Knowledge that Transforms

[This note provides a rigorous description of a game in a strategic form whose Nash equilibria are all strong equilibriaccoinciding with the Walras equilibria of the underlying Arrow-Breau pure exchange economy.]

[The theory of monetary policy is examined as it pertains to the functions of money as intermediating intergenerational trade as well as providing a useful service return. Finite economic lives are shown to alter the characterization of the optimal inflation rate from that suggested by models with infinitely long lived agents. In uncertain environments with sequential trade, policy is examined as altering the range of possible trades between agents of successive generations. In some cases, fully anticipated activist feedback policies may increase expected utility from that attainable with passive policies.]

[Methods of estimation for markets in disequilibrium have been limited to the single-market case. However, the spill-over effects of the unsatisfied demand or supply in other markets are considered to be an essential feature of disequilibrium analysis. This paper (i) develops a two-market disequilibrium model that is amenable to estimation; (ii) provides the maximum likelihood method and the two-stage least squares method for estimation; and (iii) generalizes this disequilibrium model to the n-market case, showing sufficient conditions for the existence and uniqueness of a quantity-constrained equilibrium--i.e., for its solvability as an econometric model.]

IN HIS SURVEY ON RATIONAL EXPECTATIONS, R. Shiller indicates that the difficulty of obtaining explicit solutions for linear difference models under rational expectations may have hindered their use [14, p. 27]. The present paper attempts to remedy that problem by giving the explicit solution for an important subclass of the model Shiller refers to as the general linear difference model. Section 1 presents the form of the model for which the solution is derived and shows how particular models can be put in this form. Section 2 gives the solution together with the conditions for existence and uniqueness. 1. THE MODEL The model is given by (la), (lb), and (1c) as follows:

[The purpose of this paper is to reconsider the theory of Pareto optimal redistribution from a game-theoretic point of view. We define an income redistribution game in strategic form, which may allow many varieties of utilityinterdependencies. The strategy of each individual is a vector that describes a plan of transfers from him to every other individual. The results state that while a Pareto optimal redistribution is always achieved by a Nash equilibrium in the two-person case, it is not so when there are more than two individuals. The sufficient condition we derived seems unlikely to be satisfied in general.]

The subject is retiming of lags in a system of linear difference equations. The issues are (i) the effect of retiming on stability and (ii) the effect of retiming on speed of adjustment. Regarding (i), a theorem due to Bear [1] is sharpened; and new conditions for stability to survive under a retiming of lags are obtained. Regarding (ii), the main results concern the effects of lag perturbations and spread perturbations on speed of adjustment in models with nonnegative coefficients.

A NUMBER OF ARTICLES have been written in recent as well as more distant times on the subject of limited dependent variables. This broad classification includes two particular special cases. First, the dependent variable has finite probability mass concentrated at some limit point-the so called Tobit model. This case is referred to as the censored model in the statistical literature. The second case is when the dependent variable simply has a limited range and follows a continuous density on this support-the truncated case. In this note we show that a fairly powerful technique for truncated normal distributions, first suggested over 70 years ago by Karl Pearson and Alice Lee [9], can be used in the place of more sophisticated iterative maximum likelihood or instrumental variables techniques. Approximations based upon least squares regressions can be generated which require only a calculator and the table produced here. The censored or limited variable case can also be treated in much the same way. Although the estimator is inconsistent, a consistent estimator based upon this general approach could probably be constructed. An example is given comparing this approximation with the results produced by least squares, maximum likelihood, and Amemiya's consistent estimator. The estimator suggested here compares very favorably with Amemiya's. In a more literary vein, Pearson and Lee should be given substantial credit for their work without detracting in any way from those who independently advanced the area without the benefit of reference to the rather obscure article by Pearson and Lee.2

This paper considers a problem faced by players who are involved in a sequence of games: not necessarily the same games, not necessarily with the same opponents, and not necessarily under conditions of complete information. The players are assumed to act in response to stationary Markovian hypotheses which they form about the actions of their opponents. Conditions are explored which require that these hypotheses be correct on average and that the players actions be optimal in response to their hypotheses.