Knowledge that Transforms

[The purpose of this article is to suggest and demonstrate a procedure for testing economy wide linear programming models.The suggested procedure applies the linear programming model to an historical period. In general, the model's optimal solution will not be identical to the actual historical solution. Differences between the model's optimal and the economy's actual solutions could be explained by alternative sets of hypotheses--on the one hand, market imperfections, and on the other hand, defects in the linear programming model. Ordinary statistical tests could then be applied in testing the alternative hypotheses. In order to demonstrate the procedure, a linear programming model designed for prescribing an optimal economic structure for the Greek economy during the period 1954-61 is presented and tested.]

[In this paper we are concerned with the distribution of observed or reported incomes in the context of a model that assumes underreporting. A form of `errors-in-variables' model is considered and the Pareto distribution is shown to exhibit certain invariance properties. Under this model (a) the distribution of observed incomes suitably truncated coincides with the true distribution if and only if the distribution is of the Pareto form and (b) a variable having a linear regression on true income has a linear regression on observed income also if and only if the distribution is of the Pareto type.]

This paper develops a sequential model of the individual's economic decision problem under risk. On the basis of this model, optimal consumption, investment, and borrowing-lending strategies are obtained in closed form for a class of utility functions. For a subset of this class the optimal consumption strategy satisfies the permanent income hypothesis precisely. The optimal investment strategies have the property that the optimal mix of risky investments is independent of wealth, noncapital income, age, and impatience to consume. Necessary and sufficient conditions for long-run capital growth are also given.

[The problem consists in maximizing a concave functional--given as an integral--on a class of functions. A method based on approximating optimal solutions by step functions is suggested; approximations are found by solving concave programming problems of a special type. Some convergence theorems are proved and an estimate of the error in terms of values of the objective functional is given.]

Gorman [2] has derived necessary and sufficient conditions for the existence of category expenditure functions which yield the optimal allocation of a consumer unit's income to each of a number of groups of commodities as functions of total income and group price indices. These conditions take the form of certain restrictions on the structure of the utility function. Gorman, however, did not address the problem of how these functions are derived. In this paper, we construct an algorithm (a budgeting procedure) for deriving the category expenditure functions and show that the necessary and sufficient condition for this procedure to be consistent is that the utility function be separable into homothetic parts. CASUAL OBSERVATION REVEALS that many consumers budget; that is, they first allocate their total expenditure among broad commodity categories and then decide upon the precise allocation of category expenditure to each of the commodities within the group. This type of consumer behavior is especially interesting if it is possible to carry out the broad category allocation with reference only to price indices for each of the budgeting categories, and then decide upon the intracategory allocation with reference only to commodity prices within that group. R. H. Strotz [4, 5] and W. M. Gorman [2] have examined the relationship between this type of consumer behavior and the form of the consumer unit's utility function. More precisely, they have shown that the necessary and sufficient conditions for the existence of group price indices (which depend only upon commodity prices within the group), such that category expenditures are functions only of these price indices and total expenditure, are that the utility function be (a) homothetically separable2 or (b) strongly (additively) separable (with a certain restriction on the polar form of the utility function).3 Strotz and Gorman do not address the issue of how these functions could be derived. This paper discusses a method of deriving the category expenditure functions-a budgeting procedure-which requires stronger constraints on the utility function than does the mere existence of the functions. Price indices are first derived for each budgeting category. Then the

The exact sampling distributions of estimators of structural parameters of econometric models are unknown except for a few simple cases. In this situation two alternative approaches towards evaluating finite sample properties of various estimators have been adopted in the literature: (i) Monte Carlo experiments, and (ii) the approach pioneered by Nagar and his students in which the sampling error of an estimator is expressed as the sum of an infinite series of random variables, successive terms of which are of decreasing order of sample size in probability. It is claimed that the small sample properties of the estimator under consideration can be approximated by those of the first few terms of such an infinite series. This paper shows through examples that the Nagar approach can be misleading in the sense that it can yield an estimate for finite sample bias that differs from the true finite sample bias to the same order of sample size. And it can yield estimates of bias which are finite (infinite) while the true bias is infinite (finite). The paper also draws attention to some of the pitfalls to be avoided in studying the properties of an infinite sequence of random variables.