Knowledge that Transforms

[A multivariate errors-in-variables model is used to analyze the propensity to consume from each of several sources of income for a sample of 621 families in a three year (1960-1962) panel study. The analysis provides estimates of the relationships among the transitory components of the various types of income (contemporary and intertemporal) as well as the marginal propensities to consume out of the permanent component of income from each source. Total family income is much more stable than its components, as there is a tendency for changes in head's income to be offset by opposite changes in wife's and transfer income. The marginal propensity to consume out of the permanent component of both the head's and wife's labor income is .9, a result consistent with Friedman's for aggregate income, and implying that growing labor force participation of wives should have no effect on the long run savings rate.]

[Economies with indivisible commodities admit allocations that are nearly price equilibria, provided that the number of agents is large relative to the number of commodities. In the course of the proof, it is shown that a similar result is valid if agents are insensitive to small price changes.]

[Programming theory is treated initially without any assumptions about the functions and with interpretation for production and activity analysis. By proof of a general theorem about optimal and support solutions and subsequent introduction of convexity assumptions, a new method for obtaining standard propositions and an amplification of their content becomes possible. Properties entirely peculiar to linear problems are noted. Two "shadow price" interpretations are discussed, one being the standard one in which support solutions appear as prices in a fictitious market. Consideration is also given to the law of diminishing returns. Finally, vector output, with emphasis on a concept of irreducible limit output, is treated.]

[This paper is a natural outgrowth of recent studies in markets with a "continuum" of traders. An equivalence theorem for the core of such economies was obtained, under the assumption that the measure space of economic agents is atomless. We introduce a sufficient condition under which the preceding result can be extended to economies containing "atomic" traders. The condition bears on the measure of the atoms.]

This paper develops approximations of the Gram-Charlier type to the cumulative distribution function of the instrumental variables estimator on classical assumptions. In the special case where there are only two endogenous variables in the estimated equation, exact values of the cumulative distribution function are computed by numerical integration and compared with the approximations. Although the error in the approximation depends critically on the parameters of the stochastic model, the approximation is good for the special case even for small sample size over a wide range of values of the parameters. THIS PAPER was originally conceived as a study of the finite sample distribution of two stage least squares estimates. Since it was found that the distribution of a more general class of instrumental variables estimates can be discussed in the same way with a trifling complication of the algebra, the paper was modified to cover these estimates. The basic approach is somewhat similar to that of Nagar [15], since it involves expanding the formulae for the estimator as a series of terms of 0(1), O(T-+), O(T- 1), O(T- 1+), etc., and from this a similar expansion is found for the cumulative probability of the form