According to Environmental Kuznets curve, it is expected that there is an inverse-U shaped relationship between...

 

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According to Environmental Kuznets curve, it is expected that there is an inverse-U shaped relationship between pollution and real income such that the following quadratic functional form (regression model) must be specified: Y=a₁ + a₂X+aX² + u where the variables Y and X represent respectively air pollution (CO₂) and real income (Real GDP) and u is the random error. a) Suppose a researcher wants to investigate the relationship between pollution and real income by defining a linear functional form such as Y-B + B₂X+e where e is random error. Further, suppose R² is found 0.75 from estimating quadratic form, 0.55 from linear form and 0.03 from the auxiliary regression. Given n-35, perform LM test to see whether quadratic form or linear form is the correct model specification and interpret the result. (15 point.) b) Suppose you found out that the correct specification is the linear regression. In this case, would estimating the quadratic functional form affect unbiasedness and/or efficiency property of OLS estimates? Show and explain. (15 point) According to Environmental Kuznets curve, it is expected that there is an inverse-U shaped relationship between pollution and real income such that the following quadratic functional form (regression model) must be specified: Y=a₁ + a₂X+aX² + u where the variables Y and X represent respectively air pollution (CO₂) and real income (Real GDP) and u is the random error. a) Suppose a researcher wants to investigate the relationship between pollution and real income by defining a linear functional form such as Y-B + B₂X+e where e is random error. Further, suppose R² is found 0.75 from estimating quadratic form, 0.55 from linear form and 0.03 from the auxiliary regression. Given n-35, perform LM test to see whether quadratic form or linear form is the correct model specification and interpret the result. (15 point.) b) Suppose you found out that the correct specification is the linear regression. In this case, would estimating the quadratic functional form affect unbiasedness and/or efficiency property of OLS estimates? Show and explain. (15 point)

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a To perform the LM Lagrange Multiplier test we need to compare the restricted and unrestricted models The null hypothesis H0 is that the quadratic fo... View the full answer