[Differing opinions about the specification of econometric relationships often lead to a situation in which there are competing non-nested models. This paper is concerned with the problem of testing such models. It is first assumed that tests are based upon instrumental variable estimates (so that the models can be alternative versions of an equation in a system). The tests so derived are then specialized to the case in which ordinary least squares is an appropriate estimator.]

This paper examines some implications of the observation that the same Lagrange multiplier test is sometimes appropriate for quite different alternative hypotheses. A characterization of the class of such alternatives is developed which suggests a simple approach to testing for misspecification, and the consequences for finite sample power properties are examined by Monte Carlo experiments.

[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.]

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.

[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.]

Instrumental variable tests for serial correlation can be carried out by adding lagged residuals from initial estimation to the regressors of the model under scrutiny and then checking their joint significance. It is shown that asymptotically valid tests are obtained if the lagged residuals are also added to the initial instrument set. Monte Carlo evidence suggests that useful improvements in finite sample behavior under null and alternative hypotheses can be produced when the instrument set is extended to include the relevant lagged residuals. Links with other tests are discussed and a modification allowing for conditional heteroskedasticity is described. Copyright 1994 by MIT Press.

This paper is concerned with the problem of testing the hypothesis that the disturbances of a regression model are generated by a first-order autoregressive process against the alternative assumption that they follow a first-order moving average scheme. The test proposed has the advantages of requiring only ordinary least squares estimation and of being simple to implement. Some Monte Carlo results on the finite sample behaviour of the test are provided.

L. G. Godfrey, M. R. Wickens; Testing Linear and Log-Linear Regressions for Functional Form, The Review of Economic Studies, Volume 48, Issue 3, 1 July 1981, Pa

L. G. Godfrey, Michael McAleer, C. R. McKenzie, Variable Addition and Lagrange Multiplier Tests for Linear and Logarithmic Regression Models, The Review of Economics and Statistics, Vol. 70, No. 3 (Aug., 1988), pp. 492-503