Demonstrated Interest: Signaling Behavior in College Admissions

Transcription

1 Demonstrated Interest: Signaling Behavior in College Admissions James Dearden, 1 Suhui Li, 2 Chad Meyerhoefer, 3 and Muzhe Yang 4 1 Corresponding author: Department of Economics, Rauch Business Center, Lehigh University, 621 Taylor Street, Bethlehem, PA Phone: (610) Fax: (610) jad8@lehigh.edu. 2 School of Public Health and Health Services, George Washington University; suhuili@gwu.edu. 3 Department of Economics & NBER, Lehigh University; chm308@lehigh.edu. 4 Department of Economics, Lehigh University; muzheyang@lehigh.edu.

2 Abstract In college admission decisions, important and possibly competing goals include increasing the quality of the freshman class and making the school more selective while attaining the targeted size of the incoming class. Especially for high-quality applicants who receive multiple competing offers, colleges are concerned about the probability that these students accept the offers of admission. As a result, applicants contacts with admission offi ces, such as campus visits, can be viewed positively by the offi cers as demonstrated interest in the colleges. We provide empirical evidence on the effects of demonstrated interest on admission outcomes. Specifically, we use unique and comprehensive administrative data, which include all contacts made by each applicant to the admissions offi ce of a medium-sized highly-selective university during two admission cycles. We find that an applicant who contacts the university is significantly more likely to be admitted, and that the effect of the contact on the probability of admission is increasing in the applicant s SAT score, particularly when the contact is costly to make. We further use a numerical example to explain this monotonicity result in a model of applicant signaling of preferences, university admissions, and applicant matriculation. Keywords: college admissions; signaling; demonstrated interest; on-site and off-site contacts JEL Classification: D83; I23

3 1 Introduction With recent increased competition and uncertainty in the college admissions process, selective colleges and universities are even more careful in making admission decisions. Not only do schools consider whether applicants meet admission requirements, but also whether they are good matches for their colleges and universities, and how likely they are to accept offers of admission. Schools base their beliefs about the likelihood that applicants will matriculate in part on demonstrated interest. 1 Concurrently, students who are aware that college admissions are increasingly competitive and that schools use demonstrated interest in their admission decisions have an incentive to demonstrate their interests (i.e., signal their preferences) to schools. As pointed out by Avery, Fairbanks and Zeckhauser (2004) and by Avery and Levin (2010), early-admission programs provide one opportunity for applicants to explicitly indicate their interest at one particular college or university. Other ways of demonstrating interest include visiting campus, attending school information sessions, and contacting admissions offi cers. Furthermore, campus visits take various forms such as campus tours, admissions information sessions, and personal appointments where a student has a one-to-one interaction with an admissions counselor, a professor, or a coach. While these contacts are typically characterized as means for students to gather information about whether schools are good matches, they also provide applicants with the opportunity to impress their enthusiasm about the school on admissions counselors. Even though all students have the opportunity to make contacts and signal their interest, participating in these events is costly in terms of time and money; it usually takes a whole day or a weekend for the student and their parents to visit one school. Naturally, students are willing 1 For example, Hoover s (2010) study reported in the Chronicle of Higher Education asks the following questions: How many applicants would turn down a super-selective, big-name college to attend a somewhat less-selective, less-famous one? How do you know whether a student considers your college a top choice or a safety school? How does an applicant s sense of fit with a college relate not only to matriculation, but also retention? The article continues, In recent years, such questions have prompted America s admissions teams to look more closely at demonstrated interest, the popular term for the contact students make with a college during the application process, such as by visiting the campus, participating in an interview, or ing an admissions representative. 1

4 to devote more time to visiting their preferred schools given a limited time and financial budget. Hence, these costly signals can serve as mechanisms for schools to separate those students with a greater preference for attendance from those with a lesser preference. Universities have an incentive to admit students who are more likely to attend because this allows them to make admission offers to fewer applicants overall. By reducing their acceptance rates, an important indicator of selectivity, universities increase their appeal and improve their rankings. 2 Furthermore, colleges and universities believe that applicants who signal their interest are more likely to contribute to campus activities, have more meaningful college experiences, and give back to their alma maters as alumni. Hence, colleges and universities keep detailed records of contacts made by applicants and may interpret them as signaling behavior when making admission decisions. This paper examines how applicants signaling behavior affects university admission decisions, and how this effect varies with the costs of the signals and the academic records of the applicants. We use administrative data from a medium-sized highly-selective university. One important feature of our data is the comprehensive information on the exact date and type of each contact made by every applicant throughout an admission cycle, which allows us to identify all the contacts that had occurred before the university made the admission decisions, and also to assess the impact of different types of contacts (i.e., signals) on the probability that a student is admitted by the university. We focus mainly on on-site contacts and off-site contacts: the former requires the applicant to visit campus, while the latter is less costly in terms of time and money because applicants are not required to leave their local area. Our study provides empirical evidence consistent with the hypothesis that applicants who signal their interest to a school are more likely to be admitted; the effect of the signal on the likelihood of admission is increasing in the strength of the signal, and also increasing in the quality of the applicant. Specifically, we find that on-site contacts are significantly more 2 Griffi th and Rask (2007) and Luca and Smith (2013) demonstrate that the U.S. News and World Report rankings are important to students in their application and matriculation decisions. 2

5 effective than off-site contacts in increasing an applicant s likelihood of admission, and on-site contacts made by students with high SAT scores are also more effective than those made by students with low SAT scores. Making both types of contact could increase the acceptance probability by as much as 40 percentage points for students in the highest quartile of the SAT score distribution. This is consistent with Avery and Levin s (2010) finding that applicants benefit from signaling their interest by applying under early-admission rules, although our study focuses on those applying under normal admission rules. We also verify that the university s interpretation of on-site and off-site contacts as signals of applicant interest is rational by showing that applicants who make such contacts are indeed more likely to matriculate at the university after receiving an admission offer. Perhaps our most interesting empirical result is that the effect of a costly, on-site contact on the probability of admission is increasing in the quality of the applicant. At first glance, costly signals should be most effective for applicants who are academically at the edge of admission because the best applicants should be admitted and the worst applicants should not. However, at least in the case of the American Economic Association s (AEA) jobmarket signaling mechanism used by new economics Ph.D.s, this first-glance intuition may be faulty. 3 In the AEA mechanism signals are very costly because each job market candidate is restricted to send at most two signals to prospective employers. Due to the opportunity costs of interviewing candidates, a middle-ranked university may not choose to grant an interview to a highly-sought-after applicant unless he or she has signaled the university. Hence, we speculate that in this case signaling may be most effective for the top job-market candidates. In a field experiment of an online dating market (Lee and Niederle, forthcoming) participants are randomly endowed with a finite number of virtual roses that can be used to signal special interest. In the experiment participants are rated by desirability and placed into one of three groups: top, middle, and bottom. Although Lee and Niederle (forthcoming) do not 3 The AEA signaling mechanism is described at 3

6 confirm that the effect of attaching a rose to an offered date on the probability that the offered is accepted is increasing in desirability, the analysis does uncover a result that has the same flavor as monotonicity, albeit weaker. Their hypothesis is: Participants respond more strongly to a dating request with a rose attached if the request comes from a person who is considered more attractive than they are. Consistent with this hypothesis, they find that when a participant from the most desirable group requests a date from a participant of the low or middle group, the request is significantly more likely to be accepted when it is accompanied with a rose. The same property holds for members of the middle group requesting dates from the bottom group members. The effect of a rose in all those instances is more than a 50% increase in the acceptance rate, which corresponds to twice the increase in the acceptance rate when moving the sender from the bottom to middle desirability group. Our analysis complements Avery and Levin s (2010) study in the sense that we examine a different avenue for demonstrated interest in college admissions, namely student contacts, while Avery and Levin s (2010) study focuses on early admissions. We also examine two heterogeneities in the effect of demonstrated interest on the probability of admission, which are not studied by Avery and Levin (2010): first, whether the effect is stronger for students who make costlier contacts; and second, whether the effect is increasing in student quality for on-site contacts and for off-site contacts differently. We explore this empirical result about monotonicity in student quality further with a game-theoretic numerical example. Different from traditional signaling models presented in Avery and Levin (2010), Coles et al. (2013), and Kushnir (2013), our numerical example allows a student s decision to signal to be based not only on the student s private information but also on public information. The benefit of this feature is that we can examine the relationship between a student s SAT score, which is known by all universities to which a student applies, and the effectiveness of a signal from the student. 4 4 In this paper we do not evaluate the welfare effect of the signaling mechanism; instead, we compare how signals from different types of applicants have a different impact on schools admission decisions. Our analysis of signaling behavior is related to the Dale and Krueger s (2002 and 2011) analysis of the effect of college selectivity on earnings. Dale and Krueger (2011) find that it is important to take unobserved 4

7 2 Data and Methods 2.1 Data We use administrative data from students applying for admission to a medium-sized highlyselective university in the Fall semesters of 2006 and The admissions offi ce shared with us the data recorded for each applicant throughout an admission cycle, including the number of times each applicant contacted the university, and the date and purpose of each contact. To the best of our knowledge, this study uses the most comprehensive data on the contacts each applicant made with the university. For the purpose of our study, we restrict the set of contacts to those made for the 2006 and 2007 admission cycles, but before admission decisions were finalized. These contacts were made during January 1, 2005 March 10, 2006 for the Fall 2006 admission cycle, and during January 1, 2006 March 9, 2007 for the Fall 2007 admission cycle. 5 We group contacts into three categories based largely on the perceived strength of the signal to the university: on-site contacts; off-site contacts; and contacts that do not signal interest. Table 1 reports the counts and percent frequencies of the contacts grouped into the three categories, overall and by each admission cycle. On-site contacts include various types of campus visits, which involve a higher level of effort and greater monetary cost than off-site contacts. The latter include university-sponsored events at an applicant s high school or in their local community. We postulate that costlier contacts are interpreted by the university as stronger signals of an applicant s interest. In contrast, actions such as online information requests or phone calls to the admissions offi ce involve such minor costs that they provide the university with little credible information about their interest in the university. Applicants to the university may contact the university in any of those capacities or student ability into account by controlling for the average SAT score of the colleges to which students have applied. In the context of signaling and admission decisions, the information about the sets of schools to which students have applied could be valuable to universities when making admission decisions. But, for ethical or strategic reasons, universities do not ask students for this information. 5 For the Fall 2006 and 2007 cycles, admission decisions were finalized prior to March 10, 2006 and March 9, 2007, respectively. 5

8 they may not contact the university at all. Based on all possible combinations of the three contact types (off-site, on-site, and contacts that do not signal interest), we can assign each applicant into one of the eight mutually exclusive types. 6 In our empirical analysis we focus on the following five types of applicants: (a) those who make no contact; (b) those who make off-site contacts only; (c) those who make on-site contacts only; (d) those who make off-site and on-site contacts; and (e) those who make contacts that do not signal interest. We define (a) as the control group, and use (b) (e) as four separate treatment groups, representing four signaling behaviors. We compare (a) with (b), (c), (d) and (e), respectively, to estimate four separate treatment effects. The total number of applicants in the two admission cycles is 22,700. In our study we exclude several categories of applicants. First, we exclude early-decision applicants because they enter into a contract with the university and withdraw their applications to all other institutions if they receive an admission offer. As a result, the university knows with certainty these applicants will matriculate if they are offered admission, and need not consider other signals. We keep in our sample 21,138 (or 93.12% of the original sample) students who applied under normal admission rules. Second, we exclude 1,596 foreign applicants because they face significant financial barriers to visiting campus, which is one of the most important signals. The university may also interpret some contacts differently and use different admission guidelines for foreign applicants. 7 For similar reasons, we exclude 1,275 applicants that are student-athletes, who are evaluated using different criteria from regular applicants. Third, we further exclude applicants who are the single applicant from their high schools, due to the use of high-school fixed effects in our empirical models. In the end, our final 6 These eight types of applicants are: (1) those who make no contact; (2) those who make contacts that do not signal interest; (3) those who make off-site contacts only; (4) those who make on-site contacts only; (5) those who make on-site and off-site contacts; (6) those who make contacts that do not signal interest and off-site contacts; (7) those who make contacts that do not signal interest and on-site contacts; and (8) those who make contacts that do not signal interest, off-site contacts, and on-site contacts. 7 With the exception of North Dakota, domestic applicants were from all 50 states plus the District of Columbia. 6

9 sample includes 12,501 applicants. Among them 5,539 made no contact; 1,238 made off-site contacts only; 3,384 made on-site contacts only; 1,351 made on-site and off-site contacts; and 989 made contacts that do not signal interest. 2.2 Methods We frame our empirical analysis as a binary treatment evaluation, where treated applicants make a particular type of contact, and untreated applicants (the control group) do not contact the university. In order to determine the strength of the signal provided by each treatment, we consider off-site contacts, on-site contacts, and both off-site and on-site contacts all relative to the control group separately. Applicants who make only contacts that do not signal interest are excluded from the main empirical analysis, but are used to conduct a falsification test. Although our dataset is exactly the same one used by admissions offi cers, there is important information available at the admissions offi ce that is not recorded in this dataset. For example, there is no variable in the dataset that measures the quality of an applicant s essay. If an applicant who sends a strong signal of interest (which increases the likelihood of admission) also writes a compelling essay (which also increases the likelihood of admission), then the failure to control for essay quality will result in over-estimation of the effect of signaling on the probability of admission in an ordinary least squares (OLS) regression. However, it is also possible that an applicant who writes a compelling essay makes a signaling decision that is completely independent of the essay s quality; if this is true, then the OLS estimation will not be affected by the failure to control for essay quality. Because we do not observe the quality of an applicant s essay in our dataset, we are not able to analyze the correlation between the quality of an applicant s essay and his or her decision to contact the university, which is critical in determining the magnitude of the bias from OLS estimation. Nonetheless, we use the information in our dataset that is likely to be uncorrelated with the quality of an applicant s essay, but correlated with the applicant s signaling behavior, to construct an 7

10 instrumental variable (IV). We then use an IV regression to gauge the bias from OLS due to the failure to control for essay quality. However, our IV may be correlated with other important variables used for admission decisions but unobserved to us, 8 and as a result, it is not able to identify the causal effect of making contact with the university on the likelihood of receiving an admission offer. Rather, the goal of our IV analysis is to evaluate the potential size of the bias due to the omission of essay quality variable in the OLS estimation. We construct the IV for each type of contact and for the 2006 and 2007 admission cycles separately. Specifically, we utilize the fact that our data contain information on the exact date and type of each contact made by every applicant during an admission cycle, as well as the high school where each applicant is from. For each focal applicant (e.g., the one who makes on-site contacts only) in an admission cycle, our IV is the number of applicants from the same high school who made the same type of contact during that admission cycle, but earlier than the focal applicant. 9 When the focal applicant makes multiple same-type contacts in an admission cycle, the IV is the number of applicants from the same high school who made the same type of contact during that admission cycle, but prior to the very first time the focal applicant made that contact. Note that the IV is equal to zero when the applicant fails to contact the university; when the applicant is the first person from his or her high school to make that contact with the university; or when no one else from that high school contacts the university. Descriptive statistics for the IV used in each treatment effect analysis are reported in Table 2. This instrumental variable roughly reflects the pressure from the applicant s reference (or 8 For example, in the discussion section we analyze whether our IV could be correlated with the university s preferences for proactivity, which impact the likelihood of admission. 9 To examine the case of applicants making both off-site and on-site contacts, we use the number of applicants from the focal applicant s high school who make on-site contacts earlier than the focal applicant as the IV. We do not use the number of applicants from the focal applicant s high school who make off-site contacts as an additional IV because this IV could be weak in predicting the focal applicant s on-site contacts. This is the case discussed in Angrist and Pischke (2008, pp ) and Cameron and Trivedi (2005, pp ), where adding a weak instrument will increase the finite-sample bias of the IV estimator relative to a just-identified model with one strong instrument. 8

11 peer) group, which varies with each applicant. 10 We use it to capture several factors that could affect the probability of a student contacting the university. The first factor is peer influence, which could emerge if applicants want to attend the same college fairs or visit the same colleges and universities as their peers. The second factor is competitive pressure, whereby students view other applicants from the same high school as competitors who by signaling the university (through their contacts) may gain a competitive advantage. The third factor is the information provided by students who previously contacted the university, which may influence the likelihood that other applicants initiate their contacts. While the first and second factors generate a positive correlation between the number of students making prior contacts and the likelihood that an applicant subsequently contacts the university, the third factor could result in a positive or negative correlation. However, there is an obstacle in the assignment of IV values for those who did not contact the university during the admission cycle. The strength of our IV depends on the assumption that an applicant who contacts the university faces higher pressure to do so when there are more schoolmates (i.e., peers) who have already contacted the university. Accordingly, the IV values should be monotonically increasing with the peer pressure we are trying to measure. We use a zero value for the IV for an applicant who is the first (or the only one) from his or her high school to contact the university, because there is no schoolmate who contacts the university earlier than (or other than) him or her. By monotonicity, those who do not contact the university are assumed to have lower peer pressure than the pressure faced by first-movers (or only-movers ), and therefore, the IV values should be negative for the never-movers. However, we do not observe in the dataset those negative values reflecting peer pressure. As a result, we choose to use zero values for the IV for those who do not contact the university under the assumption that the true value for peer pressure is censored, 10 The influence of peers in education is well documented. Cipollone and Rosolia (2007) provide evidence on the effect of the high-school graduation rates of male students on those of female students. Carrell, Malmstrom and West (2008) find evidence that a higher level of peer cheating leads to a significantly higher likelihood that a student will cheat. Using individual-specific peer groups, De Giorgi, Pellizzari and Redaelli (2010) suggest that college students tend to follow their peers when choosing a major. 9

12 but lower than that faced by first-movers or only-movers. We use this IV to gauge the size of the bias from an OLS estimation that does not control for the quality of an applicant s essay. In order to do so, we assume that the number of contacts made by other applicants who contact the university earlier than the focal applicant is uncorrelated with the quality of the focal applicant s essay once we control for individuallevel and area-level characteristics, as well as high school fixed effects. We add high-school fixed effects to our IV estimation to account for factors that are important to admissions offi cers and also commonly shared by students from the same high school. Such factors include the quality and reputation of a high school; a high school s effort in preparing students for college applications, such as by sponsoring college visits or holding college events at the high school; or whether a high school is a feeder school, from which a large number of students are expected to enroll. By using high-school fixed effects, we also control for the differences in signals sent by students from schools with different class sizes. Furthermore, the inclusion of fixed effects ensures that our estimates are obtained by using variation across students within the same high schools. Our regression model is specified as follows: outcome ij = β 1 treatment ij + control ijβ 2 + δ j + ɛ ij, (1) treatment ij = α 1 instrument ij + control ijα 2 + γ j + ε ij. (2) Here, outcome ij indicates whether applicant i from school j is admitted to the university; control ij is a vector of control variables; δ j and γ j denote high-school fixed effects included in the outcome equation and the treatment equation, respectively; ɛ ij and ε ij are the regression error terms. In equation (1), treatment ij (1/0) indicates whether applicant i from high school j did (equal to 1) or did not (equal to 0) contact the university, which the university may view as a signal of interest. We consider four treatment variables that indicate whether the applicant 10

13 made off-site contacts only, on-site contacts only, off-site and on-site contacts, and contacts that do not signal interest. In equation (2), instrument ij is the IV we use to estimate β 1, the effect of contacting the university on admission. In both equations the vector control ij includes gender, race (White, Black, Hispanic, and Asian), U.S. citizenship, whether the applicant s parents or grandparents attended the university (i.e., legacy applicant), combined SAT scores (and the associated quartiles), academic rank index (and the associated quartiles), 11 median zip code-level income for households of each racial category, the distance between the applicant s home zip code and the university s zip code, 12 indicators for the college to which the student applied (business, engineering, arts and sciences, or intercollegiate program), and an indicator of whether the application was submitted for the 2007, as opposed to the 2006, admission cycle. In some estimations we also include interactions of SAT score quartile dummies with treatment ij to test whether the impact of signaling on admission varies across the SAT score distribution. Throughout our estimation we cluster the standard errors at the state-level based on the applicant s high school state. This provides more conservative estimates of the standard errors than clustering at either the county, high school or zip code level (Williams, 2000). 3 Results 3.1 Main Results Table 2 reports the summary statistics for each of the five types of applicants in our sample: no-contact applicants are used as the control group and the other four types are used as treatment groups. We find that the proportion of admitted applicants is monotonically increasing in the strength of the signal represented by each contact, as is the proportion of 11 The academic rank index is created by the university from information on the applicants high school performance and their standardized test scores. 12 Note that this distance is calculated based on the applicant s home zip code; it is not invariant for applicants from the same high school. 11

14 applicants who matriculate when they are admitted. 13 There is also evidence of non-random sorting into each of the four treatment groups. For example, applicants sending stronger signals have higher combined SAT scores, and applicants making on-campus visits live closer to campus, on average. Tables 3 reports the OLS and IV estimates of the treatment effects for the following three treatments, respectively: making off-site contacts only, making on-site contacts only, and making off-site and on-site contacts. For all three treatments, the same control group is used, which includes those who made no contact. In all three cases (i.e., three treatments) we find that the focal applicant s likelihood of making contact with the university (i.e., signaling) increases by percentage points when there is one more applicant from the same high school who made the same type of contact prior to the focal applicant. This is consistent with the presence of peer (or competitive) pressure. We also find that for those who made on-site only, or both off-site and on-site contacts with the university the IV estimates of the effects of signaling on admission are smaller than the OLS estimates. This pattern suggests that the OLS estimates could be upwardly biased by our failure to control for essay quality and that the upward bias arises from those who write good application essays and also send strong signals of their interest to the university. The estimates in Table 3 also indicate monotonicity in the effect of signaling on the likelihood of admission. Making off-site contacts raises the likelihood of admission by about 11 percentage points, whereas making on-site contacts increases the chance of admission by about 14 percentage points. Those who make both off-site and on-site contacts realize the greatest increase in their probability of admission, a roughly 21 percentage point increase. Overall, these results suggest that stronger signals are given greater weight in admission decisions. We also investigate the possibility that the effectiveness of signals varies with an ap- 13 Appendix Table 1 reports the summary statistics by each treatment-control estimation sample, where we find a pattern similar to the one found in Table 2: the likelihood of being admitted appears to increase as the strength of the signal increases. 12

15 plicant s SAT score and report the findings in Table 4. Here we allow for nonlinearity in the relationship between SAT scores and the probability of admission by including the continuous SAT score as well as indicator variables for SAT quartiles and interactions of the quartile indicators with the treatment variable. Overall, the estimates suggest that the effect of signaling increases with the applicant s SAT score. This pattern is more salient for those who make on-site contacts (columns 3 and 4) and those whose SAT scores are in the third or fourth quartile of the SAT score distribution. For example, in column (4) while the effects of making on-site contacts are not statistically significant for the first and the second SAT quartiles, signaling raises the probability of admission by 21.8 percentage points for applicants in the third SAT quartile relative to the first, and by 33.7 percentage points for applicants in the top SAT quartile. Like the non-interacted models used in Table 3, the first-stage partial F-statistics reported in Table 4 indicate that the instruments are strong Discussion To assess the performance of our IV, we conduct a falsification test and report the results in Tables 5A and 5B. In these specifications we use the same model specified by equations (1) and (2), but define the treatment variable to indicate whether the applicant made contacts that do not signal interest, such as filling out online information request or calling the admissions offi ce. In both tables the OLS estimates suggest that making this type of minor contact increases the admission probability by 3.6 percentage points overall (column 1 of Table 5A), and 8.6 (or 9.2) percentage points for applicants whose SAT scores are in the third (or the fourth) quartile (column 1 of Table 5B). These results could reflect the upward bias arising from the omission of the essay quality variable in the OLS estimation. In contrast, there is no statistically significant coeffi cient of these minor contacts on the likelihood of admission in the IV estimates (reported in columns 2 of Tables 5A and 5B). Although this 14 Note that the interacted models are exactly identified by interacting the IV with each SAT quartile. The reported first-stage partial F statistics are the Angrist-Pischke multivariate F statistics for the excluded instruments (Angrist and Pischke, 2008, pp ). 13

16 falsification test cannot prove the validity of the IV, it suggests that our IV could be effective in removing the upward bias coming from omitting essay quality in the OLS estimation. In order to verify that the effectiveness of an applicant s signal is monotonically increasing in its strength, we estimate models that include treatment variables for all three types of contacts (on-site contacts, off-site contacts, and contacts that should not signal interest). The results reported in Table 6 are consistent with those obtained from the models that include a single treatment variable: the estimated effect of making on-site contacts increases the admission probability by about 14 percentage points, while the off-site contacts increase the probability of admission by about 8 percentage points, and minor contacts have no effect (column 2 of Table 6). These marginal effects are very close to the ones reported in Tables 3 and 5A. Notably, the OLS estimates in Table 6 indicate the same upward bias in the case of contacts that do not signal interest, with the magnitude (0.038, significant at the 1% level) similar to the one in Table 5A (0.036, significant at the 1% level). One important concern about our instrumental variable is that the number of applicants from the same high school who made the same type of contacts prior to the focal applicant could reflect the proactivity of the focal applicant. In other words, more proactive applicants may be among the first applicants to contact the university, resulting in a smaller value of the IV. If proactivity is detected and favored by admissions offi cers, or it is correlated with other unobservable characteristics of applicants that affect admission, such as the applicant s essay, our IV will be invalid. If the IV does in fact reflect applicant proactivity, or a first-mover advantage among applicants who contact the university, we would expect the coeffi cient of the IV in an OLS regression to be negative. We estimate such a regression and report the results in Appendix Table 2. For applicants who make off-site contacts only, we do not find any effect of our IV on admission across various specifications (columns 1 4 in Panel A). In contrast, for applicants who make on-site contacts only (Panel B) or who make on-site and off-site contacts (Panel C), we find a very small and negative effect of the IV on the admission probability. While the sign of the IV coeffi cient is consistent with the 14

17 interpretation that the IV may, in part, capture applicant proactivity, the magnitude is very close to zero (i.e., an additional visit by someone from the same high school, which is a 40 percent increase in the average value of the IV, reduces the probability of admission by at most 0.8 percentage points), suggesting that the direct impact of our proposed IV on the admission probability is minor. 15 In order to further investigate whether our IV may capture proactivity we regress each IV on applicant characteristics and report the results for each admission cycle separately in Appendix Tables 3 and 4. Overall, there are not many statistically significant correlations in these regressions. One might expect proactivity to be positively correlated with SAT and academic rank, resulting in a negative correlation between these variables and the instrument. We do not observe any such negative correlations with the SAT or academic rank quartile indicators. 16 As a result, we do not find any suggestive evidence that the small negative correlation we find between the on-site contact IV and admission is due to proactivity. Lastly, we check the coherency of our results by examining matriculation outcomes. Our finding that off-site contacts and on-site contacts increase an applicant s probability of admission implies that the university interprets these actions as signals of the applicant s interest. In order for the university s response to be rational, applicants who send signals must be more likely to matriculate after being admitted. In order to validate that signals are associated with a higher probability of matriculation, we apply OLS to equation (1) to estimate the effect of signaling among admitted applicants. In doing so, we assume that after conditioning on applicant characteristics and high-school fixed effects there are no important unobservables correlated with both the likelihood of matriculation and whether the applicant contacts the university prior to receiving an admission offer. 15 We also note that our IV is strong (the first-stage partial F -statistics reported in Table 3 range between 24 and 490), and that IV estimates based on powerful instruments are much less sensitive to violations of the exclusion restriction than those based on relatively weak instruments (Small and Rosenbaum, 2008). 16 There is actually a positive correlation between the off-site contact instrument and the third and fourth SAT quartile indicators and fourth rank index quartile indicator for the 2007 admission cycle (column 1 of Appendix Table 4), but this IV has no detectable correlation with the admission (Panel A of Appendix Table 2). 15

18 Panel A of Table 7 contains estimates of the effect of signaling on matriculation among admitted applicants from our OLS models. Signaling interest through an off-site or an onsite contact increases the probability of matriculation by approximately 7 percentage points, while the stronger signal of both on-site and off-site contacts increases this probability by about 13 percentage points. In Panel B we report the results from the models where the treatment effect is interacted with SAT score quartiles. Overall, we find that admitted applicants with higher SAT scores who signal their interest are more likely to matriculate than those who are in the same SAT score quartile but do not send a signal. These findings validate the university s admission preference for applicants who signal their interest, and justify the higher preference given to applicants who send the strongest signals. 4 An Illustrative Numerical Example In this section we use a numerical example to explore a signaling mechanism underlying our empirical results. This numerical example involves two cases that relate to our three empirical results: first, demonstrated interest increases the probability of admission; second, the marginal effect of a high-cost signal on the probability of admission is increasing in the quality of the applicant (as measured by SAT scores); and third, high-cost signals have a greater marginal effect than low-cost signals on the probability of admission. In the example students are uncertain about whether selective schools admit them and schools are uncertain whether students, if admitted, will matriculate. There is a unit mass of students, and three schools to which each student applies. Schools A and B are selective, and C accepts all students. With regard to student preferences, half of the students prefer A to B, and other half prefer B to A. All students rank school C third. Selective school i scores each applicant s academic ability on her SAT score, denoted as x, and also on a second, independent assessment, denoted as v i. Selective school i s total 16

19 assessment of an applicant is z i = x+v i. Our example has two possible SAT scores. One-third of the students scored x = 2400 on the SAT exam, and two-thirds of the students scored x = In selective school i s independent assessment, a student is either acceptable (v i = 0) or unacceptable (v i = ). All students who scored 2400 are acceptable, with v A = v B = 0. Of the students who scored 1920, one-quarter are acceptable by both schools (v A = 0 and v B = 0), one-quarter are acceptable by only school A (v A = 0 and v B = ), one-quarter are acceptable by only school B (v A = and v B = 0), and finally one-quarter are unacceptable by A and B (v A = and v B = ). We assume that school i knows its own total assessment of a representative student, z i = x + v i, but it does not know j s independent assessment x j or whether the student prefers A or B. Each student knows her SAT score and preferences. But each 1920-SAT student does know whether she is acceptable by both A and B (v A = v B = 0), only A (v A = 0, v B = ), only B (v A =, v B = 0), or neither (v A = v B = ). The model begins with students simultaneously signaling selective schools. The number of signals a particular student sends is exogenous. The proportion of the student population that sends m (m = 0, 1, 2) signals is q m, where q 0 + q 1 + q 2 = 1. The number of signals is randomly assigned, and with probability q m a representative student has m signals. Each student knows the number of signals she is exogenously assigned, whereas each school does not. In a weak perfect Bayesian equilibrium of this example, if a student has only one signal, then she signals her preferred selective school. Hence, in the equilibrium of this case the probability a student sends 0 signals to selective school i is q 0 + q 1 /2 and the probability a student sends one signal to selective school i is q 1 /2 + q 2. Following the opportunity by students to send signals, the schools simultaneously select the students they choose to admit. After receiving admissions decisions, each student decides where to matriculate. In equilibrium if a student is admitted by only one selective school, then she attends that school; and if the student is accepted by both, then she attends her 17

20 preferred school. Selective school i s utility is the weighted sum of the average quality of its entering class, denoted as x i, and its acceptance rate, denoted as r i (which with a unit mass of applicants, equals the number of admitted students). Specifically, selective school i s utility function is a x i br i. In each of the examples a = 1 and b = 50. Each of the selective schools has an enrollment target K, and in equilibrium meets this target in expectation (i.e., the expected number of matriculating applicants equals the target enrollment). The target enrollment is small enough so that in equilibrium, each selective school rejects all unacceptable students and admits only a subset of acceptable students. We construct two cases. The first is to highlight a case in which the marginal effect of a signal on the probability of admission is strictly increasing in the quality of the applicant. The second is to examine the effect of the cost of the signal, which we proxy by the distribution of the number of signals, on the effectiveness in admissions decisions of the signal. Case 1: Each student has one signal. We assume q 1 = 1. Armed with only one signal, each student signals her preferred school. If a student signals school i and is admitted, then she attends. However, if a student does not signal a school, then she attends if and only if she is rejected by the other selective school. The selective schools equilibrium admissions decisions depend on the enrollment targets, K. If K 1/6, then each school admits only students who have scored 2400 on the SAT and who have signaled the school. Specifically, the school admits 6K of the 2400-SAT students who have signaled, rejects all of the 2400-SAT students who have not signaled, and rejects all of the 1920-SAT students. If 1/6 < K 1/3, then the school admits all of the 2400-SAT students who have signaled, admits (6K 1) of the acceptable 1920-SAT students who have signaled (which translates into (6K 1)/2 of the 1920-SAT students who have signaled), and rejects all of the students who have not signaled. If 1/3 < K 5/12, then the school admits all of the acceptable students who have signaled (which translates into all of the 2400-SAT 18