[For a finite linear distribution lag model the problem of estimating the coefficients when the loss function is quadratic is considered. The explanatory variable is assumed to be generated by an autoregressive or moving average process. A result due to Szegö is used to approximate the latent roots of the sample moment matrix. The approximation is then used in a comparison of the risk of four estimators--unrestricted least squares, restricted least squares, the James-Stein estimator, and the pre-test estimator. The effect of increasing autocorrelation in the explanatory variable on the relative performance of the four estimators is also studied.]
IN THE ANALYSIS of economic data the investigator is frequently provided with only the simple sum of some elementary variables. The elementary variables are known to be perfect substitutes (i.e., to have the same effect) in some contexts, but not in all the relevant ones. Familiar examples are hours of work at possibly different jobs, hours of leisure spent at different activities, number of trips abroad, cigarette consumption (of possibly different brands). The question, naturally, is under what conditions can we expect that such aggregates will satisfy the same restrictions as those imposed by the theory on the elementary variables? As an answer we suggest the following variation of Hicks' [3, p. 33] composite good theorem: A simple sum of elementary goods can be treated as a single good if their (properly normalized) prices vary so as to keep all within group differences constant.2 We shall illustrate the proposition in the context of standard demand theory. Define the expenditure function: m (u, p) minm 1 l7pixi, subject to u(x1.. .xn) = u. Suppose that
[This paper develops a new family of biased estimators, namely the double k-class, for the parameters of the general linear regression model. We note that James and Stein[7] Stein-rule estimator in the regression context is a member of the family of double k-class. The conditions for the existence of the moments and expressions for the exact and approximate bias, moment matrix, and the risk function of the double k-class estimator are analyzed.]
[The main theorem in this paper is one in a long series of theorems which show the existence of equilibrium in economies without convex preferences, without convex consumption sets, or without complete and transitive preorderings. Here, it is proved that a competitive equilibrium exists in a large economy with not necessarily convex consumption sets and where preferences are continuous and transitive. As an additional assumption the continuity of the wealth distribution with respect to the Borel-Lebesque measure is required.]
A number of recent works have addressed the problem of describing the allocation of resources in an economy where prices are fixed at a value that does not achieve equilibrium of supply and demand in the classical sense. In the context of a model developed by Drèze, the purpose of this paper is to describe more precisely the different states of the markets (excess supply or excess demand) that may occur near a competitive equilibrium. A general analytical picture is obtained, which associates with each state of the markets the region of the price domain where it prevails. This allows us to point out an important difficulty which arises in the local comparative statics of this class of model: local unicity is not warrantied, that is, there may exist price systems very close to some competitive price, for which all the fixed price allocations are far from the competitive allocation. Examples are shown in the macroeconomic model (two aggregate agents: households and firms, and three goods: money, output, and labor); necessary and sufficient conditions for local unicity are given in this context. They require that all commodities be Hicks-substitute for the consumer, which is another way of saying that both the marginal propensities for consumption and leisure are positive and smaller than one. On the other hand, assuming local unicity, one can look for the implications of the foregoing results for the long-run determination of prices. It is easy to show that, if the economy always reaches a fixed price allocation, an increase of the price of one commodity near the competitive equilibrium is always to the advantage of the sellers and to the disadvantage of the buyers. This suggests that the determination of prices should take the form of a struggle between buyers and sellers in each market.
[It is demonstrated that, under regularity assumptions on individuals' preferences, for an open dense set of exchange economies indexed by initial endowments, the core does not possess the equal treatment property. The assumptions made on individuals' preferences are subsequently shown to characterize an open dense subject of the space of preferences.]
[This paper explores a new approach to the estimation of a joint production technology. Pseudo data, which are obtained by solving a petrochemical process model for alternative relative prices, are used to estimate a price possibility frontier with 3 inputs and 6 outputs. Unlike traditional data sources, pseudo data are not constrained by historical price variation, technologies, and environmental controls. As an econometric exercise, the approximation of the process model's detailed piecewise linear production surface by a single equation "generalized" functional form, the translog, raises a host of interesting empirical and methodological questions.]
[Arrow and Hahn's book General Competitive Analysis offers (Section 6.4) an existence theorem for non-competitive general equilibrium. Their formulation is apparently very general, but it becomes seriously restrictive in the presence of increasing returns to scale. An alternative existence theorem is presented here that obviates these shortcomings.]
[An efficient estimator for regressions in which the parameter vector can take any of several values is devised. It is shown that although the likelihood function is unbounded, the likelihood equations have a consistent root. An initial consistent estimator is provided. One Newton step provides efficient estimates. Applications to nonlinear models and contaminated normal models are suggested.]
[The paper explores some of the issues involved in constructing measures of mobility when the data are provided in the form of a transition matrix. An initial set of axioms is proposed which is inconsistent. They can, however, be reconciled if empirically unlikely transition matrices are eliminated from consideration. The paper then discusses the problem of comparing matrices not defined over the same interval. An index based on the convergence speed in a Markvov chain process is able to compensate for differing time periods.]