Does omitted variable bias affects coefficients for those variables that are not correlated with the error term? (When there is one variable that is.) I found two answers, but they appear to be contradictory, although I find both of their arguments convincing. Anyone can clarify this?
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.627.708&rep=rep1&type=pdf pdf page 13 (or manuscript page 6): answers "Yes."
https://ipcig.org/evaluation/apoio/Wooldridge%20-%20Cross-section%20and%20Panel%20Data.pdf pdf page 79 (or manuscript page 62): answers "No."