The Impact of Rural Restructuring on the Delivery of Education Services in Rural Saskatchewan
A summary of a thesis by Jacynthe Wionzek

SSTA Research Centre Report #95-03: 54 pages, $14.

The Context for Restructuring The declining rural population in Saskatchewan reduces market size for businesses located in rural areas, leading to their consolidation into fewer and geographically more dispersed centres. Analogous to businesses in the private sector is making adjustments to the size and location of elementary and secondary schools in the province to meet the future demand for education services. Decision-makers, charged with the responsibility of providing quality education to the dispersed and shrinking rural population, face important decisions regarding the consolidation of the system of schools.
The Literature Regarding the Delivery of Education in Rural Areas
The Saskatchewan Study
Research Results
Conclusions and Recommendations
References

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The opinions and recommendations expressed in this report are those of the author and may not be in agreement with SSTA officers or trustees, but are offered as being worthy of consideration by those responsible for making decisions.


Context for Restructuring

The trend toward consolidation of businesses and population into fewer, larger centres in Saskatchewan is well established. This urbanization of the rural population has been ongoing since the time of settlement; the process is illustrated in Table 1.1, along with trends in the number of farms and farm population. The rural population, representing 70 percent of the province's total population in 1936, had decreased to 37 percent in 1991. Farm population has experienced an even greater decline, falling from 88 to 44 percent of the (shrinking) rural population. By 1991, 63 percent of the province's population lived in urban centres of more than 1,000.

The evolution of the system of urban centres has been characterized by a consolidation into fewer, larger centres. Table 1.2 shows the distribution of 598 communities in Saskatchewan over six classifications in 1961, 1981, and 1990. The classification of communities is the result of considering simultaneously the number and types of business activities in the community, the infrastructure services available, and the population size.1 A large number of rural communities have lost functional status while a smaller number have gained or maintained their functions. By 1990, 419 communities were classified as Minimum Convenience, a category in which not a single business function or service is systematically available. The top four levels of the hierarchy, containing 62 centres in 1990, consist of those that have demonstrated viability, offering potential for retaining business functions, public services, and population.

The major cause of the population redistribution is the change in production, transportation, and communication technologies. Not only has farm size increased steadily since 1936, but many other natural resource activities on which the rural economy depends have also benefited from the adoption of labour-saving technology. The provision and distribution of trade and service activities have likewise consolidated in response to marketing, communication, and transportation technological change. As economic activity concentrates in fewer, larger centres and labour requirements in primary production decrease, the labour force moves to urban areas. In general, it is the younger members of the labour force who are moving to the cities or larger communities because they have more to offer in terms of employment opportunities, shopping selection, recreational activities, and education services. This, of course, further reduces the number of school age children in rural areas.

As part of the ongoing process of population redistribution, both private and public infrastructures consolidate. In the public sector the consolidation of infrastructure may occur in response to population shifts; these decisions also influence the more general spatial restructuring of business and population.

The delivery of education services to a dispersed rural population is a specific example of the challenges associated with public sector rationalization due to population redistribution. As the demand for education services -- in terms of numbers of students -- has diminished in some areas, school closures have occurred in response. Where closure is not a feasible solution, other alternatives have been pursued.

The provincial funding formula provides the framework for the consolidation of the education system. Level-specific rates are applied to enrolments to calculate the Basic Program component of Recognized Operating Expenditures. Additional Recognized Expenditures are those for transportation, special needs pupils, language programs, and northern allowance. Recognized Operating Revenues are calculated based on the local land assessment multiplied by an equalization factor (computational mill rate). When the equalization factor is less than the actual mill rate, the Recognized Operating Revenues are less than actual local revenues. For a particular school division, the difference between the Total Recognized Operating Expenditures and the Total Recognized Operating Revenues is funded by the provincial government in the form of the Basic Foundation Operating Grant.

As enrolments decrease in rural areas, the number, size, and location of small schools will be affected. Enrolment drops reduce Recognized Operating Expenditures and, for a constant level of local revenues, will reduce the provincial grant under the funding formula. In response to the revenue loss, actual costs have to be reduced. Some cost reductions can be achieved through a reduction in teaching staff, but ultimately school closures will need to be considered.

As part of the public sector, the education system is facing some form of restructuring in rural areas in order to deliver education services to a widely dispersed population. The purpose of this study is to examine how the public sector can and/or does respond to pressures for consolidation by simulating the impact of declining enrolments on the delivery of education services in rural areas. A study area containing several small schools that are expected to face declining enrolments was selected. The implications of declining enrolments, based on population projections to 2005, are examined at the level of individual schools and simulations of the impact of enrolment drops and school closures on costs, revenues, and grants are conducted. An economic interpretation of the results is offered in terms of short-run and long-run costs both at the division and the provincial level. Finally, the alternatives facing decision makers regarding the delivery of education services in rural areas are discussed, and recommendations are offered.

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The Literature Regarding The Delivery of Education in Rural Areas

Like Saskatchewan, many rural areas across North America have experienced population declines that affected the demand for public infrastructure. For example, Johnson and Beale (1992), in examining a trend of natural decrease in the nonmetro areas of the United States, found that fewer children result in less demand for education services and fewer schools. And as the economic base shrinks in local private and public infrastructures, it becomes more difficult to fund education services.

Wood and Cahape (1990) examined the rural school populations, birth rates, and population trends in Kentucky, Tennessee, Virginia, and West Virginia. The exodus out of the rural areas led to an erosion of the school age population as well as the tax base, making financing schools in rural areas more of a challenge.

A major overview of the needs of the education system in Saskatchewan by Langlois and Scharf (1991) evaluated the financing and governance of education. Due to declining enrolments over the past several years, the education system has faced several challenges in providing a quality education. Since 1930, the total enrolment in the province decreased from over 230,000 to approximately 195,000 in the 1990s. City enrolments increased by approximately 66,000 students over this period, from approximately 35,000 to over 100,000. Other areas of the province including the rural areas, small towns, and villages, experienced a decline of over 100,000 students from 1930 to 1990, decreasing from slightly over 190,000 to just over 90,000 (Langlois and Scharf 1991).

Between 1979 and 1990, over 100 schools in Saskatchewan were closed and education services were centralized so that more programs could be offered (Langlois and Scharf 1991). Small schools often lack the resources to offer a wide range of courses, particularly in the high school program, whereas students in larger schools may have more options available to them. Rural school divisions had a substantial decrease in enrolment of over 20,000 students from 1976 to 1990 and a further decline from 87,369 to 83,081 in the 1988-91 period.

Approximately one-quarter of all the Divisions have enrolments under 500 students and close to three-quarters have less than 1,500 students (Langlois and Scharf 1991). In 1979, of the 967 schools in operation, 415 of them had enrolments of fewer than 150. By 1990 the number of schools operating in the province declined to 861, with 334 of them having fewer than 150 students. Where small schools were in close proximity to large schools that offered a more diversified selection of programs, enrolment declines led to consolidation.

The Langlois and Scharf report included an evaluation of funding allocated to provincial education. They recommended that the Basic Foundation grant program be retained, but with the addition of a resource cost model to provide a more detailed account of how the money is utilized by the school division. Service levels would have to be defined and the cost of services would have to be determined in order to implement the resource cost model.

Education reform, according to Langlois and Scharf, should include a school division reorganization so that school divisions are large enough geographically to generate sufficient enrolment to offer a full service K-12 program. They recommended that the existing 92 public school divisions be reorganized into 14 or 15 divisions, with an average enrolment of 7,000, in order to reduce the variations among school division tax bases. Currently, a wide range of tax assessments exists among school divisions, which affects both the provincial funding formula as well as the school divisions' ability to raise revenue.

The Saskatchewan School Trustees Association (SSTA) established a task force in 1993 to examine education restructuring, and its major recommendation, like the Langlois and Scharf study, was that the school division size should increase. The SSTA study recommended that there be approximately 35 divisions in the province with roughly 2,500 to 5,000 students in each, in order to deliver education services effectively while reducing administrative expenses and offering a more diversified program. The study argued that divisions of this size could better withstand enrolment declines and still remain viable in the future.

To maintain stable communities, the SSTA report recommended that restructuring efforts take into account current shopping and trading patterns. A restructured division would have the resources to adopt new technologies to provide other forms of education delivery, such as distance education.

A model of cost efficiency used by White and Tweeten (1973) focuses on the optimal size school district for 27 selected Oklahoma School Districts. Long-run average (per student) cost curves were estimated at varying student densities, holding education quality constant. Quality was proxied by course content and standardized test scores of grade 11 students. Per student cost in the long run included both education and transportation costs. The optimal size school district, in terms of enrolment and student density, was determined as that size with the lowest attainable per student cost (White and Tweeten 1973).

Instructional, attendant, and transortation costs were analyzed at the school district level by White and Tweeten. Instructional costs, the major component of costs relating to education, included teacher, principal, and other salaries as well as other expenditures such as textbook and library costs. Attendant costs included fixed and variable costs: fixed costs included plant facilities and equipment; plant operating and maintenance (daily maintenance of school buildings) and administration (costs of operating the school district) were part of the variable costs. The cost of transportation, encompassing drivers' salaries, fuel, lubricants, etc., included simulated bus routes that assumed students did not spend more than one hour on the bus.

According to White and Tweeten, per unit education costs decrease as enrolment increases, and transportation costs increase as enrolment increases due to the need to collect students over a larger area. When education and transportation costs are summed, the enrolment at which the lowest per student costs are achieved can be determined. In their study, economies of size (lowest attainable per student costs) were attained at approximately 800 students, but when transportation costs were added, the optimal size was lowered to 675. This optimal size was determined for a particular student density. As the density decreases, additional transportation costs are incurred, causing the optimal (lowest cost) size to occur at a lower enrolment. Thus, lower student densities result in economies of size being reached at lower enrolments because of the diseconomies (increasing per student costs) associated with transportation.

Coleman and LaRocque (1984), in a study of school districts in British Columbia, tried to determine the causes of high operating costs. School district size was uncorrelated with per student operating costs, and although administrative costs had a strong positive correlation, they were only a small percentage of the overall costs and could not be responsible for high operating costs. Neither pupil-teacher ratios (PTRs) nor school size could account for the high per unit costs of operation, but teaching salaries were positively correlated with gross operating costs and were statistically significant.

Tholkes (1991), in a study of school district reorganization in Minnesota, determined a methodology to measure the economies of scale from school district reorganization. A cost simulation was done for scale and nonscale effects for the following categories: operating expenditures, salaries, employee benefits, purchased services, supplies and materials, and other and annualized capital expenditures. These simulations implied that per student costs would be reduced if the number of schools in operation decreased and if the PTRs increased. School closures would result in increased transportation costs, but more importantly, the travel time on the bus would place a major constraint on school district reorganization.

In summary, the question of the restructuring of the delivery of education services in rural areas experiencing population decline is not unique to Saskatchewan. Results of both Canadian and U.S. studies show that reduced enrolments result in higher per student costs and subsequent financial problems for the administration. School closures lead to students being collected over a larger geographic area, resulting in increasing per student transportation costs. Consolidation does reduce administrative costs, but as these are a relatively small component of total costs, it does not solve the financial problem of rural school districts.

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The Saskatchewan Study

The area selected for the study includes the Last Mountain, Lanigan, Long Lake, and Davidson school divisions, shown in Figure 3.1. It was chosen to reflect the circumstances of rural school divisions that serve a dispersed, largely declining rural population, that still contain small rural schools, and that, therefore, are still potentially subject to consolidation. Four contiguous divisions were chosen to avoid being constrained by existing boundaries when students are reallocated to other schools as part of a simulated closure. The Indian reserves in the Last Mountain school division permit consideration of the impact of an increasing population size, which is common to reserves, in contrast to widespread declines in the non-Native population.

Provincial population data by age and sex were obtained from Saskatchewan Health (1970-1992). Fertility (age specific) and death rates (age-sex specific) for the non-Native population were obtained from Statistics Canada (1992a, 1992b). The non-Native 1990 fertility and death rates were held constant for the population projection. Fertility and death rates projected for Saskatchewan Indians by Nault et al. (1993) were used in projecting the Indian population to 2005.

Age-sex specific population was projected to 2005 at the Rural Municipality (RM) level using a cohort survival method. Net migration rates were the result of observing past population trends in each RM compared with what the population would have been due to natural increase alone. These rates, together with death and fertility rates, were used to sequentially generate population for each age-sex group in each year from 1992 to 2005. Attendance area maps were obtained from the four school divisions in order to project school level enrolment from the RM projections.

Projected enrolments in 2005, together with the existing formulae, were used to simulate revenues and costs. Cost impacts were restricted to teaching, transportation, and plant operating. In the case of transportation costs, it was assumed that recognized transportation expenditures were the actual costs. Teaching costs were first simulated under the assumption that division-level pupil-teacher ratios (PTRs) would remain constant and then under the more realistic assumption that PTRs decline as enrolments fall. Teaching salaries were held constant at the division level. Plant and operation costs were provided by the school divisions. Recognized Operating Revenues (recognized local taxes) were assumed constant. Total Recognized Operating Expenditures for the 2005 enrolments were calculated as the sum of Basic Program, enrolment drop, sparsity, small school factor, transportation (all at the 1992 rates), and a residual category. The Basic Foundation Operating Grant was then calculated for each school division as the difference between Total Recognized Operating Expenditures and recognized local taxes.

School divisions in the study area provided the 1993/94 enrolment and the number of full-time equivalent teachers for each school, as well as teaching and plant operating and maintenance costs.

Saskatchewan Education, Training and Employment (1992, 1993, 1994) provided the necessary data to simulate the Basic Foundation Operating Grant for 2005 with the projected enrolments.

In the spring of 1994, the directors of education in each of the four school divisions were contacted to assess whether the projected 2005 enrolments seemed reasonable given their firsthand knowledge of the area. They were also asked to evaluate the viability of each school within their respective divisions based on the projected 2005 enrolments, assuming these enrolments were for the fall of 1994. The school closure simulation was carried out by assuming that no changes were made to the existing administrative and institutional framework.

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Research Results

Population Projections

At the provincial level, population was projected to 2005 by age-sex group for each RM and for each of the 62 centres in the top four levels of the trade centre hierarchy. For the study area, RM population projections were translated into school-level projections by applying the weighted 1992-2005 age-sex specific rates of growth (for each RM in each school's attendance area) to the 1993/94 school enrolment. Table 4.1 shows the results of the population projections for 2005 both with the existing set of schools and with simulated closures, as well as the actual 1993/94 enrolment figures. The grouping of grades reflects the age groups that were the basis for the projections (ages 5-9, 10-14, and 15-19).

The 2005/06 projections for the study area in total show a loss of just over 1,000 students, about 20 percent of the 1993/94 enrolment. There is, however, considerable variation among the four school divisions. Last Mountain, for example, experiences a loss of only 12 percent, while Lanigan shows a loss of 32 percent. In addition to changes in the total numbers of students, there is a change in the age structure of the student population, which reflects the combination of aging of the existing population, net migration rates, and fertility rates.

The 2005/06 projections with simulated school closures show the redistribution of the projected school populations. Division totals change because in some cases students are re-allocated across division boundaries as a result of closures. Study area totals are also different because divisions not in the study were involved in the reallocations. As the last set of four columns shows, school closures result in higher enrolments in the receiving schools. Footnotes to the table describe the reallocations of students in the simulated closure scenario.

Cost and Revenue Simulations

The school enrolments shown in Table 4.1 were the basis for projecting the implied costs and revenue implications at the school division level. The actual cost components considered were teaching, plant and operation, and transportation. For transportation, the assumption was made that actual costs would be the same as the amounts recognized by the funding formula--a combination of a rate per student and a rate per kilometre. The number of teachers was calculated assuming a constant pupil-teacher ratio, and division average teaching salaries were applied. Plant operating costs relate to actual 1992 costs. Table 4.2 shows the results of estimating these costs impacts. The last set of columns indicates the changes attributable to simulated school closures in addition to the declining enrolments.

The vast majority of cost savings in the study area were due to the reduction in teaching salaries, as 62.21 fewer teachers were required because of declining enrolment. The simulated closures led to an additional 2.56 teachers being cut. Overall, declining enrolments resulted in a $2.9 million drop in the cost items outlined in Table 4.2. The simulated school closures led led to an additional $282,757 cost reduction, the net result of higher transportation costs and reduced teaching and plant operation costs. Again, the experiences of individual school divisions vary considerably.

On the revenue side, as enrolment falls (without closures), the Basic Program recognition falls, the number of students transported falls, and sparsity, small school, and enrolment drop factors result in different recognition. Where schools are closed, the same formulae are applied but the number of students transported is higher and therefore the expenditure recognized for transportation increases. Assuming local Recognized Revenues remain the same, the changes in Recognized Expenditures translates into a reduction in the Basic Foundation Operating Grant.

The impact of declining enrolments and simulated school closures on components of Recognized Expenditures and, therefore, on the Basic Foundation Operating Grant is shown in Table 4.3. In the study area as a whole, the grant reduction due to declining enrolment alone was $3.36 million, substantially more than the cost reduction shown in Table 4.2. In the scenario with simulated closures, the grant reduction is smaller, primarily due to a higher transportation recognition and slightly greater cost reductions leading to a smaller shortfall. Comparing the 2005 scenario with only declining enrolments and 2005 with declining enrolments plus simulated closures, it is clear that the higher transportation recognition contributes substantially to increased grants as a result of closures. It should be noted that the reductions in the Basic Foundation Operating Grant are not entirely realistic since they include a "negative" grant in one division as Total Recognized Expenditures dropped below the recognized local revenues.

An assessment of the net effect at the division level requires a comparison of cost reductions and grant reductions, as summarized in Table 4.4. Clearly, the impacts vary considerably across divisions, but in all cases without school closures, the grant reductions exceed the cost reductions. With school closures, cost reductions exceed grant reductions in Last Mountain and Long Lake, and would in Lanigan if the calculated grant was not allowed to become negative.

In summary, declining enrolments have translated directly into proportional decreases in the number of teachers and, on the revenue side (via Recognized Expenditures), into decreases in the Basic Program Recognized Expenditures since these expenditures are determined as constant rates applied to enrolment. The small school, sparsity, and enrolment drop factors represent a recognition that per student costs increase as school size decreases, but these factors do not result in adjustments that equalize revenue changes and cost changes. (In the next section some of these assumptions are modified and the implications are discussed.)

Economic Interpretation

Based on the earlier literature review, decisions regarding the restructuring of education services in rural Saskatchewan have similarities to the restructuring of the private sector. Modifications to the private sector analysis need to be introduced to reflect the specific characteristics of the education system and the fact that education is a public service. Economies of scale and utilization, effects of changing market size (enrolment) on costs and revenues, and the consideration of transportation costs are important determinants of the opportunities and constraints facing decision makers. Implications derived from the economic theory of the firm can be used to focus the results presented above.

For a given size business firm, per unit (of output) costs are conventionally thought of as declining over some range until the plant is being optimally used, then rising again. There is some evidence that the education costs per student behave in a similar manner. That is, for a given school size, the greater the enrolment the lower the costs per student, up to an optimal utilization, after which per unit costs again begin to rise. The reduction in per unit costs to some level is a reflection of indivisibilities in the production process. Administrative costs, plant operation and maintenance, support staff, etc., are examples of overhead or fixed costs that will fall, on a per student basis, when the number of students increases. At some point, however, all these advantages will have been gained, and per student costs may increase as enrolment exceeds the capacity of the plant.

Given initial enrolments of varying sizes, different size schools can achieve the lowest attainable per student costs, but in general, a facility designed for larger size enrolments will result in lower per student costs than a facility designed for smaller enrolments, even when both are used optimally. This pattern is known as economies of scale. Where economies of scale are present, the larger the school the lower the attainable per student costs. Economies of scale generally arise from specialization and division of labour. An example in the education system would be an enrolment large enough to justify teachers who are subject matter specialists in a very specific area. In Saskatchewan, the Langlois and Scharf report of 1991 presents empirical evidence that the per student costs decline as school size increases, suggesting the presence of economies of scale over the enrolments observed.

As for the delivery of education services in rural Saskatchewan, however, the decision regarding plant size has already been made, and subsequent decisions relate only to how to optimally use that facility (including the closure option). When market size (enrolment) changes, what was once an optimal plant size no longer is and the per student costs will rise. At some point, the higher per student costs may lead to a consideration of school closure, which is analogous to the closure of a high cost plant in the private sector. Closure of the high cost facility and reassignment of the students will, at the same time, reduce per student costs in the receiving school, especially if it too has been experiencing declining enrolment and is therefore underutilized.

The decreasing size of the rural population in Saskatchewan, characteristic of the past several decades, has been accompanied by a consolidation of business activity into fewer places. A decrease in population in the market area (technology constant) results in a smaller demand for the goods or services being provided by area firms and downward pressure on sales, all else constant. Assuming that each of these firms was originally operating with an optimal plant size, that is, at the minimum attainable per unit costs, given the size of the market, the reduced sales resulting from the decrease in demand will result in losses and the exit of firms from the market. As firms exit, fewer "shopping centres" remain in a constant-size geographic area. Consumers dispersed over the area pay added transportation costs for the commodities they purchase. That is, the "outlay" (product price plus time and expense related to distance travelled to procure the product) made by the consumer increases for every quantity, and leads to a further decrease in demand. Firms will leave the market until the new equilibrium price, resulting from the diminished demand (due to both population decline and added transportation costs) and the smaller number of more centrally located firms, is once again equal to the lowest attainable cost. In the context of a hierarchy of central places, the function moves to a higher level centre where the market size is appropriate to the efficient delivery of the service.

In the public sector, for example, education, the consolidation process is initiated in the same way and for the same reasons. Public sector restructuring often lags behind that in the private sector and it is always more difficult because of the required collective decisions. Even so, the same trends toward centralization can be observed. In addition to the political sensitivity of public sector consolidations, differences in response to the same population decreases may be expected because of differences in the incidence of costs and benefits between private and public organizations.

Suppose that each school was initially an optimal size for the population it served and that the number of schools in a geographic area was also optimal. Thus, education services were delivered at the lowest attainable per unit cost. Let us further suppose that per student revenues available to the school through the combination of local tax revenues and provincial grants was just equal to the (minimum attainable) per unit costs. In terms of the existing funding arrangements, the Recognized Expenditures calculated by the Department of Education would be set equal to that minimum per unit costs. By definition, the Basic Foundation Operating Grant is calculated as the difference between Recognized Expenditures and recognized local tax revenue (assume that the "equalization factor" = actual mill rate).2 The size of the grant, on a per pupil basis, would thus vary according to the size of the local tax revenue.

As enrolment declines several things happen.

1. At the school level,
a) Adjustments in costs of instruction, constant PTR's:
The once optimal size schools are now operating with excess capacity and the per student costs increase. The option of building a smaller size school is not realistic, given the presence of the existing facility and (over time) the fact that the facility is already fully depreciated and has no opportunity cost. The total variable costs, however, may be reduced. Suppose teaching salaries are the only variable costs (in reality they make up about 75 percent of variable costs). If the number of teachers can be reduced in proportion to students, thereby maintaining a constant pupil-teacher ratio (PTR), the instruction cost per student will also remain constant. This is clearly possibile if the number of classes of each grade are reduced, and indeed could continue up to double- or triple-graded classrooms if these are acceptable in terms of quality standards. Ultimately, however, there will be an absolute constraint on the ability to cut instruction costs in proportion to enrolment decreases. For example, in the limit, if triple grading is the maximum acceptable combination of grades, then a K-8 school must have at least three teachers, one for each class. A constant PTR of 17 could be maintained with triple grades in a K-8 school of 51 children. At enrolments below 51, however, the PTR has to fall. This implies that the achievable instruction cost reduction is less than proportional to the reduction in enrolment and therefore average instruction costs must rise.

b) Impact of enrolment changes on PTR's:
The assumption of constant PTRs, used in the cost and revenue impact simulations above, is not realistic. Data on PTRs across school sizes consistently show higher PTRs in higher enrolment schools (Langlois and Scharf 1991). For this reason, the actual relationship between teachers and enrolment in the study area was statistically estimated.3 Since the data are those relating to existing schools they represent current practice rather than technically feasible PTR's.

Table 4.5 below illustrates the implications of the estimated equation for PTRs as the enrolment in a school changes. Changes in the implied PTRs indicate how teaching costs, at a constant average salary, can be expected to change as enrolment changes. For example, an enrolment drop from 500 to 100 leads to a 21.44 percent decrease in the PTR and therefore would represent a 27.44 percent increase in the teaching cost per student. Between enrolments of 100 and 50, there would be an additional 9.88 percent decrease in PTR based on the estimated equation and an additional 10.84 percent increase in per student teaching costs.

Table 4.5:  Estimated Relationship between Hypothetical Enrolment and FTE(T)
                                                                                                                                           
	Hypothetical	FTE(T)	Teacher-	Implied PTRs
	Enrolments	                 pupil Ratio 
                                                                                                                                             

	0.0	                 0.000	     --	--
	1.0	                 0.138	     0.1380	7.246
	10.0	                 0.977	     0.0977	10.235
	10.5	                 1.000	     0.0952	10.500
	20.0	                 1.761	     0.0881	11.357
	50.0	                 3.837	     0.0767	13.031
	100.0	                 6.916	     0.0692	14.459
	500.0	                 27.165	     0.0543	18.406
	1,000.0	                 48.964	     0.0490	20.423

The estimated increases in PTRs (decreases in teacher-pupil ratios [TPR]) in Table 4.5 can be applied to schools in the study area to approximate the understatement of costs in the previous cost simulations. Using the actual 1993 enrolments (FTE[P]) of each school, the estimated equation would yield the predicted number of teachers and implied PTRs (and teacher-pupil ratios) indicated in the second column of Table 4.6. The results represent the average relationship between school enrolment and the number of teachers that currently exists in the study area. For purposes of comparison, actual 1993 number of teachers and PTRs are shown in the first column. Variations in the PTRs across divisions are a reflection of the particular combinations of schools of different size enrolments.

Using the 2005 projected enrolments, with and without school closures, in the estimated equation generates the number of teachers (and PTRs) shown in the last two columns. The appropriate comparison in each case is the number of teachers predicted for 1993 using the equation. Without consolidation (the no closure option), the PTRs for 2005 are consistently lower in all divisions, a reflection of lower enrolments in all schools. With the simulated closures, the 2005 PTRs are consistently higher than those for the no closure scenario and, in three divisions, are also higher than the 1993 predicted PTRs.

The aggregate PTR in the study area, predicted by the equation, decreases from 15.75 in 1993 to 15.22 in 2005 without school closures. In per student terms, these figures represent 0.0635 and 0.0657 teachers in 1993 and 2005, respectively, translating into a 3.5 percent increase in instruction costs. Rates of increase in per student instruction costs, 1993 to 2005, for the individual Divisions are:

		Last Mountain	1.88 percent
		Lanigan		5.85 percent
		Long Lake	4.38 percent
		Davidson	2.70 percent

Viewed in another way, the difference in the number of teachers in 2005 between the school closure and no closure options is 9.09 (238.78 - 229.69), which translates into a cost difference of $363,600 at an average salary of $40,000.

Clearly, the increase in teaching costs, as enrolment declines and PTRs fall, is a powerful incentive to consolidate. Allowing PTRs to fall in the simulated impact of declining enrolments provides a more realistic assessment of how actual teaching costs are likely to change than do the assumptions of constant PTRs (and implied constant per student instruction costs). In addition to the instruction cost savings, the reduction in plant operating costs that are implicit in closures would add to the cost savings.

c) Reductions in non-instruction costs as enrolments decline:.

There are a number of practical reasons why it may be difficult to reduce actual costs, other than reducing the number of teachers, in proportion to enrolment decreases. That is, there are some fixed costs and indivisibilities that must be recognized. The administrative component of school costs is relatively fixed and would not decrease in proportion to the enrolment decreases. Second, as teachers are let go those with the least seniority will likely leave first so that the reduction in teaching costs at the margin is always less than the average teaching cost. Further, in high schools with, for example, five teachers representing 10 specializations (2 each), reducing the number of teachers may be even more difficult if the program is to continue to offer the previous range of topics. Any reduction in staff would imply that a part of the program would have to be obtained by another means. Finally, the plant operation and maintenance (heating, repairs, electrical, etc.) are fixed costs that cannot easily be reduced in proportion to the decrease in enrolment.

Thus, a number of sources of pressures for consolidation, not unlike those experienced in the private sector, would be present.

2. At the division level.

The decisions about the operation or closure of a school are made at the division rather than at the school level. A number of components of Recognized Expenditures and actual costs will change with enrolment drops. Some of these components are designed to compensate divisions for higher per student costs at lower enrolments. If it is possible to reduce costs in a way that matches net revenue losses, without compromising quality, declining enrolments can be accommodated without closures. For the division, a school may be considered for closure when its enrolment has declined below the level where revenue reductions can be matched by cost reductions without sacrificing quality beyond some defined minimum. In addition to the relationship between cost changes and revenue changes, the composition of revenues sources will change.

a) Small school factor recognition relative to increased costs without closures:

In recognition of the higher costs of operating small schools in sparsely populated areas, the sparsity and small school factors lead to increased Recognized Expenditures, and for a given tax base, these expenditures translate into increases in provincial grant money. They are not intended to be a substitute for consolidation, but rather compensation for higher costs where consolidation is not an option, given time-on-the-bus or quality constraints. Whether the eligibility criteria are adequate to preclude abuse of these provisions or whether the added revenues are adequate to offset higher per student costs where these are unavoidable is unclear, however.

As enrolment in a division declines, total revenue will fall since most of the Recognized Expenditures are directly proportional to enrolment, and provincial grants are the residual of these expenditures and local revenues. In the simulation of projected 2005 enrolments, Total Recognized Operating Expenditures (equal to total revenue) in the combined study area decreased by 16 percent while enrolment fell by 21 percent as shown in Table 4.7. Basic Program Recognized Expenditure, which constitutes close to three-quarters of Total Recognized Expenditures, decreased by 22 percent, very close to the percentage decrease in enrolment. The smaller percentage decrease in Total Recognized Expenditures and total revenue, relative to enrolment declines, reflects an increase in per student expenditures (revenues). This would be consistent with higher per student costs at lower enrolments.

The two components of Recognized Expenditures specifically designed to compensate for higher costs of operating small schools in remote areas are the sparsity and small chool factors.

Although these expenditures increased, especially the small school factor (by 31 percent), as a result of projected lower enrolments, the increase was small in absolute terms relative to the decrease in the Basic Program Recognized Expenditures. As Table 4.8 shows, the small school factor recognition increased revenue only modestly (4 percent of Total Recognized Operating Expenditures in 2005, no closure, compared with 3 percent in 1993). Combined, the small school and sparsity factors make up only about 5 to 6 percent of Recognized Expenditures in our study area. The component that does increase as a proportion of total expenditure between 1993 and 2005, both without and with school closure, transportation. This component increased from 13 percent of Total Recognized Expenditures in 1993 to 15 percent in the 2005 scenario without school closures, and this with an absolute decrease in the absolute amount of the transportation component. Since transportation has a per kilometre recognition, it is not as sensitive to enrolment drops as other expenditure components.

On a per student basis, the small school factor increased from $116 per student in 1993 to $192 per student in 2005, Table 4.9. The average Basic Program recognition decreased slightly from $3,332 in 1993 to $3,301 in 2005.4 Again, the transportation component per student increases significantly from $577 in 1993 to $708 in 2005 and it is primarily this increase that accounts for the increase in Total Recognized Expenditures per student from $4,474 in 1993 to $4,770 in 2005 without closure.

Since Recognized Basic Program Expenditures per student are unaffected by enrolment, the small school and sparsity factors would be expected to accommodate the increases in education (nontransportation) costs as school size decreases. The sparsity factor appears to lose its function, since the rate of compensation is close to its maximum in 1993. Because the rate is applied to the Basic Program Recognized Expenditures, which are declining, the sparsity factor recognition also declines. The small school factor, however, does result in increased Recognized Expenditures as schools become smaller. If we restrict consideration to the combination of the small school factor and Basic Program Recognized Expenditures and hold the latter constant, the increase in the small school factor results in an increase in combined Recognized Expenditures per student of 2.2 percent in the study area from 1993 to 2005.

As discussed above, the estimated relationship between number of teachers and enrolment suggests a 3.5 percent increase in per student instruction costs for the enrolment decrease experienced in the study area during the 1993-2005 period (no closures). The same enrolment decrease results in a 2.2 percent increase in Recognized Expenditures (translatable into revenues) per student. Thus, it would appear that the increase in instruction costs resulting from the declining PTR is not adequately accommodated by the small school factor. Retention of a small, "high cost" school may, nevertheless, be the efficient choice, for example where transportation costs implied by school closures (net of reduced per student costs in the receiving school due to both economies of scale and size) are greater than increased per student costs of retaining the school and operating with reduced enrolments. However, in doing so the division will find that the increased per student costs incurred are not matched by an increase in Recognized Expenditures. The rational economic choice may be discouraged by the existing administrative rules.

b) Cost and revenue changes with closure:

The cost and revenue simulations also include a scenario where some schools are closed. Using the estimated relationship between enrolment and number of teachers, PTRs were predicted for a scenario including school closures, (seeTable 4.6). As for the no consolidation option above, the estimated equation was used to predict the number of teachers implied by the enrolments in both 1993 and 2005, and consideration is restricted to the small school factor and Basic Program Recognized Expenditures. With the simulated school closures, the PTR in the study area increased from 15.75 in 1993 to 15.84 in 2005, representing a decrease in per student instruction costs of 0.6 percent. At the same time, the per student small school factor increased (1993 to 2005 with simulated closure) from $116 to $129. This increase represents a 0.4 percent increase in per student Recognized Expenditures, attributable to the combination of the small school factor plus the Basic Program in the study area. The simulated closures thus resulted in a 1 percent net improvement in expenditure recognition (which translates into a grant), less instruction costs, per student.

A more significant impact is seen in the transportation component of Recognized Expenditures, which increases from an average of $708 per student (2005) in the no closure option to $769 per student with closures. The increase in this component as a percentage of the 2005 Total Recognized Operating Expenditures (no closure) was 1.3 percent and would translate into an equivalent increase in the Basic Foundation Operating Grant, holding local tax revenues constant. Under present arrangements, assuming the transportation component is equal to actual transportation costs, transportation expenses incurred as a result of school closures represent no net cost to the division and would therefore not be a consideration, at the division level, in the decision to consolidate.

This analysis of the impact of declining enrolment on instruction costs and on the small school factor and Basic Program Recognized Expenditures suggests that, where school closure is feasible, cost savings will be realized. The accompanying reduction in the small school factor (relative to the no closure option) does not erode these potential savings. In addition, the higher transportation costs are covered through an increase in the Basic Foundation Operating Grant.

c) Redistribution of revenue sources:

Aside from the amount of revenue (Recognized Expenditures), the composition of the revenues will change with enrolment decreases (Table 4.10). Assuming the local tax revenues and other local revenue sources remain constant, a decrease in Recognized Expenditures, all else constant, will result in a decrease in the provincial grant of the entire amount. Thus, the declining enrolment in the study area resulted in a decline in the proportion of total revenues originating from the Basic Foundation Operating Grant from 36 percent in 1993 to 24 (25) percent without (with) school closures. More generally, a 20 percent decrease in recognized expenditure of $15 million in a division where funding is split 50-50 between local and provincial sources, for example, would result in a 40 percent decrease in provincial funding if local revenues remain constant. The shares would thus change to more like 40 percent provincial funding and 60 percent local.

d) Comparing cost savings with revenue loss for the consolidation decision:

At some point, as enrolment declines and revenues fall faster than costs can be reduced (and therefore costs per student rise), school closure will be considered.

At the division level, closure of a school will result in additional transportation costs and, unlike in the private sector, those costs are borne by the provider of education services rather than by the consumer (student).5 A separate component of Recognized Expenditures is based on standard rates for transportation costs calculated per student and per kilometre. This additional expenditure recognition becomes available only as a result of school closure since only then do the students whose school has closed become eligible. Given fixed local tax revenues, the increase in Recognized Expenditures due to the addition of transportation as an eligible cost translates directly into an equivalent increase in provincial grants (for a given total division enrolment). The relationship between actual and recognized transportation expenses is not clear, although Langlois and Scharf (1991) present evidence that the recognized expenditure is generous relative to actual costs. Even if the recognized transportation component correctly reflected the actual costs, school closures could still represent a financial benefit to the division because transportation expenses are covered by provincial grant money and any other operating cost savings realized by the division are retained by it.

From the division's point of view, school closure has the benefit of consolidating the students into a larger facility, thereby realizing economies of scale (lower per pupil costs). However, this benefit is not weighed against the cost of consolidation in terms of higher transportation (busing) costs since these costs are provided for through an increase in provincial grants.6 The more rational comparison in the closure decision is between the extra transportation costs and the added benefit of reduced per student costs resulting from the economies of scale realized through consolidation.

The ultimate constraint on consolidation, however, is the time spent on the bus by students. There is a range of "maximum" times, but an hour is often thought of as a workable guideline. Distance as the crow flies is, of course, a very poor approximation to time spent, as bus routes include stops, doubling back, and circuitous trips. Time can sometimes be reduced by small buses or even cars collecting children and bringing them to a common collection point. Still, time on the bus represents a very real constraint and will ultimately end the possibility of reducing costs of education through consolidation, even at the division level. When consolidation has proceeded to this limit, while enrolment continues to decrease, the per student costs of education will rise. Revenues will, however, continue to decline in proportion to enrolment decreases, with the grant revenue declining faster than the local tax revenue.

3. At the provincial level:

Viewed from the provincial level, the scope for consolidation and the evaluation of benefits and costs associated with this process has an added dimension. Administrative costs that are fixed at the division level may be considered variable at the provincial level. A reduction in the number of school divisions has been advocated by both the Langlois and Scharf report and by the Saskatchewan School Trustees Association (SSTA) report. Although costs were not a primary consideration, the reorganization did represent some reduction in administrative costs. The SSTA (1993) report shows that the per pupil administrative costs decline sharply with an increase in the number of students per division up to about 2,500, and in the presented data, continue to decline indefinitely at a slower rate beyond that number. Clearly, there is the potential for realizing economies of scale through a reduction in the number of school divisions, but several qualifications should be noted. First, division-level administrative costs represent only 4 percent of the total cost of educating students.7 Second, a significant consolidation of divisions may result in added costs in the form of travel and meeting expenses of directors and board members, partially offsetting the savings. Third, as divisions consolidate, there may be increased management demands on the school principal. Most small school principals teach part time as well, and if divisions are consolidated, additional administrative responsibilities may interfere with their teaching duties and require an offsetting increase in teachers. Fundamentally, regardless of the number of divisions, the impact of declining enrolment on small schools and many of the questions surrounding benefits and costs of consolidation will remain.

Many of the actual costs incurred by the division are not easy to interpret at the provincial level. The Langlois and Scharf report strongly suggests that "costs" are resource driven. That is, the division will spend all revenues allocated to it and thus "costs" increase when revenues increase. Also, as seen in the structure of the Basic Foundation Operating Grant, at the provincial level, calculations of costs are likely to show up as averages rather than recognizing differences among schools and/or school divisions due to local conditions, the most obvious being school enrolments, school size, and sparsity of population. Small school and sparsity factors are intended to compensate for higher costs where consolidation is not an option, but whether they are in fact related to actual costs or are functioning as intended, is not clear.

Nevertheless, some additional bases for consolidation may exist, for example, to better utilize resources or achieve common goals through the consolidation of rural school divisions with urban divisions, where feasible. It is also argued that fewer, larger divisions would tend to "level" the local tax contribution and facilitate capital planning.

Summary

The increases in per student costs that occur as enrolment declines due to population losses in rural areas are not matched by increases in Recognized Expenditures (and therefore in grants) under current funding arrangements. Actual per student costs of education are likely to vary considerably with the size of the school, the population density of the surrounding area, and the extent to which the school is operating with excess capacity. Determining equity and efficiency in the delivery of education services requires an accurate calculation, of those costs, with all considered "costs" being real costs, not provincial average "recognized expenditures" that would apply to very few, if any, actual school divisions. These costs should also be fully transparent so that rational decisions can be made and defended.

Both theory and empirical evidence suggest that there are economies of size and scale in the delivery of education services. These economies arise from the presence of fixed costs such as the operation and maintenance of the plant (school),8 the administration of the school (principal), the administration of the division (directors, their staff and facilities), the benefits of division of labour and specialization of teachers, the indivisibilities in the number of students per classroom (and therefore per teacher), etc. This necessarily implies that the per student costs of education will be higher in smaller schools and will increase in any school as enrolments fall below optimal levels.

Although consolidation into fewer, larger schools reduces the per student costs of education, it will increase transportation costs. School closure is the rational economic decision if the reduction in education costs outweighs the added transportation costs implied in consolidation. Consideration of both education and transportation costs leads to the conclusion that the optimal school size may decrease, along with increases in per student education costs, as population density falls. The present funding arrangements discourage the rational economic decision at the division level, one that would involve a comparison of cost savings with the additional costs incurred.


Conclusions and Recommendations

Summary

Based on population projections to 2005, all but 2 of the 28 schools were projected to experience enrolment drops. The growing schools were benefiting from the growth in population on a nearby reserve. Rates of enrolment change for individual schools varied from -40 percent to +11 percent over the 1993-2005 time period. In addition the age structure of the population changed, as province-wide past and present trends in (mostly) fertility rates were reflected in the profile of the age structure.

Impacts on costs and revenues under the constant pupil-teacher ratio (PTR) assumption showed that, in the existing decision framework and without school closures, revenue reductions implicit in the enrolment decreases consistently outweighed possible cost reductions as a result of reducing the number of teachers, even at constant PTRs. The implication is that local mill rates would have to be increased to make up the shortfall or that the delivery of education services are would have to change to further reduce costs. With school closures, however, cost reductions exceeded revenue loss in two of the four divisions. Of the remaining two divisions, one showed revenue reductions greater than cost savings because the funding formula generated a negative grant. In reality, grant reduction (= total grant) would be less than the projected cost saving. The more favourable budgetary impact under the closure option is partly the result of the increased transportation recognition (which translates into additional provincial grant money) implicit in school closures. In addition, closures would result in reductions in plant and operating costs.

The relationship between enrolment and number of teachers in the 28 schools in the study area was estimated to determine whether the constant PTR assumption was reasonable. The estimated relationship strongly supported the hypothesis that PTRs do not remain constant as enrolments decline but rather decrease. A decrease in PTRs at a constant teaching salary translates into an increase in per student teaching costs. The predicted PTRs from the estimated equation were used to predict the teaching costs implied by lower enrolments in per student terms. Without school closure, projected per student teaching costs in the study area increased about 3.5 percent. Since Basic Program Recognized Expenditures are constant across school sizes, increased costs attributable to small size and remoteness are addressed primarily through the small school factor. The same scenario that resulted in an increase in per student costs of 3.5 percent produced an increase in per student recognition of 2.2 percent. That is, as school enrolment falls, per student costs of education increase in a way that is not matched by increased revenues. This is analogous to the forces leading to private-sector consolidation as market size shrinks.

In the scenario with school closures, there was a net decrease to divisions in the study area of 1 percent in per student costs, showing a strong incentive to consolidate. This improvement consisted of a predicted decrease in per student teaching costs of 0.6 percent and an increase in the small school factor of 0.4 percent. Since the added transportation costs (due to additional busing) are recognized, and therefore matched by a grant, they have no influence on the decision to consolidate.

In rationalizing the delivery of education services to the rural population, the proper cost comparison, although central to the question of school consolidation, represents only part of the decision framework. Consolidation will be ultimately constrained by the time school children spend in transit. When these limits are encountered, costs per student will rise. Further, quality considerations will also be important as potential enrolments fall.

One avenue of rationalization in the delivery of education services in Saskatchewan that has been a matter of public debate is the reorganization of school divisions. Although a reorganization would likely reduce costs, the contribution of division-level administration to total costs is small and the potential cost savings much smaller. Because an administrative reorganization is unlikely to be justified in terms of cost savings, any need for reorganization has to be based on factors other than efficiency.

Conclusions

Saskatchewan's declining rural population reduces market size for businesses located in rural centres. Reduced market size leads to the consolidation of businesses into fewer and geographically more dispersed centres. In the context of the central place hierarchy, the function moves to a higher level where the market size is appropriate to the efficient delivery of the service.

The impetus for restructuring/consolidating education services is similar to that in the private sector. Pressures for consolidation result from higher per unit costs as enrolments fall due to both economies of size and of scale. That is, larger-scale schools operate with a lower per unit cost, and any size school experiences increases in per student costs as its enrolment decreases because the existing facility is used less intensively. Scale economies arise because of benefits from specialization and division of labour, as well as through economies in operation and maintenance of facilities. Economies of size are the result of spreading fixed costs over a larger number of students and the indivisibilities that lead to lower PTRs as enrolments fall. A notable difference in the public sector compared with the private sector, however, is that the provider of the service bears the added transportation cost implicit in the consolidation process. Further, in the case of schools, there is a legal obligation to deliver services to the entire population regardless of location. A consequence of combining education and transportation costs to define an aggregate average total cost per student is that costs may increase as schools are closed because students are collected from an increasingly larger geographic area. The result is that the (minimum attainable) per unit costs increase and the optimal size school (enrolment) decreases as consolidation proceeds.

When school closures are considered as a response to declining enrolments, the appropriate economic comparison would be between all per student costs with closure and those without closure. Since transportation costs are borne by the provider of the service, they should be a direct part of the consideration. As enrolment decreases generally, all existing schools are being operated with excess capacity and therefore at a higher per unit cost than if they were used to capacity. Without closures, these per student cost increases continue. When closure is considered, the higher per student costs implied in the base projection must be weighed against the combination of:
a) the cost saving due to the closure of the high cost school,
b) the cost saving in the receiving school due to the more efficient use of that facility, and
c) the increased transportation cost implied by closure.
In the existing decision framework, cost savings a) and b) are realized at the division level, leading to a strong incentive to consolidate, but the added costs represented by c) are not borne by the division since they are passed on to the provincial government. Because of the existing funding arrangements, the rational economic decision at the division level will lead to a different conclusion than it would at a level where all costs were recognized and transparent.

To arrive at the most efficient use of resources in restructuring the education delivery system, in the short run, alternatives must be compared on the basis of the least-cost method of delivering services to a declining enrolment with an evolving geographic distribution. Some additional cost savings can likely be realized by applying these critera to the existing network of rural schools.

More often, however, the choice is likely to be a constrained optimization. Quality considerations and time-on-the-bus constraints may preclude the rational choice of efficiency based only on monetary considerations. When a constrained optimization is necessary and a high cost school must be maintained, the cost implication of the alternatives should be clear and recognized in a straightforward, transparent way in terms of provincial funding. One of the greatest impediments to a rational assessment of alternatives is the absence of cost information. The constant Basic Program rate is unrealistic given the tremendous variations in enrolment size, school size and age, remoteness, and local conditions across the province. The combination of the small school factor, enrolment drop, and sparsity are apparently a response to the recognition that the flat Basic Program rate per student does not represent the real cost of education. However, these band-aids are inadequate response to an initially flawed method of recognizing costs.

Recommendations

The research results and the conclusions drawn from them suggest three possible responses to rural population decline in the delivery of education services, recognizing that the rural restructuring process is widespread. The existing distribution and size of schools are points of departure. As enrolments decline and per student costs increase, questions arise about the viability of schools. If school closure can be demonstrated to result in a net reduction in per student costs (including transportation and instructional) for a constant or improved quality of education, this would be the preferred alternative. But consolidation will not always be possible given the implied time in transit and quality considerations. Because of the size and distribution of the population, Saskatchewan will always have small rural schools. To facilitate a constrained optimum choice, three recommendations follow:

1. That the small school factor, sparsity, and enrolment drop be replaced with straight- forward techniques that compensate for high-cost small schools where these are the rational choice. A provincial average Basic Program rate may serve as a benchmark, with reductions being applied in lower-than-average-cost schools and additions in higher-than-average-cost schools.

2. That transportation costs be considered as real costs of school consolidation. School consolidation decisions should be made at the level where costs are incurred and revenues are received. Under the existing arrangement, school closures are more attractive than they would be if the added transportation costs were weighed against the cost savings due to economies of size and scale. Since transportation costs are simply passed on to the provincial government, they do not influence the consolidation decision at the division level, even though they are a real cost to provincial taxpayers. Failure to create a framework where the decision to close is made at the level where transportation costs are incurred will preclude the economically rational decision. Indeed, the right question will not even be asked.

3. That an empirical analysis of actual costs and how they vary with enrolment, location, etc., be undertaken to ensure that public expenditures on education bear some realistic relation to costs. Fundamental to a rational approach to public funding of education is the accurate identification of costs so the appropriate comparisons may be made. Actual costs are not clear in the existing data, and the illusion that no actual cost accounting is necessary follows in a system where expenditures are revenue driven. In reality, accurate cost information is necessary to improve the existing funding arrangements.

Table of Contents


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