A nested logit model of the choice of a graduate business school

Economics of Education Review 21 (2002) 471–480 www.elsevier.com/locate/econedurev

A nested logit model of the choice of a graduate business school Mark Montgomery

*

Department of Economics, Grinnell College, Grinnell, IA 50112, USA Received 10 December 1998; accepted 27 June 2000

Abstract Less than a handful of papers have used data on individuals to examine people’s decisions about which school to attend. This paper develops a nested logit model of the determinants of choice of a graduate business school. Data are drawn from a new longitudinal survey of registrants for the Graduate Management Admission Test. One finding is that elasticity of school choice with respect to tuition is fairly low, about 0.08. Another is that, even after controlling for the effects of Affirmative Action in admissions, blacks and Hispanics are substantially more attracted to top-tier institutions, while women are less attracted to them.  2002 Elsevier Science Ltd. All rights reserved. JEL classification: I21; J24 Keywords: School choice; Demand for schooling

1. Introduction The economic literature contains many articles on people’s decisions whether to go to college, but only a few on their decisions about which college to go to. This paper extends the literature on school choice in several ways. First, unlike previous studies, all of which focused on undergraduate education, this study examines the choice of a graduate management program. Second, it models the decisions whether to attend school simultaneously with the decision which school to attend, using a nested logit. Finally, this study has a richer source of data on both applicants and schools than was available to previous work. It employs a recent survey of registrants for the Graduate Management Admission Test (GMAT), sponsored by the Graduate Management Admissions Council. The GMAT survey is supplemented by published data on business schools.

* Tel.: +1-641-269-3146; fax: +1-641-269-4985. E-mail address: [email protected] Montgomery).

(M.

Our analysis yields several interesting results. For example, elasticity of business school choice with respect to tuition is surprisingly low, about 0.08. Also, even after controlling for the effect of race on admissions, blacks and Hispanics appear substantially more likely to choose a top-tier institution than whites. Women appear less likely to choose one than men.

2. The literature on school choice Most studies of school choice have relied upon institutional-level data rather than data on individual choices. A recent paper by Bezmen and Depken (1998), for example, examined how application rates at 772 US colleges responded to school characteristics like cost, size, and state unemployment rates. Several other studies have looked at enrollment or application rates for a single institution: Wetzel, O’Toole and Peterson (1998), Erhenberg and Sherman (1984), Moore, Studenmund and Slobko (1991). In comparison, less than a handful of studies have used data on individuals to model how one school is

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M. Montgomery / Economics of Education Review 21 (2002) 471–480

chosen from among a discrete set of alternative institutions. Kohn, Manski and Mundel (1976) (KMM) were the first to apply the methodology of discrete choice to this question. KMM used the SCOPE1 survey to develop a conditional logit model of the choice of a college. They found that tuition, room and board costs, and distance from home all negatively influenced the likelihood of choosing a particular school. The quality of the school increased the likelihood it would be chosen. Manski and Wise (1983) extended the KMM analysis to a multinomial logit model of choice among a set of school and non-school alternatives. They found tuition and scholarship aid to be significant determinants of whether to attend school and which one to choose. The Manski and Wise model, however, had a very restricted choice set. No information was included about schools to which the sample member had not applied or not been admitted. Oosterbeek, Groot and Hartog (1992) were able to develop a multinomial logit model using a full choice set of schools; they used data on economists in the Netherlands, which happens to have only five economics departments. Unfortunately, the only school characteristic they could include was predicted earnings for graduates at each school. This paper extends the literature on school choice by developing a nested logit model of the selection of a graduate business school. In this model the school-choice decision is one “nest” in a joint decision about whether (and how) to attend school (part-time or full-time), and which school to attend. The parameters of the separate decision functions are estimated jointly by full-information maximum likelihood (FIML).

3. The model Our econometric approach assumes that a prospective MBA student chooses a graduate business program with a two-stage process. First she decides whether to go fulltime, to go part-time, or not to go at all. If she decides to go full-time she chooses among one set of available institutions, if part-time she chooses from a (potentially) different set. A simple schematic is presented in Fig. 1. We treat part-time and full-time attendance as separate regimes because for graduate business students they are quite distinct. Part-time MBA students usually attend at night while working at a day job. Clearly the school choices of part-timers with well-established jobs are more constrained by geography than those of full-timers. Moreover, many MBA programs only offer night courses. Thus we assume an individual’s choice set for

Fig. 1.

Structure of the decision model.

a part-time program differs from that for a full-timer program. In a nested logit framework the two school-choice models (part-time and full-time) form one nest, the attendance model the other. Though estimated simultaneously, the structures of the nests are quite different and are therefore discussed separately. 3.1. The school choice model The school choice is represented by a random utility model (RUM) estimated by the conditional logit technique introduced by McFadden (1973). The RUM approach assumes that a person selects one option (in this case a business school) from among all of the options in a so-called choice set. The choice set may be specific to the individual: for example, only those schools that would admit that particular student. We assume the individual chooses the option that yields the highest utility. Formally, the model assumes that if individual i decides to go to school, say, full-time, then he or she chooses among J alternative schools in the full-time choice set. The utility of individual i of attending school j full-time can be expressed as: FT FT UFT i (School j)⫽b Zij ⫹eij , j⫽1,…, J

(1)

where Z is a vector of characteristics of the school. If we observe that individual i chooses school k we infer FT that UFT i (school k)⬎Ui (school j)∀j⫽k. The individualFT FT specific error terms (eFT i1 , ei2 ,…, eiK ), are assumed to be random, independently-distributed variables with an extreme value distribution (the Gumbel distribution). McFadden (1973) shows that under these conditions the probability that individual i chooses school j is given by: FT

eb 1

School to College: Opportunities for Post-Secondary Education, The Center for Research and Development in Higher Education, University of California, Berkeley (1966).

Prob(i chooses full-time school j)⫽

冘

Zij

.

J

e

j⫽1

bFTZij

(2)


This is the well known conditional logit model. Estimating Eq. (2) produces a single vector of parameters, bFT, that shows the effect of school characteristics Z on the probability that this student, having already decided to go full-time, will choose school j. Naturally, there is a similar equation for part-time schools. Note that demographic variables like race or sex are not included in the school-choice nest, because any variable that does not vary across schools drops out of the model — it can be factored out of both the top and bottom of Eq. (2). 3.1.1. Defining the choice set: people choosing schools versus schools choosing people The conditional logit estimates the coefficients of the RUM by comparing characteristics of the chosen option with those of the rejected options. If a certain school characteristic is systematically more prevalent in the chosen school than in the rejected ones, it is judged to positively affect the choice of a school. Important to this process, naturally, is identification of the truly rejected alternatives. A students who did not “choose” Stanford has not necessarily rejected it — more likely the reverse. To identify a person choice set, therefore, we need to identify schools an applicant could have attended, but did not. We could never observe someone’s choice set directly — she would have to apply to every single school. Therefore, we simulate the choice set imitating an approach taken by Kohn et al. (1976) (KMM). The KMM technique runs a mock admission test for each sample member at each school to decide whether that school is added to the person’s choice set. First, we estimated a probit model to predict the probability that an applicant with a given set of credentials would be admitted to a school with a given set of attributes2. This model was estimated using the outcome of sample members’ applications to their first choice school, as reported in Wave 2. We then calculated the probability of admission for each sample member at each MBA program. Next, these predicted probabilities were compared to a random number on the unit interval to see if a particular person was “admitted” to a particular school3. For example, suppose that, given her credentials, student i had a predicted 0.65 probability of admission to Wharton. A random number between 0 and 1 is drawn. If that number exceeds 0.65, Wharton is added to her choice set, if not

it is excluded. This procedure is carried out for all 573 MBA programs she could attend in the USA4. In this way a choice set was assembled for each individual in the sample. While this approach introduces some randomness into the choice sets, our RUM coefficients proved to be entirely robust across iterations of this procedure. 3.2. The attendance model The other nest in the nested logit is the model of the decision whether to go full-time, part-time, or not at all. In this case we assume that the utility levels associated with going full-time and part-time, respectively are: Ui(going full-time)⫽gFTXi⫹mFT i Ui(going part-time)⫽gPTXi⫹mPT i . We let the null choice in the logit be “not go at all.” In the attendance-decision model the vector X contains characteristics of the individual. With not-going as the null choice, the probability of attending full-time is: eg Prob(i goes full-time)⫽

Due to space constraints the coefficients of the admission model are not reported here. They are available from the author at http://www.grinnell.edu/individuals/montgome/working papers.htm. 3 Note that it is here that the model handles issues like Affirmative Action. Because race affects the probability of admission, a black student will be selecting a school from a different choice set than a white student with identical credentials.

FT

Xi

gFTXi

+eg

(1+e

PT

Xi

)

.

(3)

and correspondingly for going part-time. This is the standard multinomial logit equation. 3.3. Combining the school choice and attendance decisions To estimate the school-choice and attendance models jointly the nested logit combines (2) and (3) in the following way. The unconditional probability that individual i will choose to attend school j full-time is: Prob(i chooses j full⫺time) ⫽Prob(i chooses j|i goes full⫺time)∗Prob(i goes full ⫺time) or, using Eqs. (2) and (3) Prob(i chooses j full⫺time)

冤冘冥冋 FT

⫽ 2

473

eb

Zij

J

FT

eb

Zij

e(g (1+e(⌽

FT

(4)

FT

Xi+sFTIFT i )

Xi+sFTIFT i )

PT

+e(g

Xi+sFTIFT i )

)

册

.

j⫽1

4 There were 573 schools that had actual business programs and the requisite information listed in Barron’s. A small fraction of our GMAT takers were applying to non-business programs that required the test. We treated these people as not having attended a true business school.

474


This is just the multiple of Eqs. (2) and (3), except for the appearance of the parameter sFT and the variable IFT [see Greene (1995), pp. 512–524]. This new variable is called the inclusive value and is defined as:

冉冘冊 J

IFT i ⫽log

FT

eb

Zij

(5)

j⫽1

[Note that IFT is just the denominator of Eq. (2).] The inclusive value represents the utility associated with having available all of the schools in the full-time choice set. If the coefficient of the inclusive value, sFT is zero, then Eq. (4) reduces to the unconditional probability of choosing school j times the probability of going fulltime. In other words, if sFT equals zero there is no nesting of the decisions. In this case the choice of whether or not to go full-time is independent of the utility value of the options in the full-time choice set, and there is nothing gained by estimating the decisions jointly. Thus the coefficient sFT provides a convenient statistical test of whether the two decisions should be nested. Having specified the probabilities of the observed choices from (4), and from the corresponding equation for attending part-time, we can construct a likelihood function in the usual way. Parameters bFT, bPT, gFT, gPT, sFT, and sPT are then estimated by full information maximum likelihood. 3.4. Simplifying the model to make estimation feasible The likelihood function described above can become extremely cumbersome. First, each school characteristic added to the choice model requires two additional parameters: one for full-time; one for part-time. The same is true of personal attributes in the attendance nest. Second, the school-choice nest includes one observation per person for each school in either choice set. So if we had, for example, a thousand sample members choosing among six full-time schools and six part-time schools, the model would include 12 000 observations. Since our actual choice sets typically include nearly 600 MBA programs, the number of potential observations is astronomically large. To simplify the estimation, therefore, we eliminated the part-time school choice model. It can be argued that the part-time model is inherently less interesting because the school choice of part-time MBA students is generally quite constrained by geography — they usually have full-time day jobs. Students attending full-time have more flexibility and can presumably be choosier among school attributes. Thus we sacrificed the part-time school-choice model in the interest of tractability. We do not, however, eliminate the part-time option from the attendance model. In other words, the first step in the decision model is (still) whether to go full-time, parttime, or not-at-all as in Fig. 1. But the second step

includes only estimation of the full-time school-choice, using only those people who went full-time. 3.4.1. Obtaining a manageable number of alternative schools Even after eliminated the selection of a part-time school, there remains a prohibitive number of school choices: several hundred for each sample member. Fortunately, McFadden (1973) shows that one can obtain consistent estimates of the coefficients of a conditional logit model using a randomly drawn subsample of the full set of alternatives. In this approach the choice set includes the selected option plus a (manageable) number of others drawn at random from the rejected alternatives. We implemented this approach by drawing 14 schools at random from the rejected alternatives in the each person’s complete choice set, that is, the set of schools to which she was admitted by the mock test described above. The decision to use 15 schools (the chosen one plus 14 others) was somewhat arbitrary, but alternative models with 30 schools gave very similar estimates.

4. The data This study uses the GMAT Registrant Survey, produced by the Graduate Management Admission Council (GMAC). The Battelle Center for Public Health Research and Evaluation, in Seattle, Washington, designed the survey instruments and collected the data. The survey contacted 7400 individuals who registered to take the GMAT on test dates between June 1990 and March 1991. Of those registrants, 5602 actually took the test. The registrants were surveyed in three waves between 1991 and 1994. This study relies on the 4333 registrants who were US citizens and who completed all three waves of the survey5. Data from the survey questionnaire were supplemented with information from the GMAC’s own registration and test records, and some published sources as described below. 4.1. Data for the school-choice nest As explained in the previous section, the school choice model includes characteristics of the MBA programs; personal attributes like race and sex drop out because they do not vary among the alternatives in the choice set. The school characteristics in the school choice model include the following:

5 Since we only have GMAT registrants, this study risks some selection bias in the attendance model: we exclude people who never contemplated graduate management school. However, we expect that this will have little effect on the schoolchoice model, which is the main focus of the paper.


앫 cost: tuition, percentage of students on financial aid, whether loans are available; 앫 school quality: average GMAT at the school, average undergraduate GPA, whether the school is top ranked by US News and World Report (1994), whether it is accredited, the number of fields of specialization offered, whether it is public or private; 앫 convenience of attending: whether it is in the same region as the student’s home residence, whether there are day classes; and 앫 returns to attending: average starting salary of recent graduates6. The school characteristics were taken from Barron’s Guide to Graduate Business Schools (Miller, 1994), except for average starting salaries, which came from Peterson’s MBA Programs (Peterson, 2000). Descriptive statistics for these variables are reported in Table 1. Note that the statistics in the table are not simple averages for all schools in the country, but are weighted by the frequency of being attended full-time by sample members. Table 1 Variables in the school-choice equation: characteristics of the school actually attended by sample members who attended full-time School characteristic

Mean

Tuition to get a degree full-time 12.62 ($000)a % of students who receive financial 28.02 aid Loans available from the school 0.81 (dummy) Average GMAT score at school 450 Average undergrad GPA at school 3.11 Average starting salary of grads 45.50 ($000) Used predicted starting salary 0.58 (dummy) Total enrollment in MBA program 874 School is public (dummy) 0.60 Offers day classes (dummy) 0.83 Ranked in top 20 by US News 0.24 (dummy) Accredited by AACSB (dummy) 0.79 In same region as residence (dummy) 0.67 No. of fields of specialization offered 6.02 Sample size (No. of full-time 723

Standard deviation

475

About 30% of the schools in Barron’s failed to report a GMAT score. To these schools we assigned the average GMAT of those in the same selectivity class using a variable created by Battelle from GMAC records7. The absence of these GMAT scores is less daunting than it appears; the great majority of non-reporting schools were small, regional institutions that almost certainly had average scores near the bottom of the distribution. Similarly, average starting salary of recent graduates was published by only 271 schools, about 40% of the total. Almost all of the large well-known schools reported, smaller and less conspicuous institutions tended not to. To predict values for non-reporting schools we used a selection-corrected regression of average starting salary on other school characteristics. (These results are available from the author.) Since this regression included all of the variables in the RUM, identification of the salary effect in the school-choice model hinged upon the 40% of the schools for which actual values were reported 8. Our measure of tuition also bears discussing. This variable is the cost of tuition to obtain a degree full-time from the relevant institution, assuming the student takes the minimum number of credits. To distinguish between in-state and out-of-state tuition we had to infer state of residence based on: (1) reported address over the three waves of the survey; and on (2) the undergraduate school attended. For about 15% of the sample, no state of residence could be established. These people were assigned out-of-state tuition at every school.

10.46

4.2. Data for the attendance nest 31.04 0.40 170 0.18 11.20 0.49 776 0.49 0.37 0.43 0.40 0.47 3.16

a This variables takes account of whether the student pays in-state or out-of-state tuition.

6 These were available from Peterson’s (2000), which reported salaries for the year 1997. We deflated them back to 1992 dollars.

Table 2 gives definitions and descriptive statistics for variables in the attendance model. These variables are characteristics of the individuals, not schools — school attributes affect the attendance decision through the inclusive value, as described in Section 3. The attendance model includes the standard set of demographic characteristics: age; race; sex; marital status; number of

7 The Battelle selectivity variable estimated a minimum acceptable, or “cutoff” GMAT score. All GMAT scores sent to each school (available from GMAC records) were listed from highest to lowest. A cutoff score was then estimated from the number of students accepted. For example, if a school accepted 50 students, the 50th highest score was taken as the cutoff. For each school, the cutoff score was collected for the years 1987– 1993 and then averaged. Six categories of cutoff were constructed: below 500; 500–599; 600–650; etc. Data for the number of students accepted into the program were taken from Miller (1994). 8 Due to space constraints the coefficients of the model to predict salary are not reported here. They are available from the author at http://www.grinnell.edu/individuals/montgome/ working papers.htm.

476


Table 2 Variables in the attendance equation (all sample members) Personal characteristic

Mean

Age at wave 1 27.03 Female (dummy) 0.44 Black (dummy) 0.13 Hispanic (dummy) 0.16 Asian (dummy) 0.14 No. of kids under 18 in wave 1 0.36 Married in wave 1 (dummy) 0.33 Employed in wave 1 (dummy) 0.61 488 Total score on GMAT a Undergraduate GPA 3.01 37 Undergraduate qualityb ⱖ6 years. Work experience in wave 0.23 1 Attended B-school part-time 0.27 Attended B-school full-time 0.18 Expected parents’ help (wave 1) 0.09 Expected employer’s help (wave 1) 0.30 Sample size 4061

Standard deviation 6.32 0.50 0.34 0.37 0.34 0.77 0.47 0.49 96 0.43 31 0.42 0.44 0.38 0.29 0.46

a This is the combined verbal and quantitative score; it ranges from 200 to 800. b This is the proportion of GMAT registrants who attended an undergraduate school ranked by Barron’s Guide as less selective than that attended by the sample member. Thus the mean score of 37 implies that for the average sample member, only 37% of others went to a college ranked less selective than their own.

children; and a measure of work experience. The list also includes several measures of academic ability or performance: GMAT score; college GPA; and the quality of the undergraduate school attended. This latter measure is the percentage of GMAT registrants who attended a college or university that was ranked by Barron’s as less selective than that of the respondent. The values range from 0% (no one graduated from a less selective college) to 95% (almost everyone graduated from a less selective college).

5. Results Table 3 presents the results of the school-choice nest, Table 5 gives (selected) results for the attendance decision. While the signs and significance of the RUM coefficients in the school choice logit model have standard interpretation, the magnitudes of the coefficients do not. To help interpret the results, therefore, Table 4 reports elasticities of the probability of choosing school

j with respect to three variables of interest: tuition cost; reputation; and average starting salary of graduates9. First we consider the models of school choice. For comparative purposes Table 3 has two alternative measures of the chosen school: (1) the school actually attended, as observed in Wave 3 of the survey; and (2) the “first choice” school as reported in Wave 1. For School Attended there is a model that includes starting salary and other school quality variables, one that omits starting salary, and another that omits the quality variables. For First Choice School we have one model with, and one without, the salary variable. Most of the variables in the school choice RUMs have the expected sign and are statistically significant. As expected, higher tuition reduces the probability of choosing a given school, though the magnitude of the effect is fairly small. According to the elasticity in Table 4, for the School Attended model, doubling a school’s tuition only reduces the probability it will be chosen by about 7%10. For the First Choice model the effect is somewhat larger: doubling tuition reduces the probability by about 15%. Other aspects of cost, the fraction of students who get financial aid and the availability of loans, are highly significant only in the First Choice models, but quite insignificant in the School Attended models. This could imply that in the early stages of choosing a business school students anticipate more aid than they eventually get. Three variables in Table 4 represent measures of school quality or prestige: (1) whether the school receives a top ranking from US News and World Report; (2) the average GMAT of the student body; and (3) the average undergraduate GPA of the student body. All three have positive and highly significant effects (except GMAT in the First Choice models). According to Table 4, being one of the top 20 schools, all else constant, makes a student about 25% more likely to select a given school as her first choice, about 5% more likely to attend that school. One variable in Table 3 that does not perform as expected is the average starting salary of school graduates. Only in the School Attended model, and when other quality variables are omitted, does starting salary have the expected positive and significant effect. This almost certainly reflects the correlation between this variable and other school attributes, especially when the value is predicted. Note that schools that failed to report an aver-

9 The elasticities are measured at the sample means of all of the independent variables. 10 This is the effect conditional upon attending some school full-time. It does not include the effect of full-time tuition on the probability of choosing an alternative besides full-time schooling.

Same region as student School avg. GMAT School avg. GPA Tuition ($000) Fraction rec. Financial aid Loans available Total enrollment No. of specialties offered Day classes offered Public institution Us news tier 1 Accredited by AACBS Avg. starting salary Starting sal. is predicted Sample c2 3958 4017.9

3.23 0.02 0.70 ⫺0.03 ⫺0.00 0.06 0.07 0.06 0.68 0.21 1.51 0.35

25.58 9.55 2.32 ⫺3.19 ⫺0.06 0.46 8.28 3.39 4.97 1.69 7.75 2.42

3.22 0.02 0.71 ⫺0.03 ⫺0.00 0.04 0.07 0.06 0.61 0.19 1.62 0.31 ⫺0.00 ⫺0.42 3958 4029.3

25.63 8.28 2.29 ⫺3.02 ⫺0.40 0.28 7.74 3.20 4.32 1.46 7.68 2.12 ⫺0.46 ⫺3.25

T-statistic

T-statistic 19.61 ⫺1.32 1.90 5.20 7.64

11.42 ⫺6.11

3.28 ⫺0.01 0.35 0.61 0.06

0.05 ⫺0.95 3958 3701.7

Coefficient

2896 1625.2

0.04 ⫺0.08 0.53 ⫺0.02 0.70 0.47 ⫺0.01 ⫺0.02 0.03 0.21 1.73 ⫺0.17

Coefficient 0.37 ⫺0.83 2.62 ⫺3.55 5.92 6.79 ⫺1.56 ⫺1.33 0.51 2.96 9.15 ⫺2.05

T-statistic

Coefficient

Coefficient

T-statistic

Salary excluded

Salary included

Salary excluded

Salary only

First choice school

School attended

Table 3 Random utility models of choice of a graduate business school: School choice nest of the nested logit

0.05 0.10 0.66 ⫺0.02 0.62 0.46 ⫺0.00 ⫺0.02 0.07 0.14 2.17 ⫺0.15 ⫺0.02 ⫺0.01 2896 1649.9

Coefficient

0.53 1.08 4.06 ⫺2.62 5.20 6.67 ⫺0.12 ⫺1.42 1.04 1.88 9.96 ⫺1.81 ⫺5.11 ⫺0.10

T-statistic

Salary included

M. Montgomery / Economics of Education Review 21 (2002) 471–480 477

478


Table 4 Elasticities of probability of choosing a given school with respect to selected school characteristics Tuitiona

Full sample Men Women Black and Hispanic a b ∗ ∗∗

Starting salaryb

US News top 20a

School attended

First choice school

School attended

First choice school

School attended

First choice school

⫺0.07∗∗(3958) ⫺0.08∗∗(2203) ⫺0.08∗(1755) ⫺0.07(517)

⫺0.15∗∗(2896) ⫺0.20∗(1643) ⫺0.07(1253) 0.39(363)

1.05∗∗(3958) 1.07∗∗(2203) 1.02∗∗(1755) 1.44∗∗(517)

⫺0.07(2896) ⫺0.20(1643) 0.67∗(1253) 0.81∗∗(363)

0.05∗∗(3958) 0.10∗∗(2203) 0.05∗∗(1755) 0.25∗(517)

0.25∗∗(2896) ⫺0.20∗(1643) 0.27∗(1253) 0.35∗(363)

Using models that included all variables. Using models that omitted all quality variables except salary. The coefficient was significant at the 0.1 level. The coefficient was significant at the 0.01 level.

age starting salary were quite significantly less attractive in the School Attended models. Finally, location shows a very large impact on school choice. The coefficient on the dummy for being in the region in which the student resides is both extremely large and highly significant11. All else held constant, a student is 98% less likely to attend a given school if it is outside her region. She is 65% less likely to consider such a school her first choice.

It must be noted, however, that these estimates are based on models that exclude all school-quality variables except salary. In effect, the salary variable is serving as a proxy for all other aspects of school quality. These elasticities should be accepted cautiously, especially since a large fraction of the salary values had to be predicted.

5.2. Results for the attendance nest 5.1. School choice by race and sex The second, third and fourth rows of Table 4 report elasticity estimates for men, for women, and for blacks and Hispanics, respectively, for the three selected school characteristics. These elasticities were estimated by running separate models for the relevant demographic subset of the sample (not reported here). The elasticity of probability with respect to tuition appears fairly stable across the three groups, at least for the School Attended models. The results for prestige show more variation. The elasticity of probability of choosing a given school with respect to its being top tier is twice as large for men as for women, and more than twice as large for minorities as for all men. (Recall that this is after the choice sets are screened by an admission equation that reflects any racial preference in admissions.) Apparently blacks and Hispanics place a higher emphasis on the prestige of the institution than do whites. Possibly minorities see a degree from a top-ranked school as a means of mitigating traditional prejudice against them. On the other hand, the table shows that women are significantly less responsive to a school’s reputation than men. The elasticity of probability of choosing a school with respect to average starting salary of its graduates appears to be about unit elastic across all demographic groups. 11

For this purpose we divided the USA into 13 regions.

Space constraints prevent a detailed discussion of the attendance results, which are not the primary focus of the paper. Note, however, that in Table 5 the School Attended models contain three attendance options: went full-time; went part-time; did not go (the null choice). The First Choice model has only two alternatives: intended to go full-time, intended to go part-time (the null choice). This is because the first choice school was identified in Wave 2. In Wave 2 many students who would ultimately not to go to business school had yet to make that decision. Several results in Table 5 are worth noting briefly. First, the coefficients on the inclusive values are highly significant, which suggests the appropriateness of nesting the attendance and school choice models. Also, note that young children make it significantly more difficult to attend business school full-time. Blacks and Hispanics are more likely to go full-time (by about 0.05) and less likely to go part-time (by about 0.10) than whites. This may reflect lower opportunity cost for minorities through lower earnings or lower probability of employment. Not surprisingly, a high GMAT score significantly increases the probability of pursuing a degree. Also, as expected, people who had jobs in Wave 1 were more likely to go part-time and less likely to go full-time.


479

Table 5 Attendance nest: multinomial logit models of the attendance decision (for models 2 and 4, respectively, in Table 3)

Attendance options Independent variable Inclusive value Age Female Black or Hispanic Asian Married in wave 1 No. of kids Employed in wave 1 Work experience ⬎6 years GMAT score Undergraduate quality Expected parent’s help Expected employer’s help Sample c2

Full-time Part–time Full-time Part-time Full-time Part-time Full-time Part-time Full-time Part-time Full-time Part-time Full-time Part-time Full-time Part-time Full-time Part-time Full-time Part-time Full-time Part-time Full-time Part-time

School attended

First choice school

Went full-time, went part-time, or did not go

Intended to go full-time or to go parttime

Coefficient

T-statistic

Coefficient

0.56 ⫺0.01 0.01 ⫺0.16 0.02 ⫺0.13 ⫺0.22 0.19 ⫺0.42 0.13 0.19 ⫺0.24 ⫺0.01 ⫺0.26 0.51 ⫺0.52 0.03 0.47 0.29 ⫺0.0023 ⫺0.0030 0.79 0.04 ⫺1.27 0.69 3958 3990.0

12.10 ⫺0.71 0.73 ⫺1.58 0.23 ⫺0.91 ⫺1.86 1.17 ⫺3.28 0.99 2.02 ⫺2.61 ⫺0.18 ⫺2.40 5.49 ⫺2.74 0.23 7.64 6.27 ⫺1.34 ⫺2.18 5.44 0.26 ⫺8.14 8.23

5.3. Comparing these results with previous findings on school choice Our findings on the effect of tuition are consistent with those of earlier discrete choice studies of college selection. Kohn et al. (1976) and Manski and Wise (1983) found significant negative effects. Neither study, however, measured the impact of tuition cost on the probability that a given school would be selected. They measured the effect of tuition in “utility units”. Our results are also consistent with the several studies that used institutional data on undergraduates (Bezmen & Depken, 1998; Wetzel et al., 1998; Erhenberg & Sherman, 1984; Moore et al., 1991). These generally found that the sizes of applicant pools had low tuition elasticities. Our findings on the effect of location on choice of a graduate business school are also consistent with the results of studies of college choice. Kohn et al. (1976), Manski and Wise (1983) and Oosterbeek et al. (1992) all found distance from home to reduce the attractiveness

T-statistic

⫺0.16 ⫺0.03

⫺0.29 ⫺2.25

⫺0.18

⫺1.80

0.57

3.75

0.15

1.06

⫺0.38

⫺3.05

⫺0.21

⫺2.52

⫺1.23

⫺11.88

⫺0.31

⫺1.84

0.35

5.91

0.01

3.72

0.87

4.84

⫺3.02

⫺17.87

2896 1560.0

of an undergraduate institution. Finally, our results regarding the quality or prestige of the business school — average GMAT score, average GPA, being top ranked — are consistent with Kohn et al. (1976) and Manski and Wise (1983), who found that students were attracted to colleges and universities where the average SAT was higher than their own.

6. Conclusions This paper extended the small literature on school choice by examining the factors influencing selection of a graduate business program. The analysis was unique in several ways. This is the first paper, for example, to focus on graduate study instead of college. Also, this is the first to simultaneously estimate the attendance decision and choice of school in a nested logit framework. The highly significant coefficient of the inclusive value in the attendance equations demonstrated the value

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of nesting the two decisions. Finally, a rich new data source allowed us to examine issues that previous studies were unable to look at. For example, we were able to observe the student’s first choice school as well as the school actually attended. Several interesting findings emerged. For example, demand for a given school appears to be fairly inelastic with respect to tuition. Students apparently choose a business school mainly on grounds other than cost. On the other hand, location is a powerful determinant of school choice; even as adults, students are reluctant to go to a school outside their geographic region. Finally, we observed that black and Hispanic students were much more likely to attend a prestigious institution than were other students with similar credentials. This was not merely due to Affirmative Action in admission: minority students had stronger preferences for prestigious schools. This may reflect a perceived need by minorities for a stronger educational signal to overcome statistical discrimination.

Acknowledgements The author thanks Terry Johnson, Mary Kay Dugan and Betsy Paign of Battelle for help in securing the data, Irene Powell for helpful suggestions on an earlier draft, and Wendy Werner and Jason Bent for excellent research assistance. This research was supported in part by a grant from Grinnell College.

References Barron’s Educational Editors (1994). Barron’s profiles of American colleges. Hauppauge: Barron’s Educational Series.

Bezmen, T., & Depken, C. A. (1998). School characteristics and the demand for college. Economics of Education Review, 17 (2), 205–210. Center for Research and Development in Higher Education (1966). School to college: Opportunities for post-secondary education. Berkeley, CA: University of California. Erhenberg, R. G., & Sherman, D. R. (1984). Optimal financial aid policies for a selective university. Journal of Human Resources, 19, 202–230. Greene, W. H. (1995). LIMDEP, Version 7: user’s manual. Bellport, NY: Econometric Software. Kohn, M. G., Manski, C. F., & Mundel, D. S. (1976). An empirical investigation of factors which influence collegegoing behavior. Annals of Economic and Social Measurement, 5 (4), 391–419. Manski, C. F., & Wise, D. (1983). College choice in America. Cambridge, MA: Harvard University Press. McFadden, D. (1973). Conditional logit analysis of qualitative choice behavior. In P. Zaremka, Frontiers in Econometrics. New York: Academic Press. Miller, E. (1994). Barron’s guide to graduate business schools. New York: Barron’s Educational Series. Moore, R. L., Studenmund, A. H., & Sloboko, T. (1991). The effect of the financial aid package on the choice of a selective college. Economics of Education Review, 10, 311–321. Oosterbeek, H., Groot, W., & Hartog, J. (1992). An empirical analysis of university choice and earnings. De Economist, 140 (3), 293–309. Peterson’s MBA Programs 2000 (2000). Peterson’s Guides. US News and World Report (1994). The Best Graduate Schools: Annual Guide 1994, 116(11), 75–81. Wetzel, J., O’Toole, D., & Peterson, S. (1998). An analysis of student enrollment demand. Economics of Education Review, 17 (1), 47–54.