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.

[A process which combines a planning procedure for the allocation of final products and a multilateral nonrecontracting trading process for allocating primary and intermediate goods is defined and shown to satisfy Malinvaud's criteria for evaluating planning procedures. Central processing costs are lower than in the Malinvaud procedure since the central planner only collects information on final products.]

[The parameters of dynamic simultaneous equation models are often estimated using methods which are appropriate only when the errors of the equations are serially independent. The purpose of this paper is to propose a large sample test for serial correlation to replace the invalid Durbin-Watson test. The test requires only simple calculations and can be easily added to standard two-stage least squares/instrumental variables programs. The treatment of serial correlation is discussed. An example is given to illustrate the test procedure.]

[This paper examines the determinants of the demand for labor by fourteen two-digit manufacturing industries of India, and in particular the role of factor prices and expectations, to aid understanding of the causes of the low rates of labor absorption in the manufacturing sector. This is done within the framework of neoclassical models of factor demand. A method is suggested for measuring expectations. Our results show that adverse factor prices, long adjustment lags, low output elasticities, and the shift in the industrial structure in favor of the capital goods sector are some of the more important factors responsible for the observed low rates of labor absorption. Finally, some implications of our results for studies relating to labor demand functions in general are discussed.]

James L. Kenkel, Some Small Sample Properties of Durbin's Tests for Serial Correlation in Regression Models Containing Lagged Dependent Variables, Econometrica, Vol. 42, No. 4 (Jul., 1974), pp. 763-769

[This paper presents an axiomatic characterization of commodities for which the consumer faces a choice of quality rather than a choice of quantity. Properties of individual and market demand functions for commodities of differing quality levels are derived. Properties of comparative static price changes in response to supply changes at one or more quality levels are also developed. The analysis is then applied to price changes in housing markets.]

I N 1956 Gale [4] considered a general model of balanced growth and asserted the existence of price vectors which equate the economic growth with the technological growth rate. This model of Gale was an extension of fundamental results earlier proven by von Neumann for the case in which the production space was polyhedral. Recently Hulsmann and Steinmetz [6] demonstrated that Gale's theorem was not true by constructing a counterexample. In this paper we shall prove that Gale's theorem in a modified form is true and with a certain regularization the original theorem of Gale is valid. This regularization will be automatically satisfied by polyhedral production spaces so that as a corollary the proof for the polyhedral version of Gale's theorem will be attained. Finally we show that the counterexample of Hulsmann and Steinmetz [6] does not satisfy this regularization.