[Given n observations on a system of linear stochastic difference equations with appropriate initial conditions, and given a prior density (possibly diffuse) of its parameters, this paper obtains the predictor of the time series k periods into the future with minimum mean squared error. Completely analytical solution is given for predictions from the first-order univariate system, and, in the general higher-order multivariate case, for k up to 5.]
where y(t) represents the vector of endogenous variables, x(t) the vector of exogenous variables, u(t) the vector of stochastic disturbances, and t the tth period of observation. The matrices A, (T = 0, 1, . . . , m) of the structural coefficients are square matrices of order G. It is assumed that the conditions justifying the theorems in [3, Ch. 10] are satisfied, and that there are no nonlinear restrictions on the elements of A.. The stability of the system is determined by reference to the dominant root of the polynomial equation (2) det E Atmt) =0. t=O
[The purposes of this paper are to establish propositions about the behavior of the supply curve of labor to the individual firm and to estimate the distribution of the elasticities of this supply curve by firm. The main statistical problem faced is the possibility that labor quality increases with firm size so that one does not know how to interpret the relationship of firm size and measured wages. My solution to that problem is to look at the relationship of wages to firm size relative to population density, since I expect the "quality" and the labor supply effects to differ markedly in this respect.]
[In this paper we generalize the family of single equation k-class estimators to systems of equations. The systems k-class estimator with k = 1 is the 3SLS estimator. After developing the asymptotic properties we introduce a further member of the systems k-class, the systems LVR estimator. A systems version of Basmann's identifiability test statistic is also considered.]
T. A. Yancey, G. G. Judge, M. E. Bock, Wallace's Weak Mean Square Error Criterion for Testing Linear Restrictions in Regression: A Tighter Bound, Econometrica, Vol. 41, No. 6 (Nov., 1973), pp. 1203-1206
[Dans un article déjà ancien, les Professeurs C. Fourgeaud et A. Nataf [7] s'étaient attachés à définir la forme la plus générale prise par un système complet de fonctions de demande lorsque ces fonctions ne dépendent que du revenu réel et du prix réel du bien considéré. Ce papier retrace un essai d'interprétation et une expérience d'estimation numérique de ces fonctions. On sait que le système de Fourgeaud et Nataf constitue une généralisation intéressante du bien connu système linéaire de dépenses de R. Stone. Il permet en effet d'introduire un peu plus de flexibilité dans les effets de substitution permis par le modèle mais surtout il accroît fortement la richesse des effets revenu. Dans cette étude cette possibilité est appliquée à la prise en compte d'effets revenus de courte et de longue période, le but étant de pouvoir disposer d'un modèle de cheminement applicable aux études de planification à moyen terme.]
[The limited information maximum likelihood and two-stage least squares estimates have the same asymptotic normal distribution; the ordinary least squares estimate has another asymptotic normal distribution. This paper considers more accurate approximations to the distributions of the so-called "k-class" estimates. An asymptotic expansion of the distribution of such an estimate is given in terms of an Edgeworth or Gram-Charlier series (of which the leading term is the normal distribution). The development also permits expression of the exact distribution in several forms. The distributions of the two-stage least squares and ordinary least squares estimates are transformed to doubly-noncentral F distributions. Numerical comparisons are made between the approximate distributions and exact distributions calculated by the second author.]
[The problem of collinearity suggests the search for an alternative to ordinary least squares which, although biased, might reduce the mean square error of the coefficient of interest. Two types of estimators are examined, and the corresponding mean square error loss functions are calculated.]
An intertemporal model for the capital market is deduced from the portfolio selection behavior by an arbitrary number of investors who aot so to maximize the expected utility of lifetime consumption and who can trade continuously in time. Explicit demand functions for assets are derived, and it is shown that, unlike the one-period model, current demands are affected by the possibility of uncertain changes in future investment opportunities. After aggregating demands and requiring market clearing, the equilibrium relationships among expected returns are derived, and contrary to the classical capital asset pricing model, expected returns on risky assets may differ from the riskless rate even when they have no systematic or market risk. ONE OF THE MORE important developments in modern capital market theory is the Sharpe-Lintner-Mossin mean-variance equilibrium model of exchange, commonly called the capital asset pricing model.2 Although the model has been the basis for more than one hundred academic papers and has had significant impact on the non-academic financial community,' it is still subject to theoretical and empirical criticism. Because the model assumes that investors choose their portfolios according to the Markowitz [21] mean-variance criterion, it is subject to all the theoretical objections to this criterion, of which there are many.4 It has also been criticized for the additional assumptions required,5 especially homogeneous expectations and the single-period nature of the model. The proponents of the model who agree with the theoretical objections, but who argue that the capital market operates as if these assumptions were satisfied, are themselves not beyond criticism. While the model predicts that the expected excess return from holding an asset is proportional to the covariance of its return with the market