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.