New estimates of economies of scale and scope in higher education.

• Author: Laband, David N.

1. Introduction

   The substantially greater than inflation increases in college tuition during the late 1980s and first half of the 1990s ignited considerable discussion of the costs of higher education by both academics and nonacademics. The general discussion covered such issues as how much tuition has risen, why college costs so much (Ehrenberg 2000), the extent to which tuition fully covers costs (Winston 1998; NACUBO 2002), and what colleges are doing to cut costs (Strosnider 1998). Indeed, concern over rapidly increasing tuition spurred Congress to establish a National Commission on the Cost of Higher Education in 1997; the Commission conducted a review of college costs and issued recommendations for holding costs down.

   To economists, discussion of cost-cutting generally boils down to a simple question: What is the efficient organization of production? In a market economy, competitive pressures force profit-maximizing firms constantly to strive to produce more efficiently. Thus, information about the efficient organization of production can be deduced by observing organizations that survive and prosper (Stigler 1958). However, in the context of higher education, the answer is not so simple, for at least three reasons: (i) colleges are not profit-maximizing entities, thus market-driven pressures to minimize costs are, essentially, absent; relatedly, (ii) tuition/prices paid by students/customers do not cover the full cost of their educational experience (Winston 1998); and (iii) colleges typically produce multiple products, not just undergraduate education.

   Supposing that the individuals who run institutes of higher education (IHEs) have an interest in minimizing costs, how should they structure production to achieve this? That is, what should they produce and how much of it should be produced? Should colleges specialize and produce only undergraduate education, or produce multiple outputs, as so many currently do? Should colleges be small or large, in terms of student enrollments and/or grant research?

   These are complex questions in their own right. For example, take the question about the optimal mix of outputs to produce. Forgetting about the implications for revenues, there are a host of related empirical issues to investigate: What are the unit costs of producing different levels of only undergraduate education, graduate education, athletics, research, extension, or public services? What then, in comparison, are the unit costs of producing different levels of alternative combinations of two or more of these outputs? Knowing the answers to specific questions like these provides an essential foundation for informed decision making about the efficient organization of production in higher education.

   Estimating the cost of producing academic outputs is complicated by the fact that many, if not most, IHEs produce multiple products. Typically, the products include undergraduate and/or graduate instruction and research. (1) In addition to these basic outputs, the state land-grant institutions also produce extension services. Many institutions also produce public services such as medical services, business assistance programs, museums of various sorts, theater productions, and the like. And, of course, IHEs produce both intramural and extramural athletics. Thus, for purposes of estimating unit costs, it is essential to treat IHEs as multiproduct "firms."

   Further, it seems highly likely that the production of certain outputs affects the unit cost of producing others. For example, production of graduate instruction requires the administrators of an IHE to hire faculty with more extensive training and ability than is required to teach at the undergraduate level. Doctorally qualified faculty are more expensive to hire than non-doctorally qualified faculty, ceteris paribus. To the extent that the set of faculty providing graduate instruction and the set of faculty providing undergraduate instruction are mutually exclusive, the provision of the former has no cost spillover to the latter. However, if the graduate faculty also teach undergraduate courses, then the unit cost of providing undergraduate education will be higher at IHEs that produce both graduate and undergraduate education than at IHEs that produce only undergraduate education. On the other hand, to the extent that relatively low-paid graduate students are used to teach undergraduate courses, unit costs of the latter may actually be lower than one would find at a traditional, undergraduate education only institution. Likewise, the fact that an IHE has great athletic teams and/or facilities or strong art/music/theater programs may permit the institution to pay faculty lower salaries than would be the case in the absence of such facilities or programs.

   There is evidence that higher education is indeed characterized by (dis)economies of scope. Using data from 1981-1982, Cohn, Rhine, and Santos (1989) estimated multiproduct cost functions for 1195 public IHEs and 692 private IHEs and found (p. 287) that at the mean levels of outputs in their samples there were "economies of scope in the private sector and diseconomies of scope in the public sector." They then investigated scale and scope economies for alternative multiples of the mean outputs, given fixed(at the mean)-proportion output bundles. Public IHEs were shown to have diseconomies of scope up to 150% of the mean output level but slowly increasing economies of scope at even larger output levels. Private IHEs were characterized by economies of scope at all output levels that increased much more rapidly with higher output levels than was estimated for the public IHEs.

   These findings were derived from separate cost equations estimated for public and private IHEs, since the structural models for the two types of IHEs were found to differ significantly. However, since their data were for a single year only, Cohn, Rhine, and Santos suggest that estimations for additional years might improve our confidence in the conclusions. In this paper, we estimate multi-product cost functions for public and private IHEs using newly available data on IHE costs for 1996, employing the flexible, fixed-cost methodology employed by Cohn, Rhine, and Santos. We then investigate the extent to which production of undergraduate education, graduate education, and externally funded research are characterized by economies of scale and scope.

2. Methodology

   Following in the tradition established by Baumol, Panzar, and Willig (1982) and developed specifically in the context of higher education by Cohn, Rhine, and Santos (1989), we estimate a multi-product cost function for IHEs. Our model is specified as a flexible fixed-cost quadratic (EFCQ) function, with a dummy variable [F.sub.i] that assumes a value of 1 (0) for (non)positive amounts of the output [Y.sub.i]:

   [C.sub.i] = [a.sub.0] + [[SIGMA].sub.i] [a.sub.i][F.sub.i] + [[SIGMA].sub.i][b.sub.i][Y.sub.i] + (1/2) [[SIGMA].sub.i] [[SIGMA].sub.j] [c.sub.ij][Y.sub.i][Y.sub.j] + [[eta].sub.i].

   [C.sub.i] refers to total expenditures by IHE i in 1996, [a.sub.0], the [a.sub.i]'s, the [b.sub.i]'s, and the [c.sub.ij]'s are scalars, and [[eta].sub.i] is the error term, which is assumed to be independently and identically distributed. Output produced includes undergraduate education (measured as full-time equivalents, in thousands), graduate education (full-time equivalents, in thousands), and research (measured as the sum of federal, state, local, and private grant dollars, in millions). The [F.sub.i] variables reflect differences across IHEs with respect to the fixed costs of producing different product sets.

   Since our purpose was to update the Cohn, Rhine, and Santos estimates of economies of scale and scope in higher education using more recent data, we employed the same structural model that they used; that is, we included both linear and squared terms for the three output measures as well as the one factor price we had available (average faculty compensation). In addition, we included interaction terms between outputs and between the factor price and output measures. We...