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Description
I. INTRODUCTION
Over the last half century, the U.S. higher educational system has been transformed from a collection of local, independent college fiefdoms into a regionally and nationally integrated market in which universities compete for both resources and students as in Hoxby (1997a). Concurrently, Duffy and Goldberg (1998) contend that the most salient feature of the U.S. higher education market has been tuition increases that exceed both the rate of inflation and income growth combined with financial aid packages that increasingly emphasize merit over need. The rising real cost of college in the midst of growing competition has become a source of considerable angst for parents, university administrators, and public policy analysts who are concerned that need-blind admission goals are being sacrificed in favor of strategic enrollment management policies designed to attract the best and the brightest. Thus, McPherson and Shapiro (1998) have asked if the rapidly rising cost of college begs the question of whether universities compete on price as opposed to some other metric such as reputation or resources. This article is the first to empirically examine price-setting practices among universities by questioning whether list tuitions (i.e., the posted price) or net tuitions (i.e., the posted price minus financial aid) of private universities respond to the geographic and qualitative proximity of competitors.
There are theoretical reasons to expect that the increasing integration of the higher education sector might affect tuitions, particularly for selective private universities that are relatively unfettered by outside pricing constraints as discussed in Bowen (1967). For example, Hoxby (1997b) models integration as the opening of trade among autarkic colleges of varying quality; trade is found to reduce the monopsony power of universities over local consumers and intensify their competition for high-quality students who, because they are both inputs into and consumers of a college education, can improve institutional quality. Thus, despite applicant pools well in excess of the number of enrollment slots, Ehrenberg (2000) has documented that most selective and well-endowed institutions increasingly spend significant sums recruiting top applicants and use a combination of enrollment management tools such as merit aid, early decision policies, and campus amenities to lure top applicants to enroll.
The advent of individual college rankings further raised the enrollment management stakes by providing an easily observed quality metric. As this measure has been found in Monks and Ehrenberg (1999) to influence a student's college choice, one may anticipate that select institutions may have been afforded an ability to ramp up their list tuitions, using their substantial endowments and the tuition revenue collected from the most financially able students to price discriminate in favor of needy, academically able students as discussed in Cook and Frank (1993), Ehrenberg and Rizzo (2004), and Hill, Winston, and Boyd (2004). Nonetheless, Heller (2004) notes that the collective impact of such enrollment management practices in higher education as a whole is of particular policy concern because empirical evidence suggests needy students increasingly rely on non-need-based aid, often in the form of loans, to finance their college educations.
On the other hand, a number of studies, including those of Allen and Shen (1999), Moore et al. (1991), and Parker and Summers (1993), have documented that less-selective private institutions also appear to be cognizant that their more selective competitors have greater resources and deeper applicant pools, which yield greater demand elasticities for these institutions. Moreover, as discussed in Kane and Orszag (2003) and Rizzo (2004), less-selective private institutions must increasingly ward off the potential flight of students to lower cost public institutions that have also been forced to manage enrollments in response to declining state government support. In fact, Ehrenberg (2000) describes how, in the 1990s, a number of less-selective private institutions (e.g., Wells College, Wesleyan College, Muskingum College) found they could not fill out their freshman classes and responded by cutting tuitions for first-year students by between 23% and 30%. In general, the descriptive evidence is supportive of the theoretical predictions in De Fraja and Iossa (2002), Epple et al. (2002), and Martin (2002) that price competition should vary with selectivity.
This article speaks to the potential importance of enrollment management in college access by introducing spatial proximity into empirical models of tuition. In particular, using a detailed cross section of private universities, we first propose a spatial-autoregressive model of tuition that is common in the larger spatial-econometric literature. Given our particular questions of interest, our baseline is to regress an individual institution's tuition on the tuition levels of other institutions within the sample, which allows the data to reveal both the sign and magnitude of any spatial dependence between tuition levels. For example, an estimated spatial-lag coefficient of zero would indicate that after controlling for a detailed list of cost and demand-side factors, there is no systematic variation in tuition levels that is explained by the observed tuition levels of "nearby" institutions. In particular, as each institution's set of nearby competitors varies, our model is primed to test whether being in the neighborhood of the high-tuition institutions within the sample is associated with a given institution posting a tuition different from that would be predicted given other observable characteristics.
In short, our baseline results yield significant positive spatial relationships for both list and net tuitions, conditioned on detailed cost and demand-side controls. We then extend the spatial-econometrics literature by allowing the estimated strengths of any spatial dependence to differ across exogenous categories or groupings of observations. In our sample, this approach reveals asymmetric tuition responses, indicating that the positive estimates from the restricted spatial model are not common across qualitative classifications of institutions. Asymmetric price competition is important from a policy perspective, as it suggests that blanket rules directed at curbing the possible ill effects of rising tuition by limiting price competition may yield unintended consequences.
In the following section, we motivate and discuss the results of the restricted spatial model of tuition, where we report estimates for both list and net tuitions in order to examine if spatial price competition differs when institutional aid is taken into account. Section III then motivates the richer spatial-econometric approach that relaxes the assumption that the estimated strength of the spatial relationship be the same across all observations, in particular, across comprehensive institutions versus national and regional institutions, and reports the results of these empirical specifications for list and net tuition. Concluding remarks in Section IV summarize how the analysis contributes to a better understanding of the nature of price competition in higher education, which is currently not well understood. Overall, given the trend toward greater enrollment management and its potential influence on college access, we see our analysis as particularly timely.
II. A SPATIAL-AUTOREGRESSIVE ANALYSIS OF TUITION
In our analysis, we draw primarily on 1994 institution-level data from the National Center for Educational Statistics and its Integrated Post-Secondary Education Data System. While the potential observations are, therefore, the entire population of colleges and universities in the United States, we limit our analysis to not-for-profit private institutions. We focus on private institutions primarily due to these institutions being self-governing, especially with regard to their tuition setting. For example, unlike private colleges and universities, public institutions are constrained through legislative mandates that weigh access more heavily. Moreover, public institutions commonly operate cooperatively under state systems that fundamentally alter their tuition-setting game through interdependency. (1) Of course, fully incorporating public institutions into the analysis is further complicated by tuition and aid programs that tend to favor in-state over out-of-state students, leading to two distinct tuition levels.
Having restricted our analysis to not-for-profit private institutions within the continental United States, the sample includes a cross section of 929 institutions. Control variables not available in the above data sources are incorporated using U.S. Census data from the Bureau of Economic Analysis. We also incorporate institution-specific Pell-award data provided by the U.S. Department of Education. Sample characteristics are reported in Table 1.
A. Empirical Specification: Single Spatial-Autoregression Coefficient
In modeling list and net tuitions, we include controls for the institution's endowment, whether the institution offers graduate degrees, size (i.e., enrollment), the institution's classification in Petersen's (i.e., most selective, very selective, moderately selective, minimally selective, noncompetitive), and the proportion of undergraduate students receiving federal financial aid. For notational purposes, we capture these control variables with the matrix X. Also included in X are state-level attributes such as median disposable income, the proportion of population that is college aged, state-level unemployment rate, and performance on verbal and math Scholastic Assessment Test (SAT) (included separately), and local variants such as city size and amenities. (2) While we do not model public-tuition levels, in estimating private tuition levels, we include average in-state tuition at same-state public institutions and average out-of-state tuition at public institutions in the same Census region. (3)
In particular, we estimate the following spatial-autoregressive model of tuition:
(1) Y = X[beta] + [rho]WY + u,
where Y is a vector of either list tuition or net tuition (i.e., list tuition net of institution-provided financial assistance). Equation (1) differs from an ordinary regression model due to the spatial-autoregressive term, [rho] WY, where P is a parameter to be estimated and W is an n x n "contiguity matrix" with off-diagonal elements, [W.sub.ij], that specify the effect of [Y.sub.j] on [Y.sub.i]. While results are qualitatively robust across a number of alternative specifications, we focus on and report results using a discrete weighting mechanism such that
(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where [d.sub.ij] is the distance between institutions i and j in miles. That is, we place equal weight on all institutions within 400 miles of institution i in predicting [Y.sub.i]. Of course, to keep [Y.sub.i] from predicting itself, all diagonal elements of W are zero. We adopt a 400-mile distance as the base specification because it approximates the distance of a 1-day drive from most campuses, a metric by which parents and institutions are likely to consider institutions as possible substitutes. Letting Z = WY, Equation (1) can be rewritten as Y = X[beta] + [rho]Z + u. After following the standard practice of row standardizing the contiguity matrix, W, such that all rows sum to one, [Z.sub.i] is a simple weighted average of all... |
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