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

A analyst omits a relevant explanatory variable X2 from a regression of returns on X1. X2 has a positive true effect on returns and is positively correlated with X1. What is the consequence for the estimated coefficient on X1?

The coefficient on X1 is biased upward and inconsistent. Because the omitted variable has a positive effect and is positively correlated with X1, X1 captures part of its influence. The bias persists even as the sample grows.

  1. AIt is biased downward and inconsistent
  2. BIt is unbiased but has a larger variance
  3. CIt is biased upward and inconsistentCorrect
  4. DIt is unaffected because the intercept absorbs the omitted effect

Explanation

Omitted variable bias equals the omitted coefficient times the relationship between X1 and X2. Both are positive, so the bias is positive: X1 picks up part of X2's effect, and the bias does not vanish with sample size.

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