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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."

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The answer is "yes" as one can see by constructing a numerical example in Stata. In this example, x3 is the omitted variable which is correlated with x2, but not x1. However, the correlation between x1 & x2 makes the coefficient of x1 biased. Nonetheless, it would be nice if there was a formula for the bias in x1. set obs 10000 generate u1 = runiform() generate u2 = runiform() generate u3 = runiform() generate u4 = runiform() generate u5 = runiform() gen x1 = 0.5u1 + 0.5u4 gen x2 = 0.5u1+0.5u2 gen x3 = 0.5u2 + 0.5u3 gen y = x1 + x2 + x3 + u5 reg y x1 x2

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