tiebout mechanism, school competition and...
TRANSCRIPT
Motivations Theory Empirical Version of Theory Results Evaluation
Tiebout Mechanism, School Competition andSchool Productivity (Hoxby 2000, AER)
Lee Chanhyuck Chew Khai Yen
November 14, 2017
Motivations Theory Empirical Version of Theory Results Evaluation
Outline
1 MotivationsSchool Competition and Productivity
2 TheoryTiebout Choices
3 Empirical Version of TheoryModelIdentification Problems and IV
4 ResultsFirst StageReduced Form
5 EvaluationHoxby v. Rothstein
Motivations Theory Empirical Version of Theory Results Evaluation
School Competition and Productivity
Many elementary and secondary school reforms propose
increased parental choices.
Inter-district choices
Intra-district choices
Motivations Theory Empirical Version of Theory Results Evaluation
School Competition and Productivity
Consider the following:
1 Residential property prices captures the quality of education in
all school districts.
Residential choice of a HH determines the quality of and
expenditure on local public education (primary example of
Tiebout choices).
2 School budgets are based on property prices.
Reward / Punishment Mechanism
School Competition and Productivity
Consider the following:
1 Residential property prices captures the quality of education in
all school districts.
Residential choice of a HH determines the quality of and
expenditure on local public education (primary example of
Tiebout choices).
2 School budgets are based on property prices.
Reward / Punishment Mechanism20
17
-11
-14
Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)
MotivationsSchool Competition and Productivity
School Competition and Productivity
• If a school is productive, local property prices will increase, and theschool’s budget will also increase. If a school and collects excessive”rent”, the school will be punished by reductions in its budget.
• The incentives that schools have to be productive are generallyincreased by Tiebout choice because it gives HHs more informationand leverage in the principal-agent problem. So there is a relationbetween Tiebout choices and school productivity.
Motivations Theory Empirical Version of Theory Results Evaluation
Tiebout Choices
Private Allocative Efficiency
1 Increased choices leads to more accurate property pricing.
This raises the amount of school quality that households want
to buy.
2 Sorting
The matching quality between students’ needs and schools’
offerings increases.
Private Allocative Efficiency improves.
Student’s achievements, on average, increases.
Tiebout Choices
Private Allocative Efficiency
1 Increased choices leads to more accurate property pricing.
This raises the amount of school quality that households want
to buy.
2 Sorting
The matching quality between students’ needs and schools’
offerings increases.
Private Allocative Efficiency improves.
Student’s achievements, on average, increases.
20
17
-11
-14
Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)
TheoryTiebout Choices
Tiebout Choices
• Theory predicts that increases in Tiebout choices improve schoolproductivity. As Tiebout choices increase, HHs can raise the amountof school quality they want to buy, and decrease their expenditureon unwanted school programs. Since HHs choose the quality andamount of public education closer to their true preferences, they willbe less inclined to send their children to private schools.
• There is also a sorting effect. HH with similar educationalpreferences will gather. To the extent that greater sorting improvesmatching quality between students’ needs and schools’ offerings,Tiebout choices will raise average student achievements.
Motivations Theory Empirical Version of Theory Results Evaluation
Tiebout Mechanism
Social Allocative Efficiency
Externalities (Human Capital Spillovers)
Overall effect ambiguous
Change in Total Expenditure on Schooling
Asset-Rich vs Asset-Poor
Overall effect ambiguous
Tiebout Mechanism
Social Allocative Efficiency
Externalities (Human Capital Spillovers)
Overall effect ambiguous
Change in Total Expenditure on Schooling
Asset-Rich vs Asset-Poor
Overall effect ambiguous
20
17
-11
-14
Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)
TheoryTiebout Choices
Tiebout Mechanism
• But in terms of social allocative efficiency and changes in totalexpenditure on education, the model is inconclusive. The effects ofexternalities such as human capital spillovers are not captured sinceTiebout choices focus on private allocative efficiency. Depending onthe quality of student matching, social efficiency may increase ordecrease. This has an independent relation with school productivity.
• HH within a district have similar educational preferences, butdifferent incomes. The asset-rich will tend to decrease theireducational expenditure, while the asset-poor will tend to increasetheir educational expenditure. Depending on their preferences andpolitical mechanisms, total expenditure may increase or decrease.
Motivations Theory Empirical Version of Theory Results Evaluation
Model
Cm: measure of Tiebout choices
rm ; rm = r(Cm, ...) ; ∂r∂C > 0: reward function
Xkm = (X1km,X2km, ...): measures heterogeneity of HH
characteristics.
Model
Cm: measure of Tiebout choices
rm ; rm = r(Cm, ...) ; ∂r∂C > 0: reward function
Xkm = (X1km,X2km, ...): measures heterogeneity of HH
characteristics.
20
17
-11
-14
Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)
Empirical Version of TheoryModel
Model
• rm predicts two things: the effect of Tiebout choices on rewards andthe effect of sorting on rewards
• To eliminate the effect of sorting on rewards, Hoxby introduces thevariable X which is a vector that measures of the heterogeneity inHH characteristics, hoping it will capture the sorting effects.
Motivations Theory Empirical Version of Theory Results Evaluation
Model
Aikm
ln(Ekm)= f (r(Cm, ...),X ) (1)
Reduced Form:
Aikm
ln(Ekm)=β1Cm + Xikmβ2 + X̄kmβ3 + X̂kmβ4
+ X̄mβ5 + X̂mβ6 + εikm + εkm + εm
(2)
Motivations Theory Empirical Version of Theory Results Evaluation
Identification Problem
Omitted variable bias
If a characteristic X is omitted when it has an independent
effect on productivity, OLS leads to a biased result.
Observed choice endogeneity
Observed choices may be a product of school productivity
IV with 2SLS
Motivations Theory Empirical Version of Theory Results Evaluation
Instrumental Variables
Stream Sm
Natural boundaries which where historically used to determine
the number of school districts within a geographical area.
Related with the number of school districts, hence correlates
with Tiebout choices: Cov(Cm,Sm) 6= 0
Correlation with productivity is negligible:
Cov( Aikmln(Ekm)
,Sm) = 0
First Stage Regression
Cm = Smα1 + X̄mα2 + X̂mα3 + vm (3)
Motivations Theory Empirical Version of Theory Results Evaluation
Data Sources
School administrative data - expenditures, enrolment, staff
School-level demographic data - student gender, race,free-lunch eligibility
District-level demographic data
Mean characteristics - household income, percentages of racial/ ethnic / educational attainment groups etc.Measures of heterogeneity - Gini coefficient, Herfindahl indicesof racial / ethnic / educational heterogeneity etc.
Streams
Larger streams - measured by hand (at least 3.5 miles long),traverses multiple districtsSmaller streams1 - from Geographic Names Information System
Student achievement - 8th, 10th, 12th grade test scores;highest grade completed; earned income at age 32
1Smaller streams are frequently associated with district boundaries, but arefar too small to affect commuting times or determine local industrial history
Motivations Theory Empirical Version of Theory Results Evaluation
Measures of Tiebout Choice
Measure Mean SD SD with controls2
District index - enrolment3 0.686 0.271 0.250
District index - land area4 0.761 0.269 0.252
Districts in metropolitan area 21.132 27.611 18.751
Difference in commuting time 6.498 8.551 -
School index - enrolment 0.974 0.069 0.062
2Residuals are based on OLS regressions containing a constant, themetropolitan area’s population, the square of the population, the metropolitanarea’s land area, and the square of the land area
31 −∑K
k=1 s2km where skm = enrolmentkm
enrolmentm41 −
∑Kk=1 s
2km where skm = land areakm
land aream
Measures of Tiebout Choice
Measure Mean SD SD with controls2
District index - enrolment3 0.686 0.271 0.250
District index - land area4 0.761 0.269 0.252
Districts in metropolitan area 21.132 27.611 18.751
Difference in commuting time 6.498 8.551 -
School index - enrolment 0.974 0.069 0.062
2Residuals are based on OLS regressions containing a constant, themetropolitan area’s population, the square of the population, the metropolitanarea’s land area, and the square of the land area
31 −∑K
k=1 s2km where skm = enrolmentkm
enrolmentm41 −
∑Kk=1 s
2km where skm = land areakm
land aream
20
17
-11
-14
Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)
ResultsFirst Stage
Measures of Tiebout Choice
• Even after controlling for metropolitan population and area, the(residual) index has a standard deviation of 0.25 - degree of choicevaries widely across metropolitan areas in the US
• There is not much variation across metropolitan areas in the degreeof choice among schools
Motivations Theory Empirical Version of Theory Results Evaluation
Correlations Among the Residual Measures
(1) (2) (3) (4) (5)
(1) District index - enrolment 1
(2) District index - land area 0.86 1
(3) Districts in metropolitan area 0.45 0.42 1
(4) Difference in commuting time 0.65 0.71 0.40 1
(5) School index - enrolment 0.14 0.15 0.07 0.01 1
Correlations Among the Residual Measures
(1) (2) (3) (4) (5)
(1) District index - enrolment 1
(2) District index - land area 0.86 1
(3) Districts in metropolitan area 0.45 0.42 1
(4) Difference in commuting time 0.65 0.71 0.40 1
(5) School index - enrolment 0.14 0.15 0.07 0.01 1
20
17
-11
-14
Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)
ResultsFirst Stage
Correlations Among the Residual Measures
• Residual measures eliminate the correlation caused purely bymetropolitan-area size.
• Measures of choice among district are highly correlated. Importantdifferences among them are substantial (greater information, greaterpotential for endogeneity in the enrolment-based measure)
• Not highly correlated with the degree of choice among schools
Motivations Theory Empirical Version of Theory Results Evaluation
First Stage Results
Dependent variableDistrict choice index School choice index
# of larger streams 0.080 (0.040) -0.040 (0.045)
# of smaller streams 0.034 (0.007) 0.004 (0.004)
Demographic indicators5...
...
F2,291-statistic 24.370 0.860
n = 316
5Household income, gender, ethnicity, educational attainment, etc.
First Stage Results
Dependent variableDistrict choice index School choice index
# of larger streams 0.080 (0.040) -0.040 (0.045)
# of smaller streams 0.034 (0.007) 0.004 (0.004)
Demographic indicators5...
...
F2,291-statistic 24.370 0.860
n = 316
5Household income, gender, ethnicity, educational attainment, etc.
20
17
-11
-14
Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)
ResultsFirst Stage
First Stage Results
• The district-based choice index is statistically significantly related tothe streams variable. p-value of F-statistic of the instruments is lessthan 0.001, instruments are not weakly correlated.
• Exclusion restriction - low correlation between measures of industrialcomposition and the residual streams variable, low correlationbetween average travel time to work and the residual streamsvariables (results not shown)
Motivations Theory Empirical Version of Theory Results Evaluation
Effect of Tiebout Choice on Student Achievement
Dependent variables8th 10th 12th Highest
ln(income)reading math reading grade
Base IV3.818 3.061 5.770 1.381 0.151
(1.591) (1.494) (2.208) (0.469) (0.072)
Base OLS-0.236 -0.733 -1.434 0.323 0.055(0.493) (0.564) (0.650) (0.150) (0.029)
Base IV 4.761 2.875 5.803 1.516 0.159district area (1.429) (1.486) (2.179) (0.517) (0.073)
Base IV 61.357 -57.414 -130.577 8.031 1.436school index (44.128) (52.959) (95.960) (12.013) (2.341)
Effect of Tiebout Choice on Student Achievement
Dependent variables8th 10th 12th Highest
ln(income)reading math reading grade
Base IV3.818 3.061 5.770 1.381 0.151
(1.591) (1.494) (2.208) (0.469) (0.072)
Base OLS-0.236 -0.733 -1.434 0.323 0.055(0.493) (0.564) (0.650) (0.150) (0.029)
Base IV 4.761 2.875 5.803 1.516 0.159district area (1.429) (1.486) (2.179) (0.517) (0.073)
Base IV 61.357 -57.414 -130.577 8.031 1.436school index (44.128) (52.959) (95.960) (12.013) (2.341)2
01
7-1
1-1
4Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)
ResultsReduced Form
Effect of Tiebout Choice on StudentAchievement
• The results for the base specification suggest that studentachievement is higher when there is more choice among districts.An increase from 0 to 1 in the index of Tiebout choice generatesxxx scores that are xxx points higher. In addition, such an increasein choice generates educational attainment that is 1.4 grades higherand income at age 32 that is about 15 percent higher. All of theabove results are statistically significantly different from zero at the0.05 level, except for the educational attainment result (0.10 level).
• Effects on achievement are large if one consider an increase from 0to 1 in the choice index - relevant if thinking about the potential ofTiebout choice as a policy. However SD in the choice index is 0.27,so only a modest amount of the current variation in students’achievement is explained by Tiebout choice.
Effect of Tiebout Choice on Student Achievement
Dependent variables8th 10th 12th Highest
ln(income)reading math reading grade
Base IV3.818 3.061 5.770 1.381 0.151
(1.591) (1.494) (2.208) (0.469) (0.072)
Base OLS-0.236 -0.733 -1.434 0.323 0.055(0.493) (0.564) (0.650) (0.150) (0.029)
Base IV 4.761 2.875 5.803 1.516 0.159district area (1.429) (1.486) (2.179) (0.517) (0.073)
Base IV 61.357 -57.414 -130.577 8.031 1.436school index (44.128) (52.959) (95.960) (12.013) (2.341)2
01
7-1
1-1
4Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)
ResultsReduced Form
Effect of Tiebout Choice on StudentAchievement
• OLS results reveal the sign of the bias due to omitted variables andendogeneity - successful districts do attract households withschool-aged children and do attract other districts intoconsolidation.
• Index based on land area - less informative because it does notreflect enrolment structure, but cannot reflect some types ofendogenous behaviour. If endogeneity is remedied by IV, thenestimates should be similar to enrolment-based index - indeed thecase.
• Weak relationship between streams and school index - nomeaningful IV results.
• Effect of choice among schools is probably impossible to determine -measures of choice among schools are far more likely to beendogenous than measures of choice among districts
Effect of Tiebout Choice on Student Achievement
Dependent variables8th 10th 12th Highest
ln(income)reading math reading grade
Base IV3.818 3.061 5.770 1.381 0.151
(1.591) (1.494) (2.208) (0.469) (0.072)
Base OLS-0.236 -0.733 -1.434 0.323 0.055(0.493) (0.564) (0.650) (0.150) (0.029)
Base IV 4.761 2.875 5.803 1.516 0.159district area (1.429) (1.486) (2.179) (0.517) (0.073)
Base IV 61.357 -57.414 -130.577 8.031 1.436school index (44.128) (52.959) (95.960) (12.013) (2.341)2
01
7-1
1-1
4Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)
ResultsReduced Form
Effect of Tiebout Choice on StudentAchievement
• Partial test of exogeneity - Omnibus test - whether after eliminatingits correlation with instrumented choice and other covariates,achievement is still correlated with the streams variable - fails toreject the null hypothesis of exclusion restriction (also Hausman testfor larger streams variable)
• Conclusion: An increase in Tiebout choice has a statisticallysignificant, positive effect on measures of achievement. Naive OLSestimates of the effect of choice on student achievement are likelyto be downward biased, and the stream variables appear to be validinstruments. Evidence for effect on minority and low-incomestudents being smaller than the effect on other students is onlysuggestive.
Motivations Theory Empirical Version of Theory Results Evaluation
Effect of Tiebout Choice on Per-Pupil Spending
Dependent variablesln(per-pupil Student- Share of privatespending) teacher ratio school students
Base IV-0.076 -2.669 -0.042(0.034) (1.084) (0.018)
Base OLS-0.072 0.375 0.006(0.022) (0.268) (0.006)
Base IV -0.101 -2.582 -0.043district area (0.043) (1.122) (0.020)
Effect of Tiebout Choice on Per-Pupil Spending
Dependent variablesln(per-pupil Student- Share of privatespending) teacher ratio school students
Base IV-0.076 -2.669 -0.042(0.034) (1.084) (0.018)
Base OLS-0.072 0.375 0.006(0.022) (0.268) (0.006)
Base IV -0.101 -2.582 -0.043district area (0.043) (1.122) (0.020)
20
17
-11
-14
Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)
ResultsReduced Form
Effect of Tiebout Choice on Per-Pupil Spending
• The results for the base specification suggest that per-pupil spendingis lower where there is more choice among districts. An increasefrom 0 to 1 in the index of Tiebout choice generates a 7.6-percentdecrease in per-pupil spending. The OLS estimate is 7.2 percent,which is insufficiently different from the IV estimate to suggest bias.
• While the effects of choice on achievement appear to be significantlyaffected by endogeneity and omitted variables bias, the effects ofchoice on per-pupil spending appear to be only slightly affected.
• Again, differences in Tiebout choice (SD is only 0.27) account foronly a modest amount of the variation in the per-pupil spending.
Effect of Tiebout Choice on Per-Pupil Spending
Dependent variablesln(per-pupil Student- Share of privatespending) teacher ratio school students
Base IV-0.076 -2.669 -0.042(0.034) (1.084) (0.018)
Base OLS-0.072 0.375 0.006(0.022) (0.268) (0.006)
Base IV -0.101 -2.582 -0.043district area (0.043) (1.122) (0.020)
20
17
-11
-14
Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)
ResultsReduced Form
Effect of Tiebout Choice on Per-Pupil Spending
• The statistic for the omnibustest of the exogeneity of theinstrumental variables fails to reject the null hypothesis that streamsaffect student achievement only via their effect on choice.
• Most-striking result - an increase in district choice lowers per-pupilspending with no loss - in fact, a gain - in student achievement.
• Estimated decrease in per-pupil spending is associated with adecrease in the student-teacher ratio - based on exactly the samedata - results imply that districts that face more Tiebout choiceallocate their lower levels of per-pupil spending in such a way thatthey actually have smaller student-teacher ratios - Tiebout choicemakes districts allocate money away from other inputs and towardsreducing the student-teacher ratio - unusually productive use offunds / unusually popular policy with parents?
Effect of Tiebout Choice on Per-Pupil Spending
Dependent variablesln(per-pupil Student- Share of privatespending) teacher ratio school students
Base IV-0.076 -2.669 -0.042(0.034) (1.084) (0.018)
Base OLS-0.072 0.375 0.006(0.022) (0.268) (0.006)
Base IV -0.101 -2.582 -0.043district area (0.043) (1.122) (0.020)
20
17
-11
-14
Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)
ResultsReduced Form
Effect of Tiebout Choice on Per-Pupil Spending
• Choice among public schools is a substitute for choice of privateschools - most metropolitan areas have private-school enrolmentrates between 9 and 14 percent. That is, if exercised to its fullpotential, Tiebout choice can have a dramatic effect on thepercentage of children who attend private schools.
• The significant difference between the OLS and IV estimates givesus important evidence on the nature of endogeneity. Anunsuccessful public-school district tends to drive its students intoprivate schools. Because this phenomenon increases theconcentration of public-school students in a few districts, itendogenously lowers the choice index based on district enrolment
Motivations Theory Empirical Version of Theory Results Evaluation
Effect of Tiebout Choice on Productivity
Given previous results discussed, we expect choice to have apositive effect on productivity (achievement divided byln(per-pupil spending))
Greater productivity effects are found for measures that arerecorded later in life (e.g. income at age 32 vs 8th-gradereading score)
No statistical evidence that productivity effects are differentfor students from poor (≤ 70% of mean household income)and non-poor families
Conflicting evidence on whether productivity effects aredifferent for minority and non-minority students
Results suggest that the Tiebout choice has stronger effects instates where districts have more financial independence
Motivations Theory Empirical Version of Theory Results Evaluation
Further Evidence on Tiebout Choice and Student Sorting
Tiebout choice allows more sorting of households by districtand increases district homogeneity, which appears to havelittle net effect on achievement, per-pupil spending, orproductivity
Hoxby showed that the racial heterogeneity of a student’speers is related to the number of schools, but not to thenumber of districts in their metropolitan area (similar patternfor poverty heterogeneity)
Students are just as segregated in schools in metropolitanareas that contain few districts as they are in metropolitanareas that contain many districts
Therefore, the effect of choice on productivity is more likely tobe caused by competitive pressure among districts than bystudent sorting
Motivations Theory Empirical Version of Theory Results Evaluation
Hoxby v. Rothstein (2005)
Rothstein’s comment: Hoxby’s results are sensitive to plausiblealterations to the model, in particular the streams variables.
Smaller and insignificant estimates; little evidence ofendogeneity of the choice index to school qualitySelection bias due to exclusion of private school students?Issues of replication
Hoxby’s reply: Rothstein’s inclusion of private school studentwas based on an incorrect method that mis-assigned 40% ofall students to their home localities. Instrumentation ofstreams variables is not an issue.
Rothstein’s rejoinder (...): Hoxby’s results hold only whenrelied on her specific construction of the ”larger streams”variable. No alternatives were presented by Hoxby.
Consensus seems to be that Hoxby’s results generally still hold(?)
Motivations Theory Empirical Version of Theory Results Evaluation
Conclusion
Recap:
OLS does not account for endogeneity6 of school districtsTiebout choice among public-school districts raises schoolproductivity and reduces probability that households chooseprivate schools
Hoxby’s paper was novel for successfully using topographicfeatures as instruments for school competition
However, limited scope of Tiebout choice as a policy tool(unless initial district choice indices are at 0 and can beincreased to 1!)
Majority of literature on school competition is focused on:
VouchersPublic school choice (e.g. charter schools)Public school incentives
6Successful school districts attract households with school-aged children,thereby reducing the observed degree of choice
Motivations Theory Empirical Version of Theory Results Evaluation
References
Hoxby, C. (2000). Does Competition among Public SchoolsBenefit Students and Taxpayers? The American EconomicReview, 90(5), 1209-1238.
Rothstein, J. (2007). Does Competition among PublicSchools Benefit Students and Taxpayers? Comment. TheAmerican Economic Review, 97(5), 2026-2037.
Hoxby, C. (2007). Does Competition among Public SchoolsBenefit Students and Taxpayers? Reply. The AmericanEconomic Review, 97(5), 2038-2055.
Rothstein, J. (2007). Rejoinder to Hoxby. Retrieved from:https://eml.berkeley.edu/~jrothst/publications/
rothstein-hoxbycomment-rejoinder.pdf