Suppose that Ohio and Illinois, large states that are similar in many ways, decide in the same year (1999) to implement class size reduction state-wide so that all of their K-12 classes contain no more than 18 students.

Illinois does the reduction over 2 years, randomly choosing half of the schools in 2000-2001 school year to have reduced class size and only implementing the class size reduction policy in 2001-2002 school year for the remaining schools. No classes are reduced in 1999-2000 school year.

Ohio does the reduction all at once, so that no classes are reduced in 1999- 2000 but all classes in all grades contain 18 or fewer students in 2000-2001.

You may assume that you have data starting in 1995-1996 and ending in 2005-2006. For each student, you have data on achievement, class size, school identity, and the year in which the school was chosen for reduction (relevant in the case of Illinois).

A) How would you evaluate the effects of class size reduction in Illinois, using only the data from Illinois? Specify which research method you will use (instrumental variables, differences in differences, or regression discontinuity) and write down the equation(s) that will allow you to evaluate the effect. Which coefficient(s) from these equation(s) will give you the effects of class size reduction in Illinois?

B) How would you evaluate the effects of class size reduction in Ohio, using only the data from Ohio? Specify which research method you will use (instrumental variables, differences in differences, or regression discontinuity) and write down the equation(s) that will allow you to evaluate the effect. Which coefficient(s) from these equation(s) will give you the effects of class size reduction in Ohio?

C) Using just the data from 2003 to 2005 (when no further class size reductions are mandated but all schools just stick with the cap of 18), can you test the effects of class sizes? Specify which research method (instrumental variables, differences in differences, or regression discontinuity) you will use and write down the equation(s) that will allow you to evaluate the effect. Which coefficient(s) from these equation(s) will give you the effects of class size reduction?