Exercise 2. Suppose that the population model determining y is y = Bo + Bx +...
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Exercise 2. Suppose that the population model determining y is y = Bo + B₁x₁ + B₂x₂ + Bzx3+U And this model satisfies CLRM assumptions. However, we estimate the model that omits x3. Let Bo, ₁ and ₂ be the OLS estimators from the regression of y on x₁ and x₂. Show that the expected value of B₁ is n Σ i=1 Pixi3 E(B₁)=B₁ + B3² where f; are the OLS residuals from the regression of x₂ on x₂. Hint: In the model 9 = Bo + ₁x₁ + ₂x₂, B₁ can be expressed as ₁ residuals from the regression of x₁ on x₂. yn where fi are the OLS Plug y = Bo + B₁x₁ + B₂x2 + 3x3 + u into this equation. After some algebra, take the expectation treating x3 and f; as nonrandom. Exercise 2. Suppose that the population model determining y is y = Bo + B₁x₁ + B₂x₂ + Bzx3+U And this model satisfies CLRM assumptions. However, we estimate the model that omits x3. Let Bo, ₁ and ₂ be the OLS estimators from the regression of y on x₁ and x₂. Show that the expected value of B₁ is n Σ i=1 Pixi3 E(B₁)=B₁ + B3² where f; are the OLS residuals from the regression of x₂ on x₂. Hint: In the model 9 = Bo + ₁x₁ + ₂x₂, B₁ can be expressed as ₁ residuals from the regression of x₁ on x₂. yn where fi are the OLS Plug y = Bo + B₁x₁ + B₂x2 + 3x3 + u into this equation. After some algebra, take the expectation treating x3 and f; as nonrandom.
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Related Book For
Introductory Econometrics A Modern Approach
ISBN: 9781337558860
7th Edition
Authors: Jeffrey Wooldridge
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