FRM Part I · FRM Exam Part I · Regression Diagnostics
A researcher estimates Y = b0 + b1X1 + e, but the true model is Y = b0 + b1X1 + b2X2 + e, with true b1 = 0.50 and true b2 = 0.80. The sample regression of X2 on X1 has slope 0.25. What is the approximate expected value of the estimated b1 in the misspecified model?
Omitted variable bias equals the omitted coefficient times the slope of the omitted variable on the included one: 0.80 x 0.25 = 0.20. The misspecified regression therefore tends to estimate b1 at about 0.50 + 0.20 = 0.70, overstating the true effect.
- A0.50
- B0.30
- C0.70Correct
- D1.05
Explanation
Omitted variable bias equals b2 times the slope from regressing X2 on X1: 0.80 x 0.25 = 0.20. The estimate is expected to be 0.50 + 0.20 = 0.70. Subtracting the bias gives 0.30, a sign error. 0.50 ignores the omission. 1.05 wrongly adds 0.80 x 0.25 + 0.80 + ... rather than the bias.
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