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Consider the linear model Y₁ = B₁ + B₁X₁¡ + ß₂X2i + u; where u; is the error term and where E (u; X₁, X2i) = 0, observations (Yi, X1, X2i) are independent and identically distributed, 0 < E (Y) <∞, 0 < E (X₁) < ∞, 0 < E(X₂) < ∞ and where X2i 3X₁. Are the OLS estimators 3₁ and 3₂ of the coefficients 3₁ and 3, unbiased and = consistent?

Consider the linear model Y₁ = B₁ + B₁X₁¡ + ß₂X2i + u; where u; is the error term and where E (u; X₁, X2i) = 0, observations (Yi, X1, X2i) are independent and identically distributed, 0 < E (Y) <∞, 0 < E (X₁) < ∞, 0 < E(X₂) < ∞ and where X2i 3X₁. Are the OLS estimators 3₁ and 3₂ of the coefficients 3₁ and 3, unbiased and = consistent?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 25E
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Consider the linear model Y₁ = B₁ + B₁X₁i + ³₂X2i + u; where u; is the error term and where E (u; X1, X2i) = 0, observations (Yi, X1, X2i) are independent and identically distributed, 0 < E (Y₁₁) < ∞, 0 < E (X₁₂) < ∞, 0 < E (X₂) <∞ and where X2i = 3X₁i. Are the OLS estimators 3₁ and 3₂ of the coefficients 3₁ and 3₂ unbiased and consistent?
Transcribed Image Text:Consider the linear model Y₁ = B₁ + B₁X₁i + ³₂X2i + u; where u; is the error term and where E (u; X1, X2i) = 0, observations (Yi, X1, X2i) are independent and identically distributed, 0 < E (Y₁₁) < ∞, 0 < E (X₁₂) < ∞, 0 < E (X₂) <∞ and where X2i = 3X₁i. Are the OLS estimators 3₁ and 3₂ of the coefficients 3₁ and 3₂ unbiased and consistent?
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