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FRM Part I · FRM Exam Part I · Regression Diagnostics

Which statement about perfect multicollinearity and high (imperfect) multicollinearity in a multiple regression estimated by OLS is correct?

With perfect multicollinearity, OLS coefficients cannot be uniquely estimated because one regressor is an exact linear combination of others, making the matrix singular. High but imperfect multicollinearity keeps estimates unbiased but inflates standard errors, and it does not require a low R-squared.

  1. AWith high but imperfect multicollinearity, OLS coefficient estimates become biased
  2. BWith perfect multicollinearity, OLS coefficients cannot be uniquely estimatedCorrect
  3. CWith high but imperfect multicollinearity, the R-squared of the model must be low
  4. DWith perfect multicollinearity, the standard errors are zero

Explanation

Under perfect multicollinearity, one regressor is an exact linear combination of others, so the X'X matrix is singular and unique OLS estimates do not exist. Imperfect multicollinearity leaves OLS unbiased but inflates standard errors, and it does not force a low R-squared. Standard errors are undefined or infinite, not zero, under perfect collinearity.

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