FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
The true model is Y = 1.0 + 2.0·X1 + 3.0·X2 + e. An analyst omits X2 and regresses Y on X1 only. In the sample, the regression of X2 on X1 gives a slope of 0.40. Assuming the sample relationships hold exactly, what is the expected estimated coefficient on X1 in the misspecified model?
The expected coefficient is 3.20. The omitted variable bias equals the omitted coefficient 3.0 times the auxiliary slope 0.40, which is 1.2, and this adds to the true coefficient of 2.0 on X1.
- A0.80
- B2.00
- C3.20Correct
- D1.20
Explanation
The estimated coefficient equals the true coefficient plus the omitted coefficient times the auxiliary slope: 2.0 + 3.0 × 0.40 = 2.0 + 1.2 = 3.2. Option A (2×0.4) uses the wrong coefficient. Option D (3×0.4) gives only the bias and omits the true coefficient. Option B ignores the bias.
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