Cecilia Hyunjung Mo and Katharine M.Conn Second,we asked about feelings of closeness to mi- above the cutoff can then act as an instrumental vari- nority groups.We assessed this by asking,"Here is a list able for receipt of the treatment(D): of groups.Please read over the list and check the box for those groups you feel particularly close to-people 1, who are most like you in their ideas and interests and ifX≥c (2) feelings about things."We are interested in whether 0, ifXi<c. individuals check that they feel close to"blacks"and "Hispanics"given over 80 percent of the communities Namely,if participating in TFA is based upon a cut- TFA serves in are African American and Hispanic.We off score and the distribution of unobservable deter- also considered two additional groups to act as placebo minants of future outcomes is continuous at the selec- checks;namely,our treatment should have no effect on how close they feel toward "the elderly"and "Chris- tion threshold,our parameter of interest,t,can then be identified without bias through an RDD.TFA partici- tians."16 These questions translate to four dichotomous pation is indeed based upon a cutoff score,and as we measures,where 1 indicates whether the respondent 4 noted that he/she feels particularly close to the group will show below,pretreatment characteristics are con- tinuous at the cutoff.Note that as the cutoff differs for in question. each TFA cohort,and we consider seven cohorts,we 4 standardize the cutoff for each cohort to be zero(c=0). IDENTIFICATION STRATEGY However,TFA does not employ a sharp cutoff strat- egy.While a cutoff score is employed in the admissions To measure the causal effect of participating in TFA process,admission(rejection)into TFA is not necessar- on its program participants,we employ a quasi- ily guaranteed if an applicant scores above(below)the experimental method that exploits the fact that accep- application score cutoff;rather,the probability of ad- tance into TFA is a discontinuous function of an ap- mission dramatically increases(decreases)if an appli- 4号元 plicant's selection score.This type of design allows for cant receives an admission score that is higher(lower) an identification strategy that compares the outcomes than the cutoff,as those close to the threshold score are of those who fall just short of the threshold score(and reevaluated to ensure that the admissions recommen- are not accepted)against those who fall just above the dation based on the score should be upheld.Moreover threshold score (and are accepted into the program). while the vast majority of admitted applicants decide This is important because of selection bias concerns. to matriculate into the program,take-up of the pro- Consider the following model: gram is imperfect.For the 2007-2013 application cy. cles,the matriculation rate was 83.20 percent.As such, yi=a+tDi+ei, we employ a fuzzy RDD,which does not require a 100- percent jump in the probability of receiving the treat- 是 ment at the cutoff,and only requires the following to where i represents the individual,yi is our outcome hold: measure of interest,Di denotes receipt of the treatment (serving in TFA),&is measurement error,and t is our parameter of interest-the relationship between serv- lim Pr[D=1X=c+△]≠lim Pr[D=1X=c+△]. S5.501g ing in TFA and our outcome measures of interest.If (3) individuals select into service organizations because of As the probability of treatment jumps by less than one unobserved determinants of later outcomes,which is at the threshold,the jump in the relationship between plausible,direct estimation of r by estimating model outcome y and the score X can no longer be inter- Equation(1)would be biased. preted as an average treatment effect.As in an instru- Say that each individual receives an application mental variable setting,however,the treatment effect score X;as part of the admission score,and c is the can be estimated by dividing the jump in the relation- cutoff score for admission.We can overcome this bias ship between Y and X at c(the reduced form estimate) if the distribution of unobserved characteristics of indi- by the fraction induced to take up the treatment at the viduals just shy of being admitted and not receiving the threshold (the first-stage estimate).Thus,our treatment treatment,and the distribution of those just above the effect tF for outcome Y is the following: bar for admission and receiving the treatment,are es- sentially drawn from the same population.The follow- limaL0 E[YIX=c+△]-limato E[Y1X=c+△] TF= eys ing indicator variable for whether an individual scored limaL0 E[D1X=c+△]-limato E[DX=c+△] (4) where we assume the distribution of unobserved char- 16 Identification with Christians may not be a perfectly clean placebo. acteristics is continuous at c,Equation (3)holds,and as a majority of African Americans and Hispanics are Christian(Pew the F subscript refers to the fuzzy RDD. Research Center 2009,2014).However,while many students TFA Per Lee and Card(2008),potential concerns that the participants interact with may be from Christian homes,meaningful admission score is coarse,due to the score being dis- change in closeness to Christians is unlikely.First,TFA participants crete rather than continuous,is addressed by clustering are placed in public schools,which prohibit school-sponsored prayer or religious indoctrination.Second,religion is not salient in the way our standard errors at the admission score level.We race and income are in discussions about education inequality within control for each application year to allow for differ- the United States. ences in averages by cohort year.Finally,the choice of 728Cecilia Hyunjung Mo and Katharine M. Conn Second, we asked about feelings of closeness to mi￾nority groups.We assessed this by asking, “Here is a list of groups. Please read over the list and check the box for those groups you feel particularly close to—people who are most like you in their ideas and interests and feelings about things.” We are interested in whether individuals check that they feel close to “blacks” and “Hispanics” given over 80 percent of the communities TFA serves in are African American and Hispanic.We also considered two additional groups to act as placebo checks; namely, our treatment should have no effect on how close they feel toward “the elderly” and “Chris￾tians.”16 These questions translate to four dichotomous measures, where 1 indicates whether the respondent noted that he/she feels particularly close to the group in question. IDENTIFICATION STRATEGY To measure the causal effect of participating in TFA on its program participants, we employ a quasi￾experimental method that exploits the fact that accep￾tance into TFA is a discontinuous function of an ap￾plicant’s selection score. This type of design allows for an identification strategy that compares the outcomes of those who fall just short of the threshold score (and are not accepted) against those who fall just above the threshold score (and are accepted into the program). This is important because of selection bias concerns. Consider the following model: yi = α + τDi + i, (1) where i represents the individual, yi is our outcome measure of interest,Di denotes receipt of the treatment (serving in TFA), εi is measurement error, and τ is our parameter of interest—the relationship between serv￾ing in TFA and our outcome measures of interest. If individuals select into service organizations because of unobserved determinants of later outcomes, which is plausible, direct estimation of τ by estimating model Equation (1) would be biased. Say that each individual receives an application score Xi as part of the admission score, and c is the cutoff score for admission. We can overcome this bias if the distribution of unobserved characteristics of indi￾viduals just shy of being admitted and not receiving the treatment, and the distribution of those just above the bar for admission and receiving the treatment, are es￾sentially drawn from the same population. The follow￾ing indicator variable for whether an individual scored 16 Identification with Christians may not be a perfectly clean placebo, as a majority of African Americans and Hispanics are Christian (Pew Research Center 2009, 2014). However, while many students TFA participants interact with may be from Christian homes, meaningful change in closeness to Christians is unlikely. First, TFA participants are placed in public schools, which prohibit school-sponsored prayer or religious indoctrination. Second, religion is not salient in the way race and income are in discussions about education inequality within the United States. above the cutoff can then act as an instrumental vari￾able for receipt of the treatment (Di): Di = 1, if Xi ≥ c 0, if Xi < c. (2) Namely, if participating in TFA is based upon a cut￾off score and the distribution of unobservable deter￾minants of future outcomes is continuous at the selec￾tion threshold, our parameter of interest, τ , can then be identified without bias through an RDD. TFA partici￾pation is indeed based upon a cutoff score, and as we will show below, pretreatment characteristics are con￾tinuous at the cutoff. Note that as the cutoff differs for each TFA cohort, and we consider seven cohorts, we standardize the cutoff for each cohort to be zero (c = 0). However, TFA does not employ a sharp cutoff strat￾egy. While a cutoff score is employed in the admissions process, admission (rejection) into TFA is not necessar￾ily guaranteed if an applicant scores above (below) the application score cutoff; rather, the probability of ad￾mission dramatically increases (decreases) if an appli￾cant receives an admission score that is higher (lower) than the cutoff, as those close to the threshold score are reevaluated to ensure that the admissions recommen￾dation based on the score should be upheld. Moreover, while the vast majority of admitted applicants decide to matriculate into the program, take-up of the pro￾gram is imperfect. For the 2007–2013 application cy￾cles, the matriculation rate was 83.20 percent. As such, we employ a fuzzy RDD, which does not require a 100- percent jump in the probability of receiving the treat￾ment at the cutoff, and only requires the following to hold: lim ↓0 Pr[D = 1|X = c + ] = lim ↑0 Pr[D = 1|X = c + ]. (3) As the probability of treatment jumps by less than one at the threshold, the jump in the relationship between outcome Y and the score X can no longer be inter￾preted as an average treatment effect. As in an instru￾mental variable setting, however, the treatment effect can be estimated by dividing the jump in the relation￾ship between Y and X at c (the reduced form estimate) by the fraction induced to take up the treatment at the threshold (the first-stage estimate).Thus, our treatment effect τ F for outcome Y is the following: τF = lim↓0 E[Y|X = c + ] − lim↑0 E[Y|X = c + ] lim↓0 E[D|X = c + ] − lim↑0 E[D|X = c + ] , (4) where we assume the distribution of unobserved char￾acteristics is continuous at c, Equation (3) holds, and the F subscript refers to the fuzzy RDD. Per Lee and Card (2008), potential concerns that the admission score is coarse, due to the score being dis￾crete rather than continuous, is addressed by clustering our standard errors at the admission score level. We control for each application year to allow for differ￾ences in averages by cohort year. Finally, the choice of 728 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000412