Use the data in CATHOLIC to answer this question. The model of interest is
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where cathhs is a binary indicator for whether a student attends a Catholic high school.
(i) How many students are in the sample? What percentage of these students attend a Catholic high school?
(ii) Estimate the above equation by OLS. What is the estimate of b1? What is its 95% confidence interval?
(iii) Using parcath as an instrument for cathhs, estimate the reduced form for cathhs. What is the t statistic for parcath? Is there evidence of a weak instrument problem?
(iv) Estimate the above equation by IV, using parcath as an IV for cathhs. How does the estimate and 95% CI compare with the OLS quantities?
(v) Test the null hypothesis that cathhs is exogenous. What is the p-value of the test?
(vi) Suppose you add the interaction between cathhs ? motheduc to the above model. Why is it generally endogenous? Why is pareduc ? motheduc a good IV candidate for cathhs ? motheduc?
(vii) Before you create the interactions in part (vi), first find the sample average of motheduc and create cathhs · (motheduc – motheduc) and parcath · (motheduc – motheduc). Add the first interaction to the model and use the second as an IV. Of course, cathhs is also instrumented. Is the interaction term statistically significant?
(viii) Compare the coefficient on cathhs in (vii) to that in part (iv). Is including the interaction important for estimating the average partial effect?