Hello,
Reading in the CFA curriculum that if a variable is omitted from a regression (and was correlated to another variable in the model) then the correlation coefficient and the standard error of the remaining coefficients will BOTH be bias and inconsistent.
How is this the case? I would assume that only the standard error would be bias and inconsistent, but not sure how both would be bias and inconsistent.
_Bias ed _, not bias.
Correlation coefficient on what pair of variables? Dependent vs Independents, omitted variable vs other independents? Not sure what it is meant in the book.
Until you clarify about the correlation coefficient, I tell you that indeed the standard error of each regressor will be biased and inconsistent when a correlated independent variable (with other independent variables) is omitted from the model.
I assume you already know why. However, in short, OLS main assumption is that the model error term is NOT correlated in any way with the independent variables. If you omit a variable that is correlated with some of the other, the model error term will carry that information inside. So… error term is now correlated with the independent variables. Violates the main assumption, therefore coefficients are biased and inconsistent. Simple as that.