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Suppose you have an i.i.d. sample {( , , ): = 1, ... , }. You want to estimate the causal effect of 1 on . You first run a regression = 0 + 1i + i and get the following result:enter image description here

where the numbers in parentheses are standard errors.

Now, suppose you worry about omitted variable bias (OVB), so you are considering whether to put 2 into the regression. The only condition you can check is that whether 1 and 2 are correlated. Propose a test with the null H0: 12 = 0 based on regression. Describe what regression you would run and what the test procedure would be. Explain why the proposed test works.

I know that OVB occurs when omitting a regressor (putting the regressor in the error term UI instead of putting as a new regressor X2) that can affect Y or X1 and X2 (other omitted variable) are correlated. However, how does testing whether correlation = 0 helps to know whether this has OVB or not? I don't understand

** I encounter another question, which is how to test whether it is significant? How to obtain SE(corr(X1,X2))? I was thinking about obtaining t-statistics and compare with 1.96 since I want alpha = 0.05

gggg
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    Please add the [tag:self-study] tag & read its [wiki](https://stats.stackexchange.com/tags/self-study/info). Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. Please make these changes as just posting your homework & hoping someone will do it for you is grounds for closing. – kjetil b halvorsen Dec 07 '20 at 14:45
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    Thank you, I have just edited. I will make sure to do that before posting next time. – gggg Dec 07 '20 at 15:43

1 Answers1

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Cause omitted variables have two properties, they are correlated to the variable of the interest and they affect Y. Thus to see whether X_2 is an omitted variable, we are supposed to clarify whether corr(X_1,X_2) = 0.

Holly
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  • I understand that part, but I encounter another question, which is how to test whether it is significant? How to obtain SE(corr(X1,X2))? I was thinking about obtaining t-statistics and compare with 1.96 since I want alpha = 0.05 – gggg Dec 09 '20 at 07:06