Data and Methods

(1) Data
Panel data has been used in this study. A characteristic of panel data is that it includes time sequence information. The data used in this study was collected through two methods. One was to get the relevant data from the China Statistics Yearbook and the RTVUs Education Yearbook; the other was to directly survey accounting data from sample RTVUs at the prefecture and city level from 2002-2005. Items included in the cost data are based on the budget accounting items for public institutions in China and our prior research findings on major elements of the cost system. There are 4 major cost elements: fixed assets cost, human resources cost, study resources cost and management cost, as well as 33 cost sub-elements.

Survey samples for the research were selected based on China's different economic development levels in three different regions—East, Central and West, and only one province was selected from each of the three regions. Teaching venue samples were selected from RTVUs at the prefecture and city level from the chosen provinces. In total, 47% of the RTVU teaching venues at the prefecture and city level from Fujian, Hunan, and Xinjiang provinces were sampled, which amounted to 21 teaching venues. Cost data for 4 consecutive years was obtained for each teaching venue.

(2) Analysis methods
The research methods used for data processing and analyzing are based on Eviews software, including descriptive statistics, construction of regression functions and quadratic functions. The average cost per student uses descriptive statistics such as the mean value method. The average variable cost per student is calculated by the regression model: C=a+bx. Among them, C=total cost，a=fixed cost, b=average variable cost per student，x=number of enrolled students.

The conventional education scale-economy research model in China (Ding Xiaohao, 2000)^[11] has been applied to the research on scale economy of RTVUs and the optimal scale in student number. This study uses the following U-shaped quadratic function as its econometric model:

ACit = ai + b*Sit + c*SRit + d*STRit + e*Dit + u it , i=1,2,…21; t=1,2,3,4

ACit : the average cost per student
Sit: number of enrolled students
SRit: number of enrolled students squared
STRit: the ratio between students and teachers (Calculated by number of enrolled students /full-time and part-time instructors)
Dit: the regional dummy variable (applies to national samples only, not for provincial samples)

This econometric model isolates the average cost per student as the explained variable, while using the number of enrolled students, the number of enrolled students squared, the ratio between students and teachers, and the regional dummy variable (using the Western region as the benchmark) as the explanatory variables in a U-shaped regression model to calculate the optimal scale.

In processing the above data, cost values were normalized by factoring in the local consumer price index.

In this paper, there are 3 core research contents: average cost per student, average variable cost per student, and scale economy analysis and the optimal number of enrolled students. For each of these research contents, national samples and provincial data samples were examined and researched separately. Thus, we obtain information not only on the nationwide development of RTVUs at the prefecture and city level, but also on the specific development of such RTVUs in Fujian, Hunan and Xinjiang provinces. Moreover, the 3 provinces are representative of the 3 economic development zones (East, Central and West) of China, and so their data provides us with a general understanding of RTVUs at the prefecture and city level in China's 3 major economic development zones.

During the cost survey, we noted that the operating styles of RTVUs at the prefecture and city level vary greatly, and students recruited include ODL students, students with traditional university degrees, registered audio-visual students, vocational students and non-degree students, etc. Consequently, we needed to isolate the actual cost of students involved in ODL from the originally obtained data. Through statistics assessed by ODL experts and consultation with specialists, we confirmed that the cost coefficient after isolation is 0.75. In this article, the results of empirical research from both the original data and adjusted data have been reported to provide for reliable and high-quality research findings.

Findings of the Empirical Study

(1) The average cost per student from RTVUs at the prefecture and city level
With the expansion in enrolled students, the average cost per student from RTVUs at the prefecture and city level drops. This finding applies to both national and provincial samples. Refer to Table 1 (original data) and Table 2 (data adjusted by coefficient).

Table 1 and Table 2 show that differing economic development levels in China lead to a development imbalance in RTVUs at the prefecture and city level. The number of enrolled students falls from east to west. As for average cost per student, RTVUs in Fujian have the lowest, while RTVUs in Hunan and Xinjiang are close.

Table 1. Average cost per student from RTVUs at prefecture and city level
(unchanged prices, unit: RMB) 

Note: a. Number of enrolled students = Enrolled non-degree + enrolled degree
b. (number of teaching venues)
c. original cost data
d. Unchanged price = 100*current year cost /local CPI

Table 2. Average cost per student from RTVUs at prefecture and city level
(unchanged prices, unit: RMB) 

Note: a. Number of enrolled students = Enrolled non-degree + enrolled degree
b. (number of teaching venues)
c. Data adjusted by coefficient, cost coefficient = 0.75
d. Unchanged price = 100*current year cost /local CPI