Tiebout Mechanism, School Competition and...

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


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


School Competition and Productivity

Many elementary and secondary school reforms propose

increased parental choices.

Inter-district choices

Intra-district choices



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


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

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Tiebout Mechanism, School Competition and SchoolProductivity (Hoxby 2000, AER)

MotivationsSchool 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.


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.

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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.


Tiebout Mechanism

Social Allocative Efficiency

Externalities (Human Capital Spillovers)

Overall effect ambiguous

Change in Total Expenditure on Schooling

Asset-Rich vs Asset-Poor


Tiebout Mechanism

Social Allocative Efficiency

Externalities (Human Capital Spillovers)


Change in Total Expenditure on Schooling

Asset-Rich vs Asset-Poor


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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.


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.

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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.


Model

Aikm

ln(Ekm)= f (r(Cm, ...),X ) (1)

Reduced Form:

Aikm

ln(Ekm)=β1Cm + Xikmβ2 + X̄kmβ3 + X̂kmβ4

+ X̄mβ5 + X̂mβ6 + εikm + εkm + εm

(2)


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


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)


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


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


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

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ResultsFirst Stage


• 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


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


(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

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ResultsFirst Stage


• 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


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.

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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)


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)




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 61.357 -57.414 -130.577 8.031 1.436school index (44.128) (52.959) (95.960) (12.013) (2.341)2

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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.




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)



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ResultsReduced Form


• 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




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)



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ResultsReduced Form


• 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.


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)



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)


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ResultsReduced Form


• 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.



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)


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ResultsReduced Form


• 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?



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)


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ResultsReduced Form


• 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


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


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


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(?)


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


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

https://eml.berkeley.edu/~jrothst/publications/rothstein-hoxbycomment-rejoinder.pdf

https://eml.berkeley.edu/~jrothst/publications/rothstein-hoxbycomment-rejoinder.pdf

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