causation microeconomics

A researcher wants to study the effects of free school lunches on school attendance and test scores. The researcher works with a school that offers free lunches for students whose families make less than $30,000 per year. The researcher has data on family incomes and student test scores, and wants to learn the effects of the school lunch program on student test scores. A. The researcher rst considers modeling the relationship between test scores and lunches as 33'205lx8'li where 8,: is the test score of student 2' and 3,: is 1 if a student gets a free lunch and 0 if they do not. They then estimate the effect of school lunches on test scores as 5. Is this approach likely to overestimate or underestimate the real effect of school lunches? Discuss the role that omitted variable bias or reverse causality may have in this estimate. B. The researcher nds that the relationship between income yi, in thousands of dollars, and student test scores 8,; looks like 50 | 2%- .033}? if yz- S 30 8:: = . 73 | .0193 | 0013,11,:2 1f yz- > 30 Graph the relationship between income and test scores for family incomes less than $100,000. Calculate the regression discontinuity estimate of the effect of a free lunch on test scores