job_talk_2014-01-13_final

Exam Schools, Ability, and the E�ects ofA�rmative Action: Latent Factor Extrapolation in

the Regression Discontinuity Design

Miikka Rokkanen

Massachusetts Institute of Technology

Introduction

Latent Factor Modeling in a Sharp RD Design

Boston Exam Schools

Identi�cation and Estimation

Extrapolation Results

Counterfactual Simulations

Placebo Experiments

Conclusions

Extrapolation Problem in the RD Design

𝐸[𝑌(1) − 𝑌(0)| 𝑅 = 𝑐]

𝑅

𝐸[𝑌(1)|𝑅]

𝐸[𝑌(0)|𝑅]

𝑐

𝑌(0),𝑌(1)

Boston Exam Schools

I Three selective high schools that are seen as the �agship ofthe Boston public school system

I RD estimates show little evidence of e�ects for marginalapplicants (Abdulkadiroglu, Angrist & Pathak, forthcoming)

I Is the lack of e�ects generalizable for inframarginal applicants?

I Important question for discussion of a�rmative action atselective school admissions

This Paper

1. Develop a latent factor-based approach to the extrapolation oftreatment e�ects away from the cuto� in RD

I Nonparametric identi�cation of treatment e�ects at any pointin the running variable distribution

2. Estimate e�ects of Boston exam school attendance for fullpopulation of applicants

I Achievement gains concentrated among lower-scoringapplicants

3. Simulate e�ects of introducing minority/socioeconomicpreferences into exam school admissions

I Both reforms increase average achievement among a�ectedapplicants

Related Literature

1. Extrapolation of treatment e�ects in RD: Angrist &Rokkanen (2013); Cook & Wing (2013); Dong & Lewbel(2013)

2. Latent factor and measurement error models: Hu &Schennach (2008); Cunha, Heckman & Schennach (2010);Evdokimov & White (2012)

3. (Semi-)nonparametric instrumental variables models:Newey & Powell (2003); Blundell, Chen & Kristensen (2007);Darolles, Fan, Florens & Renault (2011)

4. E�ects of attending selective middle/high schools:Jackson (2010); Pop-Eleches & Urquiola (2013);Abdulkadiroglu, Angrist & Pathak (forthcoming)

5. E�ects of a�rmative action in school admissions:Arcidiacono (2005); Card & Krueger (2005); Hinrichs (2012)

Introduction


Boston Exam Schools




Placebo Experiments

Conclusions

Latent Factor Framework

I Running variable R is a noisy measure of a latent factor θ :

R = gR (θ ,νR)

I Potential outcomes Y (0) and Y (1) depend on θ but not onthe noise in R :

(Y (0) ,Y (1))⊥⊥ R | θ

I Example: selective school admission

I R: entrance exam scoreI θ : latent abilityI Y (0), Y (1): future achievement

Treatment Assignment in the Latent Factor Framework

𝑅 𝜃𝑙𝑜𝑤

𝜃ℎ𝑖𝑔ℎ

𝑐

Treatment Assignment in the Latent Factor Framework

𝑅 𝜃𝑙𝑜𝑤

𝜃ℎ𝑖𝑔ℎ

𝜃𝑙𝑜𝑤 + 𝜈𝑅𝑙𝑜𝑤 𝜃𝑙𝑜𝑤 + 𝜈𝑅ℎ𝑖𝑔ℎ 𝜃ℎ𝑖𝑔ℎ + 𝜈𝑅𝑙𝑜𝑤 𝜃ℎ𝑖𝑔ℎ + 𝜈𝑅

ℎ𝑖𝑔ℎ 𝑐

Extrapolation in the Latent Factor Framework

𝐸[𝑌(1) − 𝑌(0)| 𝑅 = 𝑐]

𝑅

𝐸[𝑌(1)|𝑅]

𝐸[𝑌(0)|𝑅]

𝑐

𝐸[𝑌(1) − 𝑌(0)| 𝑅 = 𝑟1]

𝑟1

𝐸[𝑌(0)| 𝑅 = 𝑟1]= 𝐸{𝐸[𝑌(0)| 𝜃]| 𝑅 = 𝑟1}

𝐸[𝑌(1)| 𝑅 = 𝑟1]

𝐸[𝑌(1) − 𝑌(0)| 𝑅 = 𝑟0]

𝐸[𝑌(0)| 𝑅 = 𝑟0]

𝑟0

𝐸[𝑌(1)| 𝑅 = 𝑟0]= 𝐸{𝐸[𝑌(1)| 𝜃]| 𝑅 = 𝑟0}

𝑌(0),𝑌(1)

Object 1: Conditional Latent Factor Distribution

𝜃

𝑓𝜃|𝑅(𝜃|𝑟)

𝑓𝜃|𝑅(𝜃|𝑟0)

𝑓𝜃|𝑅(𝜃|𝑟1)

Object 2: Latent Conditional Expectation Functions

𝜃

𝑌(0),𝑌(1)

𝐸[𝑌(1)|𝜃]

𝐸[𝑌(0)|𝜃]

Identi�cation Using Multiple Noisy Measures

I Suppose one has available three noisy measures of θ :

M1 = gM1(θ ,νM1

)

M2 = gM2(θ ,νM2

)

M3 = gM3(θ ,νM3

)

where M1,M2 are continuous, and M3 is potentially discrete

I R is a deterministic function of a subset of M = (M1,M2,M3)

I Example: selective school admissions

I R = M1: entrance exam scoreI M2,M3: baseline test scores

Identi�cation with less than three measures

Nonparametric Identi�cation: Roadmap

Goal: E [Y (1)−Y (0) | R] = E {E [Y (1)−Y (0) | θ ] | R}I Inputs: fθ |R , E [Y (0) | θ ], and E [Y (1) | θ ]

Step 1: Identi�cation of fθ ,M (and consequently fθ |R)

I Input: fMI Literature: nonclassical measurement error models

Step 2: Identi�cation of E [Y (0) | θ ] and E [Y (1) | θ ]

I Inputs: E [Y |M,D] and fθ |M,D

I Literature: nonparametric instrumental variables models

Parametric Illustration

I Suppose the measurement model takes the form

Mk = µMk+ λMk

θ + νMk,k = 1,2,3

where µM1= 0, λM1

= 1, andθ

νM1

νM2

νM3

∼ N

µθ

000

,

σ2θ

0 0 00 σ2

νM10 0

0 0 σ2νM2

0

0 0 0 σ2νM3

I Then the unknown parameters can be obtained from themeans, variances, and covariances of M

Details

Identi�cation of fθ ,M

fθ ,M identi�ed from fM under the following assumptions (Hu &Schennach, 2008):

1. fθ ,M (θ ,m) is bounded with respect to the product measure ofthe Lebesgue measure on Θ×M1×M2 and some dominatingmeasure µ on M3. All the corresponding marginal andconditional densities are also bounded.

2. M1, M2, and M3 are jointly independent conditional on θ .

3. There exists a known functional H such thatH[fM1|θ (· | θ)

]= θ for all θ ∈Θ.

4. For all θ′,θ′′ ∈Θ, fM3|θ

(m3 | θ

′)and fM3|θ

(m3 | θ

′′)di�er

over a set of strictly positive probability whenever θ′ 6= θ

′′.

5. fθ |M1(θ |m1) and fM1|M2

(m1 |m2) form (boundedly) completefamilies of distributions indexed by m1 ∈M1 and m2 ∈M2.



Step 1: Identi�cation of fθ ,M (and consequently fθ |R)√

I Input: fMI Literature: nonclassical measurement error models

Step 2: Identi�cation of E [Y (0) | θ ] and E [Y (1) | θ ]



Parametric Illustration

I Suppose the latent outcome model takes the form

E [Y (D) | θ ] = αD + βDθ , D = 0,1

and

(Y (0) ,Y (1))⊥⊥M | θ

I Then the unknown parameters can be obtained from theconditional means of Y and θ given M to the left and right ofthe cuto�

Details



Step 1: Identi�cation of fθ ,M (and consequently fθ |R)√

I Input: fMI Literature: latent factor and measurement error models

Step 2: Identi�cation of E [Y (0) | θ ] and E [Y (1) | θ ]√



Extensions

Extension 1: Latent Factor Modeling in a Fuzzy RD Design

Extension 2: Settings with Multiple Latent Factors

Introduction


Boston Exam Schools




Placebo Experiments

Conclusions

Boston Exam Schools

I Three selective public schools spanning grades 7-12(new students admitted mainly for grades 7 and 9)

I Boston Latin SchoolI Boston Latin AcademyI John D. O'Bryant High School of Mathematics and Science

I Exam schools di�er considerably from traditional BPS

I Peers, curriculum, teachers, resources

I Each applicant receives at most one exam school o�er

I Most preferred school the applicant quali�es for

I School-speci�c RD experiments for �sharp samples�

I Running variable: rank based on GPA and ISEE scoresI Admissions cuto�: lowest rank among admitted students

DA Algorithm Sharp Sample

Data and Sample

I Data sources:

I Exam school application �leI BPS enrollment �leI MCAS �leI ACS 5-year summary �le

I Sample restrictions:

I 7th grade applicants in 2000-2004I Enrolled in BPS in 6th gradeI Non-missing 4th grade MCAS scores and covariates

I Outcome: high school MCAS composite score

I Standardized average of 10th grade MCAS scores in Englishand Math

Descriptive Statistics

E�ects at the Admissions Cuto�s: First Stage

0.2

.4.6

.81

Enr

ollm

ent P

roba

bilit

y

−20 −10 0 10 20Running Variable

O’Bryant

0.2

.4.6

.81

Enr

ollm

ent P

roba

bilit

y


Latin Academy

0.2

.4.6

.81

Enr

ollm

ent P

roba

bilit

y


Latin School

E�ects at the Admissions Cuto�s: Reduced Form

−.5

0.5

11.

52

Mea

n S

core


O’Bryant

−.5

0.5

11.

52

Mea

n S

core


Latin Academy

−.5

0.5

11.

52

Mea

n S

core


Latin School

Estimates

Introduction


Boston Exam Schools




Placebo Experiments

Conclusions

Setup

I Specify a model with two latent factors:

I English abilityI Math ability

I School-speci�c running variables are functions of ISEE scores

I Reading and Verbal: Noisy measures of English abilityI Math and Quantitive: Noisy measures of Math ability

I Data also contains 4th grade MCAS scores

I English: Noisy measure of English abilityI Math: Noisy measure of Math ability

I Control for a set of additional covariates

I Application year, application preferences, GPA,sociodemographic characteristics

Measurement Scatterplots Measurement Correlations

Estimation

I Measurement model: Maximum Simulated Likelihood[θE

θM

]| X ∼ N

([µ′θEX

µ′θM

X

],

[σ2

θEσθE θM

σθE θMσ2

θM

])

MEk | θ ,X ∼ N

(µ′

MEkX + λME

kθE ,exp

(γME

k+ δME

kθE

)2)

MMk | θ ,X ∼ N

(µ′

MMkX + λMM

kθM ,exp

(γMM

k+ δMM

kθM

)2)

I Latent outcome model: Method of Simulated Moments

E [Ds (z) | θ ,X ] = α′

Ds(z)X + β

EDs(z)

θE + βMDs(z)

θM

E [Y (S (z)) | θ ,X ] = α′

Y (S(z))X + βEY (S(z))θE + β

MY (S(z))θM

I Inference: 5-step bootstrap

Introduction


Boston Exam Schools




Placebo Experiments

Conclusions

Preliminaries

Figure: Distribution of English and Math ability

Table: Factor loadings on ISEE and MCAS scores

Table: Dependence of outcomes on English and Math ability

E�ects Away from the Admissions Cuto�s

−1

01

23

Mea

n S

core


O’Bryant

−1

01

23

Mea

n S

core


Latin Academy

−1

01

23

Mea

n S

core


Latin School

Estimates

Exam School vs Traditional BPS

I Previous results about incremental e�ects of attending abetter exam school

I Latent factor model provides counterfactual predictions for allexam schools

I This allows one to study the e�ects of attending a given examschool versus a traditional BPS

Exam School vs Traditional BPS: All Applicantsextrapolation_all

Latin LatinO'Bryant Academy School

(1) (2) (3)First 0.754*** 0.948*** 0.968***Stage (0.020) (0.013) (0.016)

Reduced 0.021 0.049 0.024Form (0.037) (0.058) (0.064)

LATE 0.027 0.052 0.025(0.049) (0.062) (0.066)

N

Updated: 2014-01-13

* significant at 10%, ** significant at 5%, ***significant at 1%

3,704

Exam School vs Traditional BPS: By O�er Status

extrapolation_atu_att

Latin Latin Latin LatinO'Bryant Academy School O'Bryant Academy School

(1) (2) (3) (4) (5) (6)First 0.887*** 0.987*** 0.955*** 0.758*** 0.925*** 0.987***Stage (0.049) (0.030) (0.026) (0.017) (0.010) (0.005)

Reduced 0.334*** 0.429*** 0.428*** -0.268*** -0.300*** -0.348***Form (0.088) (0.105) (0.094) (0.066) (0.048) (0.052)

LATE 0.376*** 0.435*** 0.448*** -0.353*** -0.325*** -0.353***(0.102) (0.110) (0.098) (0.087) (0.053) (0.053)

N

Updated: 2014-01-13

* significant at 10%, ** significant at 5%, *** significant at 1%

No Exam School Offer Exam School Offer

1,777 1,927

Exam School vs Traditional BPS: By O�er Status

extrapolation_atu_att


(1) (2) (3) (4) (5) (6)First 0.887*** 0.987*** 0.955*** 0.758*** 0.925*** 0.987***Stage (0.049) (0.030) (0.026) (0.017) (0.010) (0.005)

Reduced 0.334*** 0.429*** 0.428*** -0.268*** -0.300*** -0.348***Form (0.088) (0.105) (0.094) (0.066) (0.048) (0.052)

LATE 0.376*** 0.435*** 0.448*** -0.353*** -0.325*** -0.353***(0.102) (0.110) (0.098) (0.087) (0.053) (0.053)

N

Updated: 2014-01-13


No Exam School Offer Exam School Offer

1,777 1,927

Miikka

Rectangle

Introduction


Boston Exam Schools




Placebo Experiments

Conclusions


I Simulate e�ects of two admissions reforms:

1. Introducing minority preferences (Boston 1975-1998)

I 65% of seats assigned among all applicantsI 35% of seats assigned among blacks and Hispanics

2. Introducing socioeconomic preferences (Chicago 2010-)

I 30% of seats assigned among all applicantsI 70% of seats assigned within four SES tiers

I Exam school assignment of 27-35% of applicants a�ected

I Table: Actual and counterfactual assignmentsI Table: Counterfactual admissions cuto�sI Table: Descriptives by counterfactual assignment

I Caveats (outside the scope of this paper):

I Application behavior, teacher behavior, peer e�ects

E�ect of A�mative Action on Average Achievement

cfsim12_effects

All Non- All SES SES SES SESApplicants Minority Minority Applicants Tier 1 Tier 2 Tier 3 Tier 4

(1) (2) (3) (4) (5) (6) (7) (8)All 0.023*** 0.027*** 0.017* 0.015*** 0.024** 0.011* 0.006 0.018*Applicants (0.004) (0.007) (0.009) (0.005) (0.011) (0.006) (0.005) (0.010)

3,704 2,086 1,618 3,704 737 876 901 1,190

Affected 0.062*** 0.074*** 0.046* 0.050*** 0.068** 0.044* 0.026 0.054*Applicants (0.011) (0.019) (0.025) (0.016) (0.031) (0.023) (0.024) (0.029)

1,367 754 613 1,100 265 223 208 404

Updated: 2014-01-13


Applicant GroupMinority Preferences

Applicant GroupSocioeconomic Preferences

E�ect of A�mative Action on Average Achievement

cfsim12_effects

All Non- All SES SES SES SESApplicants Minority Minority Applicants Tier 1 Tier 2 Tier 3 Tier 4

(1) (2) (3) (4) (5) (6) (7) (8)All 0.023*** 0.027*** 0.017* 0.015*** 0.024** 0.011* 0.006 0.018*Applicants (0.004) (0.007) (0.009) (0.005) (0.011) (0.006) (0.005) (0.010)

3,704 2,086 1,618 3,704 737 876 901 1,190

Affected 0.062*** 0.074*** 0.046* 0.050*** 0.068** 0.044* 0.026 0.054*Applicants (0.011) (0.019) (0.025) (0.016) (0.031) (0.023) (0.024) (0.029)

1,367 754 613 1,100 265 223 208 404

Updated: 2014-01-13


Applicant GroupMinority Preferences

Applicant GroupSocioeconomic Preferences

Miikka

Rectangle

Introduction


Boston Exam Schools




Placebo Experiments

Conclusions

Placebo Experiments

Strategy:

1. Split data on applicants with assignment Z = 0,1,2,3 in halfbased on the median of the running variable

2. Re-estimate latent outcome models to the left and right of theplacebo cuto�s

3. Repeat reduced form extrapolations to the left and right of theplacebo cuto�s

Placebo Extrapolation: Figures

−1

01

23

Mea

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No Offer

−1

01

23

Mea

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O’Bryant−

10

12

3M

ean

Sco

re


Latin Academy

−1

01

23

Mea

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core


Latin School

Fitted Extrapolated

Placebo Extrapolation: Estimatesplacebo

No Latin LatinOffer O'Bryant Academy School(1) (2) (3) (4)

All -0.057 0.080 -0.041 -0.008Applicants (0.064) (0.068) (0.062) (0.045)

1,777 563 625 793

Below -0.133 0.027 -0.028 0.027Placebo (0.099) (0.061) (0.055) (0.049)Cutoff 887 280 311 368

Above 0.020 0.133 -0.054 -0.044Placebo (0.056) (0.102) (0.097) (0.068)Cutoff 890 283 314 371

Updated: 2014-01-13


Introduction


Boston Exam Schools




Placebo Experiments

Conclusions

Conclusions

I Develop a latent factor-based approach to the extrapolation oftreatment e�ects away from the cuto� in RD

I Achievement gains from exam school attendance concentratedamong lower-scoring applicants

I A�rmative action predicted to increase average achievementamong a�ected applicants

I Latent factor-based extrapolation likely to be a promisingapproach also in various other RD designs

Identi�cation with Less than Three Measures

I One noisy measure enough for the identi�cation of fθ ,M if

I M1 = θ + νM1

I θ and νM1independent

I either fθ or fνM1known

(Carroll & Hall, 1988; Carrasco & Florens, 2011)

I Two noisy measures enough for the identi�cation of fθ ,M if

I M1 = θ + νM1, M2 = θ + νM2

I θ , νM1, and νM2

jointly independent(Kotlarski, 1967; Evdokimov & White, 2012)

Back

Parametric Illustration: Details

E [M1] = µθ

E [Mk ] = µMk+ λMk

µθ , k = 2,3

Cov [M1,Mk ] = λMkσ2θ , k = 2,3

Cov [M2,M3] = λM2λM3

σ2θ

Var [M1] = σ2θ + σ

2νM1

Var [Mk ] = λMkσ2θ + σ

2νMk

, k = 2,3

Back

Extrapolation of LATE in Fuzzy RD

Suppose

1. (Y (0) ,Y (1) ,D (0) ,D (1))⊥⊥ R | θ2. P [D (1)≥ D (0) | θ ] = 1 a.s.

3. P [D (1) > D (0) | θ ] > 0 a.s.

Then

E [Y (1)−Y (0) | D (1) > D (0) ,R = r ]

=E {E [Y (D (1))−Y (D (0)) | θ ] | R = r}

E {E [D (1)−D (0) | θ ] | R = r}

for all r ∈R

Back

Settings with Multiple Latent Factors

I Suppose the data contains 2×K +1 noisy measures of latentfactors θ1, . . . ,θK :

Mk1 = gMk

1

(θk ,νMk

1

), k = 1, . . . ,K

Mk2 = gMk

2

(θk ,νMk

2

), k = 1, . . . ,K

M3 = gW (θ1, . . . ,θK ,νM3)

Mk1 and Mk

2 , k = 1, . . . ,K , continuous, M3 potentially discrete

I R is a deterministic function of a subset of M = (M1,M2,M3)

I Extending all of the identi�cation results to this settingrequires only slight modi�cations

Back

Deferred Acceptance Algorithm

I Round 1: Applicants are considered for a seat in their mostpreferred exam school. Each exam schools rejects thelowest-ranking applicants in excess of its capacity. The rest ofthe applicants are provisionally admitted.

I Round k > 1: Applicants rejected in Round k−1 areconsidered for a seat in their next most preferred exam school.Each exam schools considers these applicants together withthe provisionally admitted applicants from Round k−1 andrejects the lowest-ranking students in excess of its capacity.The rest of the students are provisionally admitted.

I The algorithm terminates once either each applicants areassigned an o�er from one of the exam schools or allunmatched applicant are rejected by every exam school in theirpreference ordering.

Back

Sharp Sample

I Three ways for an applicant to be admitted to exam school s(given the school-speci�c cuto�s)

1. Exam school s is the applicant's 1st choice, and she clears theadmissions cuto�.

2. The applicant does not clear the admissions cuto� for her 1stchoice, exam school s is her 2nd choice, and she clears theadmissions cuto�.

3. The applicant does not clear the admissions cuto� for her 1stor 2nd choice, exam school s is her 3rd choice, and she clearsthe admissions cuto�.

I This forms the basis for the de�nition of a sharp sample foreach exam school

I Applicants who obtain an o�er from exam school s i� theyrank higher than the school-speci�c cuto�

I A given applicant can be in multiple sharp samples

Back

Descriptive Statistics

descriptives

All All No Latin Latin

BPS Applicants Offer O'Bryant Academy School

(1) (2) (3) (4) (5) (6)

Female 0.489 0.545 0.516 0.579 0.581 0.577

Black 0.516 0.399 0.523 0.396 0.259 0.123

Hispanic 0.265 0.189 0.223 0.196 0.180 0.081

FRPL 0.755 0.749 0.822 0.788 0.716 0.499

LEP 0.116 0.073 0.109 0.064 0.033 0.004

Bilingual 0.315 0.387 0.353 0.420 0.451 0.412

SPED 0.227 0.043 0.073 0.009 0.006 0.009

English 4 0.000 0.749 0.251 0.870 1.212 1.858

Math 4 0.000 0.776 0.206 0.870 1.275 2.114

N 21,094 5,179 2,791 755 790 843

Updated: 2013-11-08

Exam School Assignment

Back

Measurement Scatterplots

−2

−1

01

23

ISE

E R

eadi

ng

−2 0 2 4ISEE Verbal

.

−2

−1

01

23

ISE

E R

eadi

ng−2 0 2 4

MCAS English 4

English

−2

−1

01

23

ISE

E V

erba

l

−2 0 2 4MCAS English 4

.−

2−

10

12

3IS

EE

Mat

h

−2 0 2 4ISEE Quantitative

.

−2

−1

01

23

ISE

E M

ath

−2 0 2 4MCAS Math 4

Math

−2

−1

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ISE

E Q

uant

itativ

e


.

Measurement Scatterplots (cont'd)

−2

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Back

Measurement Correlations

measurement_correlations

Reading Verbal Math Quantitative English 4 Math 4

(1) (2) (3) (4) (5) (6)

Reading 1 0.735 0.631 0.621 0.670 0.581

Verbal 0.735 1 0.619 0.617 0.655 0.587

Math 0.631 0.619 1 0.845 0.598 0.740

Quantitative 0.621 0.617 0.845 1 0.570 0.718

English 4 0.670 0.655 0.598 0.570 1 0.713

Math 4 0.581 0.587 0.740 0.718 0.713 1.000

N

Updated: 2013-11-08

Panel B: MCAS

Panel A: ISEE

ISEE MCAS

5,179

Back

E�ects at the Admissions Cuto�s: Estimatesrd_estimates_all

Latin Latin

O'Bryant Academy School

(1) (2) (3)

First 0.781*** 0.955*** 0.964***

Stage (0.034) (0.018) (0.018)

Reduced 0.047 -0.021 -0.086

Form (0.055) (0.044) (0.052)

LATE 0.060 -0.022 -0.089

(0.070) (0.046) (0.054)

N 1,475 1,999 907

Updated: 2013-11-08

* significant at 10%; ** significant at 5%; ***

significant at 1%

Back

Marginal Distribution of English Ability

0.2

.4.6

Mar

gina

l Den

sity

−2 0 2 4English Ability

Marginal Distribution of Math Ability

0.1

.2.3

.4.5

Mar

gina

l Den

sity

−2 0 2 4Math Ability

Scatterplot of English and Math Ability

−1

01

23

4E

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h A

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y

−2 0 2 4Math Ability

Back

Factor Loadings on ISEE and MCAS Scoresfactor_loadings

Reading Verbal Math Quantitative English 4 Math 4(1) (2) (3) (4) (5) (6)

θE 1.160*** 1.180*** 1(0.033) (0.035)

θM 1.135*** 1.119*** 1(0.027) (0.028)

θE 0.081*** 0.152*** 0.016(0.020) (0.018) (0.016)

θM 0.019 -0.013 0.124***(0.018) (0.017) (0.015)

N

Updated: 2014-01-13

* significant at 10%, ** significant at 5%, *** significant at 1%5,179

Panel B: Factor Loading on (Log) Standard Deviation

ISEE MCAS

Panel A: Factor Loading on Mean

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Dependence of Outcomes on English and Math Abilitylatent_fs_rf

No Latin LatinOffer O'Bryant Academy School(1) (2) (3) (4)

θE -0.001 -0.025 -0.102* 0.003(0.011) (0.076) (0.053) (0.009)

θM -0.012 -0.059 0.012 0.027**(0.008) (0.061) (0.030) (0.012)

θE 0.446*** 0.282*** 0.217*** 0.239***(0.062) (0.067) (0.066) (0.046)

θM 0.604*** 0.346*** 0.267*** 0.158***(0.056) (0.070) (0.057) (0.044)

N 1,777 563 625 793

Updated: 2014-01-13

Panel A: First Stage


Panel B: Reduced Form

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Estimates: All Applicantsrd_extrapolation_all

Latin LatinO'Bryant Academy School

(1) (2) (3)First 0.858*** 0.962*** 0.950***Stage (0.038) (0.021) (0.018)

Reduced 0.252*** 0.279*** 0.199***Form (0.068) (0.075) (0.061)

LATE 0.293*** 0.290*** 0.209***(0.081) (0.079) (0.064)

N 2,240 2,760 3,340

Updated: 2014-01-13

* significant at 10%, ** significant at 5%, ***significant at 1%

Estimates: Below/Above Admissions Cuto�srd_extrapolation_cutoff


(1) (2) (3) (4) (5) (6)First 0.892*** 0.984*** 0.959*** 0.749*** 0.891*** 0.906***Stage (0.050) (0.027) (0.021) (0.016) (0.018) (0.031)

Reduced 0.343*** 0.362*** 0.281*** -0.021 -0.005 -0.091*Form (0.089) (0.092) (0.075) (0.034) (0.046) (0.054)

LATE 0.385*** 0.367*** 0.293*** -0.028 -0.006 -0.099*(0.102) (0.097) (0.079) (0.045) (0.053) (0.059)

N 1,677 2,135 2,601 563 625 739

Updated: 2014-01-13


Below Admissions Cutoff Above Admissions Cutoff

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Socioeconomic Tiers

I Census tracts are given a socioeconomic index based on

1. Median family income2. Percent of households occupied by the owner3. Percent of families headed by a single parent4. Percent of households where a language other than English is

spoken5. Educational attainment score

I Each component is turned into a percentile and added up toget the socioeconomic index

I BPS students divided into four tiers based on the quartiles ofthe socioeconomic index distribution

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Observed and Counterfactual Assignmentscfsim12_assignments

No Latin Latin

Counterfactual Offer O'Bryant Academy School

Assignment (1) (2) (3) (4)

No Offer 2418 221 113 39

O'Bryant 280 129 133 213

Latin Academy 88 389 268 45

Latin School 5 16 276 546

No Offer 2579 159 39 14

O'Bryant 203 319 146 87

Latin Academy 9 106 403 272

Latin School 0 171 202 470

Updated: 2013-11-08

Actual Assignment

Panel A: Minority Preferences

Panel B: Socioeconomic Preferences

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Counterfactual Admissions Cuto�scfsim12_cutoffs

Latin Latin

O'Bryant Academy School

(1) (2) (3)

Minority -14.1 -20.6 -31.9

Non-Minority 15.8 12.4 7.8

SES Tier 1 -20.4 -26.4 -32.9

SES Tier 2 -6.6 -11.7 -16.1

SES Tier 3 -2.5 -7.2 -17.1

SES Tier 4 8.0 2.1 -5.1

Updated: 2013-11-08


Panel B: Socioeconomic Preferences

Notes: This table reports the differences between the actual

admissions cutoffs and the counterfactual admissions

cutoffs under minority and socioeconomic preferences in

the exam school admissions.

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Descriptives by Counterfactual Assignmentcfsim12_descriptives

No Latin Latin

Offer O'Bryant Academy School

(1) (2) (3) (4)

Female 0.502 0.588 0.629 0.572

Black 0.430 0.440 0.386 0.274

Hispanic 0.182 0.220 0.203 0.172

FRPL 0.810 0.771 0.715 0.556

LEP 0.116 0.030 0.022 0.018

Bilingual 0.386 0.396 0.380 0.391

SPED 0.073 0.009 0.013 0.005

English 4 0.277 0.981 1.215 1.668

Math 4 0.277 0.963 1.289 1.781

Female 0.514 0.572 0.597 0.575

Black 0.499 0.360 0.295 0.203

Hispanic 0.223 0.191 0.143 0.120

FRPL 0.813 0.728 0.673 0.624

LEP 0.107 0.058 0.030 0.017

Bilingual 0.359 0.423 0.391 0.445

SPED 0.073 0.012 0.006 0.006

English 4 0.261 1.067 1.309 1.556

Math 4 0.217 1.146 1.365 1.744

N 2,791 755 790 843

Updated: 2013-11-08


Panel B: Minority Preferences

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