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Questions › DSE › DSE 2014 › Q50
2 marks, −0.666666666666667Econometrics › Misspecification and measurement error › Irrelevant variables and functional-form misspecificationHardabout 3 min

DSE 2014 Question 50: Misspecification and measurement error

Consider two models: (i) y=β0+β1X1+β2X2+uy=\beta_0+\beta_1X_1+\beta_2X_2+uy=β0​+β1​X1​+β2​X2​+u and (ii) y=γ0+γ1Z1+γ2Z2+vy=\gamma_0+\gamma_1Z_1+\gamma_2Z_2+vy=γ0​+γ1​Z1​+γ2​Z2​+v, where Z1,Z2Z_1,Z_2Z1​,Z2​ are distinct from X1,X2X_1,X_2X1​,X2​. Assume u∼N(0,σu2)u\sim N(0,\sigma_u^2)u∼N(0,σu2​), v∼N(0,σv2)v\sim N(0,\sigma_v^2)v∼N(0,σv2​), estimated by OLS. If the true model is (i), which is true?

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Consider two models: (i) y=β₀+β₁X₁+β₂X₂+u and (ii) y=γ₀+γ₁Z₁+γ₂Z₂+v, where Z₁,Z₂ are distinct from X₁,X₂. Assume u~ N(0,σᵤ²), v~ N(0,σᵥ²), estimated by OLS. If the true model is (i), which is true? (A) E[β̂₁]=E[γ̂₁]=β₁ and E[σ̂ᵥ²]=σᵤ² (B) E[σ̂ᵥ²]≥σᵤ² (C) E[σ̂ᵥ²]≤σᵤ² (D) None of the above as the two models cannot be compared

Also written as: Consider two models: (i) y=beta_0+beta_1X_1+beta_2X_2+u and (ii) y=gamma_0+gamma_1Z_1+gamma_2Z_2+v, where Z_1,Z_2 are distinct from X_1,X_2. Assume u~ N(0,sigma_u^2), v~ N(0,sigma_v^2), estimated by OLS. If the true model is (i), which is true?

Misspecification and measurement error has come up 11 times in 4 exams since 2011.

What this question tests

This question is on Irrelevant variables and functional-form misspecification, part of Misspecification and measurement error in Econometrics.

The cost of including a variable that does not belong, and of using the wrong functional form.

TestStop has 7 past-paper questions on this subtopic.

Practise Misspecification and measurement errorMore on Irrelevant variables and functional-form misspecification

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