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It is obvious to me that in a regression model with one constant and one regressor, where a problem of endogeneity exist, leads to both estimators being biased and inconsistent (since $b_1=y-b_0$) if we use OLS.

However, what about a multivariate case? If we use OLS to estimate the whole model, will also the estimators who do not suffer from endogeneity, be biased?

  • Hi: Is it a system of equations where the endogenous variables are being modelled also, like a VAR ( i.e sims idea ) ? If so, then it's okay that they are endogenous but I'm not sure if that's what you're referring to when you say "multivariate case" – mlofton Jun 03 '20 at 15:14
  • Here are a couple of questions and answers you might find helpful: https://stats.stackexchange.com/questions/455450/real-data-where-x-causes-y-and-both-variables-also-share-correlated-unobserved-c/458097#458097 and https://stats.stackexchange.com/questions/462513/does-confounding-always-imply-endogeneity/462534#462534 and https://stats.stackexchange.com/questions/464470/why-isnt-causal-inference-a-simple-specialized-regression-problem/464475#464475 – Adrian Keister Jun 03 '20 at 15:21

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