ECON 3039

Labor Economics2015-16

By Elliott FanEconomics, NTU

Elliott Fan: Labor 2015 Fall Lecture 7 1

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The first steps• To show discontinuity at the cutoff point of (1) the

treatment variable and (2) the outcome variables

• Use raw data, instead of fitted data, for graphing

Elliott Fan: Labor 2015 Fall Lecture 7

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Two validity tests for RDD• Test on whether the density of observations is continuous

around the cutoff point

• Tests on whether means of ‘other variables’ are continuous around the cutoff point

Elliott Fan: Labor 2015 Fall Lecture 7

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Empirical strategies (RDD)We adopt a standard method expressed as:

• an indicator equal to one if the individual is born between September 1st and March 3rd in the following year.

• : the standardized birthdate for individual i, which is measured by the individual’s birthdate minus the cutoff date along the dimension of calendar.

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0 1 2 3 i i i i i iUni Eligible SBD SBD Eligible

Elliott Fan: Labor 2015 Fall Lecture 7

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RDD results for university attendance

Dependant variable: Any university attendance Public university attendanceGroup level Individual level Group level Individual level

(1) (2) (3) (4) (5) (6) (7) (8)

Panel A: male siblingsmean(Y|August) 0.101 0.040

Optimal bandwidth 39.2 45.2

T (=1 if born on or after Sept. 1st) 0.0329*** 0.0329*** 0.0330*** 0.0351*** 0.0094*** 0.0094*** 0.0094*** 0.0101***

(0.0036) (0.0035) (0.0036) (0.0031) (0.0019) (0.0019) (0.0019) (0.0018)F (standardized birthdate) 0.0001 0.0001 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000

(0.0001) (0.0001) (0.0001) (0.0001) (0.0000) (0.0000) (0.0000) (0.0000)T*F 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0000

(0.0002) (0.0002) (0.0002) (0.0002) (0.0001) (0.0001) (0.0001) (0.0001)County of birth and birth cohorts -- No Yes Yes -- No Yes Yes

Family and ind. characteristics -- No No Yes -- No No Yes

Observations 79 102,330 102,330 102,330 91 117,724 117,724 117,724

Elliott Fan: Labor 2015 Fall Lecture 7

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RDD results for university attendance

Dependant variable: Any university attendance Public university attendanceGroup level Individual level Group level Individual level

(1) (2) (3) (4) (5) (6) (7) (8)

Panel A: male siblingsmean(Y|August) 0.111 0.045

Optimal bandwidth 37.7 45.3

T (=1 if born on or after Sept. 1st) 0.0354*** 0.0354*** 0.0356*** 0.0351*** 0.0060** 0.0060** 0.0060** 0.0057**

(0.0054) (0.0053) (0.0051) (0.0046) (0.0025) (0.0024) (0.0024) (0.0023)F (standardized birthdate) -0.0001 -0.0001 -0.0001 -0.0001 -0.0000 -0.0000 -0.0000 0.0000

(0.0002) (0.0002) (0.0002) (0.0002) (0.0001) (0.0001) (0.0001) (0.0001)T*F 0.0003 0.0003 0.0003 0.0002 0.0001 0.0001 0.0001 0.0000

(0.0002) (0.0002) (0.0002) (0.0002) (0.0001) (0.0001) (0.0001) (0.0001)County of birth and birth cohorts -- Yes No Yes -- No Yes Yes

Family and ind. characteristics -- No No Yes -- No No Yes

Observations 75 90,091 90,091 90,091 91 109,089 109,089 109,089

Elliott Fan: Labor 2015 Fall Lecture 7

Bandwidth• Bandwidth matters especially when linear form is

applied.

• Multiple econometrics methods can be used to select the optimal bandwidth

• It is helpful to show that the estimated effect does not vary with different bandwidth.

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Local linear regression results using different bandwidths

Elliott Fan: Labor 2015 Fall Lecture 7

Fuzzy RDD

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• In fuzzy RD designs, treatment is not entirely determined by eligibility due to existence of non-compliers

• Non-compliers are those whose decision on taking up the treatment is not affected by eligibility status

• So the likelihood does not switch from zero to one when the running variable passes the cutoff point.

1 Pr( 1| ) Pr( 1| ) 0 i i i iED C c ED C c

Elite illusion

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• The Boston and New York City public school systems include a handful of selective exam schools.

• Unlike most other American public schools, exam schools screen applicants on the basis of a competitive admissions test.

• Fewer than half of Boston’s exam school applicants win a seat at the John D. O’Bryant School, Boston Latin Academy, or the Boston Latin School (BLS)

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Fraction enrolled at Boston Latin School

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Fraction enrolled at any Boston school

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The treatment variable

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The outcome variable

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Estimating a fuzzy RDD

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1. The main difference between a sharp RDD and a fuzzy one is that for the former the discontinuity of outcome variable at the cutoff point is caused by a zero-to-one change of the treatment variable, while for the latter by a less-then-one change.

2. This implies the need of scaling.

Estimating a fuzzy RDD

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1. A two stage estimation procedure: estimating a regression for the treatment and outcome variable separately:

2. The treatment effect can be obtained by taking the ratio of

1 1 1 0 1 0

2 2 2 0 2 0

( ) [( ) ]( ) [( ) ]

i i i i

i i i i

S D s s s s D eG D s s s s D e

2

1