Simulating the OLS Consistency When X and ε are Dependent

This morning I saw an interesting tweet by Nick HK, who ran a simulation to convince himself of the fact that OLS consistency only requires Corr(X, ε) = 0 but not independence: I still find it hard to believe that OLS consistency only relies on X being uncorrelated with ε, not independent of ε, and I occasionally run a simulation to re-convince myself. I had no doubt about the conclusion, primarily because I had kindly returned most of the things I learned in the linear models class to the in...

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