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A GAME FORM IS ANY SYSTEM which makes an outcome depend on individual actions of some kind, called strategies. Prime examples are systems of voting. Where voting consists of each person's marking a ballot, a strategy is simply a way of marking one's ballot. In the case of sequential voting on a number of motions, a strategy will be a contingency plan which tells how to vote on each motion as a function of the way the votes on previous motions have gone. By no means all game forms, though, are systems of voting; any system through which people interact exemplifies a game form.' This paper deals with game forms with a special property: that each person, no matter what his preferences are, can choose his strategy without regard to what he expects others to do. Such a game form will be called straightforward. Straightforward game forms of one kind are characterized by Gibbard [2]. Call a game form determinate if it makes an outcome depend on individual strategies in a way that involves no element of chance. In the case of a determinate game form, a strategy is dominant for a player with respect to a weak ordering of the alternatives iff no matter what anyone else does, the strategy secures an outcome at least as high in that weak ordering as is any other lottery that that player can secure, with the strategies of everyone else held fixed. A determinate game form is straightforward iff each player, for each weak ordering of the alternatives, has a strategy which is dominant with respect to that weak ordering. The only straightforward determinate game forms, it turns out, are trivial: a straightforward determinate game form either restricts the attainable outcomes in advance to no more than two, or makes one player a dictator among attainable outcomes. The game forms in this paper are of a more general kind. They are systems which make an outcome depend on individual strategies in a way that may involve chance. The systems to be considered have finitely many alternatives, finitely many players, and finitely many strategies for each player. A game form
THE PURPOSE OF THIS PAPER is to consider the validity of Durbin's [1] h test when the h statistic is calculated from instrumental variable estimates of an autoregressive model. It seems useful to provide such an analysis since h tests based upon instrumental variable results have been reported in the empirical literature (for example, see McCallum [3]). The validity of the h test is investigated by deriving the asymptotic distribution (under the null hypothesis) of an estimator of the first order serial correlation coefficient of the instrumental variable residuals. The variance of this distribution is obtained using methods similar to those employed by Sargan [5, Section 3], and is compared to the value required to justify the h test. The derivation of this variance leads to a valid large sample test procedure. The statistical model examined below is a structural equation from a dynamic stnultaneous equation system, but the results obtained also apply to situations in which no 'unlagged endogenous variables appear in the regressors.
[In empirical analysis of data consisting of repeated observations on economic units (time series on a cross section) it is often assumed that the coefficients of the quantitative variables (slopes) are the same, whereas the coefficients of the qualitative variables (intercepts or effects) vary over units or periods.This is the constant-slope variable-intercept framework. In such an analysis an explicit account should be taken of the statistical dependence that exists between the quantitative variables and the effects. It is shown that when this is done, the random effect approach and the fixed effect approach yield the same estimate for the slopes, the "within" estimate. Any matrix combination of the "within" and "between" estimates is generally biased. When the "within" estimate is subject to a relatively large error a minimum mean square error can be applied, as is generally done in regression analysis. Such an estimator is developed here from a somewhat different point of departure.]
[The existence of pollution externalities calls for government intervention in developing policy measures that will improve social welfare. This paper suggests a method to predict and compare the short-run aggregate output, pollution, and labor input of a competitive industry facing various environmental policies. Assuming that the choice between alternative production technologies can only take place prior to the investment decision, the labor output ratios and the pollution output ratios are fixed in the short run but vary among plants; their distribution is the information used in the aggregation procedure. The performance of different environmental policies--taxes and standards--is examined and compared.]