1. Education 2 – Outputs © Allen C. Goodman, 2010

2. What we’ll look at Choosing Outputs –Means? –Something Else? Producing Outputs –How do we measure them? –How do we produce them? Optimal sizes –Can schools be too small? Too big?

3. Ed and Harry (drawn to scale) At age 10, Harry and Ed both have certain levels of education, 10 each. Assume that Ed (easy) can gain education at a lower incremental cost than Harry (hard). Hence, a given level of expenditures will give Ed 20 incremental points but would give Harry only 10. Suppose half of the people in the schools are like Ed and half are like Harry. 10 30 20 Ed Harry

4. Harry and Ed What if we think that Harry and Ed should have the same scores? Draw 45 degree line. 10 30 20 Ed Harry What if we think that Harry and Ed should get the same inputs? 45 o Why? S H = S E  8 S H  7; S E  13.

5. What’s the most cost-effective place? Thought experiment. Most cost effective place is where we get the highest mean score. Why? 10 30 20 Ed Harry 45 o We can draw a line with a slope of –1. This line gives us places with equal totals. Start with S = S E + S H = 10. S E +S H =10 S E +S H =20 S E +S H = max Mean = (0+10)/2 = 5 Mean = (8+8)/2 = 8 Mean = (20+0)/2 = 10 Highest mean!

6. What do we want? 10 30 20 Ed Harry 45 o S E +S H = max A B C D E Std. Dev. Mean. B' – why? A' C' D' E'

7. What do we want? Std. Dev. Mean. B' A ' Utility Functions –Leveler – Will only accept lower mean along with lower SD. –Why? Utility Functions –Elitist – Will accept lower mean with higher SD. –Why? C' E' D' L1L1 L2L2 L3L3

8. What do we want? Std. Dev. Mean. B' A' Utility Functions –Leveler – Will only accept lower mean along with lower SD. –Why? Utility Functions –Elitist – Will accept lower mean with higher SD. –Why? C' D' E3E3 E1E1 E2E2

9. What do we want? Std. Dev. Mean. B' A' So, it’s not altogether clear that we always want to raise the mean. The levelers here, want to push up the lower end, and this lowers the SD. Means fewer special programs. Lots of people feel that this characterizes the No Child Left Behind initiative. C' D' E3E3 E1E1 E2E2

10. Producing Outputs If people say, “I want a good school,” what do they mean? How is it produced? Consider a conceptual function: –Q = Q (School Inputs, Social Inputs, Other Inputs)

11. School Inputs, Social Inputs, Other Inputs School Teachers Books Computers Classroom Hours Curricula Other Students Others?

12. School Inputs, Social Inputs, Other Inputs School Social TeachersFamily BooksCultural ComputersNon-school Classroom HoursBooks at Home Curricula Other StudentsOthers?

13. School Inputs, Social Inputs, Other Inputs School Social Other TeachersFamilyInnate Smarts BooksCulturalEffort ComputersNon-school Classroom HoursBooks at Home Curricula Other Students Others?Others?Others?

14. Are we looking at changes or value added? Consider school A – Takes students from 80 th percentile to 90 th percentile. Final output = 90 th percentile. School B – Takes students from 40 th percentile to 80 th percentile. Final output = 80 th percentile. Which is the better school?

15. Thousands of Findings On average, no systematic relationship between school expenditures and student performance. Many (not AG) feel that class size is not related to student performance. Most find that there are positive attributes of teachers (verbal skills, quality of college training)  better performance. Curriculum can improve student performance.

16. School Size and Performance Fisher has a nice box in Application 19.2 Best size for elementary schools seems to be between 300 and 500 students. Some look at costs/student = ftn (size, holding output constant); others look at output/student = ftn (size, holding costs constant). We all went to elementary school – why would you think that is the case.

17. School Size and Performance Best size for high schools seems to be between 600 and 900 students. Certainly, bigger schools  more offerings, possibly more specialization. What could make them bad? We all went to high school – why would you think that is the case.

18. Too big or too small Optimal Size TOO SMALL! TOO BIG! Median = 769Mean = 897

19. Right Size In general, 40% of schools are too small. –Suggests that consolidation would be useful. On the other hand, 40% are too large. –There may be economies in subdividing schools or districts.