[This paper is concerned with linear models. In this context it gives a necessary and sufficient condition for equality of two generalized least squares estimators of any subset of the parameters. The result is applied to many kinds of problems: the Frisch-Waugh problem, equality of OLS and GLS estimators, equality of the single equation GLS and the overall GLS estimators in seemingly unrelated regressions, equality of partial and overall 3SLS, lineartransformation of a linear model, superfluous observations, and mixed estimation.]
[This paper provides a generalization of Sen's poverty measure. The generalization is motivated by the failure of Sen's poverty measure to satisfy some transfer-sensitivity axioms proposed in this paper. A numerical method of computing the alternative poverty measures is provided along with an illustration based on the data from the Australian household expenditure survey carried out during 1974.]
This paper presents a decomposition of the total effect of a change in a quantity constraint on the money income constant conditional demand function into an income compensated substitution effect and a pure income effect. The substitution effect is shown to be equivalent to the Hicks substitute-complement relation while the income effect is shown to depend directly on the extent of over- or under-supply of the constrained good. The Tobin-Houthakker results on rationing constraints can be generalized in an intuitive manner to cases of non-optimal values of the constraint when the two goods involved are: (1) Hicks substitutes, the constrained good is over-supplied and the unconstrained good is a normal good; or, (2) Hicks complements, the constrained good is under-supplied and the unconstrained good is a normal good. In the case of substitutes and under-supply or complements and over-supply, the sign of the Hicks substicute-complement relation is not sufficient to determine the sign of the partial derivative of interest. Several applications of the theoretical results are also presented.
Consider a closed economy with several deposits of an exhaustible resource, with the marginal cost of extraction differing from deposit to deposit but constant for each deposit. It is widely believed that social optimality requires that deposits be exploited in strict sequence, beginning with the lowest cost deposit. It is shown that, in a general equilibrium context, with Ricardian techniques of extraction, the validity of the proposition depends on what is meant by constancy of cost. It is also believed that if there exists a high-cost substitute for the resource then the resource should be exhausted before production of the substitute is begun. It is shown that this proposition is false.
[A general welfare framework is proposed for examining the behavior of a Tiebout type model in which consumers choose among a variety of communities providing local public services. General expressions are derived for measuring fiscal externalities and the second best nature of Tiebout taxation is explored.]
Events by Grunberg and Modigliani [3]. Economic forecasts are made to be used, and decisions based on them may affect their ultimate realization. Grunberg and Modigliani explored this problem in a model in which future aggregate supply was influenced by current decisions based on the predicted future price. They applied the Brouwer fixed point theorem to show that if the future equilibrium price is a bounded continuous function of its currently predicted value, a exists. In [8] this result was placed in a temporary equilibrium context and the notation of a correct prediction was extended to include probabilistic predictions based on estimation procedures. Again, a fixed point theorem was applied to show that the causal influence of a forecast does not always invalidate it. Although this result is a reassuring and necessary first step, the analysis is confined to a single realization of the exogeneous variables. Thus a forecast is a single point or probability distribution rather than a function or conditional distribution whose domain is the space of observable variables. Of course, if the complete exogenous specification of the economy is observable, this is no restriction since the theorems could be applied separately to each realization. However, it is more likely that the space of observable variables contains a mixture of exogenous and endogenous variables without containing the complete set of either. Then if the exogenous variables are generated stochastically, the results of the above mentioned papers do not guarantee the existence of a statistically forecasting procedure. What is needed are general equilibrium versions of the results in [10], where, in particular, the statistically forecast of a future price is derived as a function of current and past prices. It would seem natural to approach this as a fixed point problem in the space of joint distributions of the observable variables and the