ECON 3039 Labor Economics By Elliott Fan Economics, NTU Elliott Fan: Labor 2015 Fall Lecture 71

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 2Elliott 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 5Elliott Fan: Labor 2015 Fall Lecture 7

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Empirical strategies (RDD) 9Elliott Fan: Labor 2015 Fall Lecture 7

10 RDD results for university attendance Dependant variable: Any university attendancePublic university attendance Group levelIndividual levelGroup levelIndividual level (1)(2)(3)(4) (5)(6)(7)(8) Panel A: male siblings mean(Y|August) Optimal bandwidth T (=1 if born on or after Sept. 1st) *** ***0.0351***0.0094*** *** (0.0036)(0.0035)(0.0036)(0.0031)(0.0019) (0.0018) F (standardized birthdate) (0.0001) (0.0000) T*F (0.0002) (0.0001) County of birth and birth cohorts--NoYes --NoYes Family and ind. characteristics--No Yes--No Yes Observations79102, ,724 Elliott Fan: Labor 2015 Fall Lecture 7

11 RDD results for university attendance Dependant variable: Any university attendancePublic university attendance Group levelIndividual levelGroup levelIndividual level (1)(2)(3)(4) (5)(6)(7)(8) Panel A: male siblings mean(Y|August) Optimal bandwidth T (=1 if born on or after Sept. 1st) *** ***0.0351***0.0060** ** (0.0054)(0.0053)(0.0051)(0.0046)(0.0025)(0.0024) (0.0023) F (standardized birthdate) (0.0002) (0.0001) T*F (0.0002) (0.0001) County of birth and birth cohorts--YesNoYes--NoYes Family and ind. characteristics --No Yes--No Yes Observations 7590, ,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. 12 Elliott Fan: Labor 2015 Fall Lecture 7

13 Local linear regression results using different bandwidths Elliott Fan: Labor 2015 Fall Lecture 7

Fuzzy RDD 14Elliott Fan: Labor 2015 Fall Lecture 7 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.

Elite illusion 15Elliott Fan: Labor 2015 Fall Lecture 7 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)

16 Fraction enrolled at Boston Latin School Elliott Fan: Labor 2015 Fall Lecture 7

17 Fraction enrolled at any Boston school Elliott Fan: Labor 2015 Fall Lecture 7

18 The treatment variable Elliott Fan: Labor 2015 Fall Lecture 7

19 The outcome variable Elliott Fan: Labor 2015 Fall Lecture 7

Estimating a fuzzy RDD 20Elliott Fan: Labor 2015 Fall Lecture 7 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 21Elliott Fan: Labor 2015 Fall Lecture 7 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