The regression that refuses to run: the dummy variable trap

Question

Your stocks fall into four sectors. You create four 0/1 dummy variables, one per sector, and include all four plus an intercept in the regression. The software either errors out on a singular matrix or silently drops a column.

Explain why this happens and how to fix it.

Accepted Answer

The exact linear dependence. Every stock belongs to exactly one sector, so the four dummies always add up to 1 for every observation: D1 + D2 + D3 + D4 = 1. But the intercept is also a column of 1s. So the intercept is an exact linear combination of the four dummies. That is perfect multicollinearity, which is different from the merely-high correlation that inflates standard errors. Perfect collinearity makes the X'X matrix singular (non-invertible), so there is no unique least-squares solution and the software cannot proceed. This is the dummy variable trap. The fix. Break the exact dependen…

The regression that refuses to run: the dummy variable trap

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