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.

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,

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.]

16-17 year olds, or both, we estimate that these differentials would increase total teenage employment. amount of the increase is largely conjectural, since error variances in estimated parameters are large. For example, we estimate a two-standard-deviation upper bound for increased teenage employment of roughly 5% for a differential of 1.60-1.28 extended to the 14-15 year-old group, and an upper bound increase of 10% if the same differential is extended to all those 14-17 years old. lower bound in each case is roughly zero, so that a reduction in total teenage employment seems unlikely. An important question of differentials is the effect on employment of those groups to whom the differential is not extended. For a differential extended to 14-15 year-old workers, we estimate virtually no effect on employment of those 16-19 years old. substitution effects are nullified by scale effects. For a more broadly based 1.601.28 differential extended to those 14-17, the range of uncertainty concerning employment of those 18-19 is large, encompassing reductions and increases of 5%. REFERENCES Allen, R.G.D., Mathematical Analysis for Economists (New York: St. Martins Press, 1938). Hashimoto, Masanori, and Jacob Mincer, Employment and Effects of unpublished manuscript, National Bureau of Economic Research, April 1970. Kosters, Marvin, and Finis Welch, The Effects of Wages on the Distribution of Changes in Aggregate Employment, American Economic Review 62 (June 1972), 323-332. Mincer, Jacob, Unemployment Effects of Journal of Political Economy 84, part 2 (Aug. 1976), 87-104. Parsons, Donald, The Cost of School Time, Foregone Earnings, and Human Capital Formulation, unpublished manuscript, Ohio State University, Feb. 1973. Siskind, Frederic B., Minimum Wage Legislation in the United States: Comment, Economic Inquiry 15 (Jan. 1977), 135-138. U.S. Department of Labor, Bureau of Labor Statistics, Youth and Wages, Bulletin 1657 (1970). Welch, Finis, Minimum Wage Legislation in the United States, Economic Inquiry 12 (Sept. 1974), 285-318. Minimum Wage Legislation in the United States: Reply, Economic Inquiry 15 (Jan. 1977), 139-142.

Ezequiel L. Machado, Willard T. Carleton, Financial Planning in a Regulated Environment, The Journal of Financial and Quantitative Analysis, Vol. 13, No. 4, Proceedings of Thirteenth Annual Conference of the Western Finance Association, June 20-26, 1978 (Nov., 1978), pp. 759-777

Of the behavioral recommendations garnered from modern capital market theory, few, if any, generalizations have been documented as convincingly as the simple advice to hold several assets in one's portfolio. Sharpe made such a conclusion perfectly clear when he stated [27, p. 184]:If the market is efficient and if an investor is privy to no special information or predictive power, what should he do? First, and most important: diversify.

Morton I. Kamien, Nancy L. Schwartz; Optimal Exhaustible Resource Depletion with Endogenous Technical Change, The Review of Economic Studies, Volume 45, Is

Morton I. Kamien, Nancy L. Schwartz; Potential Rivalry, Monopoly Profits and the Pace of Inventive Activity, The Review of Economic Studies, Volume 45, Issue 3,