Measuring the Education Function of Government in the United States

Michael S. ChristianU.S. Bureau of Economic Analysis

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Input and Volume Approaches

Public education currently measured in United States using input approach

Value of output equals cost of inputs

Assumes productivity is constant and zero

Direct volume measurement allows for changes in productivity

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Elementary and Secondary

Most straightforward volume measure is simple count of students

Grew at annual 0.7% rate 1980-2001

Input measure grew 2.4%

Assumes all students are equal outputs

Assumes quality of education is constant

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Special Education

Growth in special education

9.4% of students in 1980, 12.1% in 2001

Chambers et al (2004): special-ed students twice as expensive

Count special-ed students double

Increases growth rate from 0.73% to 0.85%

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School Quality

Improvement in school quality

Student outcomes (test scores)

Quality of school inputs

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Test Scores

Test scores

12th grade math scores improved by about one third standard deviation over 1982-99

How should we use this to adjust volume?

What is the rate of substitution between years of education and cognitive skill?

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Test Scores to Years of Education

Use effect of education on test scores

Takes 3.3 years for average NAEP scores to rise 1 cross-sectional deviation

1 standard deviation = 3.3 years education

1/3 s.d. increase in 12th grade scores: 12 years in 1999 = 13.1 years in 1982

Upper-bound adjustment

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Adjusting With Test Scores

Test scores adjustment increases growth from 0.85% to 1.22%

Adjusting for raw scores assumes all improvements are caused by schools

Holding parents’ education constant reduces adjusted growth rate to 1.00%

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School Inputs

Quality of school inputs

Pupil-teacher ratio fell from 18.7 in 1980 to 15.9 in 2001

Inexperienced (0-1 years) teachers rose from 5.3% in 1980 to 8.8% in 2000

How do these changes affect the quality of education?

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School Inputs to Years of Education

Huge academic literature measures effects of school inputs on test scores

Multiply effects by substitution rate between test scores and years of education to make quality adjustment

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Adjusting with School Inputs

Literature on school inputs

Teacher experience important

Class size controversial

Not much evidence for others

Adjusting for class size, experience increases growth 0.85% to 1.06%

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Summary of Adjustments

Annual volume growth, 1980-2001

Direct volume measures

Count of students 0.73%

School inputs and special ed 1.06%

Test scores and special ed 1.22%

Input measure 2.41%

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Elementary/Secondary Measures

60

70

80

90

100

110

120

1980 1984 1988 1992 1996 2000

Simple count

School inputs

Raw scores

Input measure

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All Levels of Education (1)

Total education volume measure

Volume measures for all of elementary/ secondary, instruction part of higher

Input measures for rest of higher, “other”

Combined using Fisher index

Result is 90/10 volume/input hybrid index

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All Levels of Education (2)

Annual volume growth, 1980-2001

Slowest volume measure

1.08%

Fastest volume measure

1.45%

Input measure 2.47%

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All Levels of Education (3)

60

70

80

90

100

110

120

1980 1984 1988 1992 1996 2000

Slowest volume

Fastest volume

Input