion allowance on the decision to integrate vertically in the petroleum industry was presented in a recent issue of this Journal. In that paper it was shown that the combined effect of these two aspects of the corporate tax structure was the encouragement of downstream integration into refining and marketing for the crude-oil producer. A logical conclusion of that earlier analysis was that the repeal of the percentage-depletion allowance for large oil and gas producers (e.g., the tax reform which disallowed percentage-depletion tax deductions for tax years subsequent to 1974) would have the effect of slowing, and ultimately reversing, the trend toward vertical integration in the petroleum industry. The purpose of this note is to demonstrate that the effect of the combination of the corporate income tax and the windfall profit tax may be to encourage vertical integration, depending upon the interpretation and viability of the constructive sales clause of the windfall profit tax bill.