Knowledge that Transforms

[Necessary and sufficient conditions are determined under which a truncated approximation to generalized least squares is more efficient than ordinary least squares. For the general case, the necessary conditions are unlikely to be fulfilled. For a first order Markov model in a second order world, the sufficient conditions are satisfied only when one of the second order roots is very small, and therefore the first order assumption is approximately true. When the class of possible exogenous variables is limited to those typical of economic time series, the sufficient conditions are satisfied for a wider range of cases. Relative efficiencies are computed for a variety of cases.]

This paper considers the asymptotic distribution of forecasts made several time periods in the future. Such forecasts typically arise in the dynamic simulation of an econometric model.

[The economic environment (social output) is treated explicitly as a social choice variable. Individual orderings over the set of environments are derived from maximizing behavior. The influence of each individual on the choice made by society is expressed in terms of a power indice which is itself a function of the prevailing environment. These individual power indices give rise to a power rule which provides a social ordering over the set of environments, with the social choice set under any environment being non-empty. The existence of equilibrium in terms of the power rule is established.]

[This paper is concerned with "supergames" in which the action taken in a given time period by a player will affect the payoff to any other player in the subsequent period. A supergame consists of a set of players and a countable sequence of "ordinary" games. To illustrate "time-dependence," consider an economic market in discrete time. Say each firm must choose a price in each time period. This market has time-dependence if the amount demanded of a firm today is a function of the prices chosen today and of the prices chosen in the preceding period. Conditions are given for the existence of non-cooperative equilibria of two types: (i) steady state, in which the individual moves of the players converge over time to some s extasciicircum0 and (ii) balance temptation equilibria of the sort developed by Friedman [6] for games lacking time dependence.]

In long-run planning, targets may be set further in the future than economic technologies can be estimated. How costly in hindsight is limited foresight? Following Los, we say K is an e-horizon if knowledge of economic possibilities for the next K time periods permits decisions with results at most E worse than optimal. For a dynamic Leontief model, we show that any T-period efficient path is almost as big as all feasible T-period paths during the first T - K periods. Thus, given K periods notice, we can plan an E-optimal growth path no matter how technologies change after T.

1. INTIRODUCTION ANALYSES OF THE STABILITY of general competitive equilibrium2 have typically concerned themselves with the case of pure exchange. Sometimes that restriction has been inessential. In the tatonnement case, for example, if we are willing to make the assumption that all goods are gross substitutes, then it makes little difference where the excess demand functions come from.3 In less highly special cases, the restriction to pure exchange is a more serious matter. This is particularly so in the richer world of non-tatonnement processes. The difficulties raised by the abandonment of the pure exchange assumption in such models are three. First, such models, in assumptions or proofs, rest on considerations of utility maximization which are not immediately applicable to firms. Second, it is not fully natural to assume that stocks of goods are bounded, an important feature when non-tatonnement is being considered. Third, the creation and destruction of goods in the course of the adjustment process itself must be taken into account. The present paper shows how the first and, to some extent, the second of these problems can be handled in the context of the most appealing of the non-tatonnement models, that of the Hahn process.4 The third problem, that of the creation and disappearance of goods during the adjustment process is far more difficult. It is also not special to the introduction of firms, since the pure exchange models do not allow consumption to take place until equilibrium has been reached. Thus, this

[This paper demonstrates how the short-run static stability conditions of the two-sector growth model can be derived by converting the problem into a two-person, two-good exchange model. It is shown that the only necessary and sufficient condition for short-run stability is the Marshall-Lerner condition, and that the Drandakis (sufficient) condition follows easily from the former.]

R. L. Basmann, D. H. Richardson, R. J. Rohr, An Experimental Study of Structural Estimators and Test Statistics Associated with Dynamical Econometric Models, Econometrica, Vol. 42, No. 4 (Jul., 1974), pp. 717-730

[This paper looks at some aspects of the three stage least squares approach to estimating simultaneous econometric models. Three stage least squares is derived along the lines of best linear unbiased estimators in classical regression, whereby it is indicated that the usual assumption of non-singularity of the disturbance covariance matrix is unnecessary. Consistency of the estimator is shown as is the irrelevance of exactly identified equations to the estimation of other equations in a model when three stage least squares is used. Also included are an easily computed test for the validity of all specified overidentifying restrictions, and a method of efficiently estimating the reduced form using only the information contained in structural equations that are thought to be well specified.]