Journal Article On Tobin's Multiperiod Portfolio Theorem Get access Guy V. G. Stevens Guy V. G. Stevens Federal Reserve System Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 39, Issue 4, September 1972, Pages 461–468, https://doi.org/10.2307/2296514 Published: 01 September 1972

Journal Article A Comment Get access Frederick V. Waugh Frederick V. Waugh Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 86, Issue 3, August 1972, Page 499, https://doi.org/10.2307/1880807 Published: 01 August 1972

Jerome Stein's article in a recent issue of this Review is subject to misinterpretation which could lead to seriously misleading results. He makes several arguments against the Council's conclusion that Many, though not all, pollution problems are local in character, and therefore determination of the appropriate level of environmental quality in these cases is likely to be more accurate if it is done locally rather than by the Federal Government . (quoted by Stein, p. 532). One of his arguments is that local pricing (effluent charges) would result in inefficiency because the marginal product of pollution would then differ from region to region. Possible confusion results from the fact that two separate measures of pollution are not consistently distinguished. The first is a physical measure like pounds of biochemical oxygen demand or tons of sulfur oxide discharge. The other is the dollar value of damage. In Stein's Figure 1, the horizontal axis represents pollution damage and what is demonstrated is that a dollar's worth of damage must be charged for at the rate of a dollar if efficiency is to prevail. This is emphatically not the same as saying that every pound of discharge should be charged for at the same rate, no matter where in the nation it occurs. But the latter is a conclusion that could easily be inferred from Stein's discussion. instance, Stein says, For example, if the firms were ordered to reduce the rate of pollution by Ax, . (p. 533) where the correct reference is to pollution damage. A similar sliding over from pollution emission to pollution damage occurs again in the first full paragraph of page 535. The translation of pounds of discharge into dollars of damage depends, among other things, on meteorological and hydrological conditions and on the presence and preferences of receptors. Charging a dollar for a dollar's worth of damage requires quite different rates of charge per pound of discharge depending upon the locality. A uniform national charge might be defended on other grounds (see Kneese) but not as a requirement for efficiency strictly speaking. Charges which reflect local conditions could in principle be set locally or nationally. If the Council's argument is right, and I am not trying to assess it here, that the optimum level of environmental quality is more likely to be accurately determined locally, then, problems of implementation aside, more efficient charges could be set locally.

"Inl statistical inference proper, the model is never questioned.... The methods of mathe-matical statistics do not provide us with a means of specifying the model. " 1

IN THE GROWTH model of Kemeny-Morgenstern-Thompson [2, pp. 115-135], the production space is a closed convex and polyhedral cone in R2, with some further properties. In the growth model of Gale [1, pp. 285-303], the production space has to fulfil the same assumptions except that the cone need not be polyhedral. Therefore the model of Gale can be regarded as a generalization of the KMT-model. In this paper it will be shown that in contradiction to a central theorem of Gale, the existence of an optimal price vector cannot be guaranteed in this generalized production space. To describe the difficulty in the growth model of Gale, we enumerate the properties of the production space and the basic definitions given by him. The technological possibilities of production are described by the production space

Wallace and Hussain (1969) considered the use of an error components regression model in the analysis of time series of cross-sections and developed an estimator of the coefficient vector based on an estimated variance-covariance matrix of error terms. In this paper, we have shown that under the set of assumptions adopted by Wallace and Hussain there are an infinite number of estimators which have the same asymptotic variancecovariance matrix as the Wallace-Hussain estimator and also that it is not possible to choose an estimator on the basis of asymptotic efficiency. We have developed an alternative estimator of the variance-covariance matrix of error terms and have used this estimator in developing a feasible Aitken type estimator for the coefficient vector. We have derived some small sample properties of this estimator and have compared them with those of other estimators of the coefficient vector.