Education 2 – Outputs © Allen C. Goodman, 2014 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? Ed and Harry (drawn to scale) • At age 10, Harry and 30 Ed both have certain levels of education, 10 each. • Assume that Ed (easy) Ed 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. 10 • Suppose half of the people in the schools are like Ed and half are like Harry. PP frontier 10 20 Harry Harry and Ed SH 7; SE 13. 30 • What if we think that Harry and Ed should have the same scores? Draw 45 degree line. 45o Ed SH = SE 8 • What if we think that Harry and Ed should get the same inputs? 10 • Why? 10 20 Harry What’s the most cost-effective Why NOT place? here? Highest mean! 30 Mean = (20+0)/2 = 10 • Thought experiment. Most cost effective place is where we get the highest mean score. Why? • We can draw a line with a slope of –1. This line gives us places with equal totals. Start with S = SE + SH = 10. 45o SE+SH= max Ed SE+SH=20 Mean = (8+8)/2 = 8 SE+SH=15 SE+SH=10 10 Mean = (0+10)/2 = 5 10 20 Harry What do we want? E Mean. 30 D 45o SE+SH= max D' Ed E' C' C B' – why? B A' A 10 10 20 Harry 0 Std. Dev. What do we want? • Utility Functions – Leveler – He’ll accept a lower mean if it comes with a lower SD – Why? L3 L2 Mean. L1 D' E' C' B' A' • Utility Functions – Elitist – He’ll accept a lower mean if it comes with a higher SD. – Why? Std. Dev. What do we want? • Utility Functions – Leveler – He’ll accept a lower mean if it comes with a lower SD – Why? Mean. E3 D' C' E2 B' A' • Utility Functions E1 – Elitist – He’ll accept a lower mean if it comes with a higher SD. – Why? Std. Dev. What do we want? • What if all we care about is the mean? Mean. E3 D' C' E2 B' A' E1 Std. Dev. What do we want? • 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. Mean. E3 D' C' E2 B' A' E1 Std. Dev. 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) School Inputs, Social Inputs, Other Inputs School Teachers Books Computers Classroom Hours Curricula Other Students Others? School Inputs, Social Inputs, Other Inputs School Social Teachers Books Computers Classroom Hours Curricula Other Students Family Cultural Non-school Books at Home Others? Others? School Inputs, Social Inputs, Other Inputs School Social Other Teachers Books Computers Classroom Hours Curricula Other Students Family Cultural Non-school Books at Home Innate Smarts Effort Others? Others? Others? Are we looking at changes or value added? • Consider school A – Takes students from 80th percentile to 90th percentile. Final output = 90th percentile. • School B – Takes students from 40th percentile to 80th percentile. Final output = 80th percentile. • Which is the better school? 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. 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. 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. Too big or too small Median = 769 Mean = 897 Enrollment Intervals for Michigan HS - 2004 25 Percentages 20 15 10 TOO SMALL! TOO BIG! Optimal Size 5 0 127406 406624 624769 769951 Enrollment Intervals 9511416 14162596 Percent 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.