[This paper addresses the problem of estimating unknown regression coefficients when erroneous data and other violations of the standard assumptions are possible. An estimator which has a limited sensitivity to these departures from the assumptions is presented, and some of its properties are derived. This estimator is shown to have a certain efficiency property relative to other estimators with the same sensitivity to erroneous data.]

This paper develops a test of the rational expectations hypothesis advanced by Muth [18]. The framework considered here allows for multiperiod expectations of several endogenous variables, with or without lagged exogenous variables. In conventional (linear) models, the hypothesis implies that the expectations are linear in certain relevant variables, and restricts the coefficients of these variables to be certain functions of the parameters in the imbedding model. The test is developed as a test of the validity of these restrictions. The paper also treats the estimation problem in some details, under the alternative hypothesis which is taken as simply the negation of the rational expectations hypothesis.

Events by Grunberg and Modigliani [3]. Economic forecasts are made to be used, and decisions based on them may affect their ultimate realization. Grunberg and Modigliani explored this problem in a model in which future aggregate supply was influenced by current decisions based on the predicted future price. They applied the Brouwer fixed point theorem to show that if the future equilibrium price is a bounded continuous function of its currently predicted value, a exists. In [8] this result was placed in a temporary equilibrium context and the notation of a correct prediction was extended to include probabilistic predictions based on estimation procedures. Again, a fixed point theorem was applied to show that the causal influence of a forecast does not always invalidate it. Although this result is a reassuring and necessary first step, the analysis is confined to a single realization of the exogeneous variables. Thus a forecast is a single point or probability distribution rather than a function or conditional distribution whose domain is the space of observable variables. Of course, if the complete exogenous specification of the economy is observable, this is no restriction since the theorems could be applied separately to each realization. However, it is more likely that the space of observable variables contains a mixture of exogenous and endogenous variables without containing the complete set of either. Then if the exogenous variables are generated stochastically, the results of the above mentioned papers do not guarantee the existence of a statistically forecasting procedure. What is needed are general equilibrium versions of the results in [10], where, in particular, the statistically forecast of a future price is derived as a function of current and past prices. It would seem natural to approach this as a fixed point problem in the space of joint distributions of the observable variables and the

We investigate the structure of optimal policies in general multiperiod multiasset consumption-investment problems in the presence of transfer costs. A number of objectives such as utility of a consumption stream, utility of terminal wealth, and multiattribute utility are encompassed by the formulation. The general problem is first formulated as a stochastic dynamic program. The one-period subproblems are then analyzed using convex duality theory. The principal result is the characterization of a not necessarily convex of no for each period. If in any period the entering asset position is in this set, no transactions are made. Each point of the set is the vertex of a cone such that if the entering asset position is outside the set, the optimal policy is to move to the vertex of the cone in which the entering asset position lies. It is shown that the region of no transactions is a connected set and that it is a cone when the utility function is assumed to be positively homogeneous. In the latter case, the optimal decision policy and induced utility IN THIS PAPER we study a general class of multiperiod, multiasset investmentconsumption problems. Our purpose is to characterize the structure of optimal policies in the presence of transaction costs. Related problems have been studied by several authors, e.g., Constantinides [2, 3], Fama [5], Eppen and Fama [4], Kamin [7], Magill and Constantinides [10], Zabel [17], Hakansson [6], Merton [11], Samuelson [14], and Mukherjee and Zabel [12], and in these papers optimal policies have been characterized for a number of special cases. Our methodology significantly generalizes and sharpens many of the above results. For example, much of the previous work has been limited to the two-asset case or to particular utility functions, whereas our formulation allows any number of assets and general concave utility functions. The principal result of this paper, in the case of proportional transaction costs and concave utility functions, is the characterization of the optimal policy in each period and the set of entering asset positions from which no transactions should be made. This set or of no (RNT) can take on many forms ranging from a simple halfline to a nonconvex set. (See examples in Section 3.)

Lung-Fei Lee, G. S. Maddala, R. P. Trost, Asymptotic Covariance Matrices of Two-Stage Probit and Two-Stage Tobit Methods for Simultaneous Equations Models with Selectivity, Econometrica, Vol. 48, No. 2 (Mar., 1980), pp. 491-503

It was conjectured by Pigou that an increase in real national income, as reckoned in the prices of either the initial or the terminal period, would always correctly indicate an improvement in national welfare provided the increase referred to the aggregate income of a given group of persons with fixed preferences and a fixed proportional distribution of income among them. We show that if the individual preferences are assumed to be homothetic, and if by a welfare improvement one means respectively a potential improvement (in which losers can be compensated by gainers) or an actual improvement (in which all are gainers), then on either of these respective criteria Pigou's conjecture holds true under these conditions if and only if individual preferences are identical.

This paper reports both theoretical results and also computational experience with a method for approximating a competitive equilibrium in a piecewise linear economy. The algorithm consists of solving a sequence of linear programs, alternating between: (a) a problem which ensures a balancing bundle of choices and generates a price vector; and (b) a problem which indicates the maximum level of utility attainable by each household--given the initial resource endowments-and also given the prices generated at the current iteration of the master problem. Each subproblem provides a utility vector. The master problem determines a convex combination of the utility vectors generated at previous iterations. This convex combination is chosen so as to minimize the distance between the quantityconsistent and the price-consistent set. For the sequence of sub and master problems to approach a competitive equilibrium, this distance must approach zero. Thus far, the algorithm has failed whenever all equilibria are unstable, and it has converged rapidly when there are stable equilibria. It will be shown that the algorithm does not cycle. It will also be shown that if the sequence of solutions (obtained from the algorithm) converges, then it converges to a Walrasian equilibrium.