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

A risk manager models quarterly loss rates using an intercept and three seasonal dummy variables (Q2, Q3, Q4) with Q1 as the base period, and also includes a dummy for Q1. What is the most likely consequence?

Perfect multicollinearity, known as the dummy variable trap. Including an intercept plus a dummy for every one of the four quarters makes the dummies sum to the constant column, so the regressors are linearly dependent and OLS coefficients cannot be uniquely estimated.

  1. APerfect multicollinearity (dummy variable trap), so the coefficients cannot be uniquely estimatedCorrect
  2. BHeteroskedasticity in the residuals that biases the coefficients
  3. COmitted variable bias in the Q2-Q4 coefficients
  4. DSerial correlation that makes the intercept inconsistent

Explanation

The four seasonal dummies sum to one for every observation, which equals the intercept column. This produces perfect multicollinearity, so OLS cannot be computed uniquely. The fix is to drop one dummy or the intercept. The other options describe different problems unrelated to this redundancy.

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