Suppose you are tasked to study the variations in income earnings of Namibian black and white individuals. The Data sampling process (DSP) is given by: y = βo + βlnx+ β₂x₂₁+ β₂D₂ + e,i = 1,.,1801 (1) where y₁ = earnings, x₁ = education, xz experience and D, is a dummy 11 black variable such that
(D₁ = | 1 for black individuals)
| 0 for white individuals)
Using a sample of 1801 individuals, the following earnings equation has been estimated: Iny, = 7.059 +0.147lnx₁ +0.049x2-0.201D, (2); R² = 0.179 (0.135) (0.008) (0.007) (0.036) where standard errors are reported in parenthesis. Answer the following questions:
a) What are your prior expectations on the signs of B₂ and B,? Please motivate your answer.
b) Interpret the coefficients in equation (2)?
c) Test the hypothesis that there is no difference in expected earnings between black and white individuals.
d) with reference to the concept of multiple linear restrictions, suppose you drop experience and the dummy variable i.e. Di, and obtained the following estimate instead: R² = 0.153; n = 1801 Inŷ = 6.703 +0.1517Inx₁ (0.182) (0.012)
Use the concept of exclusion restriction to test if experience and the dummy variable are jointly significant in the original equation.