OLS with Autocorrelation: Key Consequences

When autocorrelation is present in the error terms of a regression model, it violates a key assumption of the Ordinary Least Squares (OLS) method. This violation leads to specific consequences:

Analysis of Potential Consequences:

• i. Coefficients estimates may be misleading: This statement is incorrect. While OLS is no longer the most efficient estimation method (not BLUE), the coefficient estimates ($\hat{\beta}$) themselves remain unbiased and consistent even in the presence of autocorrelation. They are not systematically wrong.
• ii. Hypothesis tests could reach the wrong conclusions: This statement is correct. Autocorrelation leads to incorrect standard error estimates. Standard OLS formulas for standard errors assume independent errors, which is violated. Using these incorrect standard errors in t-tests, F-tests, and other hypothesis tests can lead to erroneous conclusions about the significance of variables.
• iii. Forecasts made from the model could be biased: This statement is incorrect. Since the OLS coefficient estimates remain unbiased, the point forecasts derived from them ($\hat{y} = X\hat{\beta}$) are also unbiased. However, the uncertainty around these forecasts (prediction intervals) will be incorrectly estimated due to the faulty standard errors.
• iv. Standard errors may be inappropriate: This statement is correct. This is a direct consequence of violating the independence assumption. The standard formulas used to compute the variance-covariance matrix of the OLS estimators are based on the assumption of zero correlation between error terms. When this correlation exists, the computed standard errors are biased and inconsistent, making them inappropriate for inference.

Conclusion on Consequences:

Based on the analysis, the likely consequences of using OLS in the presence of autocorrelation are that hypothesis tests may yield incorrect results (ii) and the calculated standard errors become inappropriate (iv).

Therefore, the correct options are ii and iv only.