Mobility Costs and College Enrollment for Students with Disabilities

Unintended yet desirable eﬀects of centralized college admission: Mobility costs and college enrollment for students with disabilities

By Aline Dalcin1, Guilherme Stein2, and Hugo Jales3

1Department of Economics, PPGE/UFRGS 2Business School, Unisinos 3Department of Economics, Syracuse University

Abstract: We study the eﬀects a centralized university admission system (Sisu) on the demographic distribution of students admitted to higher education institutions, with focus on a particular type of disadvantaged group: students with disabilities. Centralizing the application process diminishes mobility costs that are salient in the decision of individuals with a disability to apply to a university. We ﬁnd that the percentage of entrants with a disability on institutions that have adopted Sisu for seven years was 0.63 percentage point higher than those that have not adopted. This result is sizable considering that, in 2016, the percentage of entrants with disabilities was only 0.77%. JEL: I23, I28, D47 Keywords: Higher education, disabilities, special needs

Recently, policymakers have started to pay more attention to the particular issues faced by people with disabilities and special needs. In 2007, 160 countries signed the UN’s Convention on the Rights of Persons with Disabilities, which is a treaty designed to protect the human rights of people with disabilities. In addition, the World Bank has recently increased its eﬀorts to promote disability-inclusive development by appointing a disability advisor to the World Bank Group. In several diﬀerent countries, in both the developed and the developing world, policies are also being designed with the aim of helping individuals with disabilities to engage in certain aspects of society. Many of such laws focus on regulation regarding the adaptation of facilities to ensure that disabled individuals can access buildings and use public services. Other policies focus on providing conditions for individuals with special needs - and incentives for those who interact with them, such as employers and educational institutions - to make sure that these individuals are able to study and to work. The rationale behind a large number of these public policies is to reduce costs associated with physical access to buildings. Wheelchair access ramps, information in braille, pathway markers for people with visual impairments are examples of accessibility improvements that are aimed at reducing mobility costs. 1 2

Explicit accessibility policies, however, are not the only mechanism capable of lowering mobility costs. Oftentimes, these costs change as a byproduct of advances information technology combined with institutional changes that alter the way information is produced, stored, processed, and shared. Policies that reduce the overall necessity of dislocation might have an unintended yet desirable effect of helping people with disabilities, even if they have not been explicitly designed with that goal. With that in mind, we study the impact of the Brazilian Unified Selection System (Sisu) on access to higher education for students with disabilities. Sisu centralized the college admission process, unifying entrance exams across participating institutions around a single exam named National Exam of Upper Sec- ondary Education (Enem). Sisu’s implementation dramatically reduced mobility costs of a college application. Before, students that wished to apply to several universities across the country could only do so by taking the specific admission exams of those institutions. The need to travel to several cities provided barriers for low-income individuals who did not have resources to pay for expenses, but also to special needs individuals who require special attention to travel and thus have lower mobility. To guide our analysis, we formulate a decision-theoretic model designed to capture the trade-offs associated with the decision to apply to a higher education institution under a decentralized system. Our analysis highlights the forces that lead individuals to apply to none, a few, or many different institutions. We argue that, under certain conditions, a decline in the marginal costs of a college application will increase the likelihood of joining a higher education institution, particularly for those who would otherwise engage in few applications. Our empirical strategy is based on an intention-to-treat analysis. By lowering mobility costs, Sisu has affected disproportionately individuals for which the transportation costs to take multiple admission exams are large. Therefore, we expect an increase in the number of college applications from individuals with disabilities through the Sisu, but also, ultimately, an increase in the share of entrants with special needs on these institutions. Our results show that exposure to the Sisu by an institution-degree pair has a significant and sizable effect on the share of entrants with disabilities. Institution-degree pairs that have been exposed to seven years of Sisu have a share of entrants with disabilities 0.63 percentage point higher than institutions-degree pairs that have not been exposed. This is a sizable effect considering that the total percentage of entrants with disabilities in 2016 was on average 0.77%. This paper is divided into six sections after this introduction: (1) related literature; (2) institutional background; (3) model; (4)data; (5) empirical strategy; (6) results; (7) final remarks. DISABILITY AND ACCESS TO COLLEGE 3

I. Related Literature

This paper relates to a few different branches of the literature. First, it is in line with the studies on the effects of the adoption of the Sisu system. In this literature, Machado and Szerman (2017) and Li (2016) investigate the impacts of Sisu on migration, student sorting, enrollment, and college dropout. Machado and Szerman (2017) find that higher education institutions under a centralized system can attract students that score one-third of a standard deviation higher and that interstate mobility of admitted students increases by 2.5 percentage points. Li (2016) finds that, with a centralized admission method, interstate mobility of students increases by 2.9 percentage points, but intrastate mobility decreases by 4.0 percentage points. She also finds that the college dropout increases by 4.5 percentage points. Machado and Szerman’s (2017) results also relate to our paper because the authors investigate if the composition of students changes with the adoption of Sisu. They test to see if individuals with disabilities have a higher probability of entering university programs that use Sisu as the admission system. They find some evidence of this effect. However, their paper only studies the short-run effects of Sisu and not long-run effects. In our empirical exercise, we test and explore the presence of heterogeneous effects of different length of exposure to the Sisu. Our main contribution to this literature is, thus, to investigate the role of Sisu in explaining the rise in the share of students with disabilities in higher education in recent years. Second, our paper relates to the literature concerning students with disabilities and the policies oriented to increase their achievement, inclusion and ultimately success. For example, Hanushek, Kain, and Rivkin (2002) argue that classes with children with disabilities might receive additional resources which can pos- itively affect student performance. Seeking to empirically evaluate this relationship between peers with disabilities and the cognitive abilities of their classmates, Hanushek, Kain and Rivkin (2002) find that an increase of 10 percentage points in the proportion of students with disabilities in the class increases the achievement of other students in 1.6% of a standard deviation in elementary school.1 Moreover, our paper sheds light on the economic determinants of college application and, more generally, human capital accumulation (Mincer (1958), Becker (1962)). This literature so far has devoted greater focus on the study of student/college match quality (Dillon and Smith, 2017), college completion (Light and Strayer, 2000), returns to college (Black and Smith (2006), Arcidiacono (2004), and many others), and other dimensions of the investment in higher education. We analyze college applications as an investment in a risky asset, for which the value is only realized in the event in which the agent is admitted and chooses to enroll. We characterize the optimal number of college applications as

1Friesen, Hickey, and Krauth (2010), Fletcher (2009, 2010) and Gottfried (2014) also evaluate this relationship between having a peer with disabilities and the (cognitive or non-cognitive) abilities of the other classmates. 4 a function of the parameters of the student’s environment, namely the likelihood of success, application costs, and value of the degree. We study the forces that shape college application choices - both in the exten- sive margin (whether or not to apply) and on the intensive margin (how many applications to make). We show how these decisions are sensitive to the institutional setting in which these choices are made, and how they ultimately lead to differences in enrolment in higher education institutions. Since differences in college entrance and completion play a notable role in explaining the earnings gap among certain demographic groups, it is important to think about the economic forces that shape college application decisions - and, ultimately, college admission - and how sensitive these decisions are to changes in policy (Pallais, 2015). Lastly, there has been recently an effort to understand the implications of decentralized college admission. Che and Koh (2016) study the case in which student’s preferences are uncertain, Hafalir et. al. (2014) investigate the role of pre-application investments in terms of student effort, and Chade, Lewis, and Smith (2014) study the general equilibrium problem of determining application thresholds and acceptance probabilities from the distribution of college seats and student’s attributes in a Bayesian game setting. Our model is cast in a simple decision-theoretic framework and thus does not incorporate the general equilibrium effects studied on Hafalir et. a. (2014), Che and Koh (2016) and Chade et. al. (2014). However, we believe that the simplified decision-theoretic model we use provides an elegant and tractable framework to think about the particular mechanisms we are interested in investigating in this paper. We discuss to what extent our results would have to be qualified if we were to incorporate general equilibrium effects. Our results also relate to Pallais (2015), who showed that small changes in the costs of sending out applications could generate sizable effects on the number of applications sent out by students. Our setting, however, is somewhat distinct since we believe that the costs of application for students with disabilities are non-trivial.

II. Institutional Background

A. The Enem Exam and the Sisu System

The National Exam of Upper Secondary Education (or Enem) is currently the main access instrument to ascend to Brazilian public higher education, which consists of around 275 institutions (federal, state and municipal) that do not charge tuition fees but oﬀer a limited number of seats. Enem was created in 1998 as a tool to evaluate school performance at the end of secondary education. From its ﬁrst edition until 2008, the Enem was held annually with the application of a single test composed of 63 interdisciplinary questions. During this period, some higher education institutions began to use it as an entrance examination to select their students. DISABILITY AND ACCESS TO COLLEGE 5

Figure 1. : Evolution of the number of entrants by the Enem and the vestibular

Source: Elaborated by the authors, based on data from Inep.

In 2009, a reform took place to boost Enem’s use as an admission exam: the number of questions increased to 180. These questions were divided into four groups encompassing the fields of knowledge around which basic education is organized in the country (languages, mathematics, social sciences, and natural sciences), plus an essay. Soon after, the government started to nudge institutions to adopt it as an admission instrument. The Enem then began to be used by most public higher education institutions. Before these reforms, the vestibular was the most popular access instrument. Students applied directly to the desired institutions and took the specific exam (vestibular) of each one. Candidates with the best scores in the vestibular exam, stratified by major, were offered seats.2 Importantly for our later analysis, the admission was decentralized across institutions. That is, if a student were to apply to, say, ten different institutions, he would have to take ten different exams

2Different from college admissions in North America, majors are chosen at the time of application. Another feature is that admission decisions are made solely based on the outcome of the entrance exam. Thus, extracurricular activities, faith, family ties to the university, non-academic skills such as musical talent, none of these factors are taken into account when institutions make admission choices. In a large number of cases, the admission exams are graded in a double-blinded manner, so the individuals grading the exam cannot know the identity of the student being evaluated. These features are mostly unaltered until today, with the notable exception of student demographic characteristics such as race which affect admission choices through the affirmative action reserved seats (known as “quotas”). 6

Figure 2. : Evolution of the number of institutions participating in the Sisu

Source: Elaborated by the authors, based on data from MEC. and would likely have to travel to several different cities in the process. After Enem’s reform, the exam took the role previously played by the vestibular entrance exams. The difference, however, is that the same score became the criteria of admission across different institutions. The Enem has since become one of the main access instrument to ascend to Brazilian public higher education, a change that centralized and unified the admission system. In 2010, the admission system centralized even further with the creation of the Unified Selection System (called Sisu), an online platform through which public higher education institutions offer seats to students that are selected based on their score obtained in the last Enem exam. Students choose, in order of preference, up to two institutions among the options offered by the participating institutions of the Sisu system. Seats are then offered on the basis of the students’ rankings among the applicant pool.3,4 The number of students who entered through the Enem in undergraduate degrees (excluding online education) attended by the public institutions increased from around 20 thousand in 2009 to over 250 thousand in 2016, as shown in

3Institutions are free to decide the number of seats oﬀered through the Enem exam. Also, they can use the Enem in diﬀerent ways for student selection: 1) Enem scores through the Sisu system; 2) Enem scores without the Sisu system, and 3) some combination of Enem and vestibular scores. 4Machado and Szerman (2017) provide further details about the Sisu platform. DISABILITY AND ACCESS TO COLLEGE 7

Figure 3. : Evolution of the number of students taking the Enem.

Source: Elaborated by the authors, based on data from Inep.

Figure 1. In 2014, the Enem passed the vestibular and became the main access instrument to enter Brazilian public higher education. Much of this result was due to the Sisu: the number of institutions participating in the Sisu went from 59 in the ﬁrst edition, in 2010, to 130 in 2018 (see Figure 2). As a result, it is also noticeable that the number of Enem inscriptions grew rapidly, reaching 8,627,367 in 2016, more than twice as many as in 2008 (see Figure 3).

B. Disabilities and Higher Education in Brazil

According to the Demographic Census of 2010, in Brazil, there are approximately 4 million people (around 2% of the population) with some serious disability (people that are unable to see, hear, move or with any intellectual disability). Access to education for this group is yet a great challenge for the country. For example, only 6.7% of people with disabilities aged over 15 have completed higher education compared to 10.4% of people without disabilities aged over 15, and less than 1% of students enrolled in higher education have any form of disability. Between 2009 and 2016, the total number of people with disabilities in higher education rose substantially (see Figure 4), from 16,911 in 2006 to 28,725 in 2016. This represents an increase of 70%. For comparison, the growth in overall enrollment in the same period was only 28%. As a result, the fraction of people 8

Figure 4. : Evolution of the number of people with disability in Brazilian higher education

Source: Elaborated by the authors, based on data from Inep.

with disabilities in higher education increased from 0.33% to 0.44% (see Figure 5). During this period, there was also some progress in terms of policies aimed at providing access to education for people with disabilities. Along with the Federal Constitution of 1988, the National Policy on Special Education in the Perspective of Inclusive Education of 2008, and other documents that aim to ensure the right to education (both primary education and higher education) to people with disabilities, public policies explicitly focused on higher education emerged. In this sense, the Programa Incluir and affirmative action policies for people with disabilities stand out: (a) The Programa Incluir, created in 2005, proposes actions that aim to guarantee the access and permanence of people with disabilities in federal higher education institutions in Brazil. Among the main actions of the program, there are the creation and consolidation of accessibility centers that guarantee the removal of architectural and communication barriers, fulfilling the legal requirements of accessibility. (b) The Law 13,409/2016, in force since the academic year of 2017, establishes that people with disabilities must be included in the affirmative action policies DISABILITY AND ACCESS TO COLLEGE 9

Figure 5. : Evolution of the percentage of people with disability in Brazilian higher education

Source: Elaborated by the authors, based on data from Inep. of federal institutions of higher education, which already included students from public schools, low-income students, black students, and indigenous students. The number of aﬃrmative actions seats (or “quotas”) set aside for people with disabilities in federal institutions must be proportional to the presence of this group in the census of each state.5

III. Model

To help understand the mechanisms underlying the changes associated with the centralized admission system, here we outline a simple decision-theoretic model of application behavior. Our goal is to characterize the optimal number of college applications as a function of the parameters of the environment. Then, we consider how these choices change as the application environment varies. Let the value of being admitted to a college be given by V , the cost - both the application fee, transportation costs, and the opportunity cost of time devoted to the application and exams - be given by k, and the likelihood of being admitted

5In addition to this law valid for federal institutions, some states have previously created laws that are valid for state institutions, and some institutions have established quotas for people with disabilities on their own initiative. 10 given that the student applied to be given by p, which we assume to be inside the (0, 1) interval.6 These parameters might be heterogeneous across different groups or individuals, and they will likely be different across different institutions, but carrying this distinction will not change the nature of our arguments. Thus, to ease the discussion, we will omit the dependence of (V, k, p) on the institution and across individuals.7 On the Mathematical Appendix, we discuss how the results have to be adjusted when we add varying degrees of heterogeneity on the problem. Importantly, we show that the key insights from this simplified setting still apply, with minor qualifications, in the more general case. In this environment, the student’s problem is to choose n, the number of applications. The expected utility is then:

E[U(n; V, k, p)] = (1 − (1 − p)n)V − nk The student’s problem is then:

n∗ = arg max E[U(n; V, k, p)] n At an interior solution, the optimal choice of n, which we denote by n∗, is given by the largest number of applications for which:

∗ V (1 − p)n −1p − k ≥ 0, where here we used the assumption that the student will attend, at most, one institution. The optimality condition can, in words, be stated as: The student will keep on increasing the number of applications as long as expected utility associated with the event in which he fails to be admitted to each and every university he applied so far but manages to get into the very last one is larger than the costs of adding this last application.8 That is, he includes the nth application to his set as long as the probability of ending up going to this university is larger than the ratio of the cost to the beneﬁt of this application. The solution to this problem has several intuitive properties. An increase in the value of college - for example, an increase in the college/high school earnings gap - will induce individuals to (weakly) increase the number of applications. A decline in the costs of applying to a college will (weakly) increase the number of applications. The next remark shows how the magnitude of this eﬀect is functionally related to the odds of a successful application, p.

6Whenever p is zero, it is trivially optimal never to apply. Whenever p is one, the individual will make a single application as long as V > k. 7That is equivalent to assuming that there is a class of institutions that are considered roughly of the same quality for the applicant, whereas all others outside this set have an expected value lower than the student’s outside option. We relax this restriction on the Mathematical Appendix. ∗ 8A more complete characterization of n∗ is given by the following inequalities: V (1 − p)n p < k < n∗−1 n∗−1 pV (1−p) 1 ∗ V (1 − p) p. These can be rearranged into 1 < k < 1−p . In other words, n is the last application for which the expected beneﬁt is larger than the cost. DISABILITY AND ACCESS TO COLLEGE 11

Remark 1. Let ∆n∗ be the change in the optimal number of applications after a change in the environment. Then, if the student is at an interior solution, the change in the optimal number of applications is given by: a) Increase in the value V of college:

1 ∆n∗ ≈ [% Change in V] p b) Decrease in the costs k of an application:

1 ∆n∗ ≈ [% Decline in k] p c) A change in the p, the probability of a successful application:

1 1 n ∆n∗ ≈ − | ln(1 − p)| p 1 − p

Note that while changes in V and K have a clearly defined effect on the optimal number of applications, the same is not true for changes in p. The effect of changes in p on n∗ has two components: The first is 1/p. This term is identical to the effect of a change in V or k. The intuition is that the expected value of a college application lottery is going to increase if either the payoff V goes up or the odds of success p go up. Thus, the first term represents the increase in the value of going to college due to change in the likelihood of entering, conditional on applying. The second component, which does not appear in parts a and b of Remark 1, is the decline in value of marginal application due to the increase in the likelihood that each infra-marginal application will result in acceptance. This effect is negative. Note that the second term is zero for those that before the change in p did not apply.9 An increase of p will induce an increase the number of college applications for certain students and decrease it for others. Furthermore, for certain individuals, the response will be less than proportional to the changes in p, while for others, it will be more than proportional to the changes in p. The next remark characterizes which individuals will have an elastic response, which individuals will have an inelastic response, and which individuals will have a negative response. In the discussion that follows, we will simplify our analysis by assuming that n∗ can be chosen continuously instead of discretely. This allows us to take deriva- tives and compute elasticities, which are useful to characterize the individual’s responses to changes in the environment. These objects are to be understood as approximations to the discrete changes in n∗ (∆n∗) that will result from changes in the environment.

9This result is similar to the labor supply effect of a change in the wage in the neoclassical theory of labor supply. The income effect is zero for those out of the labor force and, because of that, the sign of the labor supply effect of a change in the wage is well-defined for those individuals. 12

∂n∗ p ∗ Remark 2. Let ηp ≡ ∂p n∗ be the elasticity of college applications n with respect to p. Then: a) ηp < 0 if, and only if, n(p + 1) > 1. A suﬃcient condition for ηp to be negative is that np > 1. b) Conversely, ηp > 0 if n(p + 1) < 1. ∗ ∗ 1−p 1−p c) ηp is larger than one (n is elastic to p) if n < p+(1−p)|log(1−p)| ≈ p+(1−p)p

It is useful to note that np is the mean of the binomial distribution that characterizes the number of successful applications. Thus, the first part of Remark 2 shows that students that expect to be admitted will reduce the number of applications, n∗, to an increase in p. Conversely, those such that n(p + 1) is smaller than one will react to an increase in p by increasing the number of admissions. Lastly, the students that will have an elastic response to a change in p, that is, the change in n∗ will be more than proportional to the change in p, are those such ∗ 1−p that n < p+(1−p)|log(1−p)| . Note that a necessary, but not sufficient, condition for this to hold is that np < 1, so the individual is expected to have a number of successful applications that is smaller than one. A sufficient condition for n to be elastic to p is n∗ to be equal to zero.10

∂n∗ V ∗ Remark 3. Let ηV ≡ ∂V n∗ be the elasticity of college applications n with respect ∂n∗ k ∗ to V . Similarly, let ηk ≡ ∂V n∗ be the elasticity of college applications n with respect to k. Then: a) ηV ≥ 1 if, and only if, n| ln(1 − p)| < 1 ( aprox. np < 1 for small p). b) |ηk| ≥ 1 if, and only if, n| ln(1 − p)| < 1 ( aprox. np < 1 for small p).

Remark 3 characterizes the individuals that will be more sensitive to changes in V and k: The students that are expected to have a number of successful applications smaller than one (np < 1). These are individuals that either apply to one or none institutions, or those that have a chance of success p smaller than the inverse of the number of applications (p < 1/n). Note that, to the extent that individuals with disabilities are more likely than those without disabilities to choose n∗ = 0 (not to apply), the result above suggests that individuals with disabilities will have a stronger reaction to declines in k.11

10 ∗ For any n ≥ 1, a necessary condition for ηp > 1 is p < 0.5. Similarly, for any student that engages in two or more applications, a necessary condition for n∗ to be elastic to p is that his chances of success p are smaller than 1/3. 11It is possible to make this argument more formally: Suppose that there are two groups: individuals with disabilities, which have a much higher k than those without disabilities. Then a decline to zero of the transportation costs of an application will induce a change in n∗ for each member of these groups. The average change in n∗ among members of either group is approximately equal to the (group average) of ηk times the change in k. This change is equal to the covariance between ηk and the decline in k plus the product of the average of ηk and the change in k. This is, in turn, smaller than the product of the average of ηk and the average change in k, which implies that the change in n in each group will be at least as large as the change k, which we expect to be much larger for individuals with disabilities, multiplied by the average elasticity in that group, which we also expect (based on remark 3) to be larger for those with disabilities. DISABILITY AND ACCESS TO COLLEGE 13

Remark 4 (Aggregation). Consider a group of individuals, indexed by i, that are 12 characterized their values of (Vi, ki, pi). Then the change in the average number of applications among member of this group following a change in the distribution of values of ki among members of this group is approximately given by: 1 E[ ] × E[%Change in ki] log(1 − pi) This result states that the change in the number of applications in diﬀerent demographic groups will be a product of two terms.13 One is related to the average percentage change in k in those groups. Ceteris paribus, groups that experience on average a larger percentage decline in k will have a larger response in n∗. The second component states that the response will also depend on the average responsiveness of n∗ to k in that group. This component is roughly equal to the inverse of p, so groups that have, on average, a lower probability of success will have a larger response (to the same average percentage change in k). This last remark implies that individuals with a disability are expected to increase their optimal number of college applications by a number that is larger than individuals that do not have a disability, after the introduction of the centralized admission system. The main force is that the percentage decline in the costs of application is expected to be on average larger for the disabled group. Secondly, to the extent that individuals with a disability also have, on average, a smaller chance of a successful application – or, to be more precise, a larger absolute value of E[ 1 ] – they are also going to have larger responsiveness log(1−pi) of n∗ to changes in k, even if these changes in application costs were to be on average the same across groups. The results we obtain for the optimal number of applications can be used to characterize how other objects of our interest will change after a change in the environment. Our main interest lies in the number of successful applications and the probability of being admitted to at least one school. The next remark describes how these objects will react to changes in the environment:

Remark 5. Denote by n˜ the optimal number of applications after a change in the student’s environment (through a change in either V or k). Then: a) Change in the chances of being admitted:

∗ ∆P r[Being admitted] ≈ p(1 − p)n −1(˜n − n∗)

12 For simplicity, we assume that ki and pi are independent of one another, although this assumption is not crucial for our result. It, however, allows us to unambiguously say that a shock in k aﬀects the individual through the change in the costs of application only. If k and p are correlated, then a change in k could also lead to other (mechanism induced) changes in behavior through the dependence of p on k. This is essentially the same argument that in Vector Autoregressive models the fundamental shocks only have meaningful interpretations when these shocks are assumed to be independent of one another. The result is essentially unaltered if one changes it to an assumption that k and p are conditionally independent, as long as we care about the changes on the conditional expectation of n. 13This result can be obtained once one recognizes that Cov( 1 , ∆ki ) is zero. log(1−pi) ki 14

b) Change in the number of successful applications:

∆[Expected number of admissions] ≈ p(˜n − n∗)

Lastly, we obtain the changes in ex-ante expected utility associated with changes in the environment: Remark 6. Change in utility associated with an increase in the value of being admitted V :

∂E[U(n∗(k, V, p))] ≈ 1 − (1 − p)n∗ ∂V Change in utility associated with an increase in the costs of application k:

∂E[U(n∗(k, V, p))] ≈ −n∗ ∂k Change in utility associated with an increase in the probability of a successful application p:

∗ ∂E[U(n (k, V, p))] ∗ ≈ n(1 − p)n −1V ∂p A mass of students might end up at the corner solution, either setting n to zero, or to max{n}. These are students for which neither the first application is worthwhile to entertain, or all of them are. At a simple, decision-theoretic level, the centralized admission system is a decline to zero the marginal costs of application for any n greater than one. In other words, provided that the student decides to apply to one university, the incremental costs of applying to any number beyond that will be close to zero. The limitation of this argument, however, is that the centralized admission system will induce this change in the costs of application for all students. The chances of being admitted, which students take as given when deciding their applications, will change when the system undergoes such a substantial change. In other words, the change to a unified application system induce both changes in application costs from the point of view of the student, but also general equilibrium effects through the behavioral changes of all students. One approach to tackle the general equilibrium effects of centralization would be specifying an equilibrium model that takes the decision of institutions to offer seats, the decisions of students to apply to these distinct institutions, and the equilibrium determination of score thresholds that determine admission. However, as long as we are interested in whether a student will ultimately be admitted - and not other outcomes such as the welfare comparison between the two systems - one does not need to fully specify the decision of other agents and institutions. With respect to the likelihood of ultimately being admitted and entering a higher education institution, p and n act as sufficient statistics. This means that the only DISABILITY AND ACCESS TO COLLEGE 15 piece of information that we must add to investigate the changes in the likelihood of admission is the general equilibrium effects that operate through changes in p.14 The condition that characterizes whether an individual will be more likely to enter a university after a change in the environment is given by:

n˜ log(1 − p∗) p∗ ≥ ≈ n∗ log(1 − p˜) p˜ This condition has an intuitive interpretation: As long as the percentage change in the number of applications is larger than the (general equilibrium) percentage decline in p - the likelihood of a successful application - the individual will be more likely to be admitted to a higher education institution. There are many direct implications of this result: The first is that individuals at the corner solution (n∗ = 0) are (weakly) more likely to being admitted to college after the change. Individuals that are relatively more sensitive to changes in k the costs of application are more likely to being admitted to a college. Individuals with a relatively smaller number of applications are more likely to being admitted after the policy change. These results allow us to conjecture which groups are more likely to benefit from the centralized admission system. The most obvious groups are the ones in which a substantive fraction of the students before the policy optimally choose to engage in zero applications. Thus, we expect individuals with disabilities to increase the number of applications, and we expect that this increase will trump any general equilibrium effects associated with changes in tightness since many of these students engage in zero applications at the decentralized system.

IV. Data

We use the Brazilian Higher Education Census from the years 2009 to 2016, an annual administrative dataset. It contains information of all higher education institutions in the country, including details about majors and characteristics of the student body. We make some sample restrictions in the data. Since private and municipal institutions cannot participate in the Sisu system, we keep in the sample only federal and state institutions. We consider only information about on-campus degrees and entrant students. In addition, we exclude degrees with less than ten entrants. We also excluded federal institutes from our sample. Established by federal law in 2008 (Lei 11.892/2008), their creation is contemporaneous to the establishment of the Sisu admission system. For that reason, we exclude degres of federal institutes from our sample so our results are not driven by the changes

14This result does not require the value of college to be invariant to the policy changes, neither the restrictions in the heterogeneity in the p, V , and k that we make above to simplify our discussion. 16

Figure 6. : Institutions by academic type

Source: Elaborated by the authors, based on data from Inep. associated with enrolment in these institutes.15 To the census data, we add to our sample the information, provided by the Ministry of Education, on whether and when institutions joined Sisu. This tran- sition is made voluntarily by each institution and, most importantly, there are institutions that use the Sisu system for certain majors and vestibular for others. Therefore, the variable of our interest varies at the institution-major-year level, which allows us to control for a wide range of unobservables that are constant over time across institutions. Our interest lies in the following variables: a dummy variable indicating if the entrant is a student with disabilities in an institution-degree pair; student’s gender and age; dummy variables indicating the time of exposure of that institution- degree pair to Sisu; the General Index of Evaluated Degrees of the Institution (GIC) (a quality indicator that evaluates Brazilian higher education institutions); a dummy variable indicating if that institution-degree pair oﬀers accessibility conditions for people with disabilities; and dummy variables indicating the institution’s length of exposure to aﬃrmative action policies.

15Higher education institutions consist of ﬁve groups: universities, university centers, colleges, federal education centers, and federal institutes. Figure 6 shows that the vast majority of higher education institutions are universities. DISABILITY AND ACCESS TO COLLEGE 17

Our sample consists of 2.932 million observations of entrant students in federal or state public institutions’ degrees between 2009 and 2016 (see Table 1). Table 2 reports annual descriptive statistics. The percentage of entrants with disabilities has increased considerably, almost doubling in seven years. In the same period, we also saw a rapid increase in the share of institutions using Sisu as an admission method, quotas for people with disabilities and a growing number of degrees oﬀering accessibility accommodations. These three factors are possible candidates that might help explain the increasing share of entrants with disabilities in college rises from 0.40% to 0.77% in a few years.

V. Empirical Strategy

In this section, we describe the methodology of our empirical exercise. Our preferred speciﬁcation is

8 X j 0 Dicst = γjDEScst + Xicstδ + αcs + αtt + icut j=1

where Dicst is one if the student i enrolled in major c at institution s and year j t has a disability and zero otherwise. The dummy variable DEScst assumes the value one if the degree c of the institution i at time t has been exposed to the Sisu admission system for j years (and zero otherwise). We allow for the impact of adopting the Sisu admission system on the entrance of individuals with disabilities to take time to emerge. The term Xicst is a vector with control variables. We include in the vector of controls two student’s characteristics: (1 ) the student’s age and (2 ) gender. We also include characteristics of the institution and of the degree: (1 ) the General Index of Evaluated Degrees of the Institution (GIC) and (2 ) a dummy variable that assumes the value one if the degree provides accessibility accommodations for people with disabilities. Finally, we also include and dummy variables indicating the institution’s exposure time to affirmative action policies in the same way as the Sisu admission dummies. The model also includes institution by degree fixed effects (αcs), time fixed effects (αt), and state linear time trends, αet, where e is the state. We explore the time variation in the length of exposure to Sisu in order to identify the impact of the adoption of the Sisu and the existence of possible heterogeneous effects as a function of the length of exposure. Our identification assumption is that, conditional on control variables, time and fixed effects and state linear time trends, the path of the proportion of entrants with disabilities in degrees that have adopted Sisu would be identical to the ones that have not adopted Sisu, if the system were not implemented 16.

16 As a placebo test, we ran regressions for the year 2009 (before the adoption of Sisu) with Dicst on a dummy that is 1 if the degree will adopt Sisu in some time in the future and 0 if it will never adopt. When we controlled for institutions fixed effects, the Sisu dummy had no statistically significant impact. Results are available upon request. 18

Institution by degree fixed effects control for characteristics of distinct majors that do not vary over time and might be related to the dependent variable and to the adoption of the Sisu. Year fixed effects control for common shocks in each year that affect all institutions and degrees at the same time. Lastly, state linear time trends control by state characteristics that vary over time. We also try a specification in which we do not allow for heterogeneous effects P8 j of Sisu over time. In this case, we substitute the element j=1 γjDEScst by a dummy Dcst which is one if the degree c in the university s was participating of Sisu at time t.

VI. Results

Figure 7. : Heterogeneous eﬀects as a function of the time of exposure

Source: Elaborated by the authors.

We present our results in Tables 3 to 5. In the Table 3, we present four different regression results. Our preferred model is (6), where our variables of interest are dummy variables indicating the time of exposure to Sisu, and institution-degree pair and year fixed effects and state linear time trends are present. The effect is not statistically significant in the first two years of adoption. After the second year of adoption by a degree, the percentage of entrants with disabilities increases by 0.01 percentage point. Considering that the fraction of entrants with disabilities DISABILITY AND ACCESS TO COLLEGE 19

Figure 8. : Heterogeneous eﬀects as a function of the time of exposure by Enade quantiles

Source: Elaborated by the authors.

is on average 0.61% (see Table 1), this implies a relative increase of 1.6%. The effect increases in the fourth year of expousure to 0.59 percentage points and remains above 0.3 percentage points afterwards. As expected, Table 3 shows that the presence of accessibility accommodations has a positive impact on the fraction of students with disabilities. In Figure 7, we plot the heterogeneous effects over time. The impact of exposure to Sisu rises over the years expousure. This result is consistent with the hypothesis that the impact of Sisu takes time to affect the share of entrants with disability. A back of the envelope calculation shows that the impact of a seven-year exposure to Sisu represents roughly eighty percent (80%) of the proportion of entrants with disabilities in 2016 (see Table 2), a sizable increase. The structure of our dataset - containing the information of disability status for individuals that entered college - allows us to investigate whether the presence of Sisu changes the proportion of individuals with a disability. Sisu, however, does not induce any student to acquire a disability; the causality lies in the opposite direction. Here we discuss how to interpret the effects on the changes on the proportion of students with disabilities in terms of components related to the effects that Sisu induces on the choices made by students with disabilities and 20 the ones without them. An application of the Bayes’ rule shows that the changes in the proportion of students with disabilities associated with Sisu can be decomposed into three components: One associated with the differential effect of Sisu on the likelihood on applying to college across individuals with disabilities and individuals without it. The second component is associated with the differential effect of Sisu on the likelihood of a successful application across students. Lastly, a third component associated with the differential effect of Sisu on the likelihood of entrance. Together, these three terms add to the total change in the proportion of students with disabilities across schools that use the Sisu system and the ones that do not. With a richer dataset,17 we could hope to separately identify the terms of this decomposition, that is, to disentangle both where in the chain of events the Sisu effects are larger, but also to what extent the changes are happening in the set of students without disabilities as well. A couple of insights come from this decomposition: The first is that for the proportion of students with disabilities to change when Sisu is introduced, it is not enough that students with disabilities will be more likely to apply, be accepted, and ultimately enter. It must be the case that these changes are larger than the effects that the system has on the students that do not have a disability. For example, if the only change that the system induces is to increase by 10% the likelihood that a student will apply, and this effect also occurs in the population of students with no disability, then although the system does have a positive effect on the probability of applying to college, the fraction of students with disabilities in college will remain the same after the policy is implemented. Thus, the effects we capture here should be interpreted as changes relative to the changes that the system induces in the set of students with disabilities, as compared to students without them. In conclusion, although we can only obtain estimates of the change in the proportion of students with disabilities, the changes in this proportion can be easily mapped into changes in the likelihood of an application, acceptance, and entrance; the outcomes we are ultimately interested on investigating.

A. Heterogenous Eﬀects on Quality of Institution-Degree pairs

Our model suggests that the value of the institution is an important factor that inﬂuences the number of applications. Thus, we conjecture that the adoption of Sisu should have heterogeneous eﬀects regarding the quality of the institution and degree. In order to measure the presence of this heterogeneity, we use the ENADE ranking, which grades institution by majors regarding their quality, to divide our

17The ideal setting would be a dataset in which we observe all students (regardless of whether they entered college), their disability status, whether they apply to college, whether they apply through Sisu, and whether they were accepted and which institution they ultimately entered. DISABILITY AND ACCESS TO COLLEGE 21 data into three subsamples: the bottom third institution-degree pairs, which we label as the third quantile, the middle institution-degree pairs, which we label as the second quantile, and the top third institution-degree pairs, which we label as the first quantile. Results are reported on Table 4 and summarized on Figure 8. The effect of Sisu seems to be greater in the bottom quantile of the quality distribution. In fact, the first quantile institution-degree pairs that have adopted Sisu have, for some years at least, experienced a reduction in the chance of having entrants with disabilities. The effect of Sisu adoption on the middle quantile is positive, but lower than the effect in the Bottom quantile. We warn, however, that the standard errors for these comparisons are large, so the null hypothesis of no difference would not be rejected for several of these different coefficients. A deeper investigation of the heterogeneity of effects across different margins could be a fruitful area for future work.

B. Placebo test

Since Sisu was implemented in 2010, the proportion of graduating students with disabilities should only be aﬀected by this system from 2014 onwards, when the students that entered in higher education in 2010 began to graduate. Thus, as a placebo check, we repeated our analysis using as the outcome variable the percentage of graduating students with disabilities for the years 2009 to 2013. Table 5 describes the results of this exercise. The results show, unsurprisingly, that the Sisu did not consistently aﬀect the percentage of graduating students with disabilities for those that applied and entered the institutions before the system was implemented.

C. The Enem eﬀect

Before Sisu, students could use their Enem exam score to apply for some universities. Even though the main entrance instrument was the vestibular exam in most universities, it is possible that Enem had a similar effect of reducing application costs. Therefore, it is relevant to disentangle the impact of Enem exam alone and Sisu admission system. Table 6 sheds light on this problem. The table shows the share of students with and without disabilities by entrance method from 2009 to 2016. Before Sisu, when students could use the Enem exam in a few universities, about 5.6% of students without disabilities have accessed higher education through Enem, in contrast with only 0.65% of students with disabilities. In 2010, after Sisu’s implementation, the Enem score became much more relevant as an admission method. The reason is that now using Enem allowed students to apply through the Sisu system. Table 6 shows that the share of students without disabilities that access higher education through Enem rose to 20.2%, about four times greater than in 2009. The increase, however, was much more significant when considering students with disabilities. The share of students with a disability that accessed higher education rose from 0.65% in 2009 (before Sisu) 22 to 10.16% in 2010, increasing by 15 fold. Moreover, the rate of increase through the following years was faster for students with disability. This fact means that accessing a higher education institution using Enem became much more relevant after Sisu. The centralized admission process was crucial to nudge students to start using their Enem Score and not taking the Vestibular exam. That was especially true for students with disabilities because their sensibility to Sisu implementation was much higher. This consistent with our theoretical model: students with higher mobility costs would have a more significant response to a cost reduction of a college application. To capture the effect, we run a simple diff-in-diff regression with two groups: individuals with and without disabilities. We run the following regression:

ln(Ed,t) = αSd,t + βDd,t + γSd,tDd,t + σt + εd,t

Variable ln(E)d,t is the log of the number of entrants that have used Enem at time t and belong to group d ∈ {0, 1} where d = 1 for the group of students with disability and zero for the groups of students without disability. Sd,t is a dummy indicating if at t Sisu existed, D is a dummy indicating if the group has disabilities or not, and σt is time fixed effects. This simple model illustrates what could be inferred from Table 6. Results (Table 7) shows that the effect of Sisu implementation on the number of students with disabilities that accessed higher education through Enem was higher than students without disabilities.

VII. Final Remarks

We study the effects of centralizing the college admission process on human capital investment decisions by individuals with disabilities. We conjecture that the decrease in the marginal costs of college applications associated with moving towards a centralized admission process would have a disproportionally larger effect for the populations that these costs are larger. We find that the change to a centralized admission system led to an increase in the proportion of students with disabilities (compared to the control group) for the institutions that participate in the centralized mechanism. This result suggests that, on top of other documented benefits of such a system (Machado and Szerman, 2017), an unintended but positive consequence of such an admission system is to substantially improve access to higher education for individuals with special needs.

References

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Table 1—: Descriptive Statistics

Obs Mean Std. Dev Min Max Entrants with disability 2932633 0.0061269 0.0780345 0 1

Age 2932633 22.8657 6.814003 12 95

Sex (male = 1) 2932633 0.4818908 0.499672 0 1

Participation in the Sisu 2932633 0.4749885 0.4993741 0 1

Exposure time to Sisu 2932633 1.495935 2.008635 0 7

GIC 2932633 3.246023 0.5855563 0.565132 4.686605

% degrees with acessibility 2932633 0.6495231 0.4771194 0 1

Quotas policy 2932633 0.2172287 0.4123596 0 1

Exposure time to quotas policy 2932633 0.7530833 1.680662 0 7

ENADE 2112787 2.938169 0.478998 0.6461 4.7846

PCC 2151043 3.034623 0.9251551 0 5

Mathematical Appendix

Alternative modelling assumptions

Here we discuss how the main results can be interpreted when one allows for varying degrees of heterogeneity. To start, recall that under the absence of heterogeneity in (V, p, k), the optimality condition is:

∗ (1 − p)n −1pV ≥ k Now, consider the setting in which the agent faces no heterogeneity in (V, p), that is, the likelihood of a successful application and the value of an oﬀer, but faces heterogeneous application costs. Heterogeneity in application costs might be due to either changes in the marginal value of wealth as resources are spent; or due to the need to travel longer distances to take the admission exams. Let k(i) be the cost of application for institution i, and assume that the k is sorted in an increasing order (from lower k to higher k). Then, the optimality condition becomes:

∗ (1 − p)n −1pV ≥ k(n∗) That is, the agent keeps on increasing the number of applications up to the point that the marginal increase in the expected value is equal to the marginal increase in the expected costs. DISABILITY AND ACCESS TO COLLEGE 25

Table 2—: Descriptive Statistics by Year

2009 2010 2011 2012 2013 2014 2015 2016 Entrants with disability 0.0039961 0.0048664 0.0034055 0.0047608 0.0056103 0.0084221 0.0091091 0.0077443 (0.0630881) (0.0695896) (0.0582573) (0.0688339) (0.0746917) (0.0913848) (0.0950063) (0.0876601)

Age 22.4902 22.66975 22.68533 22.99103 22.78366 23.15084 23.15268 22.85826 (6.28249) (6.537309) (6.61587) (6.905879) (6.820741) (7.146458) (7.098802) (6.848494)

Sex (male = 1) 0.4739359 0.4660392 0.4715483 0.467597 0.4803278 0.4870345 0.4989945 0.5037127 (0.4993211) (0.498846) (0.4991905) (0.4989496) (0.4996135) (0.4998325) (0.4999996) (0.4999868)

Participation in the Sisu 0 0.2119958 0.4266178 0.4158339 0.4707392 0.6299767 0.7085297 0.76852 (0) (0.4087225) (0.4945864) (0.4928658) (0.4991437) (0.4828112) (0.4544402) (0.4217789)

Exposure time to Sisu 0 0.2119958 0.5987538 0.9794006 1.44493 2.002089 2.644519 3.403278 (0) (0.4087225) (0.76454) (1.210405) (1.657245) (1.991882) (2.299514) (2.581916)

GIC 3.12069 3.213146 3.253245 3.22483 3.269418 3.27087 3.275334 3.304432 (0.621143) (0.6383521) (0.5696176) (0.5679835) (0.555152) (0.5899431) (0.5735525) (0.5605336)

% degrees with acessibility 0.3045805 0.5676449 0.6343927 0.6606683 0.6688846 0.7318297 0.7479206 0.7777823 (0.4602303) (0.4954037) (0.4816007) (0.4734831) (0.4706151) (0.4430073) (0.4342072) (0.4157372)

Quotas policy 0 0.1299421 0.1912538 0.2008348 0.2474343 0.2827409 0.2946112 0.3204768 (0) (0.3362402) (0.3932889) (0.4006252) (0.4315218) (0.4503321) (0.4558683) (0.4666605)

Exposure time to quotas policy 0 0.1299421 0.3118944 0.5285593 0.7515491 1.032164 1.318862 1.615133 (0) (0.3362402) (0.6752027) (1.080013) (1.434472) (1.834684) (2.230341) (2.622573) Standard errors in parentheses

Now instead assume that costs of application are approximately the same for the applicant. However, institutions aren’t viewed as perfect substitutes. In this setting, let V (i) be the value of obtaining an admission oﬀer from institution i and assume that institutions are ranked in descending order of value. The optimality condition is then:

∗ (1 − p)n −1pV (n∗) ≥ k The intuition for this result is the same as before. The student will progressively increase the number of college applications up to the point in which the increase in the expected utility is zero. That is, up to the point in which the marginal beneﬁt is equal to the marginal cost. Lastly, assume now that institutions are roughly perfect substitutes and costs of application are approximately the same. This surely is not the case when one considers the entire set of higher education institutions, but it might be a good approximation for the subset of institutions the individual is seriously considering to apply. Now, let pi be the institution speciﬁc probability of a successful application, and assume that institutions are ordered in a descending order (from high p to low p). Then, the optimality condition is:

n∗−1 Y ( (1 − pi))pn∗ V ≥ k i=1 26

Table 3—: Main Results

(1) (2) (3) (4) (5) (6) Sisu 0.00000668 -0.000373 (0.000237) (0.000259)

Quotas policy 0.000626 0.000239 (0.000444) (0.000419)

One year in the Sisu 0.000481∗ 0.000190 0.000459∗ 0.000337 (0.000246) (0.000288) (0.000264) (0.000288)

Two years in the Sisu -0.000206 -0.000602∗ -0.000494 -0.000548 (0.000287) (0.000352) (0.000305) (0.000349)

Three years in the Sisu 0.00127∗∗∗ 0.00112∗∗∗ 0.000705∗∗ 0.000998∗∗ (0.000320) (0.000414) (0.000346) (0.000413)

Four years in the Sisu 0.00632∗∗∗ 0.00626∗∗∗ 0.00530∗∗∗ 0.00590∗∗∗ (0.000723) (0.000762) (0.000711) (0.000742)

Five years in the Sisu 0.00449∗∗∗ 0.00470∗∗∗ 0.00351∗∗∗ 0.00440∗∗∗ (0.000719) (0.000790) (0.000739) (0.000776)

Six years in the Sisu 0.00305∗∗∗ 0.00363∗∗∗ 0.00228∗∗∗ 0.00342∗∗∗ (0.000730) (0.000841) (0.000738) (0.000839)

Seven years in the Sisu 0.00398∗∗∗ 0.00640∗∗∗ 0.00300∗∗∗ 0.00629∗∗∗ (0.000951) (0.001169) (0.000934) (0.001166)

One year with quotas policy -0.000234 0.000584 0.0000478 (0.000399) (0.000409) (0.000401)

Two years with quotas policy 0.000729 0.00131∗∗ 0.000726 (0.000502) (0.000528) (0.000506)

Three years with quotas policy 0.000109 0.00115∗ 0.000413 (0.000605) (0.000618) (0.000607)

Four years with quotas policy -0.000488 0.000743 -0.000191 (0.000578) (0.000602) (0.000577)

Five years with quotas policy -0.00105 -0.000449 -0.000730 (0.000708) (0.000713) (0.000702)

Six years with quotas policy -0.00198∗∗ -0.00148∗∗ -0.00154∗ (0.000791) (0.000735) (0.000789)

Seven years with quotas policy 0.000455 0.00147∗ 0.00109 (0.000979) (0.000760) (0.000978)

Age 0.000249∗∗∗ 0.000249∗∗∗ 0.000249∗∗∗ 0.000248∗∗∗ 0.000248∗∗∗ (0.000012) (0.000012) (0.000012) (0.000012) (0.000012)

Sex (male = 1) 0.00141∗∗∗ 0.00140∗∗∗ 0.00139∗∗∗ 0.00141∗∗∗ 0.00140∗∗∗ (0.000109) (0.000109) (0.000109) (0.000109) (0.000109)

GIC 0.00145∗∗ 0.00222∗∗∗ 0.00315∗∗∗ 0.00208∗∗∗ 0.00288∗∗∗ (0.000619) (0.000517) (0.000550) (0.000657) (0.000546)

Courses with accessibility 0.00464∗∗∗ 0.00345∗∗∗ 0.00435∗∗∗ 0.00314∗∗∗ (0.000375) (0.000298) (0.000341) (0.000274)

State linear time trends NO YES NO YES NO YES N 2,932,633 2,932,633 3,122,070 2,932,633 2,932,633 2,932,633 F 84.64 43.72 37.69 35.12 48.30 34.70 r2 0.0451 0.0462 0.0455 0.0463 0.0453 0.0464 Standard errors in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 Note: All regressions are controlled for institution-degree pairs fixed effects, time fixed effects and State linear time trends. DISABILITY AND ACCESS TO COLLEGE 27

Table 4—: Results by Enade quantiles

(1) (2) (3) (4) (5) (6) Sisu -0.00130∗∗∗ 0.000364 0.00119∗∗ (0.000397) (0.000476) (0.000566)

Quotas policy -0.000581 0.00137∗ 0.000516 (0.000528) (0.000799) (0.000934)

One year in the Sisu -0.000429 0.000138 0.000833 (0.000417) (0.000560) (0.000600)

Two years in the Sisu -0.00186∗∗∗ 0.000990 0.00134 (0.000542) (0.000773) (0.000843)

Three years in the Sisu -0.00143∗∗ 0.00266∗∗∗ 0.00492∗∗∗ (0.000633) (0.000930) (0.001071)

Four years in the Sisu 0.00455∗∗∗ 0.00418∗∗∗ 0.00666∗∗∗ (0.001041) (0.001412) (0.001492)

Five years in the Sisu 0.00325∗∗∗ 0.00289∗ 0.00416∗∗ (0.001087) (0.001728) (0.001932)

Six years in the Sisu 0.000196 0.00341∗∗ 0.00445∗∗ (0.001404) (0.001601) (0.001764)

Seven years in the Sisu 0.00341∗∗ 0.00466∗∗ 0.00573∗∗ (0.001533) (0.001974) (0.002262)

One year with quotas policy -0.000730 0.00117 0.0000819 (0.000556) (0.000957) (0.001063)

Two years with quotas policy 0.000155 0.00153 0.00200 (0.000653) (0.000937) (0.001244)

Three years with quotas policy -0.000777 0.00143 -0.000627 (0.000748) (0.000925) (0.001362)

Four years with quotas policy -0.000880 0.000313 -0.000845 (0.000829) (0.001029) (0.001720)

Five years with quotas policy -0.00150 -0.0000597 -0.000611 (0.001030) (0.001412) (0.001830)

Six years with quotas policy -0.00163 -0.00173 -0.00268 (0.001187) (0.001482) (0.002139)

Seven years with quotas policy 0.00175 -0.000482 -0.000508 (0.001614) (0.001626) (0.002576)

Age 0.000269∗∗∗ 0.000275∗∗∗ 0.000246∗∗∗ 0.000270∗∗∗ 0.000276∗∗∗ 0.000245∗∗∗ (0.000021) (0.000028) (0.000030) (0.000021) (0.000027) (0.000030)

Sex (male = 1) 0.000888∗∗∗ 0.00213∗∗∗ 0.00166∗∗∗ 0.000895∗∗∗ 0.00213∗∗∗ 0.00166∗∗∗ (0.000163) (0.000280) (0.000286) (0.000163) (0.000280) (0.000287)

GIC 0.00181∗∗ 0.00186 0.00305∗∗ 0.00136∗ 0.000921 0.00203 (0.000779) (0.001368) (0.001468) (0.000745) (0.001254) (0.001368)

Courses with accessibility 0.00373∗∗∗ 0.00185∗∗∗ 0.00117∗∗ 0.00402∗∗∗ 0.00206∗∗∗ 0.00148∗∗∗ (0.000429) (0.000475) (0.000523) (0.000468) (0.000504) (0.000535) N 1362168 485056 303819 1362168 485056 303819 F 19.25 9.729 6.025 23.64 12.06 . r2 0.0217 0.0169 0.0132 0.0214 0.0168 0.0129 Standard errors in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 28

Table 5—: Results - Placebo

(1) (2) (3) (4) (5) Sisu -0.000637 -0.000348 (0.000445) (0.000571)

Quotas policy 0.00124∗∗ -0.000654 (0.000565) (0.000653)

One year in the Sisu -0.0000796 -0.000196 0.0000222 (0.000427) (0.000418) (0.000493)

Two years in the Sisu -0.00150∗∗∗ -0.00191∗∗∗ -0.00168∗∗ (0.000532) (0.000544) (0.000697)

Three years in the Sisu 0.000437 -0.000240 -0.0000458 (0.000976) (0.001000) (0.001384)

Four years in the Sisu -0.00357∗∗∗ -0.00440∗∗∗ -0.00363∗∗∗ (0.000865) (0.000985) (0.001277)

One year with quotas policy 0.000661 -0.00120∗ (0.000573) (0.000711)

Two years with quotas policy 0.00229∗∗∗ -0.000198 (0.000771) (0.000832)

Three years with quotas policy 0.00156∗ -0.00134 (0.000936) (0.001046)

Four years with quotas policy -0.00184∗ -0.00533∗∗∗ (0.001015) (0.001215)

Age 0.000119∗∗∗ 0.000118∗∗∗ 0.000120∗∗∗ 0.000119∗∗∗ (0.000018) (0.000018) (0.000018) (0.000018)

Sex (male = 1) 0.000815∗∗∗ 0.000825∗∗∗ 0.000812∗∗∗ 0.000822∗∗∗ (0.000175) (0.000175) (0.000175) (0.000174)

GIC -0.00177∗∗ 0.00124∗ -0.00211∗∗∗ 0.000856 (0.000720) (0.000724) (0.000735) (0.000718)

Courses with accessibility 0.0000132 -0.000106 0.0000421 -0.000166 (0.000301) (0.000311) (0.000308) (0.000310) N 747448 747448 800480 747448 747448 F 18.46 8.234 8.211 12.42 7.580 r2 0.0324 0.0331 0.0340 0.0326 0.0333 Standard errors in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 DISABILITY AND ACCESS TO COLLEGE 29

Table 6—: Share of Students that have accessed an University using Enem (%)

Year Students without Disabilities Students with Disabilities 2009 5.67 0.65

2010 20.19 10.17

2011 25.63 17.53

2012 32.23 34.13

2013 36.11 35.9

2014 47.09 62.27

2015 50.55 64.9

2016 54.91 63.34

Table 7—: Results - The Enem Eﬀect

(1) (2) Sisu 2.075∗∗ - (0.870265)

Disabilities -7.718∗∗∗ -7.718∗∗∗ (1.151253) (0.676135)

Interaction 2.520∗ 2.520∗∗ (1.230741) (0.722818)

2010 1.002 (0.599329)

2011 1.248∗ (0.599329)

2012 1.921∗∗ (0.599329)

2013 2.064∗∗ (0.599329)

2014 2.706∗∗∗ (0.599329)

2015 2.823∗∗∗ (0.599329)

2016 2.763∗∗∗ (0.599329) N 16 16 F 72.34 73.11 r2 0.948 0.991 Standard errors in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 30

The expression for the optimality condition becomes a little more cumbersome, but the intuition is still the same. Note, also, that the expression collapses to our usual one when all ps are assumed to be the same. These results show that the results from the baseline version of the model are quite robust to changes in the environment. The baseline version of the model displays a simple, tractable version of the setting that displays the key trade-offs involved in choosing the number of applications. The limitation of this exercise here is, however, that as long as the student can unambiguously rank universities before the applications: being it due to differences in p,V , or k, then the solution to the problem will suffer little modification. However, if there is no unique ranking of institutions - that is, they are not perfect substitutes, and neither the ranking based on p, V , and k are identical, then the setting changes. If the agent’s ranking of V , p, and k displays no ambiguity, then, the optimality condition becomes:

n∗−1 Y ∗ ∗ ( (1 − pi))pn∗ V (n ) ≥ k(n ) i=1

B1. A general framework

In our baseline model, the student’s problem is to decide n∗, the number of applications. This is a well-defined question in our setting because institutions are viewed as perfect complements, both in terms of value, costs of application, and the likelihood of obtaining an offer. When we add heterogeneity to the problem, the structure remains virtually the same, as long as the student can unambiguously decide ex-ante on a ranking of these institutions. This is so because, in that case, the problem can be split into two parts: The first part is to sort institutions in descending order of value. The second is to decide the number of applications to send. However, in the setting with unrestricted heterogeneity, then the problem cannot be reduced to simply choosing how many applications to send. The problem is also to decide where to send these applications. In this setting, n∗, the optimal number of applications is not quite well-defined unless we specify clearly which institutions the individual will be applying to. Assume that there is a continuum of institutions indexed by x ∈ [0, 1]. One can think of x as the overall perception of the quality of the institution. Let V (x) be the value that the student attaches to attending institution x and let p(x) be the probability of being admitted to this institution. The only interesting case, where a trade-off is actually present, is in the regions in which p0(x) < 0 but V 0(x) > 0, DISABILITY AND ACCESS TO COLLEGE 31 that is, better institutions are harder to get into.18,19 The student problem is to choose the (quality of) the institution for which he will apply to. In this case,

x∗ = arg max p(x)V (x) − k x The solution to this problem is given by the following condition:

V 0(x)p(x) = −p0(x)V (x) Multiplying x on both sides of this equation and rearranging terms, we obtain:

Elasticity of V(x) = − Elasticity of p(x) In words, the student will choose the institution quality at the point in which the gain in expected value obtained by marginally increasing the quality of the institution that he is applying for is exactly balanced by the decrease in the likelihood of being admitted to that institution.

B2. General model

Now, putting all these pieces of information together, here we lay out the problem of a student that must decide on both which institutions to apply for and also how many applications to send. Assume, as before, that institutions are characterized by a quality index x, that the density of x is continuous and positive everywhere in the (0, 1) interval, and that the costs of an application might be a function of n the number of applications, but not of x, the quality of the institution. Finally, assume that the student will ﬁrst decide on the quality of the institutions he will apply for, then how many institutions of the chosen quality he will engage.20. Then the student problem becomes:

(n∗, x∗) = arg max E[U(n; V (x), p(x), k(n)] (n,x)

E[U] = (1 − (1 − p(x))n)V (x) − k(n) The solution to this problem is characterized by the following system of equations:

V 0(x∗) P 0(x∗) x∗ = x∗ V (x∗) P (x∗)

18Here and henceforth we implicitly assume that the density of x is continuous and the functions V (x) and p(x) are continuous and twice diﬀerentiable. 19 Also, since k is designed to capture both the monetary costs of application and also the time and distance taken to perform the exams, we assume that k is not a function of x, although it is easy to generalize the results for this case as well. 20It is possible to relax this assumption as well, which results in a messier characterization of the optimal application behavior. 32

∗ (1 − p(x∗))n −1p(x∗)V (x∗) ≥ k(n∗), where P (x∗) = (1 − (1 − p(x∗))n∗). These conditions, as before, state that at the optimum, the student cannot increase his utility neither by moving laterally on the quality index (increasing or decreasing the quality of the institutions that he is applying for), nor by increasing the number of applications for the universities of the quality that he has chosen. It is again useful to note that the main characterization of the optimal number of applications is still present in this general setting.