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To continue the discussion that began in the previous blog posts about HEQCO’s report on The Differentiation of the Ontario University System let’s at look some significant matters of fact insofar as what the report calls “financial sustainability” is concerned.

The largest university in the University of California system – Berkeley – is two times larger than the smallest – Santa Cruz.  The University of Toronto is more than two times larger than Berkeley. Santa Cruz is 13 times larger than Algoma – Ontario’s smallest university — and about the same size as Queen’s, which is Ontario’s smallest “research intensive” university as categorized in HEQCO’s report. The message here is not that Ontario should or should not adopt the California model.

The message is that a highly respected system of higher education pays a lot of attention to institutional size, and has done so since the inception of it first master plan more than 50 years ago. Size matters, and it matters because of cost, economy of scale, and economy of scope.

Cost

Ontario tends to think of cost in two ways. The first is cost to government. HEQCO’s report presents the provincial government’s capacity to afford higher education as a de facto parameter of cost, as if there were some kind of functional identity between what universities spend and what the government spends on them. But what is cost to government is revenue to universities. The second is the ’ characterization of cost as the cost of attendance, which in turn is largely an artifact of government regulation.

Neither is really about cost. Both are functions of enrolment and a capitation formula that is based on enrolment weighted nominally to reflect cost. In other words, they are more about volume than the unit costs of performance or output. Neither seriously addresses how universities make decisions about balancing revenue and expense, or, in the context of differentiation, what change costs.

Here are some examples of what we know about cost that illustrate the difference between cost as a function of revenue and cost as a function of spending. The number of programs drives costs more than the numbers of students and faculty in some large areas of expense, most notably libraries and student information systems. If a university were to seek “financial sustainability” by increasing enrolment, the cost of expansion by adding students to programs that already exist will be much less than those of adding programs to attract more students.

The same works in reverse: costs will be reduced more by eliminating programs than by reducing enrolment incrementally. There is an important lesson to be learned here: almost all sources of revenue follow linear progressions – each additional or fewer student generates the same marginal revenue — while many costs follow step functions, for example, once the cost of coding a student information system to accommodate a new program is incurred the cost will not change as the number of students rises or falls, but the cost will change if a new program is added.

Perhaps the HEQCO report’s reference to “program approvals” was not as off-hand as it appears. To locate this is in recent Ontario context, neither the Advanced Technology Opportunity Program (ATOP) nor the graduate expansion program recognized this distinction, nor does the Council of Ontario Universities’ persistent insistence on “average cost funding.” Given the track record of ignoring opportunities to promote differentiation, one wonders whether or not HEQCO’s report on differentiation should have been directed more to the government – that is, politicians –  and universities collectively – that is, the COU – than to universities as autonomous entities.

We also know that the cost of research is largely unrelated to the cost of instruction. One does not need to spend much time examining the results of the or the Center for College Affordability and Productivity reports – both in the U.S. – to understand how different the cost functions of research are from the cost functions of instruction. In Ontario, universities – “research intensive” by HEQCO’s standard or not — are funded almost entirely on the basis of enrolment – that is, instruction – as a surrogate for all cost. Universities do not report the expense of instruction separately from the expense of research. Internally, most universities neither know nor budget for the full cost of the research that they conduct. The cost of instruction is itself problematic because class size appears to have a greater effect on cost than enrolment at large.

Space, the unit costs of which vary a lot between instruction and research, is often regarded either as a free good or as an highly aggregated average that disguises real costs. This gets in the way of benchmarking as a means of determining efficiency and economy of scale.

As data about space inventories in Ontario are now collected and assembled, comparisons are at best only possible building by building, and sometimes only campus by campus. This is a cost problem for two reasons. First, we know that different kinds of space – wet research laboratories, for example – within a single building are more expensive to maintain and depreciate than other kinds of space in the same building. Second, enrolment as a driver of cost does not apply to all categories of space, particularly to some of the most expensive in terms of energy intensity and depreciation.

In terms of the unit costs of space, use may thus trump volume. In terms of “financial sustainability” the cost of “inefficient use of space” may be greater than the cost of too much space.

Economy of Scale and Scope

One of the explicit mandates of the California master plan was “to set forth as accurately as possible minimum, optimum, and maximum sizes in terms of enrolments of [colleges and universities].” Nevertheless, one still might ask whether the concept of economy of scale in higher education is only a hypothesis, or does size in fact matter?

One way of answering this entirely legitimate question is to look at the track record of mergers and consortia among colleges and universities. With the exception of South Africa, all mergers in higher education have been predicated at least partly on the realization of economy of scale or of scope, and often of both. Mergers have been a successful means of reducing costs by realizing economy of scale in libraries, information systems, utilities, class size, program “diseconomies,” and all “shared” or “backroom” services, for example financial services.

Another way of answering the question is to examine IPEDS data from the United States to determine whether or not universities exhibit economies of scale. Why not do this with Canadian data? American universities separate the costs of instruction and research, and report the indirect or overhead costs of research as well as the direct costs. Canadian universities do not. This is very significant.

Let’s look at some graphs courtesy of Kevin Stolarick. Figures 1 and 2 present the total number of students and the average cost per student for all US institutions.

The first noticeable phenomenon is something that is generally but, often surprisingly, true of economy of scale: size can be either too low – as intuitively expected — or too high – which is the surprise – to realize optimal unit costs. In other words, economy of scale for a university can be depicted as an inverted J with size being smallest on the left and rising to the largest on the right.

The second, and more important, is that unit cost per enrolment initially falls as enrolment rises but then rises again as enrolment grows beyond certain higher levels. In fact, unit costs later increase at a faster rate than they initially decreased.  Figure 3 displays the same data but with the sample split at the median.  The lowest cost – that is to say, the bottom of our inverted J – is at an enrolment of about 14,000. This is, of course, only an average and only a proximate one at that. There are outliers in both directions. But with regard to the question, it demonstrates that economy scale is more than an hypothesis when applied to universities.

Most studies of optimal university size indicate an optimal range of – 10,000 to 25,000 – which coincides closely with the lower end of the ranges indicated by Figure 3. But we must remember that this study and others separate instruction and research. One could say that “primarily undergraduate” in de facto terms is the equivalent of “instruction only” in HEQCO’s terms.  But that is as far as one could go in terms of specific applicability to Canada. There should, however, be no doubt that economy of scale can be applied to universities in Canada, and that it applies to public as well as to not-for-profit private universities.

What are the implications for planning a differentiated system?  First, and least popular among Ontario universities, is that “average cost funding” is inherently problematic given the current range in size among Ontario universities.

Second, it is even more problematic for “research intensity” which has an entirely different cost structure and which is almost entirely unrecognized by the current funding regime. All the HEQCO report says about this phenomenon is that it should be “enhanced” and, in the case of the University of Toronto, “assured.”

The University of Toronto to the system planner is something like the bumblebee: it should not be able to fly, but it does. If HEQCO were to take into account the University of Toronto’s multi-campus structure, it and York would still be outside the economy of scale parameters but to approximately the same extent.  All the “research intensive” universities, the remaining “in between regionals” and two “primarily undergraduate” – Brock and Laurier, are within the optimal range at the bottom of the inverted J curve. Laurentian would just make it into the optimal range if it were either to revert to its previous structure that included Algoma and Nipissing as colleges or enter “shared services” agreements with them.

This sorting of institutions may or may not be correct – it’s like a parlour game that anyone can play – but an undeniable fact remains: if the universities were categorized on the basis of size and economy of scale the categorization would not look like the one proposed by HEQCO.  To sharpen the point, there is no fiscal reason to expect, as the report promises, that differentiation will promote “financial stability” at the institutional level.

To conclude where this discussion began, this is a problem that the California master plan foresaw and had the discipline to control. It is too late now for Ontario, not because the economy of scale horse is far outside the barn, but because it never got out of the barn in the first place. HEQCO’s report refers expressly to “capitalizing” on the current array of institutional strengths and missions rather than changing any. In this context the report could have referred to current sizes as well. It did not, but it could have, particularly with regard to the assertion that financial stability can be realized by “reducing duplication of expenditure.”

The report does not say whether this refers to government expenditure or institutional expenditure. If it is the latter, economy of scale could have a major role in determining the realistic parameters of reducing duplication. For the universities that are already within the optimal curve there is little reason to believe that further efforts towards efficiency – involving duplication or not – will produce significant results. There are a few, however, at either end of the curve that are very close to becoming too small or too large, and thereby at risk of losing economy of scale.

Then there are universities that are outside the curve, either too small to realize economy of scale or too large to retain economies of scale previously realized. These institutions may or not be able to make a significant contribution towards system-wide financial stability by moving in directions that will reduce unit costs, but if they do it will be by becoming less different insofar as size is concerned.

In other jurisdictions that have faced a dilemma like this the answer has been to eschew size as a desirable differentiating factor, and provide funding to institutions that were either too small or too large on the deliberate and explicit assumption that they were an optimal size – that is, within the curve – even if they were not. HEQCO, instead, appears to favour granting an economy of scale amnesty.

Isn’t economy of scope simply an offshoot of economy of scale? It isn’t, and it is different in a way that has a particular relevance to higher education. With apologies for using an industrial example, here is a simple illustration of the difference. An automobile manufacturer seeks economy of scale to reduce cost of producing a certain kind of vehicle that the firm is already producing. The same manufacturer alternatively seeks economy of scope by designing and manufacturing a different kind of vehicle using the same workforce and assembly line that produced the original vehicle. In both cases, savings in unit costs may be realized.

Another example is the previously noted difference between increasing enrolment in existing programs and adding programs to increase enrolment. The former as a means of unit cost reduction is an example of economy of scale. The latter is an example of economy of scope.

What else could be done to recognize the role of cost in financial sustainability?

What else could HEQCO propose now? First, there are some possibilities: separate the funding regimes for instruction and research; introduce a flat “marginal cost” instead of “average cost” formula that assumes an optimal size as an incentive to “right size;”  introduce a formula that separates and funds costs in two categories, ones that follow a linear progression and ones that follow a step function; promote “shared service” consortia, especially among or with under-capacity institutions; cap funded enrolment at the main campuses of Toronto and York; promote student mobility with a structured tuition fee schedule that lowers fees (and commensurately raises grants) according to distance away from home; promote mergers between below capacity universities and below capacity colleges; and take a look at the Bovey Commission’s proposal for “research intensity” not for the detail but as an example of a flexible and responsive metric.

Second, there are lessons here for HEQCO’s proposed reliance on a revitalized round of Strategic Mandate Agreements () as an instrument of differentiation. Specialization is not enough. To realize economy of scope an institution’s specializations should have some degree of affinity among them. On the institutional side, universities should accept not having to be organizationally specialized in order to deliver specialized programs and research. This a lesson to which the very large universities and those nearing the upper end of the J curve could usefully give some thought. It also is a lesson to which PEQAB and the Quality Assurance Council should give some thought: “each [program] tub on its own bottom” might not be optimal in terms of resource utilization and taking full advantage of differentiation to enhance quality.

Finally, a “stir the pot” question: why isn’t HEQCO promoting a companion discussion about the college system, in which several colleges are already talking in terms of “polytechnic” status, and in which economy of scale and economy of scope are just as problematic, if not more so?