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Questions › DSE › DSE 2014 › Q47
2 marks, −0.666666666666667Econometrics › Dummy variables and functional forms › Dummy variables and the dummy variable trapModerateabout 2 min

DSE 2014 Question 47: Dummy variables and functional forms

Consider the linear regression yi=β1D1i+β2D2i+εiy_i=\beta_1 D1_i+\beta_2 D2_i+\varepsilon_iyi​=β1​D1i​+β2​D2i​+εi​, where D1i=1D1_i=1D1i​=1 for one group of observations and 000 for the other, and D2=1−D1D2=1-D1D2=1−D1. Can this model be estimated using least squares?

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Consider the linear regression yᵢ=β₁ D1ᵢ+β₂ D2ᵢ+εᵢ, where D1ᵢ=1 for one group of observations and 0 for the other, and D2=1-D1. Can this model be estimated using least squares? (A) No, because D1 and D2 are perfectly collinear (B) Yes, and it is equivalent to running two separate regressions of y on D1 and y on D2 respectively (C) No, because there is no variability in D1 and D2 (D) Yes, provided an intercept term is included

Also written as: Consider the linear regression y_i=beta_1 D1_i+beta_2 D2_i+epsilon_i, where D1_i=1 for one group of observations and 0 for the other, and D2=1-D1. Can this model be estimated using least squares?

Dummy variables and functional forms has come up 20 times in 6 exams since 2011.

What this question tests

This question is on Dummy variables and the dummy variable trap, part of Dummy variables and functional forms in Econometrics.

Using 0-1 variables for categories, how to read their coefficients, and the trap of too many.

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Question from the DSE 2014 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.