John Whalley, Philip M. White, A Decomposition Algorithm for General Equilibrium Computation with Application to International Trade Models: A Correction, Econometrica, Vol. 53, No. 3 (May, 1985), p. 679
[A general problem faced by both private firms and public enterprises is how to allocate the costs of common facilities fairly among the different goods and services produced. Any such cost accounting method can create incentives among product managers within the firm for altering the production function to their advantage. It is therefore both reasonable and desirable that a method reward increased efficientl by attributing lower unit costs to products whose marginal cost of production uniformly decreases. It is shown that there is only one "symmetric" method that satisfies this "monotonicity" principle--namely, the Aumann-Shapley price mechanism based on the Aumann-Shapley value for nonatomic games. This provides a new and simple axiomatization of this method without resorting to the usual assumption of additivity.]
A two-period (0 and T) Arrow^Debreu economy is set up with a general model of uncertainty.We suppose that an equilibrium exists for this economy.The Arrow-Debreu economy is placed in a Radner [31] setting; agents may trade claims continuously during [0,T].Under appropriate conditions it is possible to implement the original Arrow-Debreu equilibrium, which may have an infinite dimensional commodity space, in a Radner economy which has only a finite number of securities.This is done by opening the "right" set of securities markets, a set which effectively completes markets for the continuous trading Radner economy.
On decrit une representation tabulaire simplifiee qui fait ressortir une hypothese structurale implicite importante dans des modeles de selection bases sur la censure
An action in an extensive game that has a suboptimal payoff in every sequential equilibrium is said to be useless. There are sequential equilibria in which beliefs at each information set assign positive probability only to those nodes reached by the fewest useless actions. An action is second order useless if it is not useless but is strictly suboptimal in every equilibrium satisfying this condition on beliefs, and there exist sequential equilibria in which beliefs assign positive probability only to those nodes reached by the fewest useless actions, and, in this set, only those nodes requiring the fewest second order useless actions. Higher order uselessness is defined inductively, and beliefs satisfying the associated sequence of conditions are said to be justifiable. The existence of sequential equilibria with justifiable beliefs is demonstrated.
[Caves and Christensen [16] have provided a procedure for displaying the regular regions of a flexible functional form in the 2-good homothetic and nonhomothetic cases and in the 3-good homothetic case. We extend the procedure to the nonhomothetic 3-good case, and we apply the extended procedure to the translog, generalized Leontief, and minflex Laurent flexible functional form. In addition, we acquire the regular regions for the minflex Laurent model in the 2-good nonhomothetic case and superimpose the resulting regions on those already found by Caves and Christensen for the translog and generalized Leontief models. We find that the new minflex Laurent model generally has the largest regular regions of the three flexible functional forms. In addition, the regular region of the minflex Laurent model is found to expand as real income increases. As a result, that model is particularly well suited for use with time series data, which typically is characterized by positive long term growth trends in real income. In such applications, all recent data and future forecasts can be expected to lie within the regular region of the minflex Laurent model. Although it is possible for some of the earliest data to fall outside that regular region, the model's regular region nevertheless is sufficiently large to hold even all of those earliest data points in many data sets. The regular region of each of three models moves when the model's parameters are changed. With the generalized Leontief or translog model, the regular region's shape, location, and size are unpredictable without prior knowledge of the model's parameters. With either of those two models, the intersection of the model's regular regions, as the parameters are changed, is contained within a very small neighborhood of the one point at which we require the model to be regular. With the minflex Laurent model, the primary properties of the regular regions are invariant to the values of the parameters, and the intersection of the displayed regular regions is a very large unbounded set. The width of that intersection increases without limit as real income increases.]
Does a pure exchange economy with an infinite time horizon have determinate perfect foresight equilibria? When there is a finite number of infinitely lived agents equilibria are generically determinate. This is not true with overlapping generations of finitely lived agents. We ask whether the initial conditions together with the requirement of convergence to a steady state locally determine an equilibrium price path. In this framework there are many economies with isolated equilibria, many with continua of equilibria, and many with no equilibria at all. With two or more goods in every period not only can the price level be indeterminate but relative prices as well. Furthermore, such indeterminacy can occur whether or not there is fiat money and whether or not the equilibria are Pareto efficient. THIS PAPER CONSIDERS whether infinite horizon economies have determinate perfect foresight equilibria. This question is of crucial importance. If instead equilibria are locally indeterminate, not only are we unable to make comparative static predictions, but the agents in the model are unable to determine the consequences of unanticipated shocks. The idea underlying perfect foresight is that agents' expectations should be the actual future sequence predicted by the model; if the model does not make determinate predictions, the concept of perfect foresight is meaningless. We consider two extreme cases: the first with a finite number of infinitely lived consumers and the second with an infinite number of finitely lived consumers, an overlapping generations model. Both are models of stationary pure exchange economies. No production, including the storage of goods between periods, can occur. These models are unrealistic but are the easiest to study. Extensions of the results of this paper to models with production, infinitely lived assets, and mixtures of the two types of consumers are presented by Muller and Woodford [29]. When there is a finite number of infinitely lived consumers, we argue that equilibria are generically determinate. This is because the effective number of equations determining equilibria is not infinite, but equal to the number of agents minus one and must determine the marginal utility of income for all but one agent. Generically, near an equilibrium, these equations are independent and exactly determine the unknowns. When there are infinitely many overlapping generations, this reasoning breaks down: An infinite number of equations is not necessarily sufficient to determine
Different definitions of noncausality (according to Granger, Sims, Haugh and Pierce,...) are analyzed in terms of orthogonality in the Hilbert space of square integrable variables. Conditions, when necessary, are given for their respective equivalence. Some problems of testability are mentioned. Finally noncausality is also analyzed in terms of rational expectations, extending previous results of Sims. (Author)