Economies of Scope in Distance Education : The Case of Chinese Research Universities

With the rapid development of information technologies, distance education has become “another form of product differentiation in the output mix produced by the multi-product university or college” (Cohn & Cooper, 2004, p. 607). This article aims at analyzing the economies of scope of distance education (as an educational output) in Chinese research ist in distance education programs offered by Chinese research universities; b) there are economies of scale in distance education; and c) there are weak cost complementarities between distance education and research output, meaning that distance education and academic research can promote each other to reduce the costs in Chinese research universities.


Introduction
Before the 1960s, distance education had been on the margin of the contemporary education system around the world. Distance education was provided by private, profit-oriented institutions to disadvantaged populations as a means to support their desire for achieving greater equity and equality of opportunity to access education. Since then, distance education has been popularized by various governments with unprecedented passion. Advocates firmly believe that distance education will not only achieve greater equity and equality in higher education, but also take control of the cost of education and maintain it at a manageable level. In particular, the development of information technologies has revolutionarily expanded the range of distance education, resulting in a general improvement in its attractiveness, quality, effectiveness, and efficiency (Siaciwena, 2008).

Fengliang Li and Xinlei Chen
Tsinghua University, Beijing, PR China

118
In recent years, some researchers have argued that the development of information technologies, especially the Internet, has enabled Internet-based distance education to become "another form of product differentiation in the output mix produced by the multi-product university or college" (Cohn & Cooper, 2004, p. 607) and allowed research-intensive universities to benefit from distance education (Garrison & Anderson, 1999). However, prevailing current studies on the input and output of distance higher education have focused on their economies of scale 1 (Rumble, 1976(Rumble, , 1997Wagner, 1977;Abrioux & Ferreira, 2009) rather than their economies of scope 2 which regards distance higher education as part of a multiproduct 3. In response, Cohn and Cooper (2004, p. 609) suggest it is necessary to study distance education as a "product mix of the typical university and college." Two recent studies also investigate the economies of scope in distance education through theoretical analyses and discussions 4 (Bramble & Panda, 2008;Morris, 2008). However, these researchers do not seem to have conducted the empirical analyses of the economies of scope of distance education by higher education institutions (HEIs hereafter) as one of multiple outputs; although, they acknowledge the importance of distance education as an educational output and the necessity of inquiring into the cost relations of distance education with other educational outputs 5 as well as research outputs of HEIs. With an objective to fill this research gap, this article adopts the methodology of Cohn et al. (1989) and focuses on an empirical study on the economies of scope of distance education in research universities in China 6 .
The paper is structured in the following way: introduction of distance higher education in China, methodology (multiproduct cost function), data, results, and conclusions. 1 Economy of scale, in microeconomics, refers to the decrease in average cost (cost per unit) due to expansion of the scale for a single product type in an organization.
2 Economy of scope is conceptually similar to economy of scale. It refers to cost advantages for an organization in producing two or more products. Economy of scope can arise from the sharing or joint utilization of inputs and lead to reductions in unit costs. An example would be the benefits of teaching from academic research in universities.

3
According to economics of education, universities are typical multi-product organizations since universities usually tend to have a broader set of products, such as teaching and academic research.

4
These two studies focus on the economies of scale and scope of online learning or e-learning. However, according to Siaciwena (2008), although distance education has been widely carried out, it does not have a unified definition of consensus because of the multiplicity of service purposes and the variety of media utilized.
In fact, terms such as opening learning, flexible learning, and online or e-learning have been used as substitutions. In this article, online learning or e-learning is regarded as equivalent to distance education if there is no special explanation.

5
The distance education studied in this article refers to degree programmes, which should be regarded as an educational output of HIEs, instead of nondegree programmes, (i.e., training programs which should be regarded as a public service output).

6
If there is no special explanation, China in this article refers to mainland China which does not include Hong Kong, Taiwan, and Macau.

Distance Higher Education in China
Distance higher education in China is a later initiation than that of the developed countries; yet, it has been paid close attention by the Chinese government since the establishment of P.R. China in 1949. In the early 1950s, Renmin University of China and Northeast Normal University began to provide distance higher education. By the early 1960s, different provinces nationwide had witnessed the establishment of specific distance education institutions and the Radio and Television Universities (Ding, 2001, p. 91). During the Cultural Revolution (1966)(1967)(1968)(1969)(1970)(1971)(1972)(1973)(1974)(1975)(1976), the contemporary education system in China was almost destroyed. In the years after the Cultural Revolution, the Chinese government realized the importance of quickly recovering and upgrading the shattered education system. One of the benchmarks is the establishment of the Central Radio and Television University of China in 1979, leading the development of distance education nationwide. The Central Radio and Television University of China, directly led by the Ministry of Education (MOE hereafter), is dedicated to distance higher education, whose main role is to From 1979 to 1998, the task of providing distance higher education was mainly shared within the national Radio and Television University system, that is the specific institutions for distance higher education, including the Central Radio and Television University of China and other provincial or municipal Radio and Television Universities.
In the year 1998, the MOE decided to allow general HEIs to become involved in distance higher education, with Tsinghua University 8 , Zhejiang University, Beijing University of Posts and Telecommunications, and Hunan University as the first four institutions piloting the scheme. In April 2000, the MOE decided to further enlarge the scale of general HEIs providing distance education due to the information technology boom in China at that time.
Thirty more general HEIs were added to the list of distance higher education providers of degree programs (Ding, 2001, p. 100). By 2009, sixty-eight HEIs had been approved as degree program providers by means of distance education by the Ministry of Education (MOE, 2009).

7
For more information about the Central Radio and Television University of China, please refer to its homepage http://en.crtvu.edu.cn/about/general-information. Now it will be renamed National Open University. 120 The scale of distance education in general Chinese HEIs has been expanding (see Figure 1, which indicates the enrollments of distance education in general HEIs by year). Distance education has become an important educational output for the participating general HEIs as well as an important component of the total cost of these HEIs, making it possible for us to include distance education in the multiproduct function 9 in HEIs so as to conduct an empirical study on the characteristics of its cost complementarities 10 with other outputs and the product-specific economies of scope of distance higher education. Methodology Baumol et al. (1982) pioneered the invention of a comprehensive set of cost-efficiency analysis methods for multiproduct organizations, pointing out the three most frequently used functions: quadratic, CES (constant elasticity of substitution) and hybrid translog cost function 11 . This set of analysis methods has been widely applied in banking, transportation, public facilities, telecommunication, and health care as well as many other multiproduct organizations.
Additionally, Cohn et al. (1989) applied this set of analysis methods to the study of HEI outputs which investigated the economies of scope of US public and private HEIs with the help of the quadratic cost function. The majority of empirical studies on the economies of scope of higher education so far have adopted quadratic cost function (Lewis & Dundar,9 In microeconomics, a multiproduct function is a function that specifies costs of two or more outputs for all combinations of inputs in an organization.

10
In a multiproduct organization, cost complementarities exist when the marginal cost of producing one output is reduced when the output of another product is increased.
The primary objective of this research is to study the economies of scope of distance education provided by general HEIs rather than to compare the advantages and disadvantages of the various functions mentioned above. In light of this point, this article adopts the quadratic cost function due to its wide application.
Thus, the cost function is as follows: where C is the total cost of producing k products, and q i is the output of the ith product.
Generally economies of scope are divided into global and product-specific economies of scope 12 . Global economies of scope measure how much can be saved from joint production of multiple products compared with a separate process, which means that a certain HEI can produce all products more cheaply than a combination of separate HEIs can.
Global economies of scope are defined as follows: Product-specific economies of scope are also to be examined since scales of all products may not increase (or decrease) proportionally. Product-specific economies of scope are given by: Product-specific economies of scope associated with product k exist if k SC is greater than zero, which means a certain HEI can produce product k more cheaply with other products than a combination of separate HEIs can.

12
The product-specific economy of scope exists when the product can bring cost advantages for the multiproduct organization. 122 For a multiproduct organization, the interaction items of cost functions indicate the existence of cost complementarities in joint production. For doubly differentiable cost function, weak cost complementarities exist if the two products k and l meet the following inequality:  There are three highlights in Table 1. First, although public service is an important output of HEIs, the data constraint has been a major obstacle to include them in the cost functions in the studies carried out so far. Therefore, this article does not consider it. Second, some studies have controlled for production quality (de Groot et al., 1991;Glass et al., 1995;Stevens, 2005;Johnes et al., 2008), and some scholars have tried to take better control of other input factors through including the average staff salary or teaching costs in their studies (Hashimoto & Cohn, 1997;Koshal et al., 2001;Laband & Lentz, 2003;Cesar, 2006). However, given the limitation of data accessibility, this study does not control for either of the two variables mentioned above. Third, as pointed out by Cohn et al. (1989) and some other scholars, there is no consensus on appropriate measures of output, especially the research output; and there should be a high correlation between research output and research expenditure. In the absence of a better alternative, many empirical studies used research expenditure as the measure of research output (Cohn et al., 1989;Koshal & Koshal, 2000;Stevens, 2005;Hou, et al., 2009). Our study also follows the practice of existing empirical studies.

13
In China, presently there is no master or doctoral degree program available through distance education.

Results
First we use the OLS method to estimate the flexible fixed cost quadratic (FFCQ) function.
The FFCQ function is in the following form: where TC is total cost, Q k is the kth output, and F k is the dummy variable which assumes the value 1 for positive amounts of the output Q k and the value zero otherwise. 0 α is constant, k α and kl α are coefficients, and µ is an error term. Note: *** Denotes 1% level of significance;** Denotes 5%

level of significance
As this study is conducted on the basis of cross-sectional data, the presence of heteroscedasticity should be tested. Through the White heteroscedasticity test, we found that the presence of heteroscedasticity cannot be rejected. One way to correct for heteroscedasticity is to compute the weighted least squares (WLS). The regression of weighted least squares is shown in Table 3.
The following can be concluded through the estimation of weighted least squares. As shown in Table 3, the relation among the coefficients is QD < QU < QG, which indicates that when educational outputs are of small scales, the relation of their average cost is that distance education < undergraduate education < graduate education. This indicates that when the distance education of a research university remains at a small scale, the average cost of it is lower than that of general undergraduate education. There are two possible explanations.
One is that distance education has cost advantages compared with general education. The other is that distance education is equivalent to low-quality education compared with general education (Siaciwena, 2008). Other conclusions are as follows. Table 3, the coefficient of QDSQ is negative and significant, meaning that with the expansion in scale, the average costs of distance education are decreasing.

As shown in
This implies that in research universities in China, when their distance education has reached a certain scale, the average cost would be further reduced, confirming the findings of the existence of economies of scale in distance education in previous studies (Rumble, 1976(Rumble, , 1997Wagner, 1977). Table 3, the coefficients of interaction items of QD and other educational outputs are all positive (with the coefficient of IQDQG being insignificant and the coefficient of IQDQU being significant), rejecting the existence of cost complementarities between distance education and general undergraduate education and graduate education respectively. That is to say, in current Chinese research universities the increase in output of general education does not result in the decrease of the cost of distance education. This result is inconsistent with many scholars' viewpoint because generally speaking, the facilities, faculty, and management of the two forms of education can be shared in the same university (Morris, 2008). Then why do the cost complementarities not exist in the case of Chinese research universities? The most possible reason might be that in those universities there are two independent subsystems for general and distance education with separate education resources including facilities, faculty, and education management platforms. Therefore, it is expected that the cost complementarities of the two subsystems will appear when they are increasingly combined in the future.

As shown in
3. Nevertheless, the coefficient of IQDQR is negative and significant, indicating the exis- 126 academic and research level. Although research and distance education are of different subsystems, the higher the research level, the higher the level of information technology, providing high-quality technical support from the subsystem of research to the subsystem of distance education at a relatively low cost. Second, universities of higher academic level usually have highly qualified faculty who can teach distance courses, reducing the cost of hiring high-quality faculty outside the school because it would cost the universities much more to do so due to the salary system of higher education in China. Meanwhile, since distance education brings considerable tuition to the universities, this money can be used to boost research output. Table 3, the coefficient of CSIZE is significantly negative, which can be interpreted as the significant influence over cost by the student-teacher ratio, and the higher the ratio, the lower the cost, which indicates the intrinsic economies of scale in teaching.

As shown in
Now the question is whether specific-product economies (hereafter PSE) of scope in distance education exist when provided by Chinese research universities. The formula is as follows: Firstly, we conduct the calculation under the 100% output level 14 , which results in PSED = 0.0933. Thus it can be concluded that presently the product-specific economies of scope for distance education exist in Chinese research universities and that providing distance education, on top of general education and research output, is conducive to reducing the cost and increasing the total output of a university.
Secondly, we analyze the PSE D for different levels of output. Calculations have been conducted based on two different scenarios: 1) HEIs only make changes to the scale of their distance education; and 2) the scale of every HEI output changes by the same proportion.
The results are shown in Table 4.
From Table 4 we can see that at the output level from 50% to 140%, PSE of scope do exist in the output of distance education among the Chinese research universities, which shall disappear either when the output of distance education reaches a 220% level of its present scale in scenario 1 or when all outputs reach a 150 % level of their present scale in scenario 2. Therefore, research universities should consider the subsystems of general education and research when planning distance education, or they may wrongly estimate the reasonable boundary of economies of scope so that diseconomies of scope may arise.
14 Those who are interested in the detailed calculation process may contact the author.

Conclusion
As distance education has become an important educational output of general HEIs, some scholars believe that it is necessary to study its economies of scope (Cohn & Cooper, 2004;Morris, 2008). Since Chinese universities started to offer distance higher education in 1998, 70 general universities have been qualified as providers. These universities, research- and so on (Morris, 2008). However, the empirical results in this article do not support 128 such general opinion, which we believe is due to the operational mechanism of distance education in research universities. There are essentially two independent subsystems for general and distance education with separate facilities, faculty, and education management platforms and little communication and interaction between them.
If economies of scope do not result from the cost complementarities of distance and general education, what do they come from? What we have found is the existence of weak cost complementarities between distance education and research output, meaning that research output can reduce the average cost per student of distance education, enabling the university to produce more output with the same cost. As stated above, we find that distance education and academic research can promote each other, which has rarely been mentioned in previous studies and discussions on the economic issues of distance education. Such phenomenon evinces the feasibility of providing a new type of output (i.e., distance education on top of general education and research output). It also verifies that as multiproduct organizations, general research universities have been suitable institutions for the pilot programs of distance higher education launched by the Chinese Ministry of Education.
Furthermore, the results show that the average cost of distance education is lower than that of undergraduate or graduate education and is negatively correlated with the increase of its output. Therefore, scale production is economic for distance education, confirming the conclusion of the existence of economies of scale in distance education by previous studies (Rumble, 1976(Rumble, , 1997Wagner, 1977).
In conclusion, there are economies of scope in distance education due to the weak cost complementarities between distance education and research output. However, the boundary of economies of scope does exist, and research universities therefore should avoid excess growth in distance education so as not to cross the boundary. We also find that there is no complementarity between general and distance education. The most possible reason might be that the universities have two independent subsystems for general and distance education. Therefore, we suggest that universities should promote the integration and resourcesharing of the two systems so as to lower the cost, increase the output, and achieve greater economies of scope.