Showing papers in "Econometrica in 1975"

Other solutions to nash's bargaining problem

Abstract: A two-person bargaining problem is considered. It is shown that under four axioms that describe the behavior of players there is a unique solution to such a problem. The axioms and the solution presented are different from those suggested by Nash. Also, families of solutions which satisfy a more limited set of axioms and which are continuous are discussed. WE CONSIDER a two-person bargaining problem mathematically formulated as follows. To every two-person game we associate a pair (a, S), where a is a point in the plane and S is a subset of the plane. The pair (a, S) has the following intuitive interpretation: a = (a1, a2) where ai is the level of utility that player i receives if the two players do not cooperate with each other. Every point x = (x1, x2) e S represents levels of utility for players 1 and 2 that can be reached by an outcome of the game which is feasible for the two players when they do cooperate. We are interested in finding an outcome in S which will be agreeable to both players. This problem was considered by Nash [3] and his classical result was that under certain axioms there is a unique solution. However, one of his axioms of independence of irrelevant alternatives came under criticism (see [2, p. 128]). In this paper we suggest an alternative axiom which leads to another unique solution. Also, it was called to our attention by the referee that experiments conducted by H. W. Crott [1] led to the solution implied by our axioms rather than to Nash's solution. We also consider the class of continuous solutions which are required to satisfy only the axioms of Nash which are usually accepted. We give examples of families of such solutions.

Congestion tolls for poisson queuing processes

Abstract: The relationship between Pareto optimal (0s) and revenue maximizing (Or) tolls is examined for queuing models that permit balking. When customers have the same value for waiting time, Q, =Or provided the entrepreneur can impose a simple two-part tariff. With heterogeneous values for waiting time, Or can be greater than, equal to, or less than H,. Expanding the number of servers and charging multi-part tariffs are shown to be alternative methods for segmenting the market, and the welfare implications of these two strategies are explored.

Production and Demand Models with Direct or Indirect Implicit Additivity

Abstract: Direct or indirect additivity of production or utility functions implies dependence of substitution effects on income effects. This dependence is eliminated by implicit additivity, or strong separability along isoquants or indifference surfaces. The present study proposes and analyzes two models, with direct and indirect implicit additivity, respectively, which are generally non-homothetic, non-CES, and include less than 3n parameters for n goods. They give rise to log-linear systems of estimable demand relations. Many other models, such as Cobb-Douglas, CES, Direct and Indirect Addilog, CRESH, CDE, and Non-homothetic CES, are simple, testable special cases of either or both of these models.

Estimation of the two-limit probit regression model

Abstract: Some economic variables are restricted by an upper and lower limit but are continuous between the two limits. Measurements of such variables are sometimes available in their natural form and sometimes only in the form of three categories where information concerning the middle category is suppressed (unemployed, employed part time, employed full time, for example). Where such a variable is a continuous function of other variables between the two limits, the function can be estimated from data of either sort provided the function and the distribution of errors can be specified. WHEN THE LIMITED dependent variable technique developed by Tobin [3] is extended to provide for cases in which the dependent variable in a regression is subject to both an upper limit and a lower limit, a surprising property of the statistical model emerges.1 Estimates of the regression function can be obtained whether or not the exact values of the dependent variable are known for the nonlimit cases. Provided the functional form can be specified correctly, classification of the dependent variable into upper limit, lower limit, and non-limit observations provides enough information, along with observed values of the independent

Pareto optimality in non-convex economies

Abstract: This article uses the concept of "cone of interior displacements," which extends the notion of differentiability, to set up a characterization of Pareto optima in non-convex economies. A general theorem asserting that a Pareto optimum is a PA equilibrium is given and specifications are discussed. It is finally argued that the usual formulation of the doctrine of "marginal cost pricing"as a doctrine for achieving Pareto optimal states in a non-convex decentralized economy has unsatisfactory logical basis, and a way of defining a minimum degree of centralization inherent to non-convex economies is suggested. THE MAIN RESULTS of the economic theory of allocation of resources rest upon assumptions of convexity: convexity of production sets, and convexity of preferences. The relevance of these assumptions is often doubtful; even if in a many consumer economy the classical statements can be extended to the case of nonconvex preferences (this idea, pointed out first by Farrell [13] and Rothenberg [24], was developed in the general framework of economics with a continuum of agents as introduced by Aumann [4]; see W. Hildenbrand [18 and 19]), the indivisibilities arising in production are often large and create non-convexities that cannot be overlooked. Furthermore, non-convexities may arise with externalities (see Baumol [5], Kolm [20], and Starrett [25]), exchange of information (see Radner [23]), or stock markets (see Dreze [10]). Even if one must take the risk of producing less elegant results, a relevant economic theory cannot ignore non-convexities.

An instrumental variable approach to full-information estimators for linear and non-linear econometric models

Abstract: FIML is shown to be an instrumental variables estimator where the instruments embody all the over-identifying a priori restrictions. FIML is compared to the two alternative estimators 3SLS and full information instrumental variables. 3SLS differs from FIML in not using all a priori restrictions in forming the instruments. The full information instrumental variables estimator when iterated to convergence yields the FIML estimate. For the case of nonlinearity in the parameters a nonlinear 3SLS and a nonlinear full information instrumental variables estimator are proposed. Both estimators are asymptotically efficient. THIS PAPER UNDERTAKES an investigation of asymptotically efficient estimators for linear and nonlinear simultaneous equation econometric models. By using an instrumental variable approach the equivalence of previously proposed linear estimators to full information maximum likelihood (FIML) follows in a straightforward manner, and a class of new estimators which includes a nonlinear three stage least squares estimator (NL3SLS) and nonlinear full information instrumental variables estimator are proposed and shown to be asymptotically equivalent to FIML. First, an instrumental variable interpretation of FIML is developed by investigating the first order conditions for the maximum of the likelihood function without first concentrating the likelihood function. The essential difference between 3SLS and FIML then becomes evident. The difference between the two estimators is first that FIML uses all over-identifying restrictions in forming the instruments while 3SLS ignores some of these restrictions. Also, FIML uses an estimate of the covariance matrix in forming the instruments which is consistent in the sample with the parameter estimates. Thus the instruments used by FIML are mutually consistent with the parameter estimates in the given sample, while for other estimators the instruments are consistent with the parameter estimates only asymptotically. While this difference in forming the instruments is of no importance asymptotically as is known by the earlier results of Sargan [10] and Rothenberg and Leenders [9], in finite samples there seems to be no reason for not using all known prior information. The use of the a priori restrictions gives a more useful criterion than Dhrymes' [3] recent interpretations of a difference in "purging" the endogenous variables since all other proposed estimators can be shown to be equivalent by simply proving asymptotic equivalence of the instruments used to those instruments used by the FIML estimator. Then using the instrumental variable interpretation, a relation between FIML and the class of estimators recently proposed by Dhrymes [2], Lyttkens [5, 6], and Brundy and Jorgenson [1] is established. The full information instrumental

Values of markets with a continuum of traders

Abstract: It is shown that in markets with a continuum of traders, the allocations associated with the Shapley value are the same as the competitive allocations

The distribution of tenant benefits in public housing

Abstract: In this paper we estimate the Hicksian equivalent variation of consumer's surplus for a sample of public housing tenants and examine the distribution of these surpluses by household characteristics To do this we estimate the parameters of a generalized CES utility function (imposing second order constraints as needed) and of a Cobb-Douglas utility function The Cobb-Douglas specification is rejected statistically and benefit estimates based on it follow a significantly different distributional pattern than those estimated with the generalized CES, although there is not much difference in average benefits

A note on the underestimation and overestimation of the leontief inverse

Abstract: Suppose that the coefficients of an input-output matrix, A, are random variables but that we have ascertained their expected values, EA. What will be the relation of the Leontief inverse of EA, (I EA) ', to the expected value of the inverse, E(I A) "? Will one or the other be uniformly greater? We will show that if all coefficients of A are independent, then the expected value of the inverse is uniformly greater than or equal to the inverse of the expected value. If, on the other hand, the column and row sums of the coefficient matrix are fixed, and smaller than one, so that the variables are not independent, then, in the two-by-two case, the opposite is true of the off-diagonal elements.

Nonstandard exchange economies

Abstract: Edgeworth's conjecture that as the number of traders in an exchange economy increases the core approaches the set of competitive equilibria has been formalized both as a theorem about a sequence of finite economies, and as a theorem about an economy having an infinite number of agents. This paper, using nonstandard analysis, provides a synthesis of these two approaches. It is shown that the core and the set of competitive equilibria are equivalent within a non-standard exchange economy. This theorem implies a asymptotic theorem concerning the core and competitive equilibria of sequences of finite economies. (Из Ebsco)

GRAM-CHARLIER APPROXIMATIONS APPLIED TO t RATIOS OF k-CLASS ESTIMATORS

Abstract: This paper obtains Edgeworth or Gram-Charlier expansions for the t ratio of instrumental variable and k-class estimators, and uses them to give approximations to the confidence intervals obtained from these t ratios. These confidence intervals for large sample size are more accurate than the usual asymptotic confidence interval. Charlier expansions is applied to the t ratio of 2SLS and non-stochastic k-class estimators. Previous general theorems in this field, with the exception of those given by Chambers [2], such as those in [3] have assumed that the statistic has moments of appropriate orders. The theorem proved here assumes only that it can be expressed as a function of other variables with moments of all orders with appropriate properties in some neighborhood of the origin. It can be applied to a wide range of

Error Analysis in Nearly-Completely Decomposable Stochastic Systems

Abstract: The purpose of this paper is to analyze the accuracy of the Simon-Ando approximation for stochastic nearly-completely decomposable systems. Relations are established defining this accuracy as a function of the maximum degree of coupling (e) between aggregates, the conditioning and the indecomposability of these aggregates. A procedure is derived by which estimates in c2 may be computed from aggregate eigencharacteristics. Finally, the Simon-Ando approximation is shown to be optimal in block-stochastic matrices, and the accuracy achievable by higher-order aggregation is examined.

An adaptive learning rule for multiperiod decision problems

Abstract: Zellner [11], and Chow [3], is to deal with the uncertainty by treating the model parameters as independent, identically distributed random variables in each period,' yielding what Zellner calls "sequential updating" rules. Although the sequential updating rules do capture the uncertainty, they ignore the possibility of ongoing estimation in the formulation of decision rules. The purpose of this paper is to develop an adaptive learning decision rule for the multiperiod problem. This rule incorporates the effect of policy variables on the learning which is expected to occur throughout the remainder of the planning period. It is a generalization of the rules described above in the sense that both of them can be derived as special cases of this rule. Finally, this decision rule yields to economic analysis in terms of the stock and value of information, a feature which is not found in previous work. Section 2 of the paper describes the multiperiod decision problem with unknown parameters, discusses the assumptions associated with the certainty equivalence and sequential updating rules, and then presents the assumptions employed in this paper. Adaptive learning decision rules are derived in Section 3 and a mathe

The graph of the walras correspondence

Abstract: THE WALRAS CORRESPONDENCE associates the set equilibrium price vectors with an economy. The purpose of this paper is to study some topological properties of the graph of the Walras correspondence such as connectedness and contractibility. This is done once the graph is given the structure of a bundle. The mathematical notations used in this paper are given in Section 2. The bundle structure of the graph is proved in Section 3. The contractibility of the graph is then a straightforward result proved in Section 4. Finally, variable demand functions are introduced in Section 5 and connectivity is then proved.