Serial correlation causes the OLS estimates of the SE(b)s to be biased in hypothesis testing. True False
The correct answer and explanation is:
The correct answer is True.
Serial correlation, also known as autocorrelation, occurs when the residuals (errors) from a regression model are correlated across time or space. This violates one of the key assumptions of the ordinary least squares (OLS) method, which assumes that the residuals are uncorrelated. When serial correlation is present, the OLS estimates of the coefficients themselves (the bs) remain unbiased, but the estimated standard errors of these coefficients are not accurate. This leads to problems in hypothesis testing and can cause Type I or Type II errors.
To explain in more detail, hypothesis testing relies on the accurate estimation of standard errors because these standard errors are used to compute test statistics (like t-values) and confidence intervals. If serial correlation is present and ignored, the OLS formula for standard errors underestimates their true value. This means the t-statistics will be inflated, leading to an increased likelihood of incorrectly rejecting the null hypothesis (a Type I error). In other words, we might falsely conclude that a variable has a statistically significant relationship with the dependent variable when it does not.
Serial correlation is often present in time series data, where observations close in time tend to be correlated. This can happen in economics or financial data where past events influence future outcomes. To correct for serial correlation, economists and statisticians use methods like Newey-West standard errors, which adjust the standard errors to account for autocorrelation.
In conclusion, serial correlation does cause bias in the OLS estimates of the standard errors, and this is why hypothesis testing results may be invalid when serial correlation is present in the data. However, the coefficient estimates themselves will not be biased.