Looking through misspecification principle through the exam, I noticed they discuss how one misspecification is that the independent variables is correlated with the residuals. However, they discuss something more along the lines of serial correlation:

“Lagged dependent variables and forecasting the past result in residuals being correlated with eachother, thus regression coefficients will be biased and inconsistent”

Does this imply that the independent variables being correlated with the residuals the same thing as serial correlation?

Serial correlation does not imply that an independent variable is correlated with the error term. Independent variable correlation with the error term does not imply serial correlation.

Serial Correlation only occur when the dependent variable and the error term are correlated. The error term is expected to be independent all through, thus it cannot be correlated with both the dependent and independent variables.

Thus when the independent variable is correlated with the error term, then you most likely have an incorrect model specification, your result will be spurious and unreliable.

By definition, independent variable correlated with residual means correlation between Independent variable and Residual. Serial correlation in the lines you quote means residuals correlated with each other; or, correlation between Residual and Itself. So, it’s different.

Serial correlation simply means a variable is correlated with its own lagged values. The independent terms being correlated with errors is a totally different problem.

Also note that the dependent variable and the error term always have a non-zero correlation.

I always get a kick out of how many people need to say the same thing in a slightly different way. Is it to boost the post count or do people think the original post lacked something important? It’s one thing if something is wrong and needs to be corrected, or if there is additional, pertinent information, but often times, people are saying the same thing with little to no additional value.