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Q2. Alice wants to study the effect of getting more education on income. Suppose she can observe a cross section of individuals' income and the number of years of education. a) Alice does not think a univariate regression of income on years of education yields a consistent estimate for the return to education. Can you help her to briey explain why? b) Suppose kids cannot attend primary school unless they are already six years old. Assume that at every stage of education, the probability of getting into the next stage of education decreases with age. Suppose Alice can also observe in which month an individual was born. She constructs a dummy SecondHalf E {1,0} where SecondHalfi = 1 if and only if the kid was born after June. Explain why S econdH at f can be used as a proxy for years of education. c) Alice believes that the 12 zodiac signs may affect kids' income as well. Therefore, the effect obtained by using SecondHalf to proxy years of education may be a mixture of the true return to education and the effects of the zodiac signs in the second half of the year. Therefore, she also creates 12 dummies, one for each month. For instance, dummy jun,- equals 1 if individual i was born in June, and equals 0 otherwise. Suppose she runs a regression as follows: Incomei = ljani + zFebi + BlzDeci + ySecondHalf + u,- Does this regression suffer from perfect multicollinearity? Prove or disprove your claim. Also, if you think it does suffer om perfect multicollinearity, explain what you can do to eliminate the