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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?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 25EQ
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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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