Handout 15. Omitted Variable Bias CASE: Pay for Performance Some people think that we should pay money to high school students who perform well on a test, a program called "Pay for Performance". Supporters think this gives students an incentive to learn and try hard. However, some people oppose paying students to learn, saying it is costly and that it crowds out "intrinsic motivation" (that is, it takes away love of learning). Boloxia is a large city that has a metropolitan-area-wide school district. There are already some schools in the district that chose to implement the " Pay for Performance" program in 2008 and have been using it for several years. The other schools chose not to offer the pay for performance program. The school superintendent hires your consulting firm to evaluate the program and give a recommendation about continuing with the program (based on the effect on test scores). You gather a dataset of all the schools in the region (in Questrom Tools-) Resources-)DatasetsHandout 15 Pay for Performance) with the following variables: 0 SCORE: Score on the Math Test in 2012 . OLD_SCORE: Score on the Math Test in 2000 . PAY_PROGRAM= 1 if the school offered the " Pay for Performance" program from 2003 through 2012, 0 otherwise . POVERTY RATE : (0 to 100) = the poverty rate in the school neighborhood Part 1: Simple Regression 3. Using a simple regression, find the average difference in scores between schools that offered PAY_PROGRAM and those that didn't. Is this difference statistically significant? b. Write here the regression that you used to answer part "3", including standard errors or t-stats in parentheses under each coefficient, and the adjusted R-squared off to the side. c. Is the coefficient on PAY_PROGRAM the sign you were expecting? How can you explain the counterintuitive result? d. Is this exercise enough evidence to give a recommendation about whether to continue the program? Explain