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      Question

      In an OLS regression with severe multicollinearity, R²

      = 0.94 but no individual coefficient is significant at 5%. The researcher drops one collinear variable. Which consequence should she anticipate?
      A Remaining coefficients unbiased, standard errors fall — model now correctly specified Correct Answer Incorrect Answer
      B If the dropped variable is relevant (non-zero true coefficient), remaining coefficients will be biased (omitted variable bias), but standard errors will fall — a bias-variance trade-off Correct Answer Incorrect Answer
      C Dropping the variable eliminates multicollinearity and restores BLUE properties without any cost Correct Answer Incorrect Answer
      D R² will rise because the model is more parsimonious Correct Answer Incorrect Answer

      Solution

      Classic multicollinearity remedy trade-off: If the dropped variable truly belongs in the model, its omission causes OMITTED VARIABLE BIAS in remaining coefficients. However, standard errors fall (multicollinearity reduced). The researcher faces: Option (A) ignores OVB. Option (C) is wrong — BLUE requires correct specification; dropping a relevant variable violates this. Option (D) is wrong — R² generally falls when a variable is dropped.

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