Knowledge that Transforms

[The purpose of this paper is to present a model which explains the formation of firms in a market economy. This is done by unifying two recent developments in economic theory: the labor-managed market economy and the coalition production economy. D. Sondermann's model [30] of a coalition production economy with "increasing returns to coalition" is generalized. Specifically, the concept of coalition structures is introduced, so that the model can be naturally interpreted to represent a labor-managed market economy. Two kinds of specific interpretation are considered: one is a type of socialistic economy and the other a capitalistic economy.]

[This paper considers (i) the robustness of the @t and Durbin-Watson bounds tests for first-order autocorrelation when disturbances in the linear regression model are heteroskedastic and (ii) the robustness of the Goldfeld-Quandt and Glejser tests for heteroskedasticity when the disturbances follow a first-order autoregressive scheme.]

[Under classical assumptions, characterizations are given for two classes of instrumental variable estimators of an equation in a simultaneous system. IV estimators where all instruments are nonstochastic are expressed in terms of multinormal random vectors in exactly the same way as the 2SLS estimator of a just-identified equation. These estimators have no finite moments of positive integral order. The second class, consisting of IV estimators based on certain stochastic instruments, includes the OLS, 2SLS, and modified 2SLS estimators. The inadmissibility (under squared-error loss) of some estimators in this class is considered when the equation being estimated contains two endogenous variables.]

IN THIS PAPER we show that application of the traditional theory of the true cost of living index to Lancaster's new approach to consumer theory (cf. [6 and 7]), i.e., to shadow prices of characteristics rather than to ordinary prices of goods, opens a possibility for a convenient treatment of quality changes and of the introduction of new goods. Section 2 is a statement of the relevant properties of Lancaster's model. In Section 3 this model is used to derive a cost of living index, which is not only price compensating but also quality compensating. However, the Laspeyres index which corresponds to this true index and which in principle might be observable, is not always an upper bound on this true index. In this section the relationship to the hedonic price index is also noted. Section 4 contains some concluding remarks.2

[A choice function is defined to exist if there is a "best" (under a binary relation R) element in all non-empty compact subsets of S, the set of all possible alternatives, whereas a demand correspondence exists if there is a "best" element in only the budget sets of S. Some basic restrictions on R are considered. First, if the "at least as good as" sets are closed, then none of the standard restrictions on R are shown to be necessary for the existence of a demand correspondence: the "domination" of finite sets is necessary and sufficient. This is shown to imply that acyclicity of R is necessary and sufficient for the existence of choice functions. Second, if either there is a restriction on convergent P monotone sequences or if R satisfies a regularity condition, then a condition on cyclical sets of alternatives is enough to guarantee the existence of demand correspondences. For the existence of rational choice functions, however, reflexivity, completeness, and transitivity of R, together with the above-mentioned condition on P-monotone sequences, are necessary and sufficient. Finally, if the strictly preferred sets are taken to be convex, then under a restriction weaker than the first, a best element in budget sets exists.]

SAMUELSON MADE THE CONJECTURE stated above in his 1967 paper [7]. He also formalized there the axiom of independence of irrelevant alternatives for cardinal preferences, used here. Preference are cardinal if their representation by a numerical function is invariant under, and only under, positive linear transformations. One may think that the disregard for intensity of preferences, embedded in Arrow's treatment of profiles of ordinal rankings of alternatives, leads to the impossibility result. Samuelson's conjecture points out that this is not the way to refute the conclusions of Arrow's theorem. There is also interest per se in aggregation of cardinal preferences. Such preferences are usually considered as von Neumann-Morgenstern utility, i.e., numerical representation of preferences over lotteries [11]. Since uncertainty is the rule and not the exception whenever decisions are involved, it is of some importance to obtain a social N-M utility over risky outcomes. Given such a utility, the society will be able to choose a best alternative among the several feasible risky actions (i.e., lotteries). However it is not necessary to restrict the interpretation of cardinal preferences to those induced by ordinal ranking over lotteries. One can think of cardinal preferences derived from comparisons between pairs of alternatives (as in an axiomatization of a regret relation). See Alt [1] for an early work of this kind. When working with cardinal preferences a continuity assumption is needed, in addition to unanimity and independence (see the example at the end of the next section). A standard reference for Arrow's theorem is the last chapter of his book [2]. For a general discussion of aggregation of cardinal preferences, see ShapleyShubik [10]. Some other impossibility results involving different notions of cardinal preferences appear in the works of Sen [9], DeMeyer-Plott [4], Schwartz [8], and Fishburn [5]. A model dealing with aggregation of cardinal preferences into social cardinal prefereiLces, as here, is that of Harsanyi [6]. However he is interested in 1 The work of the first author was done at Northwestern University and the work of the second author began at the University of Illinois in Urbana-Champaign and it was completed at the University of Minnesota in Minneapolis. Both authors are on leave from Tel-Aviv University. The authors wish to express their thanks to E. A. Pazner, M. A. Satterthwaite, J. Kelly and the referees for helpful comments. This research was partly supported by NSF Grant # SOC-75-05317.

A wide variety of economic models include as explanatory variables either expectational variables or variables representing the result of some decision-making process. The first category includes both expectations about the future values of variables, e.g., next period's sales, the level of unemployment two quarters ahead, etc. and other subjective variables such as permanent income or the "normal" level of prices and interest rates. Examples of the second type are "desired" capital stock, planned production, or inventory accumulation, and so on.

is misleading if o-2 $ o-2 and n, and n2 are both small, where Y, and Xi are ni x 1 and ni x k observation matrices, ,li is a k x 1 coefficient matrix, and ei is an n, x 1 error matrix for i=1,2. A valid asymptotic test may easily be obtained by regarding (1) and (2) as seemingly unrelated regression equations. In this paper we establish a small sample test which may readily be extended to a test of some of the coefficients in the two regressions.