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If OLS is used in the presence of auto-correlation, which of the following will be likely consequences…

In a classical linear regression model with exogenous explanatory variables, if Ordinary Least Squares (OLS) is used when the error terms are autocorrelated: - The OLS…

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If OLS is used in the presence of auto-correlation, which of the following will be likely consequences ? i. Coefficients estimates may be misleading. ii. Hypothesis tests could reach the wrong conclusions. iii. Forecasts made from the model could be biased. iv. Standard errors may be inappropriate.

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Correct answer A

In a classical linear regression model with exogenous explanatory variables, if Ordinary Least Squares (OLS) is used when the error terms are autocorrelated: - The OLS coefficient estimators remain unbiased and consistent, so Statement (i) ('Coefficients estimates may be misleading') is false in terms of unbiasedness. - Point forecasts based on the OLS estimators remain unbiased (though inefficient), so Statement (iii) ('Forecasts made from the model could be biased') is false. - However, the standard OLS variance formulas are biased, making the estimated standard errors inappropriate (Statement iv is true). - Because the standard errors are biased (typically downward under positive autocorrelation), t-statistics and F-statistics are invalid, so hypothesis tests can reach wrong conclusions (Statement ii is true). Therefore, (ii) and (iv) only is the correct answer.

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