The sign of the bias of when omitting X in the estimation of Y =...
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The sign of the bias of ₁ when omitting X₂ in the estimation of Y = Bo + BiX + B2X2 +u can be summarized in the table below. B₂>0 B₂<0 Corr (X1,X2) >0 + Corr (X1,X₂) <0 + This exercise will help you work through the cases above by illustrating them with examples of your own. For two cases, follow the steps below. Assume the regression equation you would like to estimate is Y = Bo + B₁X₁ + B₂X₂ + u, but for some reason (lack of data or knowledge, for example), you end up omitting X₂ from the regression. Feel free to draw on examples from class but do not copy directly. 1. Describe the hypothetical variables Y, X₁, and X₂. 2. Indicate the sign of the correlation between X₁ and X₂, and explain why you would expect such a sign. 3. Indicate the sign of P2, and explain why you would expect such a sign. 4. Indicate the sign of the bias if you were to omit X₂ from the regression. 5. Indicate how your estimate of ₁ is likely to change when omitting X₂ from the regression, i.e. will it get larger or smaller relative to when you estimate the full regression (with both X₁ and X₂ as explanatory variables)? Explain your reasoning both in technical terms (using your answers to the previous sub-questions) and in terms a policymaker can understand. The sign of the bias of ₁ when omitting X₂ in the estimation of Y = Bo + BiX + B2X2 +u can be summarized in the table below. B₂>0 B₂<0 Corr (X1,X2) >0 + Corr (X1,X₂) <0 + This exercise will help you work through the cases above by illustrating them with examples of your own. For two cases, follow the steps below. Assume the regression equation you would like to estimate is Y = Bo + B₁X₁ + B₂X₂ + u, but for some reason (lack of data or knowledge, for example), you end up omitting X₂ from the regression. Feel free to draw on examples from class but do not copy directly. 1. Describe the hypothetical variables Y, X₁, and X₂. 2. Indicate the sign of the correlation between X₁ and X₂, and explain why you would expect such a sign. 3. Indicate the sign of P2, and explain why you would expect such a sign. 4. Indicate the sign of the bias if you were to omit X₂ from the regression. 5. Indicate how your estimate of ₁ is likely to change when omitting X₂ from the regression, i.e. will it get larger or smaller relative to when you estimate the full regression (with both X₁ and X₂ as explanatory variables)? Explain your reasoning both in technical terms (using your answers to the previous sub-questions) and in terms a policymaker can understand.
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Answer The answer to the above question is as per the below Case 1 B0 Corr X X 0 Suppose we woul... View the full answer
Related Book For
Financial Markets and Institutions
ISBN: 978-0077861667
6th edition
Authors: Anthony Saunders , Marcia Cornett
Posted Date:
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