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For example, I conduct an OLS regression and a regressor turns out to be statistically significant. When I conduct the same regression but with a GMM to account for serial correlation - I get a regressor (of a value slightly different from that of the OLS) that is not biased and is statistically significant.

Why can a biased estimate still be statistically significant?

Richard Hardy
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Santi
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    What do you mean by "biased" in this question? – Tim Dec 21 '19 at 16:00
  • In the example above, endogeneity causes bias in an OLS – Santi Dec 21 '19 at 16:46
  • But my question is general - why can a bias in a model (from whatever source) still provide statistically significant estimates? – Santi Dec 21 '19 at 16:47
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    To be socratic: why wouldn't a biased model be able to return statistically significant estimates? What's your reasoning for why such a thing should not be possible? – Matthew Drury Dec 21 '19 at 17:09
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    The insight that [*p* values get arbitrarily small as sample size increases](https://stats.stackexchange.com/questions/108911/why-does-frequentist-hypothesis-testing-become-biased-towards-rejecting-the-null/108914#108914) should be illuminating. – Alexis Dec 21 '19 at 17:48

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