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

An analyst regresses a firm's monthly excess return (Y) on the market excess return (X1) and omits a relevant variable X2 that is positively correlated with X1. The true coefficient on X2 is positive. What is the expected effect on the estimated coefficient on X1?

The estimated coefficient on X1 is biased upward. The omitted variable has a positive true effect and is positively correlated with X1, so the bias term is positive, and X1 absorbs part of X2's effect on the dependent variable.

  1. AIt is biased upwardCorrect
  2. BIt is biased downward
  3. CIt is unbiased but has a larger standard error
  4. DIt is unbiased and consistent

Explanation

Omitted variable bias in the X1 coefficient equals the true coefficient on X2 times the slope from regressing X2 on X1. Both are positive, so the bias is positive and X1's coefficient is overstated. Unbiasedness only holds if the omitted variable is uncorrelated with X1.

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