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

A risk manager models quarterly loan loss rate with a regression that includes an intercept and three seasonal dummy variables for Q2, Q3 and Q4, with Q1 as the omitted base. The estimated coefficients are: intercept 1.20, Q2 0.30, Q3 -0.10, Q4 0.50. What is the expected loss rate in Q4 and what happens if a fourth dummy for Q1 is added while keeping the intercept?

Expected Q4 loss rate is 1.70, the intercept 1.20 plus the Q4 coefficient 0.50. Adding a Q1 dummy alongside the intercept makes the four dummies sum to one, the constant column, creating perfect multicollinearity known as the dummy variable trap.

  1. A1.70; perfect multicollinearity (dummy variable trap) arisesCorrect
  2. B0.50; the model becomes more efficient
  3. C1.70; the coefficients become unbiased
  4. D0.50; perfect multicollinearity arises

Explanation

Q4 expectation = intercept + Q4 coefficient = 1.20 + 0.50 = 1.70. Including all four seasonal dummies plus an intercept makes the dummies sum to the constant column, causing perfect multicollinearity, so the model cannot be estimated uniquely.

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