According to Environmental Kuznets curve, it is expected that there is an Inverse-U shape relationship between pollution and real income such that the following quadratic functional form (regression model) must be specified: Y = a1 + a2 X + a3 X² + u where the variables Y and X represent respectively air pollution (CO2) and real income (RGDP). 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 = B1+ B2 X+e. Show technically how you test whether quadratic form or linear form is the correct model specification using Ramsey's Reset test. b) Suppose R² is found 0.75 from quadratic form, 0.55 from linear form and 0.73 from the auxiliary regression. Given n=35, carry out Reset test and interpret the result. c) Suppose you found out that the correct specification is the quadratic regression. In this case, would estimating the linear functional form result in an unbiased estimate of the slope parameter (B2) ? Show and explain.
According to Environmental Kuznets curve, it is expected that there is an Inverse-U shape relationship between pollution and real income such that the following quadratic functional form (regression model) must be specified: Y = a1 + a2 X + a3 X² + u where the variables Y and X represent respectively air pollution (CO2) and real income (RGDP). 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 = B1+ B2 X+e. Show technically how you test whether quadratic form or linear form is the correct model specification using Ramsey's Reset test.
b) Suppose R² is found 0.75 from quadratic form, 0.55 from linear form and 0.73 from the auxiliary regression. Given n=35, carry out Reset test and interpret the result.
c) Suppose you found out that the correct specification is the quadratic regression. In this case, would estimating the linear functional form result in an unbiased estimate of the slope parameter (B2) ? Show and explain.
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