(a) We first estimate the following model using simple OLS regression: childreni =Bo + Bleduci + Bagei + Byage, + BAurbani + Batvi +Bocatholic; + B7knowmethi + Bgusemethi + ui, i = 1, ..., n, where our focus is on the parameter B1. Suppose at first that all the assumptions for OLS are satisfied and estimate the model accordingly. Use heteroskedas ticity robust standard errors. Report the value for the estimators of the regression coefficients, their standard errors, and significance level. (b) Do you think that Cov(educi, ui) = 0? Explain. (c) frethalf is a dummy variable equal to one if the woman was born during the first six months of the year, and zero otherwise. Explain what is required for frethalf to be a valid instrumental variable for educ. Do these assumptions seem reasonable? (d) Estimate the first step regression of educ on firsthalf and verify that the coef- ficient associated to firsthalf is significant. Use heteroskedasticity robust standard errors. (e) Estimate the second step regression and compare the TSLS estimator of B1 with the OLS estimator. Is the value of B1 higher/lower than before? Explain