On the existence of random measure preserving bijections

This paper establishes the existence of an invariant probability measure on the set Π of measure-preserving bijections of the unit interval. In fact, the measure may be further restricted to be a Baire-measure. This result is compared with Aumann's (1967) and Aumann and Shapley's (1974) impossibility theorems.     

On the existence of equilibrium in social systems with coordination

Social systems with coordination were introduced by Vind (1983) as a general model of economic institutions. The present paper gives a general existence theorem for equilibria in social systems with coordination extending Vind's result.     

On the two armed bandit with one probability known

Summary The dynamic programming approach to the solution of the two armed bandit problem with one probability known is discussed, for a general prior distribution for the unknown probability. Properties of the objective function and of the stopping boundaries are obtained. The problem of costly observations is discussed.     

On the existence of locally mvu estimators

It is proved that there exists an unbiased estimator for some real parameter of a class of distributions, which has minimal variance for some fixed distribution among all corresponding unbiased estimators, if and. only if the corresponding minimal variances for all related unbiased estimation problems concerning finite subsets of the underlying family of distributions are bounded. As an application it is shown that there does not exist some unbiased estimator for θ^k+c(ε≥0) with minimal variance for θ =0 among all corresponding unbiased estimators on the base of k i.i.d. random variables with a Cauchy-distribution, where θ denotes some location parameter.     

On characterizing the probability of survival in a large competitive economy

We consider a Walrasian exchange economy in which an agent is characterized by a utility function, a random endowment vector, and a function that specifies the minimum expenditure necessary for survival at a given price system. If at any equilibrium price system, the income of the agent is no more than the minimum expenditure for survival, it is ruined. The main results characterize the probability of ruin when the number of agents is large. The implications of stochastic dependence among agents are explored.     

Estimation of a finite population total in varying probability sampling for multi-character surveys

The problems of estimating population total in multi-charter surveys are considered in a unified set up. Alternative estimators for Rao-Hartley-Cochran (1962), Midzuno-Sen (1952,53) and other varying probability sampling schemes are proposed when the measure of size is not well related to the study variables. Some of the proposed estimators are found superior to the existing alternatives. A numerical study is carried out to investigate the performances of the proposed alternatives.     

On the existence of bivariate moments of lower order given the existence of moments of higher order

Dit artikel geeft een voorbeeld van een twee-dimensionale waarschijnlijkheidsdcht-heid met de eigenschap, dat het bestaan van momenten van de vorm E(g^ky^l ) niet het bestaan garandeert van alle momenten van lagere orde, E(g^myⁿ ) met 0myⁿ ) met 0 < m < k en 0 < n < l is, dat de drie momenten E(x^k), E(y^l ) en E(x^ky^l ) bestaan, alsmede een iets algemener resultaat.     

On the existence of equilibria in economies with an infinite dimensional commodity space

We prove an infinite dimensional extension of the Gale–Nikaido–Debreu lemma which includes all necessary limiting processes and allows a proof of the existence of equilibria under standard assumptions in an economy with infinitely many commodities which exactly parallels the proof of Debreu (1959) for the finite dimensional case.     

On the existence of walrasian equilibrium in large-square economies

An existence theorem for Walrasian equilibrium is demonstrated for an economy with a continuum of consumers and an infinite-dimensional commodity space, such as l₁ or c₀, having an ‘order-compatible’ basis.     

On the existence of moments of the partially restricted reduced-form estimators from a simultaneous-equation model

This article proves the existence of all moments of the partially restricted reduced-form estimator. It highlights this estimation method as it appears to be the only reduced-form estimator to possess finite moments, and is thus a valid alternative to restricted reduced-form estimation (where the moments do not exist). The estimation method is described briefly and then the existence proof is formulated, first, for the case of two included endogenous variables in the structural equation and then, we extend the result for any number of included endogenous variables.     

On the probability of entry in potential competition cases

This paper explores, both theoretically and empirically, the extent to which having ‘other potential entrants’ to a market injected into potential-competition cases has been a worthwhile enterprise. This two-pronged attack leads to the conclusion that (he attempt to specifically identify potential entrants probably results in our deluding ourselves as to the likelihood that entry will occur, and that unless a convincing argument can be made to the effect that any given potential entrant from a stockpile of unnamed potential entrants is ‘reasonably likely’ to elect the entry option, expanding lhat stockpile will be similarly misleading.     

On the existence of the ex post symmetric random entry model

This paper studies symmetry among countably infinitely many agents who randomly enter into a stochastic process, one for each period. Upon entry, they observe only the current period signal and try to draw inference about the underlying state governing the stochastic process. We show that there exist random entry models under which agents are ex post symmetric. That is, all agents have identical posterior belief about the underlying states, although they are not ex ante symmetric. The form of the posterior belief is uniquely pinned down by ex post symmetry and a stationarity condition. Our results provide a common prior foundation for the model studied in Liu and Skrzypacz (2014).     

On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach

For the problem of adjudicating conflicting claims, a rule is consistent if the choice it makes for each problem is always in agreement with the choice it makes for each “reduced problem” obtained by imagining that some claimants leave with their awards and reassessing the situation from the viewpoint of the remaining claimants. We develop a general technique to determine whether a given two-claimant rule admits a consistent extension to general populations, and to identify this extension if it exists. We apply the technique to a succession of examples. I gratefully acknowledge support from NSF under grant SBR-9731431 and SES 0214691, and the comments of Carmen Bevia, Rodrigo Velez, Chun-Hsien Yeh, and a referee.     

On the existence of moments of partially restricted reduced form coefficients

In this paper ridgelike Bayesian estimators of structural coefficients have been used to form the partially restricted reduced form estimators. These partially restricted reduced form estimators are simple in form and possess finite sampling moments and risk in contrast to other restricted reduced form estimators that possess no finite moments and have infinite risk relative to quadratic loss functions. The usual k-class implied partially restricted reduced form estimators with 0≦k≦1 do not posses finite moments unless the degree of overidentification (or the excess of sample size over the number of coefficients) of the structural equation being estimated is suitably restricted.     

On the existence,uniqueness and stability of spatial equilibrium in an open city with externalities

This paper deals with the existence, uniqueness and stability of a spatial equilibrium in an open city with external diseconomies like air pollution generated by manufacturing activities. First, assuming that both production functions and utility functions are Cobb-Douglas, we prove the existence of a spatial equilibrium under some reasonable assumptions. It is shown, however, that the uniqueness and stability of the equilibrium may not be obtained, unless the degree of externality is sufficiently small. In fact, none of the equilibria will be stable for a certain set of speeds of adjustment in the labor market and the land market, if the degree of externality is relatively large. Finally, some implications of our results are derived in regard to the application of the hedonic price concept within the context of a spatial equilibrium model.     

On the normality of probability distributions of inflation and GNP forecasts

This study analyzes mean probability distributions reported by ASA-NBER forecasters on two macroeconomic variables, GNP and the GNP implicit price deflator. In the derivation of expectations, a critical assertion has been that the aggregate average expectation can be regarded as coming from a normal distribution. We find that, in fact, this assumption should be rejected in favor of distributions which are more peaked and skewed. For IPD, they are mostly positively skewed, and for nominal GNP the reverse is true. We then show that a non-central scaled t-distribution fit the empirical distributions remarkably well. The practice of using the degree of consensus across a group of predictions as a measure of a typical forecasters' uncertainty about the prediction is called to question.     

Is Giffen behaviour compatible with the axioms of consumer theory?

A family of direct utility functions is constructed which exhibit the characteristic of Giffenity, while satisfying the axioms of convexity and monotonicity. The approach starts by specifying a price offer curve, C₀, with a required backward-bending segment. Then a set of convex indifference curves is constructed having price offer curve arbitrarily close to C₀.     

小企业存在原因的一般分析

长期以来,规模经济理论阻塞了经济学家们对小企业存在和发展原因的分析,经济学家们面临要么承认规模经济导致的垄断性市场结构,要么肯定小企业的存在和发展的两难选择。本文将从协调规模经济与小企业存在之间矛盾的角度,分析小企业存在的一般原因。     

A remark on the existence of equilibria in markets without ordered preferences and with a Riesz space of commodities

We show the existence of competitive equilibria in economies without ordered preferences and a Hausdorff locally convex solid Riesz space of commodities. Our principal assumptions are that the commodity space has a predual and that its positive cone has a non-empty interior.