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Questions › IIT JAM › IIT JAM 2026 › Q13
2 marks, −0.667Econometrics › Dummy variables and functional forms › Dummy variables and the dummy variable trapModerateabout 2 min

IIT JAM 2026 Question 13: Dummy variables and functional forms

For a sample of employees participating in an annual appraisal, the effect of the participants' performance on their wages is studied. Variables are defined as: WageiWage_iWagei​ = wage of employee iii; Passi=1Pass_i=1Passi​=1 if employee iii passes and 000 otherwise; Faili=1Fail_i=1Faili​=1 if employee iii fails and 000 otherwise. Which one of the following regression models CANNOT be estimated? (A) Wagei=α+βPassi+γFaili+u1iWage_i=\alpha+\beta Pass_i+\gamma Fail_i+u_{1i}Wagei​=α+βPassi​+γFaili​+u1i​; (B) Wagei=βPassi+γFaili+u2iWage_i=\beta Pass_i+\gamma Fail_i+u_{2i}Wagei​=βPassi​+γFaili​+u2i​; (C) Wagei=α+γFaili+u3iWage_i=\alpha+\gamma Fail_i+u_{3i}Wagei​=α+γFaili​+u3i​; (D) Wagei=α+βPassi+u4iWage_i=\alpha+\beta Pass_i+u_{4i}Wagei​=α+βPassi​+u4i​

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For a sample of employees participating in an annual appraisal, the effect of the participants' performance on their wages is studied. Variables are defined as: Wageᵢ = wage of employee i; Passᵢ=1 if employee i passes and 0 otherwise; Failᵢ=1 if employee i fails and 0 otherwise. Which one of the following regression models CANNOT be estimated? (A) Wageᵢ=α+β Passᵢ+γ Failᵢ+u₁ᵢ; (B) Wageᵢ=β Passᵢ+γ Failᵢ+u₂ᵢ; (C) Wageᵢ=α+γ Failᵢ+u₃ᵢ; (D) Wageᵢ=α+β Passᵢ+u₄ᵢ (A) Wageᵢ=α+β Passᵢ+γ Failᵢ+u₁ᵢ (B) Wageᵢ=β Passᵢ+γ Failᵢ+u₂ᵢ (C) Wageᵢ=α+γ Failᵢ+u₃ᵢ (D) Wageᵢ=α+β Passᵢ+u₄ᵢ

Also written as: For a sample of employees participating in an annual appraisal, the effect of the participants' performance on their wages is studied. Variables are defined as: Wage_i = wage of employee i; Pass_i=1 if employee i passes and 0 otherwise; Fail_i=1 if employee i fails and 0 otherwise. Which one of the following regression models CANNOT be estimated? (A) Wage_i=alpha+beta Pass_i+gamma Fail_i+u_(1i); (B) Wage_i=beta Pass_i+gamma Fail_i+u_(2i); (C) Wage_i=alpha+gamma Fail_i+u_(3i); (D) Wage_i=alpha+beta Pass_i+u_(4i)

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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