Regression Discontinuity Design Using Maimonides’ rule

University Rovira I VirgiliDepartment of Economics

Regression Discontinuity Design

Using Maimonides’ ruleMarina M Bánnikova


• Thistlethwaite & Campbell (1960)• Goldberger (1972)• Berk and Rauma (1983)• Hahn (1998)• Joshua D. Angrist and Victor Lavy (1999)• Van der Klaauw (2002)• Lemieux & Milligan (2008)• Lalive (2008)• Card, Dobkin & Maestas (2008)


Descriptive statistics

Variable MeanStd. Dev. Min Max

Quantiles0.10 0.25 0.50 0.75 0.90

Enrollment77.8

6839.060 5 226 31 50 72 100 129

Class size29.9

546.598 5 47 21 26 31 35 38

Average math score

67.323

10.032 0181.

254.8 61.1 67.8 74.1 79.4

Average reading score

74.445

8.077 34.8187.

664.2 69.9 75.4 79.8 83.3

Percent disadvantaged

14.091

13.485 0 76 1.0 4.0 10.0 19.0 35.0


The class size as a function of enrollment

enrollment

class

siz

e


The function of Maimonides' rule

enrollment

class

siz

e

41

20.5

81

27


Class sizes: actual and predicted by Maimonides’ rule

enrollment

class

siz

e


Average class size and predicted by Maimonides’ rule

enrollment

class

siz

e


The histogram of the differences between actual class size and predicted by the rule.


OLS estimation. Regressor: absolute difference between

actual class size and predicted by Maimonides' rule

Reading comprehension Math score

Coefficient -0.102 -0.100

St. error 0.035 0.048

p>|t| 0.004 0.036


OLS estimation

Regressors Reading comprehension Math score

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

Class size0.2203

6-

0.0279-

0.02420.3241 0.0865 0.0230

Percent of disadvantaged

-

0.3458-

0.3463

-0.3309

-0.3220

Enrollment

-0.0011

0.0192


Sharp RD design

enrollment

pro

babili

ty o

f bein

g t

reate

d


Sharp design in 3 discontinuities

1 2 3

enrollment

class

siz

e


Regressors Reading comprehension Math score (1) (2) (3) (4)

First discontinuity (threshold when enrollment=40)fsc -0.0607509 -0.0404945 -0.0472943 -0.0516246Percent of disadvantaged

-0.3433815 -0.3439759 -0.335075 -0.3349479

Enrollment -0.0367843 0.0078636Number of observations 445 445

Second discontinuity (threshold when enrollment=80)fsc -0.1600848 -0.1571057 -0.1431432 -0.1080707Percent of disadvantaged

-0.3262798 -0.3255215 -0.2922873 -0.2833603

Enrollment 0.0055505 0.0653448Number of observations 391 391

Third discontinuity (threshold when enrollment=120)fsc -0.3042367 -0.2508187 -0.1994336 -0.145723Percent of disadvantaged

-0.4811178 -0.4617891 -0.486871 -0.4674365

Enrollment 0.0891202 0.0896083Number of observations 137 137


Fuzzy RD design

enrollment

pro

babili

ty o

f bein

g t

reate

d


RegressorsReading comprehension Math score (1) (2) (3) (4) (5) (6)

Class size -0.15626-

0.27904-

0.27851-

0.00251-

0.22298-

0.27674Percent of disadvantaged

-0.36790-

0.36503-

0.36503-

0.34536-

0.34009-

0.34011

Enrollment 0.02333 0.02298 0.04285 0.07865Enrollment squared/100

0.00015 -

0.01626

Number of observations

2024 2024

Fuzzy RD design: instrumented-variable 2SLS regression


Conclusions• OLS showed us that small classes are not always

better in scores• Following the rule has positive influence on the

scores

• Sharp RD design showed that the less is the cutoff the better are scores

• Fuzzy RD design indicate a significant association between being in smaller classes and achieving higher scores

• The question of finding the right threshold remains opened

Regression Discontinuity Design Using Maimonides’ rule

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