An over-identified model could be defined as an exactly identified model that is subject to over-identifying restrictions. One could therefore define a constrained indirect least squares estimator for systems of equations similar to generalized least squares estimators under constraints for single equations. The estimator differs from three stage least squares in using the indirect least squares estimated covariance instead of the two stage least squares estimated covariance. With linear constraints, the estimator is linear. Under the overall null hypothesis with all constraints obtaining, the constrained indirect least squares estimator has the same asymptotic properties as the full infornhtation maximum likelihood estimator. The main advantage of the estimator lies in its easy adaptability to the multiple comparisonist's preferred testing procedure given the exactly identified model as maintained hypothesis. In this paper we stay with the likelihood principle and the corresponding preliminary Wald-type multiple X tests. 1. PROPERTIES OF SEQUENTIALLY CONSTRAINED MAXIMUM LIKELIHOOD ESTIMATORS BELOW WE DEFINE a family of estimators obtained by adding one or a group of constraints after another. To verify the properties of these estimators, we first compare the covariances in the asymptotic distribution of maximum likelihood estimators of models that differ in the number of prior constraints on the structural parameter. References are [1, 13, and 14], but we state the comparisons in a form that shows more of the details. Let f( ; xt, 0) be the density of the endogenous variables yt E R G conditional on the exogenous variables x, E R K and the reduced form parameter 0 E R m. For a sequence (yt), t = 1, . n of n independently selected endogenous variables,

Since dynamic regression equations are often obtained from rational distributed lag models and include several lagged values of the dependent variable as regressors, high order serial correlation in the disturbances is frequently a more plausible alternative to the assumption of serial independence than the usual first order autoregressive error model. The purpose of this paper is to examine the problem of testing against general autoregressive and moving average error processes. The Lagrange multiplier approach is adopted and it is shown that the test against the nth order autoregressive error model is exactly the same as the test against the nth order moving average alternative. Some comments are made on the treatment of serial correlation.

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.

[There has been increasing concern recently over the use of the simple first order Markov form to model error autocorrelation in regression analysis. The consequence of misspecifying the error model will be especially serious when the regressors include lagged values of the dependent variable. The purpose of this paper is to develop Lagrange multiplier tests of the assumed error model against specified ARMA alternatives. It is shown that all of the tests can be regarded as asymptotic tests of the significance of a coefficient of determination, and a table is provided which gives details of two general tests and several special cases.]

We consider dynamic choice behavior under conditions of uncertainty, with emphasis on the timing of the resolution of uncertainty.Choice behavior in which an individual distinguishes between lotteries based on the times at which their uncertainty resolves is axiomatized and represented, thus the result is choice behavior which cannot be represented by a single cardinal utility function on the vector of payoffs.Both descriptive and normative treatments of the problem are given and are shown to be equivalent.Various specializations are provided, including an extension of "separable" utility and representation by a single cardinal utility function.