1. INTRODUCTION

Microeconomics manuals teach that, in equilibrium, the amount demanded for a good or service must equal the amount supplied. In the higher-education market, this principle does not hold. Instead, many higher-education institutions (HEIs) limit the number of available slots to guarantee permanent excess demand. The same phenomenon can be observed in other markets, especially service markets, but the rationale behind excess demand in higher education does not apply to restaurants or large events. In education, the student is not only the consumer, but also he or she is a factor of production. As consequence, the quality of the output is a function of the quality of the student body. For this reason, given the characteristics of HEI and the quantity of available slots, the institution charges tuition below equilibrium price to increase the quantity of appliers and, thus, to benefit from greater selectivity.

The Brazilian market for HEIs is predominantly composed by private enterprises. Among 2.281 HEIs in 2006, 89% were private, and 74.6% of all students were enrolled in these private schools. Additionally, the majority of private HEIs (52%) are for profit (2006 Higher Education Census – Ministry of Education). Despite the lack of official data on the amount of donations received by HEIs, it is known that the resources derived from this source are limited, as are the resources available to fund research. In this context, most Brazilian private HEIs primarily raise funds from student tuition payments. Those are little known outside their area and, although they charge low tuitions, have empty slots. They coexist with some HEIs with good reputation, which charge high tuitions and have hotly disputed selection processes. Among private Business Administration schools in São Paulo in 2006, for example, the fees range from R$ 170 to R$ 2.250 (or from US$ 106 to US$ 1,415^{(}^{1}^{)}), and the ratio of candidates to slots ranges from 0.17 to 11.5.

The sector has been going through substantial transformation over the last years. There has been a large increase in the number of students enrolled in higher education: from 1.3 million in 1995 to 3.8 million students in 2003 and 7.0 million in 2012 (2012 Higher Education Census – Ministry of Education). Despite the consistent growth observed over the last decades, there has been a substantial slowdown in the growth rate. The number of enrolled students more than tripled from 1995 to 2003, while it less than doubled from 2003 to 2012.

The players and their size have also changed. A fast consolidation process has taken place, with some large educational groups (Anhanguera, Estacio and Kroton, among others) buying local institutions. So, the observed trend nowadays is from a market with local and independent HEIs to a market dominated by large chains. Kroton and Anhanguera had 11% of the Brazilian market in 2011, and 14% in 2012, which means a growth of 27% in one year. However, the majority of supply still comes from local and independent institutions.

This article analyzes the HEI market and attempts to answer four interrelated questions:

How do we theoretically understand the existence of the HEI that opts for the strategy of maintaining permanent excess demand?

Which HEIs’ characteristics affect the demand for their business courses?

How big is the group of HEIs that really invest in selectivity?

How much revenue does the HEI give up to increase the selectivity of its admissions process and, consequently, the quality of its students?

Through two adaptations of the ideas of ^{Becker (1991)}, we attempt to explain why some HEIs maintain permanent excess demand while others do not. Next, using a database of business schools in the state of São Paulo^{(}^{2}^{)} (see section 3 for a detailed description of the dataset) we estimate the demand for higher education. The empirical results show that the quality of the student body, the tuition, and the quality of the lecturers are relevant in determining the demand of the market. The relevance of the quality of the student body justifies the strategy of an HEI that opts for excess demand and confirms the theory that will be developed in the next section: demand for the school hinges on the quality of the students and, ultimately, responds positively to the selectivity imposed by the HEI. Finally, using the results of econometric models, we present the total “investment” in selectivity made by São Paulo HEIs in their business programs. This total, which surpasses R$ 5 million (or US$ 3.14 million – 7.6% of the revenue) per year, can be understood as an investment in differentiation.

While ^{Becker (1991)} theoretically shows why some restaurants having long queues for tables do not raise prices, this paper estimates the “investment on queues”. The higher education market is specially appropriated for this study because there is data about all the candidates, including those students that failed in the selecting process. In a restaurant-market context, it would be as if we knew the numbers of clients **and** the number of people who give up eating at a given restaurant because of its long queues.

The selection of better students in higher education is well documented by literature, but how to measure its impact on the education output is a controversial question (see ^{Winston & Zimmerman, 2003}). Instead of measuring this effect, the focus of this work is to better understand how the **existence** of those effects modifies the market equilibrium. Thus, we estimate (a) on one side, how the selectivity of HEIs (considering the quality of incoming students as a proxy) affects the demand curve, and (b) on the other side, how much the HEIs invest in selectivity to maximize their long term profits by maintaining permanent excess demand.

There is a broad and well-established literature that studies the decision to pursue college education, with emphasis on the impact of tuition on college decision. An earlier study by ^{Bishop (1977)} analyzes the decisions of high school students. He found that tuition has a more severe negative impact on lower income groups. ^{Ehrenberg (2004)}presents a review of this literature, corroborating the notion that a higher tuition and fewer financial incentives, such as scholarships, reduce the motivation to study at an HEI. Other characteristics that may affect student preferences are less studied.

Another branch of this literature (^{Belzil & Hansen, 2002}; ^{Hartog & Diaz-Serrano, 2007}; among others) analyzes higher education as an investment, and how earnings risk affects students’ choice. The results are not conclusive: Belzi and Hansen find a positive correlation between risk and the decision to attend college, while other authors find a negative relationship.

Four papers follow this line of research and are closely related to our study. ^{Gallego and Hernando (2008)} also use a discrete choice model in Chilean high schools to estimate the effects of the voucher system on student well-being and socio-economic segregation. ^{Monks and Ehrenberg (1999)} use panel data to evaluate the impact on the demand for universities of the U.S. News and World Report rankings, the most traditional ranking in the U.S market. They conclude that a lower position in the ranking is detrimental to the university: fewer accepted students decide to enroll; the quality of new classes decreases, as measured by the admissions test; and the net tuition paid by the student is lower because the university has to be more generous in granting financial aid to attract students from the smaller group of applicants.

^{Long (2004)} examines how different cohorts of students in the United States choose which HEI to attend based on their own characteristics and those of the HEI, such as tuition, quality of the student body, percentage of lecturers with doctorates and student/lecturer ratio. Long’s study concludes that the quality of the faculty is the most important factor in the student’s decision, a result we also find here.

^{Kelchtermans and Verboven (2009)} study college choice in the Belgium region of Flandres. They conclude that courses are close substitutes, and that a tuition increase would not affect the decision of whether to study but affect the decision of where to study.

^{Flannery and O’Donoghue (2013)} use a nested logit model with three choices: to attend college, to work or to work and study part time. They recognize two key features. First, college choice is a discrete choice problem where tuition and college quality variables are important in students’ choices. Second, there is a trade off between studying and working.

Other papers – such as ^{Frenette (2009)}, ^{Chowdry, Crawford, Dearden, Goodman, and Vignoles (2010)}, ^{Spiess and Wrohlich (2010)}, among many others – investigate different aspects that affect college attendance. Despite the fact that all these papers also estimate a demand for educational institutions, the details of the method we employ and our goals are quite distinct from the others. We chose to restrict our analysis to business administration courses only. Implicitly, we assume that business administration is not a substitute with other courses, such as biology or engineering. Moreover, our final goal is both to identify the group of HEIs that invest in selectivity and to estimate the investment.

The rest of this article is organized as follows. In the next section, we discuss why a HEI could use the strategy to operate with excess demand. Sections 3 and 4 explains the methodology and data employed. The results are presented in Section 5. The final section concludes the analysis.

2. THEORETICAL DISCUSSION

The fundamental hypothesis of ^{Becker (1991)}, who studies the causes of excess demand in the restaurant industry, is that the individual’s demand depends on the other individuals’ demand. The author suggests that eating out, attending a cultural event or discussing a book are social activities in which people consume the product or service together, and therefore, the number of people sharing the same product influences the utility of the individual consumer.

While in Becker’s model the decision of attending a cultural event is a function of the queues’ size because of social aspects; in the present paper, the choice of a HEI depends on the HEI’s capacity of selecting the best students. In both situations, excess demand creates demand.

More specifically, in the case of higher education, we claim that the Becker’s argument becomes even stronger because both the actual quality and the reputation of a graduate course are functions of the quality of its students. In terms of quality for enrolled students, the qualification and performance of the cohort affect learning (the peer effect, which does not occur in the case of restaurants). Also the success of the graduates serves as signals to the market of the quality of the HEI. Therefore, excess demand allows HEI to select good students, who tend to be good graduates, which contribute to the reputation of the institution. Thus, in contrast with restaurants, the quality of enrolled students is fundamental to the choice of the potential students. Because greater selectivity increases the quality of the incoming class, we may conclude that excess demand creates demand, which should be considered in the maximization process of long-term profit. As result, the long-term equilibrium may present permanent excess demand.

In any market, one should expect higher demand for high-quality products than for low-quality products given the same price. However, in a “traditional” market, the equilibrium is reached by increasing price of high-quality products until eliminating excess demand.

The coexistence of HEIs with different strategies — with or without excess demand — can be understood using Becker’s model (1991). ^{Becker (1991)} does not distinguish between the short and long term, but his analysis corresponds to what we consider to be long term here.

This differentiation seems important with respect to higher education because we assume that permanent excess demand builds the HEI’s reputation, which in turn determines its short-term demand curve. The idea is that, in the short term, tuition set below equilibrium generates excess demand (and greater selectivity), which, in the long term, will shift the short-term demand curve to the right. It happens because, in this analysis, each short-term curve is determined (and sustained) by a given level of excess demand.

For the HEI that maintains excess demand, this movement is sufficiently large for a given interval of prices, and consequently, the long-term demand curve will be positively inclined in this interval (Figure 1). When the price reaches a sufficiently high level, the large shifts in demand stop, and the long term demand becomes negatively sloped. In this case, the tuition rate that maximizes profit (P3) will be below the short term equilibrium price (P4).

Yet, in the case of the HEIs that do not maintain excess demand, the long-term demand curve will be negatively sloped because excess demand does not create a sufficiently large shift in the short term (Figure 2).

In analyzing Figure 1, an initial equilibrium in P1 is determined by the D1 demand and supply S. Next, an HEI reduces its price to P2 and creates an excess demand of *ab*. In the long term, for this excess demand, the short-term demand curve turns out to be D2, which allows the HEI to charge tuition equal to P3, while maintaining the same excess demand. Note that the excess demand *ab* generates a shift of demand curve (from D1 to D2), which implies a higher quantity demanded for P2. In order to maintain both the same excess demand (*ab*) and, consequently, D2 as the short-term demand curve, HEI can increase price to P3, reducing the quantity demanded to the previous level (Figure 1). In this step, demand is positively inclined.

If the HEI decides to lower the price below P3, the shift of short-term curve due to an increase in excess demand will be smaller and, as consequence, the long-term demand curve will be negatively inclined (from D2 to D3). In this case, the long-term equilibrium will be in P3, while in the short term (only!) the price P4 maximizes the profits of the HEI.

Following the same sequence in Figure 2, suppose there is an initial equilibrium in P1. A new price P2 would create an excess demand for *ab*, which would shift the short-term demand curve to D2. However, in this case, long-term demand (d1) is negatively inclined, since any price higher than P1 generates excess supply. Hence, the equilibrium price is the initial price – P1.

3. EMPIRICAL METHOD

The methodological challenge of this project, given the specifics of this market, is to propose estimation strategies through models of discrete choice and the utilization of instrumental variables that can surpass (at least in part) the econometric difficulties arising from the particularities of the market. These strategies are to:

redefine the question in order to avoid the problem in which, in the higher education market, the student not only chooses the HEI but is also chosen by the HEI, and so be able to use the Aggregate Logit Model;

define the demand for the HEI;

obtain instrumental variables to correctly estimate the model.

3.1. Econometric model

The methodology used in this paper to estimate the demand for undergraduate business programs in the state of São Paulo is based on the literature of discrete choice applied to the estimation of demand in markets with differentiated goods. There is a vast range of references, from the seminal work of ^{Lancaster (1971)} and ^{McFadden (1974)} to more recent contributions well known in the field, such as ^{Berry (1994)}, ^{Berry, Levinsohn and Pakes (1995)} (BLP, as they are referred to from here onward) and Nevo (2001). In this paper, we will use the Aggregate Logit Model^{(}^{3}^{)}.

This methodology has two important characteristics. The first of these is that despite being a model of discrete choice, it is based only on aggregated or market data. The second is that the method projects the goods (HEIs, which hereafter refer specifically to São Paulo business schools) in the space of characteristics, and the dimension of this space is the relevant one. In this sense, the problem of dimensionality is resolved when the system of demand equations for differentiated goods is estimated, wherein the price of all goods must appear in every equation.

Before describing this methodology, it is necessary to evaluate if it is adequate for the HEI market. Models of discrete choice assume that the consumer chooses the good or service. This assumption does not match this market, in which the student not only chooses the HEI but also is chosen by the HEI. The fact that a student goes to study at an HEI indicates that there was a matching between them. This interpretation of the process suggests that models of discrete choice are not appropriate for this sector.

In order to avoid this problem and be able to apply a discrete choice model, we redefine the question of interest. Instead of asking the question “at which HEI will students study”, we turn to the question “to which HEI will students apply”. Hence, instead of using the number of registered students as the measure of demand, we use the number of student applications. This approach can be understood in terms of the student calculating an *ex ante* utility of studying in a given HEI, before the decision of the HEI of accepting or not him as its student. This approach allows us to use the traditional methods of discrete choice to analyze this market.

The primary idea behind this method is that students classify HEIs according to their characteristics. We initially assume that the function of *ex ante*indirect utility that a student has upon applying to an HEI depends on the HEI quality (*qe*), the quality of the students that attend the HEI (*e*), the price of studying at the HEI (*p*) and the difficulty of being accepted to the institution (*sel*). We can then write that the utility that the student *i* has upon registering at the HEI *j* is represented as

where *ε _{ij}* is a non-observable characteristic of individual

*i*in relation to HEI

*j*, for example, if the HEI is close to the residence of

*i*. We assume that the HEI quality depends on both observable characteristics (

*x*) and non-observable characteristics (

*ξ*), then

*qe*=(

*x,ξ*). Assuming that the utility function is linear, we find that the utility a student

*i*has on choosing school

*j*is represented by

where α, γ and φ are scalars, β is a vector with dimension K, ξj is an unobserved characteristic of the HEI (*j*), and *ε _{ij}* is a characteristic idiosyncratic to consumer i in relation to HEI

*j*.

The student chooses between (*N*+1) options: the N different HEIs available in the market and the option to not study business (which means studying in a different higher-education program or no higher-education program). The utility of each option for the consumer is represented by the following system:

From among the available options, the student chooses the option that grants the best utility. We normalize the utility of the option of not studying business as zero, as is usual. Additionally, we assume that the idiosyncratic characteristic ε*i _{j}* is distributed as a

*type I extreme value distribution,*which transforms the problem into the well known

*logit*

^{(}

^{4}

^{)}.Then a consumer chooses alternative

*j*if uij > uik , k ≠ j, k = 0, 1,...

*N*.

If information about the choice of the consumers were available or if we had microdata, then this study would use the hypothesis of logistically distributed errors to calculate the probability of the consumer choosing each alternative. In that case, the model would be the traditional Multinomial Logit Model. Unfortunately, microdata on consumer choices were not available – only the total number of students that chose a determined HEI. Therefore, a model based on aggregated data is used.

With this aim, we define:

where *x*. = (*x*_{1},... *x _{N}*),

_{p}. = (

*p*

_{1},...

*p*),

_{N}*e*. = (

*e*

_{1},...

*e*),

_{N}*sel*. = (

*sel*

_{1},...

*sel*) and

_{N}*x*. = (

*x*

_{1},...

*x*) are, respectively, the observable characteristics, the price vector, the student quality vector, the selectivity vector and the vector of the non-observable characteristics of all

_{N}*N*HEIs existing in the market. Group

*A*defines the group of individuals who choose alternative

_{j}*j*. It is important to note that individual

*i*is defined by vector (

*e*

_{i}_{0},

*e*

_{i}_{1}...

*e*). Aggregating all individuals

_{iN}*i*present in group Aj, or integrating the distribution e over group

*A*, one obtain the

_{j}*market share*of product

*j*:

where *f*(.) is a density function of the extreme value distribution. This hypothesis on distribution means that the defined integral in [5] has a closed functional form, represented by the following equation (see Train, 2003, pp. 78 and 79 for the algebraic manipulation that transforms the equation from [5] to [6]):

Using the log in equation [6], we reach a linear expression of the fraction of consumers that opt for HEI j, which is the model estimated in this paper:

where *s _{j}* is the

*market share*of HEI

*j*, and

*s*

_{0}is the

*market share*of the option to not pursue a higher education or to undertake a program in an area other than business. Two points should be mentioned. Initially, despite the non-linearity of the initial problem, the hypothesis of logit distribution and the aggregation allowed us to reach a linear equation, which simplifies the estimation process.

Secondly, the non-observable characteristic (by the econometrists) of the HEI, x, is the random term of the estimation model. Observing that this term captures the characteristics of the HEI not included in vector x, it is intuitive to suppose that this term has a positive correlation with the price, the quality of the students and the selectivity of the HEI. HEIs with better non-observable characteristics in equilibrium charge higher prices, attract better students, and can be more selective. This fact generates a correlation between these variables and the econometric error, resulting in problems of endogeneity for all of them, so instrumental variables are needed to estimate the model. We discuss this issue in the next subsection.

Finally, with respect to the econometric technique, it is necessary then to use those models that permit the use of instrumental variables. We will use the method of two-stage least squares (2SLS).

3.2. Instrumental variables

According to the literature on estimating demand for homogeneous goods, the valid instrument to correct for the endogeneity of the price variable is a set of variables that affect business costs and are unrelated to demand shocks. In theory, the same type of instrument can be utilized in markets with differentiated goods. However, there are rare situations in which cost variables of firms are related to only one differentiated good, without being correlated with all of the market goods. Therefore, another type of instrument should be used.

In literature, there are two possible solutions to this problem. The first, derived by BLP, uses the exogenous characteristics of the firm’s own product as instruments for themselves and the sum or average of the rivals firms’ product characteristics as instruments for the price. According to Bertrand’s oligopoly model with differentiated goods, in market equilibrium, the better the quality of the rival goods, the lower the equilibrium price of the firm in question.

The second solution, introduced by ^{Hausman (1996)}, advocates the use of the same product’s price in another market as an instrument for the price^{(}^{5}^{)}. In the problem analyzed here, one HEI is different from another, not having a product brand appearing in different markets, nor two HEIs in different cities. This forces us to opt for the first solution, in which we use the average of the characteristics of the other HEIs as an instrument for the price.

The quality of enrolled students and HEI selectivity are also endogenous variables. We will use the same group of instrumental variables that we use for price: competitor characteristics, and the age of the HEI. The age must be related to the reputation of the school, the hypothesis being that the older HEIs are more likely to have better reputations.

4. DATASET

As mentioned in the previous section, the model represented by equation [7] will be estimated in this work. We will explain the variables utilized in this estimation, as well as the source of the data.

At the onset, it is important to define the dependent variable or the market share of the HEIs (variable *s _{j}* in equation [7]). This is equal to the ratio between the number of students that want to study at an HEI and the number of potential students in the market where the HEI is located.

To reach the market share denominator, it is necessary to explain *a priori* the markets in which the HEI participates. In the present work, we assume, in a simplifying manner, that each municipality with at least one business program corresponds to a market^{(}^{6}^{)}. At the same time, to reach the number of potential consumers of an HEI, the study takes into consideration the fact that the consumer has completed secondary education, is between 18 and 25 years old, and is being confronted with three possibilities: to attend a business program, to attend a higher-education program in another field or to not attend a higher-education program at all. All of the students who opt for one of these alternatives and who live in the municipality where the HEI is located are part of the HEI’s potential market.

The 2006 Higher Education Census from the *Ministério da Educação e Cultura* (MEC – Ministry of Education) provides information, by municipality, on the number of students in the first two options, the business program or the program in another field. In addition, the 2010 Population Census carried out by the *Instituto Brasileiro de Geografia e Estatística* (IBGE – Brazilian Bureau of Statistics) shows that 27% of individuals between 18 and 25 years old who have finished secondary education do attend an HEI. Therefore, knowing the number of students in the first two groups and the participation percentage of the third group, we can estimate the number of potential consumers, which will be the denominator of the market-share formula of the HEI in the municipality. This number is then equal to the ratio between the number of students enrolled in any undergraduate degree (business and others) in the municipality and 0.27.

It is difficult to define the numerator of the market-share formula of the HEI. As we discussed in the econometric model section, we use the number of students who take the entrance exam for the business program at an HEI^{(}^{7}^{)}, in order to avoid the fact that in the education sector not only the students chooses the HEI but also is chosen by it. We are aware that there is a problem with this alternative: many students take various exams, for different HEIs, in the same year. Thus, the average might overestimate the demand for the HEI.

A possible alternative is to use the number of registered students in the HEI business program. The problem with this alternative is that the HEIs that are more selective, that is, that have higher candidate/slots ratios, tend to work with excess demand. As discussed in section 2, they do not adjust the tuition to balance the amount demanded with the amount offered. The reason, as was already discussed, is that in the education sector, the consumer (the student) is also an input in the productive process. The better quality the registered students are, *ceteris paribus*, the better the quality of the students educated at the HEI. This occurs in large part because students can benefit from interacting with the other students, through what is known as the peer effect, and because the quality of the HEI supplies a signal about the quality of the graduate in the job market after completing higher education^{(}^{8}^{)}. Moreover, the HEIs with excess demand certainly would have a better market share if they were to have a less rigorous selection process and accept more students. Therefore, the number of registered students as a measure of the numerator for the market-share formula underestimates the demand for the HEIs with higher selectivity. Last but not least, with this alternative, we could not apply the models of discrete choice, as pointed out in the econometric model section. Hence, we do not consider this alternative.

The data of the number of student applicants to each HEI comes from the 2006 Higher Education Census of the MEC.

This study now proceeds to a discussion of the different observable characteristics related to the variable quality of the HEIs that can affect the choice of the student and are used as explanatory variables (variable *x _{j}* in equation [7]) in the empirical model. Two variables are related to the quality of the faculty body: the percentage of lecturers with doctorates (perc_doutor) and the percentage of full-time lecturers (perc_int). These variables are collected from the 2005 Faculty Body Census. At first, a high percentage of lecturers with doctorates and full-time lecturers might signal the quality of the program; however, the business student certainly is also interested in their lecturers’ business experience, which often competes with the full-time dedication of a university lecturer. Therefore, whether a superior title means better academic quality in the program (maintaining constant the rest of the variables) is questionable. For example, a lecturer who is also the director of a large company may attract more candidates to a business course than a full-time lecturer with a Ph.D. degree.

Other observable characteristics related to the variable quality of the HEIs used as explanatory variables are the ones related the conditions of the infrastructure offered by the HEI. The models in this paper consider three variables: the quality of the overall physical structure (qual_infra), the quality of the library (qual_libr) and the availability of computers (qual_comp). These three variables are obtained from a socioeconomic survey administered to undergraduate students during the* Exame Nacional de Desempenho de Estudantes* (Enade – National Student Performance Exam), carried out by the MEC and compiled at the 2006 Enade Census. The students grade each of these variables and an average score for each of those is obtained. In the case of these three physical- -infrastructure variables, the signs of their coefficients are expected to be positive; that is, better infrastructure should correspond to a greater market share.

The authors collected pricing information during the first semester of 2008. A negative sign for the tuition coefficient is expected.

Every new undergraduate student in business (and in other programs as well) must take an exam that encompass specific and general knowledge, the Enade. The average score of the students in a given HEI is used in this paper as a proxy for the quality of the student body that the student will find if he chooses this HEI. This variable comes from the 2006 Enade Census. This variable might signify that the students take into account the effect of their peers (peer effect) in their choice of HEI. Additionally, schools with better students have a better reputation, generating better results for their students in the job market after graduation. In both cases, the higher the Enade score is, the more qualified the group of students and the higher the demand for the HEI.

The selectivity variable is defined as the number of candidates divided by the number of vacancies. On the one hand, a higher selectivity implies less likelihood that the student will be accepted by the HEI. Hence, we expect that this variable will have a negative effect on the choice of the student. On the other hand, this variable may be seen as another proxy for the quality of the student body. In this regard, the higher Enade score is, the higher is the demand for the HEI. Therefore, the sign of the coefficient of the variable selectivity is unclear from a theoretical point of view.

In terms of the market (municipality) in which the HEI is located – as identified by the 2006 Higher Education Census – the model includes the Gross Domestic Product (GDP) *per capita* of the municipality (GDP-pc) for the year 2007, as obtained from Ipeadata^{(}^{9}^{)}. In terms of the location, a dummy variable (SP) assumes the value one when the HEI is in the market of the capital, the city of Sao Paulo, and zero otherwise. As the density of business programs in relation to the total population is smaller in the capital than in other cities, an inferior market share is expected in the capital.

Our sample contains 298 observations of HEIs located in 130 municipalities (or markets) in Sao Paulo state. As previously mentioned, each market is defined as a municipality.

Table 1 shows the distribution of programs in the different markets. In 83 markets (municipalities), or in 63% of markets, there is only one undergraduate business program. Two HEIs share students in 25 markets, and 97 programs are distributed through 21 markets, each containing between 3 and 11 competitors. Additionally, the principal market is certainly the municipality of Sao Paulo, where there is a concentration of 22.8% (n=68) of all programs in the state.

Table 2 presents a statistical summary of the variables used in the analysis, with the average and standard deviation of each one. The average of the dependent variable, i.e., the market share, is equal to 6.9% once the total market includes all of the individuals of university age who have completed secondary school, whether enrolled in a business program or not. The HEIs are, on average, 9.2 years old, and practically all offer a bachelor’s program rather than a technical program.

Variable | Average | Standard Deviation |
---|---|---|

Market Share (%) | 6.9 | 11.2 |

Enade Score (0-100) | 39.5 | 4.3 |

Price (R$) | 506,85 | 249.2 |

Lecturers with Doctorates (%) | 8.5 | 9.3 |

Full-time Lecturers (%) | 12.5 | 15.1 |

GDP per capita (R$) | 28.750,95 | 18.200,1 |

Age | 9.2 | 12.2 |

Bachelor's Degree Offered (%) | 94.8 |

The average Enade score of the registered students is equal to 39.5 (on a scale of 0 to 100). Considering only the 20 programs with the highest candidate/vacancy ratios, the Enade average rises to 44.6.

The average tuition is equal to R$ 506,85 (or US$ 318), and the municipalities’ average GDP *per capita* is equal to R$ 28.750,95 (or US$ 18,082). Additionally, among the HEIs analyzed, the average percentage of lecturers with doctorates and full-time lecturers are, respectively, 8.5% and 12.5%.

Table 3 shows the distribution of the average scores of the variables related to the conditions of the infrastructure: the quality of the overall physical infrastructure, the library, and computer availability. The second, third and fourth columns present the number of programs with evaluation, respectively, “worse than average by one standard deviation (sd)”, “average ± one sd”, and “better than average by one sd”.

Variable | Worse than average by one standard deviation | Average ± one standard deviation | Better than average by one standard deviation | Total |
---|---|---|---|---|

qual_infra | 48 | 201 | 49 | 298 |

qual_comp | 42 | 204 | 52 | 298 |

qual_libr | 46 | 206 | 46 | 298 |

Finally, Figure 3 summarizes the data sources.

Variable | Source |
---|---|

Population | Population Census - Brazilian Bureau of Statistics (IBGE) |

Applicants and enrolled students and by IES, course | 2006 Higher Education Census - Ministry of Education (MEC) |

Percentage of lecturers with doctorates and full-time lecturers | 2005 Faculty Body Census - Ministry of Education (MEC) |

Quality of computers, infrastructure and library | 2006 ENADE (National Student Performance Exam) - Census |

Average HEI quality | 2007 ENADE (National Student Performance Exam) - Census |

Per capita GDP in 2007 | IPEADATA |

Name and location of a HEI | 2006 Higher Education Census - Ministry of Education (MEC) |

HEI Tuition | Collected by the authors in 2008 |

5. EMPIRICAL ANALYSIS

In this section, we show and discuss the empirical results. In the first part, various estimates will be presented, which vary according to the explanatory variables used. Here, we aim to explain which factors are considered by students when choosing a HEI. In the second part, using the coefficients estimated, the HEI’s investment in excess demand is calculated.

5.1. Results of the regressions

Table 4 shows the results of the different estimation models. Model (1) is estimated via OLS. Models (2) through (5) are estimates with instrumental variables (IVs) for the price, Enade score and selectivity via 2SLS.

(1) | (2) | (3) | (4) | (5) | |
---|---|---|---|---|---|

OLS | 2SLS | 2SLS | 2SLS | 2SLS | |

Price | -0.000642 | -0.0319 | -0.0192** | -0.0322 | -0.0214** |

(-1.07) | (-1.60) | (-3.00) | (-1.55) | (-2.96) | |

Enade | 0.0199 | 0.0888 | 0.736* | 0.770* | |

(0.65) | (0.09) | (2.15) | (2.13) | ||

Selectivity | 0.369*** | 6.314 | 6.742 | ||

(4.35) | (0.89) | (1.26) | |||

Doctorates | -0.366 | 4.776 | 12.06* | 4.247 | 13.20* |

(-0.27) | (0.33) | (2.14) | (0.30) | (2.14) | |

Full-time | 0.602 | -7.175 | -1.111 | -7.466 | |

(0.84) | (-0.91) | (-0.61) | (-0.99) | ||

qual_instal | -0.346 | -0.795 | -0.665 | -0.789 | |

(-1.18) | (-0.56) | (-1.01) | (-0.52) | ||

qual_comp | -0.502 | 7.937 | -0.808 | 8.580 | |

(-0.80) | (0.77) | (-0.55) | (1.14) | ||

qual_libr | 0.491 | 0.745 | 1.929 | 0.667 | 1.242 |

(1.12) | (0.27) | (1.70) | (0.24) | (1.08) | |

saopaulo | -4.599*** | 0.251 | -2.568** | 0.413 | -2.209* |

(-17.11) | (0.07) | (-2.64) | (0.12) | (-2.06) | |

GDP-pc | -0.00575 | 0.0654 | 0.0294 | 0.0670 | 0.0329 |

(-0.43) | (0.81) | (0.92) | (0.82) | (0.94) | |

_cons | -4.551** | 11.35 | -23.25 | 15.28 | -22.55 |

(-3.03) | (0.24) | (-1.86) | (1.18) | (-1.79) | |

N | 298 | 298 | 298 | 298 | 298 |

Notes: t statistics in parentheses.

^{*}p < 0.05,

^{**}p < 0.01,

^{***}p < 0.001.

As mentioned in the previous section, OLS is not the indicated method in this case, but we present the result of this estimate to highlight the effect of the instrumental variables. The comparison between model (1) and the others allows us to identify a substantial difference when we use IVs for the estimate of the models. In particular, the coefficients of the variables price, Enade and selectivity change substantially when the 2SLS method is employed.

For models (2) through (5), the IVs used is the average values of the other HEIs (the rivals) for the following characteristics: the percentage of lecturers with doctorates (ivdoc), the quality of the infrastructure (ivinstal), the quality of the computers (ivcomp), the quality of the library (ivbibl) and the percentage of full-time lecturers (ivintegr). Moreover, we use the age of the HEI itself as a measure of its reputation, which should have a direct impact on students’ choices and Enade scores. We observe in the correlation of variables in Table 5 that the Enade scores as well as the price of the HEI show a correlation of around 0.3 with the age of the institution.

MS | Price | Enade | Selectiv | Doctor | Full-Time | qual_inst | qual_comp | qual_libr | Age | |
---|---|---|---|---|---|---|---|---|---|---|

Ms | 1.00 | |||||||||

Price | -0.21 | 1.00 | ||||||||

Enade | -0.14 | 0.60 | 1.00 | |||||||

Selectivity | 0.04 | 0.39 | 0.32 | 1.00 | ||||||

Doctor | -0.11 | 0.51 | 0.42 | 0.36 | 1.00 | |||||

Full-Time | -0.12 | 0.16 | 0.22 | 0.23 | 0.27 | 1.00 | ||||

qual_instal | -0.03 | 0.17 | 0.22 | 0.06 | 0.12 | 0.14 | 1.00 | |||

qual_comp | 0.01 | 0.27 | 0.30 | 0.04 | 0.24 | 0.15 | 0.58 | 1.00 | ||

qual_libr | 0.06 | 0.24 | 0.27 | 0.13 | 0.13 | 0.18 | 0.58 | 0.60 | 1.00 | |

Age | -0.14 | 0.25 | 0.28 | 0.18 | 0.23 | 0.24 | 0.00 | 0.14 | 0.07 | 1.00 |

The results of the first stage of the models (2) through (4), which contains all of the variables, are presented in Appendix 1. Importantly, some of the IVs are significant and exhibit the expected sign, configuring instruments that present a significant (conditional) correlation with the endogenous variable.

Tuition, Enade scores, and selectivity are all endogenous variables, and they represent the market equilibrium of the HEI. Some difficulties arise with this fact. First, at equilibrium, these variables are positively correlated: better HEIs charge a higher tuition, are more selective, and attract better students, implying a positive correlation between these three variables (see Table 5). Secondly, as discussed, the instruments used in the identification of the model are made up of the exogenous characteristics of the HEIs that determine the market equilibrium and, therefore, are the same for these three variables. In contrast, BLP uses the group of instruments to identify only one endogenous variable, instead of three in this case.

All of these factors complicate the identification of the effect of these three variables, as can be observed in model (2) of Table 4. This specification includes all of the explanatory variables, including tuition, Enade scores, and selectivity. None of these is significant in this specification. The positive correlation between them complicates the correct identification of the parameters. To avoid this problem, we estimate the model with only Enade (models (3) and (5)) or selectivity (model 4) as the explanatory variable, apart from tuition.

The only difference between models (3) and (5) is the fact that some control variables (full-time, qual_instal and qual_comp) are excluded in the last model. The results of models (3) and (5), which exclude selectivity, are similar to each other. The coefficients of the price variable are approximately -0.02, and those of the Enade score variable are approximately 0.74. The percentage of lecturers with doctorate degrees is also statistically significant, with a coefficient close to 13. The coefficients of the other variables are also robust compared to the different specifications. The results in these models suggest the importance of the price variable for student choice.

In the case of the Enade score variable, the positive, robust, and significant effect shows that the students take into account the quality of the student body when they choose where to study. The primary justification for this fact is that employers on the job market do not perfectly observe the quality of the student or the recent graduate. The reputation of the student’s school provides a sign about his or her quality. In equilibrium, HEIs with more qualified students would have a better reputation and would signal a higher quality to the market. Thus, the candidates would ultimately prefer an HEI with a better student body^{(}^{10}^{)}. Another explanation for the importance of the quality of the student body on the choice of the applicant has to do with what the literature calls the peer effect. This effect consists of the positive externality that qualified colleagues have on the learning process. In other words, studying and living with intelligent and studious individuals contributes to the student’s ability to learn. For this reason, the quality of the students in the HEI affects the decision of the applicants^{(}^{11}^{)}. With the available data, it is not possible to define which of the alternatives better explains the decision to take the entrance exam; we limit ourselves to the conclusion that students have a preference for better peers.

In model (4), in comparison with model (2), we exclude the variable Enade. The variable “selectivity” is not statistically different from zero. As we mentioned before, this variable captures two effects. On the one hand, a higher selectivity implies less likelihood that the student will be accepted by the HEI and a negative sign is expected. On the other hand, this variable is a proxy for the quality of the student body, and a positive sign is expected. The empirical result suggests that the net effect is zero.

In Table 4, we still observe that the percentage of full-time lecturers shows is not significant in all models, similar to the coefficients for computer access and infrastructure quality. Business students might prefer to take classes with lecturers who are professionals in the market, and therefore part-time at the HEI, rather than with lecturers with a full time academic profession. This may explain the non-significance of the percentage of full-time lecturers in the students’ choice.

The percentage of lecturers with doctorates, in contrast, seems to be a relevant variable to the student decision-making process. This variable has a positive value and is statistically significant in all of the estimate specifications via IVs that do not include selectivity. Taken together, the results obtained by the characteristics of the faculty – the percentage of lecturers with doctorates and the percentage of full-time lecturers – indicates that students take into account faculty quality, but that lecturers do not need to be academics in the traditional sense, i.e., dedicated solely to research and teaching.

The quality variables of the HEI are not significant. A possible cause for this is the high correlation that exists between them, close to 0.6 (Table 5). For this reason, we remove infrastructure quality and computer access from the specification (5) of the model, but the results do not change substantially. The quality of the library coefficient continues to be non-significant in this specification.

Aside from the variables mentioned, we include controls for characteristics of the counties: GDP *per capita* and a dummy for the city of São Paulo. We believe that the São Paulo dummy makes the value of the price coefficient more accurate. Without this differentiation, the regression might overestimate the impact of price because the correlation between lower tuition and greater participation in the market might be partially explained not by a causal relationship but by the fact that these characteristics are typical in the markets of smaller cities. Yet, the programs in the city of San Paulo, a city with a higher cost of living, tend to have smaller market shares, since the market-share denominator is the number of potential applicants, which is enormous for the São Paulo’s market. Therefore, the higher prices of the São Paulo programs and their smaller market share might intensify the impact of prices on the market-share, if the regression were not to include a dummy for the city of São Paulo. The interpretation seems clear: the programs in the city of São Paulo tend to present a market share smaller than the others and are, on average, more expensive (R$ 663,9 or US$ 417 in the capital *versus*R$ 460,3 or US$ 289 in the other cities). Therefore, if we had not controlled for location (capital *versus* countryside), we would have created an overestimation of the importance of the price in the determination of the market share.

5.2. Estimation of the “investment” in excess demand

According to the results presented in the prior section, one can estimate the total volume of revenue that a specific HEI gives up by maintaining a lower tuition in order to generate excess demand and, therefore, selectivity of the applicants for the business program. The procedure is simple. Using the price coefficient estimated in the previous section, one can calculate the necessary price increase that would reduce the HEI market share in order to eliminate the excess demand. In other words, the price increase that would make the number of applicants equal to the number of offered slots. The amount of revenues that the HEI gives up is equal to the difference between the price that would eliminate the excess demand and the actual price charged multiplied by the number of slots available.

Before presenting the results, a methodological procedure deserves mention. This estimation should be made only for the HEI that has a number of offered spaces lower than the number of applicants, which is a condition necessary but not sufficient for the characterization of excess demand. Furthermore, the applicants should fill all of the spaces because some institutions present a number of applicants greater than the number of slots but without all the slots being filled, which does not allow us to identify excess demand. Therefore, it is important that there are no unfilled slots. However, in some cases, the HEIs present an applicant/vacancy ratio much greater than one, but only one or two spaces are not filled. Clearly, in this case, the unfilled space is not a consequence of demand scarcity for the program but simply an operational question or a registration cancellation. For this reason, we considered programs with a number of applicants greater than the total number of vacancies and with at least 98% of the slots occupied.

Figure 4 present the amount of revenues that the HEIs give up in order to operate with excess demand. The calculation is done using the price coefficient estimated in model 3. This is the model chosen because the variables “Enade” and “Price” have significant coefficients and all control variables are present. The values correspond to the annual revenue that the HEI gives up in the year 2006 with regard to the first-year class.

There are 39 HEIs with excess demand, and the value of the “lost” revenue is presented for each HEI in a growth curve. In model 3, 39 HEIs in the state of Sao Paulo gives up, in the short term, a total of R$ 5.499 million (or US$ 3,458 million) per year by “investing” in the selectivity of their students. Considering the 39 HEIs with excess demand, this amount corresponds to 7.6% of the total revenue coming from a freshman class.

6. CONCLUSION

This article analyzes the private higher education sector and attempts to explain and quantify some particularities of this sector, such as the strategy of some institutions to maintain permanent excess demand and the strong segmentation that exists in this market. To achieve this objective, various peculiarities in this sector had to be taken into account in the analysis, requiring specific theoretical and empirical treatment, which we explain throughout the paper.

On the empirical part, there are two aspects that make the analysis more complex. First, the HEI’s market is a *matching* market, which consists of students choosing the HEI as well as the HEI selecting the students. To avoid this problem, we changed the student’s question from “at which HEI to study” to “at which HEI to apply.” Instead of using the number of registered students as a measure of demand, we use the number of applicants in the selection process. This avoids the problem of the **matching** market because the application precedes the HEI’s selection process.

The second difficulty results from the fact that some variables that determine the decision of the student are endogenous, such as tuition, quality of the student body and the HEI’s selectivity. These variables are determined by the market equilibrium, so that there is no causal relationship between them and the firm’s market share. We use the solution proposed by BLP, using the characteristics of the competitors, in addition to the age of the HEI itself, as instruments for the endogenous variables of the model.

Using data from all business-administration programs in the state of São Paulo, the study shows that the most relevant factors for student choice are the tuition charged by the institution and the quality of the lecturers and students. The other characteristics, such as the quality of the infrastructure or computer access, are shown to be insignificant. In a general way, we found evidence that the tuition and quality of both lecturers and the student body define an institution and its position in the market.

Besides estimating the importance of some HEI characteristics for students’ choices, this paper estimates the indirect HEI’s investment on student quality. As already mentioned, the empirical strategy is to measure the revenue amount that HEIs give up to be able to select the best students. As far as we know, estimating the investment on student quality – which means higher peer effect and better graduates – by using the methodology proposed here, is quite new.

The results show that, among the small group of 39 HEIs with positive investment, the total amount is significant only for very few of them. Instead of dividing the business courses into two groups – with positive and zero investment on student selection – the results suggest the existence of three groups: (1) HEIs with no investment; (2) HEIs with very small investment; and (3) HEIs with significant investment. It is hard to think of HEIs of the second group as institutions really willing to invest on student quality; rather the excess demand seems to be occasional. Therefore, of the total of 298 courses, only three or four institutions – depending on the criterion chosen – invest on the quality of their students.

It is worth examining the possible strategies for those courses of the first and second groups that do not invest on selection. One strategy is to reduce costs as much as possible so that they can attract students by reducing prices. An alternative strategy would be to invest on both physical resources (modern labs and equipments) and hiring good lecturers. However, in this market, as mentioned, the demanders (students) can be understood as input and complementary to physical resources and lecturers. As HEIs of the first and second groups do not invest on student quality, one should expect that the return of their investment on any other input will be lower than the return of the investment made by a selective HEI.

This scenario suggests that the market of business courses in Brazil is, in fact, composed by only two types of HEIs: those that invest zero or little on selection – more than 95% – and compete by reducing costs and prices, with little attention on quality; and those – three or four institutions – that invest on quality and reputation.

Surely, the present study does not attempt to exhaust the subject; rather, the idea is to open topics for further research that may answer important questions that were not central to the objective of this article. The demand estimated in the first section, using cross-sectional data, with an observation on each institution, corresponds to what we consider throughout the article to be short-term demand. A new investigation that estimated the size of external diffusion (network externality) in the higher-education sector would be extremely valuable. Additionally, alternative solutions from the point of view of econometric methodology might also be tested.