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# B1 absence of disturbance term serial correlation the

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B:1: ABSENCE OF DISTURBANCE TERM SERIAL CORRELATION: The consequences of estimating the regression model by OLS when the assumption of no serial correlation between equation disturbances is not valid depend upon the properties of the regressors. Consider first the case where all the LRM assumptions and the regressors are non-stochastic). Serial correlation results in the

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10 OLS estimator no longer being BLUE. In these circumstances, the OLS estimator is inefficient although still unbiased. Stating that an estimator is inefficient means that the estimator has a higher variance than some other unbiased estimator. If the error term did in fact exhibit serial correlation, the OLS estimator would be making no use of this information. It is the failure of the estimator to use that information that explains the inefficiency. Another (and probably more serious) consequence of disturbance serial correlation is that the standard errors of the OLS estimators are in general biased. This means that the use of t and F statistics to test hypotheses is misleading or invalid. If the researcher knew the true structure of the serial correlation, then an alternative estimator - the Generalised Least Squares (GLS) estimator - could be used instead of OLS, and would yield unbiased and efficient parameter estimates. Note that in practice the researcher will not be able to use GLS as such because the researcher will not know the true structure of the serial correlation,; he or she will have to assume a structure, estimate its parameters, and then use "feasible least squares". Where the regressors are stochastic, serial correlation will also result in efficiency losses, and may also lead to OLS being inconsistent. The error term could be serially correlated (or autocorrelated) in many different ways. One structure that might be taken is given by the following specification of the equation disturbance term: t t-1 t u = u + ρ ε ( 65) where ε t is assumed to be a "white noise" error term (that is, it has a zero mean, is serially uncorrelated and has a constant variance). This equation states that the disturbance term u t is generated by a first order serially correlated (autoregressive) process. We denote the process described by (32) as an AR(1) process, where AR is used to mean autoregressive . The assumptions of the NCLRM or LRM imply that ρ =0, so that u t = ε t . INSPECTION OF RESIDUALS Visual inspection of a graph of the regression residuals may be a useful starting point in indicating whether there is a potential problem of serial correlation. However, any inference from such inspection should be backed up by the use of a formal test statistic. THE DURBIN-WATSON (DW) TEST The Durbin-Watson test can be used to test the null hypothesis that the error term is serially uncorrelated, against the alternative that each disturbance term is correlated with the disturbance term in the previous period. In this alternative case, the disturbance is said to be serially correlated of order one. The required null
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