Demonstrated Interest: Signaling Behavior in College Admissions 1

Transcription

1 Demonstrated Interest: Signaling Behavior in College Admissions 1 James Dearden, 2 Suhui Li, 3 Chad Meyerhoefer, 4 and Muzhe Yang 5 1 The authors thank the microeconomics seminar participants at the Penn State University. All errors are our own. 2 Corresponding author: Department of Economics, Rauch Business Center, Lehigh University, 621 Taylor Street, Bethlehem, PA Phone: (610) Fax: (610) jad8@lehigh.edu. 3 School of Public Health and Health Services, George Washington University; suhuili@gwu.edu. 4 Department of Economics & NBER, Lehigh University; chm308@lehigh.edu. 5 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 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 throughout two admissions 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. This monotonicity result that the effect of demonstrated interest on the probability of admission is strictly increasing in the quality of the applicant at first glance is counterintuitive. Therefore, to explain these empirical results, we produce a numerical example based on a sequential model of applicant signaling of preferences, university admissions, and applicant matriculation.

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 admissions 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 American 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 ranking. 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 behaviors 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 purpose of every contact made by each applicant throughout an admission cycle, which allows us to identify all the contacts that had occurred before the university made the admission decisions. We use this information 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. We hypothesize that applicants who signal their interest to a school are more likely to be admitted; furthermore, 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. By implication, a school s response to signals is only rational if applicants who signal the school are more likely to matriculate upon receiving an admission offer. 2

5 Taking into account the endogeneity of both types of contacts, we find that on-site contacts are significantly more 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 increases the acceptance probability by as much as percentage points for students in the highest quartile of the SAT 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 strictly 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, especially for those who are familiar with the American Economic Association s (AEA) job-market signaling mechanism used by new economics Ph.D.s, this first-glance intuition may be faulty. 2 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 choose to grant an interview to a highly-sought-after applicant only if he or she has signaled the university. Hence, in this case, signaling may be most effective for the top job-market candidates. We explore this empirical result about monotonicity in student quality in an example of a theoretical signaling model. Different from traditional signaling models discussed in Avery and Levin (2010), Coles et al. (2013) and Kushnir (2012), in our numerical example we 2 The AEA signaling mechanism is described at 3

6 allow the decision to signal to be based not only on the sender 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. 3 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 These data contain all applicant information submitted to the admissions offi ce, and also 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 during the admissions cycle, but before admission decisions were finalized. These contacts were made during January 2005 March 10, 2006 for the Fall 2006 admission cycle, and during January 2006 March 9, 2007 for the Fall 2007 admission cycle. 4 We group contacts into three categories based on the 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, by each admission cycle and overall. On-site contacts include various types of campus vis- 3 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 decisions. Our analysis of signaling behavior is related to the Dale and Krueger s (2002, 2011) analysis of the effect of college selectivity on earnings. Dale and Krueger (2011) find that in determining the effect of college selectivity on earnings, it is important to take unobserved 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. 4 For the Fall 2006 and 2007 cycles, admission decisions were finalized prior to March 10, 2006 and March 9, 2007, respectively. 4

7 its, 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 no credible information about their interest in the university. Applicants to the university may contact the university in any of those capacities or 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. 5 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. Using a binary treatment evaluation framework, 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 bar- 5 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. 5

8 riers 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. 6 For similar reasons, we exclude 1,275 applicants that are student-athletes, who are evaluated using different criteria from regular applicants. Third, as previously discussed we restrict our sample periods to be January 2005 March 10, 2006 (for the Fall 2006 admission cycle) and January 2006 March 9, 2007 (for the Fall 2007 admission cycle), and we focus on the five out of the eight types of applicants. We further exclude applicants who are the single applicant from their high schools, for the use of high-school fixed effects. In the end, our final 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 separately relative to the control group. Applicants who only make contacts that do not signal interest are excluded from the main empirical analysis, but are used to conduct a falsification test validating our identification strategy. Although our data do contain the same coded information used by admissions offi cers, there are two potentially important pieces of information that are not represented: the applicant s essay and the results of candidate interviews with admissions staff. 7 These two pieces of unobservable information could result in a biased estimate of the effect of signaling 6 With the exception of North Dakota, domestic applicants were from all 50 states plus the District of Columbia. 7 Interviews were generally conducted at the request of applicants, and only 2.8% of applicants were interviewed by admissions staff. 6

9 on admission. For example, if applicants who send the strongest signals of interest also write the most compelling essays, then the impact of signaling on admission would be overestimated by an ordinary least squares (OLS) regression. As a result, we require additional information to identify the effect of signaling on admission; specifically, an instrumental variable that is correlated with signaling, but not directly correlated with the admission decision, or the unobservable determinants of admission. In order to construct an instrumental variable (IV) for each type of signal, or contact, we utilize the fact that our data contain the information on the exact date and type of every contact made by each applicant during an admission cycle, as well as the high school where each applicant is from. For each type of the focal applicant (e.g., the one who makes on-site contacts only), our IV is the number of applicants from the same high school who made the same type of contact prior to the focal applicant. 8 In the case that the focal applicant makes multiple same-type contacts, the IV is the number of applicants from the same high school who made the same type of contact prior to the first time the focal applicant made that contact. Note that the IV is equal to zero when the applicant was the first person from his or her high school to make that contact with the university, or when no one from that high school made that contact with the university, or when the focal applicant did not make that contact. Descriptive statistics for the IV used in each treatment effect analysis are reported in Table 2. Our instrumental variable roughly reflects the size of the applicant s reference group, which is specific to each applicant. 9 It also captures several factors that are hypothesized to 8 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 the 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 the off-site contacts as an additional IV because this IV could be weak in predicting 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, and just-identification with one strong instrument should be used. 9 The influence of peers in education is well documented. Cipollone and Rosolia (2007) provide evidence on the causal effect of the high-school graduation rates of male students on those of female students. Carrell, Malmstrom and West (2008) find evidence that the greater level of peer cheating leads to a significant higher likelihood that a student will cheat. Using individual-specific peer groups, De Giorgi, Pellizzari and Redaelli (2010) suggest that college students tend to following their peers when choosing a major. 7

10 affect the probability that a student signals the university. The first factor is peer pressure, which exists 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 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 contact. 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. We add high-school fixed effects to our IV estimations, to account for factors that are important to admissions and also commonly shared by students from the same high school. Possible factors include the quality and reputation of a high school, the school s effort in preparing students for college applications, such as sponsoring college visit trips or holding college events at the high school. By using the high-school fixed effects, we also control for the difference in signals sent by students from schools with different class size, and the within-school variation across students is used as the source of identification. The first and second stages of our proposed IV estimator are 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 is the endogenous dummy variable (1/0) indicating whether 8

11 applicant i from high school j contacted (equal to 1) the university, which the university may view as signaling behaviors. Our empirical analysis considers five types of applicants who make the following contacts, respectively: no contact (used as the control group), 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 used to identify β 1, the treatment effect of signaling 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 (legacy applicant), combined SAT scores (and the associated quartiles), academic rank index (and the associated quartiles), 10 median zip codelevel income for households of each racial category, the distance between home and campus zip codes, 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 models 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 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 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 10 The academic rank index is created by the university from information on the applicants high school performance and their standardized test scores. 9

12 increasing in the strength of the signal represented by each contact, as is the proportion of applicants who matriculate when they are admitted. Table 3 reports the summary statistics by each treatment-control estimation sample. And, 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. In both tables 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. Applicants making on-campus visits also live closer to campus, on average. Tables 4 6 report the 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. Columns (1) (4) of Panels A and B report β 1 (in equation 1) and α 1 (in equation 2), respectively, across various specifications. For comparison purpose, columns (5) of these three tables report the OLS estimates. In all three tables we find that the focal applicant s likelihood of making contact with the university (i.e., signaling) can increase 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, suggesting the presence of peer pressure. We also find that the estimated effects of signaling on admission are largely robust across four specifications (columns 1 4). In particular, estimates with high-school fixed effects included (column 4) are uniformly smaller than those without (columns 1 3). This pattern is consistent with the possibility that high schools make an effort in preparing their students for the college applications, such as encouraging campus visit trips or holding college events at the high schools. The estimates in Tables 4 6 also indicate a monotonicity in the effect of signaling on the likelihood of admission: making off-site contact could raise the likelihood of admission by about percentage point (Table 4), whereas making on-site contact could raise the admission likelihood even more, by about percentage points (Table 5); for applicants 10

13 who make both off-site and on-site contacts, the likelihood of admission will increase the most, by about percentage points (Table 6). These results suggest that stronger signals have greater impact on increasing the likelihood of admission. For the estimated effects of making on-site contacts on admission (reported in Tables 5 and 6) we also find that the OLS estimates (column 5) are larger than the IV estimates (columns 1 4). This is consistent with the possible over-estimation by OLS because the omitted variables such as the quality of applicants essays may induce a positive selection bias: applicants who write more compelling essays are more likely to signal the university their interest and also are more likely to be admitted. We further investigate another monotonicity in the effect of signaling on admission: the effect is increasing in the applicant s SAT score. Similar to the design of Tables 4 6, Tables 7 9 report the estimates of the treatment effect, and the effects of the treatment interacted with SAT quartile dummies. In this analysis we also allow for nonlinearity in the relationship between SAT scores and the probability of admission by including the continuous SAT score as well as the quartile dummies. Overall, estimates reported in Tables 7 9 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 (Tables 8 and 9) and whose SAT scores are in the third or fourth quartile of the SAT score distribution. For example, in column (4) of Table 8, while there is no statistically significant difference between the effects of making on-site contacts for applicants in the first and second SAT quartile, signaling raises the probability of admission by 21.8 percentage points for applicants in the third SAT quartile relative to the first quartile of the SAT distribution, and by 33.7 percentage points for applicants in the top SAT quartile. Like the non-interacted models used in Tables 4 6, the first-stage partial F-statistics of Tables 7 9 indicate that the instruments are strong, and the estimates reported in columns (2) (4) are robust to the alternative specifications 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 ). 11

14 3.2 Robustness Checks To gauge the validity of our IV identification strategy, we conduct a falsification check and report the IV estimates in columns (1) (4) of Tables 10 and 11. For comparison purpose we also report the OLS estimates in columns (5) of both tables. Here, we use the same model specified by equations (1) and (2) except that the treatment considered is making contacts that do not signal interest, such as filling out online information request or calling the admissions offi ce. Surprisingly, the OLS estimates suggest that making such a minor contact could increase the admission probability by 3.6 percentage point (column 5 of Table 10), and the effect would be an increase of 8.6 (or 9.2) percentage points for applicants whose SAT scores are in the third (or the fourth) quartile (column 5 of Table 11). These results indeed highlight the over-estimation problem of the OLS because the effects suggested by the OLS could be fully explained by the high quality of applicants, who are likely to fill out online information request and who are also likely to be admitted. In contrast, our IV estimates reported in Tables 10 and 11 do not indicate the effect of making such a minor contact on the likelihood of admission, suggesting a removal of the spurious correlation. We further check the monotonicity in the effect of signaling on admission, which varies with the strength of the signal, by estimating the model jointly. Here, we simultaneously include in our IV estimator three treatment dummies for on-site contacts, off-site contacts, and contacts that should not signal interest, respectively. The results reported in Table 12 are consistent with the ones obtained from the separate estimations: the estimated effect of making on-site contacts (or making off-site contacts) on the admission probability, an increase of (or of 8 11) percentage points, are very close to the ones reported in Table 5 (or Table 4); contacts that should not signal interest have no effect on admission. Like Tables 10 and 11, Table 12 also highlights the over-estimation problem of the OLS in the case of making contacts that do not signal interest. One 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 12

15 represent the proactivity of the focal applicant, which may be observable to the admission offi cers, for example through the application essays. In this case smaller values of the IV would indicate a more proactive student, who is probably better prepared for the application and wants to take a first-mover advantage, and consequently who is more likely to be admitted. If this is true, then we would expect a negative coeffi cient of the IV included in the OLS regression. We conduct such a regression and report the results in Table 13. For applicants who make off-site contacts only, we do not find any effect of our proposed IV on the admission probability 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 modest effect of the proposed IV on the admission probability: the sign of the effect is negative, which is consistent with the proactivity interpretation; however, the magnitude is small and very close to zero, suggesting the direct impact of our proposed IV on the admission probability could be minor. Next, we check the possibility that our proposed IV actually represents an applicant s proactivity. To do so, we regress our IV on the characteristics of the applicant for the two admission cycles separately, and report the results in Tables 14 (the 2006 cycle) and 15 (the 2007 cycle): negative coeffi cients indicate that applicants who have certain characteristics could have fewer classmates from their high school who made the same type of contact earlier than them a possible result of being more proactive. In both Tables 14 and 15, we find very few negative coeffi cients. In particular, for applicants in the third or fourth (the highest) quartile of the SAT distribution, the coeffi cient is either insignificant (all three columns of Table 14, and columns 2 and 3 of Table 15) or actually positive (column 1 of Table 15), which suggests that our proposed IV at least is not likely to be a measure of proactivity for this group of applicants who can be proactive. Lastly, we check the coherency of our results by examining the matriculation outcomes. Here, we apply OLS to equation (1) to identify the effect of signaling among admitted applicants. This is based on the assumption that after we control for the characteristics 13

16 of applicants and include high-school fixed effects in the regression, there are no important unobservables correlated with both the likelihood of matriculation and whether an applicant contacted the university prior to receiving an admission offer. Our finding that off-site contacts and on-site contacts (such as campus visits) increase an applicant s probability of receiving an admission offer 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 signal the university must be more likely to matriculate after being admitted. We test this hypothesis using a matriculation model based on equation (1). Panel A of Table 16 contains estimates of the impact of signaling on matriculation among admitted applicants from our OLS treatment effect models. Signaling interest through an off-site or an on-site contact increases the probability of matriculation by bout 7 percentage points, while the stronger signal of both on-site and off-site contacts increases this probability by about 13 percentage points. 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. In Panel B we report the results from the interacted models. Overall, we find that admitted applicants with higher SAT scores who actually signal their interest are more likely to matriculate than those who are in the same SAT score quartile but do not signal their interest. 4 An Illustrative Theoretical Example In this section we use a numerical example, which is related to a model presented in the Appendix, 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 sig- 14

17 nals 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 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 are 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 15

18 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 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 α x i βr i. In each of the examples α = 1 and β = 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. 16

19 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 students and one-half of the 1920-SAT students who have signaled), admits (12K 4) of the acceptable 1920-SAT students who have not signaled (which translates into (12K 4)/2 of the 1920-SAT students), and rejects all of the 2400-SAT students who have not signaled. Table 17 contains the admissions probabilities for each of the three target enrollment regions: K [0, 1/6], (1/6, 1/3], or (1/3, 5/12]. In each of these three regions, signaling increases the probability of admission by a greater amount for the 2400-SAT students than for the 1920-SAT students. That is, the marginal effect of signaling on the probability of admission is strictly increasing in the applicant s SAT score. We observe this monotonicity in part because the selective school rejects all 2400-SAT students who have not signaled. It does so because either it fills its class with 2400-SAT students who have signaled (K 1/6) or it cannot attract any 2400-SAT students who have not signaled (K > 1/6). If K > 1/6, a school cannot attract the 2400-SAT students who have not signaled because they all signal the school s selective competitor, where they are admitted and subsequently matriculate. Case 2: Zero, One, or Two Signals. We demonstrate by means of this case that the schools base their admissions decisions on the students signals only if the signals are suffi ciently informative. In Case 1 above, the signals or lack thereof are informative because the signaling behavior perfectly conveys 17

20 student preferences. Alternatively, if a signal is too fuzzy, then the selective schools ignore the students signals when making admissions decisions. For example, suppose that each student has either zero or two signals to send, but not one signal (i.e., q 0 + q 2 = 1). If a school receives a signal from a student, then it knows she has two signals, and therefore knows that the signal conveys no information about the student s preferences. Also, if the school receives no signal from a student, then it knows she has zero signals, and therefore lack of a signal once again conveys no information about the student s preferences. In this case, we set each school s capacity K = 4/15. We also fix the number of students who send zero signals at q 0 = 1/10, and we examine the effect of increasing the number of students with one signal, q 1, and decreasing the number of students who send two signals, on the equilibrium admissions strategies. (Note in this example that q 2 = 9/10 q 1.) For any values of q 1 and q 2 = 9/10 q 1, each selective school ranks at the top the 2400-SAT students who have signaled the school. Therefore, because K > 1/6, each selective school admits all 2400-SAT students who have signaled the school. Furthermore, each selective school ranks next to the bottom the 1920-SAT students who have not signaled the school. (All unacceptable 1920-SAT students are ranked at the bottom.) Because K < 5/12 each selective school rejects all 1920-SAT students who have not signaled the school. Whether a selective school s ranks the acceptable 1920-SAT students who have signaled the school above or below the 2400-SAT students who have not depends on q 1 and q 2. Specifically, the selective school ranks the 1920-SAT students who have signaled the school above the 2400-SAT students who have not if and only if q 1 > (or q 2 < 0.467). The school does so because if q 1 is large and q 2 is small, then a student who signals is likely to matriculate, and a student who does not signal is unlikely to matriculate. If matriculation is important to the school (because the school strongly prefers to reduce its acceptance rate), then the school admits 1920-SAT students who have signaled before admitting 2400-SAT students who have not. As shown in Table 18, consistent with Case 1, if q 1 = 0.65 (which is large) and q 2 =

21 (which is small), then the marginal effect of a signal on the probability of admission is strictly increasing in the quality of the applicant. If, however, q 1 = 0.15 (which is small) and q 2 = 0.75 (which is large), then a signal affects the admissions decisions for only 1920-SAT students. We use Case 2 to build an argument that high-cost signals have greater influence on admissions decisions than do low-cost signals. Suppose there are two populations of students: those who know about the possible effect of demonstrated interest (i.e., signaling) on admissions decisions and those who do not. The uninformed send zero signals, regardless of the cost. In Case 2, we have assumed that one-tenth of the students are uninformed about the process. For the remaining nine-tenths of the students the well-informed ones as the cost of signaling increases, they send fewer signals. In this stylized example, therefore, as the cost of signaling increases, q 1 increases and q 2 decreases. If the high-cost signaling case corresponds to q 1 = 0.65 and q 2 = 0.25 in Table 18, then for the high-cost signaling case, the marginal effect of the signal on the probability of admission is strictly increasing in the quality of the student. If the low-cost signaling case corresponds to q 1 = 0.15 and q 2 = 0.75, then for the low-cost signaling case, the signal is ineffective for the high-sat applicants. 5 Conclusion Our study provides empirical evidence consistent with the hypothesis that a selective university gives preference to applicants who signal their interest because these applicants are more likely to matriculate upon receiving an admission offer, and that the effect of the signal on the likelihood of admission is increasing in the quality of the applicant. Our empirical analyses use administrative data on admission, which include all the contacts made by applicants to the admission offi ce of a medium-sized highly selective university. Some contacts, such as campus visits, are more costly to applicants than contacts initiated from an applicant s home community. By considering these contacts separately, we show that the university places the 19

22 greatest weight on the most costly contacts. In particular, off-site contacts increase the probability of admission by percentage points, while making both an on-site and offsite contact increases the probability of admission by percentage points. Applicants who make the most-costly contacts are also the most likely to matriculate. For example, the likelihood of matriculation is 12.7 percentage-point higher for an applicant who made an off-site and on-site contact, but only 7.2 percentage-point higher for one that made just an off-site contact. Our empirical analyses also confirm that the effectiveness of each signal is increasing in the quality of applicants. For example, sending a strong signal (an off-site and on-site contact) increases the probability of admission by 4.4 percentage points if the applicant is in the lowest SAT quartile, but by 37.3 percentage points if the applicant is in the highest SAT quartile. We use a numerical example to further explore a potential mechanism underlying our empirical findings: schools attempt to attract the most qualified applicants possible, so a signal given by a very high quality applicant induces the school to give an admission offer to that applicant whom it might otherwise consider out of reach. Overall, our results suggest that signaling is an effective strategy used especially by topranked applicants in large part because their preferences are private information. We suspect that the heterogeneity we uncovered about the effectiveness of applicant signals carries over to other environments. Consider the American Economic Association (AEA) job signaling mechanism in which job market candidates interviewing for Ph.D. positions at the annual AEA meetings can signal at most two hiring institutions. 12 In this environment, a middleranked university is likely to interview a good, middle-ranked candidate without having received a signal from the candidate. However, the same university is willing to interview a top-ranked candidate if and only if the university receives a signal from the candidate. Hence, for obtaining interviews from middle-ranked universities, a top-ranked candidate s signal could more effective than a good, middle-ranked candidate s signal. Of course, our conjecture is open to empirical verification. Coles et al. (2010) study the role of AEA 12 See 20

23 signaling mechanism in the job market and find evidence that sending a signal increases the likelihood of receiving an interview. While Coles et al. (2010) do not examine heterogeneity in the effect of a signal on the probabilities of schools making offers, their analysis does offer evidence of heterogeneity and strategic behavior in the signals that candidates send. Specifically, they offer evidence of a tendency of job-market candidates from higher-tiered schools to signal departments in lower tiers. Costly signals by university applicants or job applicants could be important to universities and employers not only as signals of the probability of acceptance of offers, but also of the candidates enthusiasm or ability. Simply put, candidates who are more likely to expend effort to send a costly signal could also be more hard-working, better-organized, or more willing to take on costly activities all attractive attributes. If these better attributes were the reason why the university in our empirical analysis placed positive weight on costly signals in its admission decisions, then we would suspect that this weight would be unrelated to SAT scores. If so, then the effect of a student sending a costly signal to a university would be non-monotonic. The students most-qualified academically would be admitted and the least-qualified students would not. Costly signals would be most effective for students in the middle. Our empirical result that the effect of applicant signals on the probability of admission is increasing in the quality of applicants indicates that the school in our model is concerned about matriculation probabilities when making admission decisions. We want to stress that the cause of the monotonicity result that signals are most effective for top applicants is that the schools must have an opportunity cost of admitting applicants. In the case of our model, the opportunity cost is created by the schools objectives of reducing their acceptance rates. In the case of the AEA signaling mechanism, the opportunity cost is that schools have a limited number of interview slots. While our analysis can carry over to the case for certain cost functions and school utility functions in which the numbers of signals and acceptances are endogenous, a more general analysis would be interesting. One question is whether the very top universities would accept 21