FRM Part I · FRM Exam Part I · Linear Regression
A researcher models quarterly sales growth using seasonal dummies for Q1, Q2, Q3 and Q4 plus an intercept in the same regression, estimated by OLS. What is the consequence?
Including an intercept and all four seasonal dummies creates perfect multicollinearity, because the dummies sum to the intercept column in every observation. OLS cannot give unique estimates. The fix is to omit one dummy, which becomes the base category.
- APerfect multicollinearity, so the regression cannot be estimated uniquelyCorrect
- BHeteroskedasticity in the residuals
- CBiased slope estimates for all non-dummy variables
- DSerial correlation in the error terms
Explanation
The four dummies sum to one in every observation, equal to the intercept column. This is the dummy variable trap: perfect multicollinearity, so X'X is not invertible. Drop one dummy or the intercept.
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