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      Question

      In a linear regression model estimated using OLS,

      suppose the disturbance term follows a first-order autoregressive process AR(1) with parameter ρ>0, while maintaining constant variance. Which of the following statements is most accurate?
      A OLS estimators become biased and inconsistent Correct Answer Incorrect Answer
      B OLS estimators remain unbiased but lose efficiency, and usual standard errors are inconsistent Correct Answer Incorrect Answer
      C OLS estimators remain BLUE due to constant variance Correct Answer Incorrect Answer
      D GLS and OLS estimators coincide asymptotically Correct Answer Incorrect Answer

      Solution

      Autocorrelation violates the Gauss-Markov assumption of independence of errors, not the zero-mean or exogeneity condition. Hence: OLS estimators remain unbiased and consistent.  However, they are no longer efficient (not BLUE) because variance is not minimum.  More importantly, the estimated standard errors are biased, leading to unreliable t-tests and F-tests (typically underestimated → inflated significance). GLS (or feasible GLS) becomes the efficient estimator in such cases.

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