Card (1995) use a dummy variable indicating whether there is a college near one's residence as an instruments to estimate the impact of education on wage. We want to replicate his results using the data set Card.dta. The data set includes the following variables: Iwage: the natural log of wage educ: years of education nearc4: a dummy variable indicating whether there is a college near one's residence (1 = yes, 0 = no) exper, exper2: work experience and its square smsa: whether lives in urban areas (1 = urban, 0 = rural) motheduc: mother's years of education Use the data to answer the following questions (you need to write your own codes) (a) Estimate the model using OLS (assume heteroskedasticity and report robust standard errors). What's the coefficient and standard error of educ? 1wage = Bo + Beduc + exper+ Baexper2 + Basmsa + smotheduc + u. (b) We want to use nearc4 as an IV for educ. Use regression to determine whether nearc4 satisfies the instrument relevance condition. (e) Do you think nearc4 is a valid IV? Briefly discuss your answer. (d) Use nearc4 as the instrument for educ, and estimate the model using 2SLS. Assume heteroskedasticity and report robust standard errors. What's the coefficient and standard error of educ? (e) Compare the OLS estimates and the IV estimates of 31. Which is larger? Which has a larger standard error?