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.
Answer and explanation
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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UGC NET Economics