Question;1. Education Production Functions. Consider the following education production function:test i = b 1 + b 2 class _ size i + b 3 free _ lunch i + b 4 class _ size i? free _ lunch,?where test i represents student i?s predicted test score in percentil points, class _ size i is i?s class size, and free _ lunch i equals 1 if i receives a federally subsidized lunch at school, 0 otherwise.a. Suppose that b3 = 0.05. Interpret this finding. (Hint: Evaluate the production function forfree _ lunchi = 0 and for free _ lunchi = 1.)b. Suppose that b2 =?0.01 and b4 =?0.005. Interpret this finding. Are the class size effectslarger for students on free lunch, larger for students not on free lunch, or the same for both?Explain. (Hint: Same as above.)c. Suppose that the education production function above is estimated using data from ProjectSTAR. Does b 2 give a biased estimate of the true causal effect of class size on test scores? Whyor why not?d. Suppose once again that the education production function above is estimated using data fromProject STAR. Does b 2 tell us anything about how test scores would be affected by a large-scaleclass-size reduction program? Why or why not?2. Replication of Card and Krueger (1996) analysis. The below table presents findings from areplication of the Card and Krueger?s analysis, but for two different southern states (Alabama andMississippi) and for a different measure of school resources (average term length, measured in days).Answer the following questions using the information reported in this table and the data on the?question 1? worksheet of exercise2.xls.a.Using the data given in the question 1 worksheet, plot average term length for blacks in Alabamaand for blacks Mississippi (y-axis) against year (x-axis). (Note: The resulting figure will looksomething like Figure 3 in the original paper, but with only 2 lines. To create this graph, useChart Wizard in Microsoft Excel, and choose line graph.)b. On the basis of the graph created in part (a), would you say that school resources havehistorically been lower for blacks in Alabama or in Mississippi?c. Mississippi produced more cotton than Alabama during the antebellum (pre Civil War) period.i. Does this help to explain the trends seen in the figure produced in part (a)? Explain.ii. Suppose that the cropping patterns in Alabama and Mississippi were largely a result of differences in soil types or climate. Describe how this historical accident might create a ?natural experiment? that can be used to estimate the effect of school resources on skill. d. Using the data given in the question 1 worksheet, plot average educational attainment against birth cohort by state of birth for blacks. Do the trends in educational attainment appear to be consistent with the trends in term length described in part (b)? Explain. (Note: The resulting figure will look something like Figure 4 in the original paper. To create this graph, use Chart Wizard in Excel, and choose line graph.)e. The attached table shows the differences between Alabama and Mississippi in average educational attainment and average term length for five birth cohorts, separately by race. Using this table, answer each of the questions below.i. For blacks, which of the differences in average educational attainment are statistically significant?ii. What is the implied effect of term length on educational attainment for blacks? [For each cohort, find the ratio of the AL-MS difference in educational attainment to the AL-MS difference in term length.]3. Understanding Peer Effects and the Social Multiplier. Sacerdote (QJE, 2001) estimates the following equation:GPAi =? 0 +?1GPAir +? 2 SATir +? 3 SATi +?iwhere GPAi represents student i?s predicted grade point average, GPAir is i?s roommates? GPA andSAT represents scores on the Scholastic Aptitude Test.a. How do you interpret? 2 the coefficient on roommate SAT. If individuals chose their roommates in the sample, would you be concerned with the estimate of? 2? Why or why not?b. Now suppose that roommates are randomly assigned. How do you interpret?1 the coefficient on roommate GPA? What concerns might you have regarding potential biases in this estimate?c. Now suppose the equation is re-estimated excluding roommate GPA and,? 2, the coefficient on roommate SAT is positive and statistically significant. Could the University use this information to better sort individuals into roommate pairs? Why or why not? Fully explain.
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