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

A model of portfolio returns omits a relevant variable X2 that is positively correlated with the included variable X1, and X2 has a positive true coefficient. What is the effect on the estimated coefficient of X1?

The estimated coefficient on X1 is biased upward and inconsistent. Omitting a relevant variable that is positively correlated with X1 and has a positive true coefficient lets X1 pick up part of X2's effect, and the bias persists even in large samples.

  1. AIt is biased upward and inconsistentCorrect
  2. BIt is biased downward but consistent
  3. CIt is unbiased but has a larger variance
  4. DIt is unbiased and consistent, but the R-squared is lower

Explanation

Omitted variable bias equals the omitted coefficient times the correlation-driven term, here positive times positive, so the X1 estimate is biased upward. The bias does not vanish with larger samples, so it is also inconsistent. Unbiasedness only holds for irrelevant-variable inclusion, not omission.

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