It is useful to have bounds on expected utility in situations in which the relevant distribution is skewed. This paper assumes that the third moment of the distribution is known and uses knowledge of the first three moments to derive upper and lower Tchebycheff bounds.

In an interesting paper B. Singh and H. Drost (S-D) (1971) gave two iterative methods for estimating the parameters in two different specifications of Friedman's Permanent Income Hypothesis (PIH). As to their Method I comments have been given by Rao ( 1973, p. 261 ) and Pesaran ( 1973, pp. 259261), and this method will not be taken up in this paper. It has been shown by Pesaran and the present author (1974) that (S-D) 's iterative Method II is easily solved algebraically. The iterative procedures proposed by (S-D) are applications of WAold's NIPALS (nonlinear iterative partial least squares). Furthermore (S-D)'s alternative approach is a direct application of the NIPALS modelling of an errors-in-variables model given by Wold (1966, pp. 438-439). However, as should be clear from Wold (1966, p. 439) the NIPALS procedure designed by Wold rests upon an assumption, the importance of which has been overlooked by (S-D). The contribution by Pesaran (1973) is to show the necessity of this assumption for the estimate of the marginal propensity to consume to be consistent. As has been shown by the present author, the scope of the NIPALS procedure designed by Wold (1966) is easily broadened. Retaining the definition of variables made by (S-D) we have the following model