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FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables

A risk manager has a regression with two highly correlated regressors whose coefficients are individually insignificant. Which statement about the consequences and treatment of this perfect-to-high (but not perfect) multicollinearity is correct?

Under imperfect multicollinearity, OLS estimates stay unbiased but their standard errors are inflated, so individual t-tests lose power. A joint F-test on the correlated variables can still show they are significant together, and the model can still forecast well if the correlation pattern persists.

  1. AOLS coefficient estimates become biased, so the model must be discarded
  2. BForecasts from the model are necessarily invalid even for observations with the same correlation structure
  3. CCoefficient estimates remain unbiased but have inflated standard errors, and a joint F-test on the two coefficients can still show they matterCorrect
  4. DThe R-squared of the regression is mechanically forced to be close to zero

Explanation

With imperfect multicollinearity, OLS remains unbiased and consistent, but standard errors rise, making individual t-tests unreliable. A joint F-test on the correlated variables can still detect their combined significance. Forecasts can remain reasonable if the correlation structure persists. R-squared is not forced down.

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