[2] Many studies have measured the impact of per capita income (1) on per capita sulfur...

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[2] Many studies have measured the impact of per capita income (1) on per capita sulfur dioxide emissions (SO₂), typically finding at low income levels a positive relationship between income and sulfur dioxide, but at high income levels a negative relationship between income and sulfur dioxide. Suppose you wish to assess whether or not such a relationship exists for California, and as such you collect annual California data on I and SO₂ for the period 1945-2010 (i.e., 66 observations). A. Consider the following specification: SO₂ = Bo + B₁1 + B₂1². What conditions on B, and B₂ (i.e., greater than zero, less than zero, or equal to zero) would be consistent with a positive relationship between income and sulfur dioxide emissions at low income levels and a negative relationship between income and sulfur dioxide emissions at high income levels? B. Utilizing the data you collected for California, imagine a simple plot of SO, against I (with SO₂ on the vertical axis and I on the horizontal axis) illustrates a positive relationship between SO₂ and I prior to 1975 (i.e., 1945-1974 (30 years)) but a negative relationship between SO₂ and I since 1975 (i.e., 1975-2010 (36 years). Accordingly, you obtain the following two regression results: Period 1 (1945-1974): SO₂ = 20 + 1.03-7 Period 2 (1975-2010): SO₂ = 100 - 1.05-I (n=30) (n = 36) Now, utilizing the data for the entire 1945-2010 period, suppose you wish to estimate the following specification: SO₂ = Bo + B₂D + B₂I+ BDI, where D = 1 from 1975 onward and 0 prior to 1975. What conditions on Bo, B₁, B2, and B3 (i.e., greater than zero, less than zero, or equal to zero) would be consistent with the estimates provided above? [2] Many studies have measured the impact of per capita income (1) on per capita sulfur dioxide emissions (SO₂), typically finding at low income levels a positive relationship between income and sulfur dioxide, but at high income levels a negative relationship between income and sulfur dioxide. Suppose you wish to assess whether or not such a relationship exists for California, and as such you collect annual California data on I and SO₂ for the period 1945-2010 (i.e., 66 observations). A. Consider the following specification: SO₂ = Bo + B₁1 + B₂1². What conditions on B, and B₂ (i.e., greater than zero, less than zero, or equal to zero) would be consistent with a positive relationship between income and sulfur dioxide emissions at low income levels and a negative relationship between income and sulfur dioxide emissions at high income levels? B. Utilizing the data you collected for California, imagine a simple plot of SO, against I (with SO₂ on the vertical axis and I on the horizontal axis) illustrates a positive relationship between SO₂ and I prior to 1975 (i.e., 1945-1974 (30 years)) but a negative relationship between SO₂ and I since 1975 (i.e., 1975-2010 (36 years). Accordingly, you obtain the following two regression results: Period 1 (1945-1974): SO₂ = 20 + 1.03-7 Period 2 (1975-2010): SO₂ = 100 - 1.05-I (n=30) (n = 36) Now, utilizing the data for the entire 1945-2010 period, suppose you wish to estimate the following specification: SO₂ = Bo + B₂D + B₂I+ BDI, where D = 1 from 1975 onward and 0 prior to 1975. What conditions on Bo, B₁, B2, and B3 (i.e., greater than zero, less than zero, or equal to zero) would be consistent with the estimates provided above?

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A In order for a positive relationship between income and sulfur dioxide emissions at ... View the full answer