An analysis of the optimization algorithm of comprehensive budget performance management for budgeting in higher education institutions

In recent years, the continuous investment of provincial finance in the double first-class construction of colleges and universities has enabled colleges and universities to receive more financial support by striving for project funds [1-2]. These inputs have greatly promoted the sustainable development of the cause of colleges and universities and brought unprecedented development opportunities. However, this also brings greater management pressure and challenges. Colleges and universities need to use these funds more efficiently and transparently, strengthen project management and performance evaluation, and ensure the rationality and effectiveness of the use of funds [3-4]. At the same time, colleges and universities also need to strengthen financial management and risk prevention, do a good job of risk assessment and control, and guarantee the safe and stable use of project funds [5-6].

In the process of financial system reform, comprehensive budget performance management plays an important role, but it is also an important manifestation of the financial management system and management functions [7-9]. China’s education department and finance department jointly issued relevant regulations, requiring universities to strictly implement and build the “three full” budget performance system. The use of comprehensive performance management in university programs should strengthen the daily management and ensure that the management work is meticulous in order to improve the overall effectiveness of university programs [10-11]. Colleges and universities are administrative institutions, but it has some special characteristics, so in the process of project management should pay attention to the allocation and utilization of funds [12-15]. Therefore, colleges and universities to carry out project management, the use of comprehensive budget performance management can effectively solve the financial problems and play the role of funds for the promotion of the project [16-17].

Colleges and universities should grasp this historical opportunity, strengthen management innovation and system construction, promote the sustainable development of the cause of colleges and universities, and make greater contributions to the realization of high-quality development [18-20]. At the same time, the requirements of project expenditure management are becoming more and more stringent, which puts forward higher requirements for the level of project management in colleges and universities, and makes the financial management of colleges and universities encounter unprecedented difficulties [21-23].

In this paper, the comprehensive budget performance management work of 10 colleges and universities in 10 provinces from 2014 to 2023 is selected as the research object, and the optimization of budgeting in colleges and universities is analyzed horizontally and vertically dynamically and statically under the Data Envelopment Analysis (DEA) and Malmquist index model respectively. Subsequently, the logistic regression model is used to regress and compare the factors that affect the input and output efficiency of colleges and universities. Finally, four safeguards are proposed for the management of budgeting in colleges and universities, namely, the quality of staff, the level of budgeting, the accuracy of data and the implementation of budget performance management in the whole process.

2

Performance measurement and impact factor analysis model for budgeting

2.1

Theoretical approach to evaluation

2.1.1

The Data Envelopment Analysis (DEA) method

Data Envelopment Analysis [24] (DEA) is a new statistical analysis method based on multiple input-output units, which can estimate the effectiveness of units with multiple inputs and multiple outputs at the effective boundary of the output. There are two models for data envelopment analysis, CCR and BCC. 1)

CCR model (constant returns to scale) efficiency measurement methods

Assume that there is n college budgeting that produces S outputs using M inputs, x_i is the input for performance management in the i th college, and y_i is the output for performance management in the i th college.

Using linear programming dyadic theory and introducing positive and negative deviation quantities s⁺, s⁻, the following equation can be obtained: (1) $M i n i m i z e θ - ε (\sum_{i = 1}^{m} s_{i}^{-} + \sum_{i = 1}^{s} s_{r}^{+})$ (2) $s t . {\begin{array}{l} \sum_{j = 1}^{n} x_{i j} λ_{j} + s_{i}^{-} = θ x_{i 0}, i = 1, 2, ..., m \\ \sum_{j = 1}^{n} y_{i j} λ_{j} - s_{r}^{+} = y_{r 0}, r = 1, 2, ..., s \\ λ_{j} \geq 0, j = 1, 2, ..., n \\ s_{i}^{-} \geq 0, s_{r}^{+} \geq 0 \end{array}$

where ε is a non-Archimedean infinitesimal, x_i represents the inputs of the comprehensive budget performance management of the i rd university, and y_i is the outputs of the comprehensive budget performance management of the i th university. s⁻ represents the vector of slack variables for the input variables and s⁺ represents the vector of slack variables for the output variables.

When θ = 0 and s⁻ = 0, s⁺ = 0 represents the inputs are efficient and the input-output ratio is maximized, and vice versa. 2)

BBC model [25] (variable returns to scale) efficiency measurement method the only difference between the variable returns to scale model and the efficiency measurement method under the constant returns to scale model is the addition of a condition: $\sum_{i} = 1^{n} λ_{i} = 1$ , which is: (3) $M i n i m i z e θ - ε (\sum_{i = 1}^{m} s_{i}^{-} + \sum_{i = 1}^{s} s_{r}^{+})$ (4) $s t . {\begin{array}{l} \sum_{j = 1}^{n} x_{i j} λ_{j} + s_{i}^{-} = θ x_{i 0}, i = 1, 2, ..., m \\ \sum_{j = 1}^{n} y_{r j} λ_{j} - s_{r}^{+} = y_{r 0}, r = 1, 2, ..., s \\ \sum_{j = 1}^{n} λ_{j} = 1, λ_{j} \geq 0, j = 1, 2, ..., n \\ s_{i}^{-} \geq 0, s_{r}^{+} \geq 0 \end{array}$

At this stage, the initial value of budgetary efficiency value is obtained by using BCC model, on the basis of which the efficiency value obtained is called comprehensive technical efficiency (TE), based on variable returns to scale, there are two types of comprehensive technical efficiency: pure technical efficiency (PE) and scale efficiency (SE), i.e., TE = PE × SE. In this case, the pure technical efficiency is the productivity of HEIs which is affected by the managerial ability and technical level of HEIs, whereas the Scale efficiency refers to the output efficiency of HEIs that is affected by the size of HEIs under different modes of operation.

2.1.2

Malmquist exponential modeling

Since the DEA model is only applicable to the cross-sectional comparison of efficiency in performance management of universities, the Malmquist index model was invoked, and then the longitudinal analysis of the productivity of universities was launched, and its dynamic analysis was carried out so as to dynamically analyze the change of the time trend of efficiency.

Malmquist productivity index based on Shepherd’s distance function, which is a production technique with multiple inputs and multiple outputs that does not need to state a specific behavioral criterion (e.g., minimum cost and maximum benefit). The distance function is determined in the direction of outputs, or in the direction of inputs. The input distance function is defined as follows: (5) $D_{0} (x, y) = \max {ρ : (x / ρ, y) \in p (y)}$

Use x, y to describe the matrix of input and output variables, use ρ to describe the input-oriented efficiency indicators, and define the set of possible outputs as p(y).

The value of the function will be 1 or greater if and when x is an element of p(y). When x is at the outer edge of a set of possible production, then the function value is 1; conversely, when outside p(y), then the function value will be smaller than 1.

Total factor productivity refers to the ratio of the total output of a system to the actual inputs of all factors of production and the Malmquist index, which is the change in total factor productivity, is the geometric mean of the Malmquist productivity index for periods t and t + 1: (6) $M I (x_{t + 1}, y_{t + 1}, x_{t}, y_{t}) = [\begin{matrix} D_{0}^{t} (x_{t + 1}, y_{t + 1}) \\ D_{0}^{t} (x_{t}, y_{t}) \end{matrix}] \times \frac{D_{0}^{t + 1} (x_{t + 1}, y_{t + 1})}{D_{0}^{t + 1} (x_{t}, y_{t})}$

Where: M denotes the Malmquist productivity index, x_i denotes the input vector in period t, x_i+1 denotes the input vector in period t + 1, y_i denotes the output vector in period t, y_i+1 denotes the output vector in period t + 1, and $D_{0}^{t} (x_{t}, y_{t})$ and $D_{0}^{t + 1} (x_{t + 1}, y_{t + 1})$ are the input distance functions of the production point in periods t and t + 1 respectively. If the total factor productivity is higher than 1, it means that the total factor productivity of the university is higher in period t + 1 than in period t; on the contrary, if it is less than 1, then its total factor productivity is lower in period t + 1 than in period t.

According to Fare, the total factor productivity index (MI) is decomposed into technical change (TC) and technical efficiency change (EC), while EC contains pure technical efficiency change (PTEC) as well as scale efficiency change (SEC). Then there are: (7) $M I = T C \times E C$ (8) $M I = P T E C \times S E C$

And a further decomposition of TC yields output-biased technical change (OBTC), input-biased technical change (IBTC) and technical scale change (MATC), which can be expressed as: (9) $O B T C = {[\frac{D_{0}^{t} (x_{i + 1}, y_{i + 1})}{D_{0}^{t + 1} (x_{i + 1}, y_{i + 1})} \times \frac{D_{0}^{t + 1} (x_{i + 1}, y_{i})}{D_{0}^{t} (x_{i + 1}, y_{i})}]}^{\frac{1}{2}}$ (10) $I B T C = {[\frac{D_{0}^{t + 1} (x_{i}, y_{i})}{D_{0}^{t} (x_{i}, y_{i})} \times \frac{D_{0}^{t} (x_{i + 1}, y_{i})}{D_{0}^{t + 1} (x_{i + 1}, y_{i})}]}^{\frac{1}{2}}$ (11) $M A T C = \frac{D_{0}^{t} (x_{i}, y_{i})}{D_{0}^{t + 1} (x_{i}, y_{i})}$

Technical changes can be derived as: (12) $T C = O B T C \times I B T C \times M A T C$

Where MATC refers to a change in the scale of technology, a neutral technological progress. OBTC refers to the effect of technological progress in contributing to multiple outputs in different proportions. In addition, when there is a single output indicator for HEIs, OBTC is 1. When OBTC > 1, it indicates that technical progress is tending to raise unintended outputs. IBTC reflects the change in the marginal rate of substitution of technical progress for each input factor. If IBTC > 1, it suggests that input-biased technological progress will cause total factor productivity to continue to rise when the share of other factors is small.

Assuming two input factors x₁ and x₂, when $x_{2}^{t + 1} / x_{1}^{t + 1} > x_{2}^{t} / x_{1}^{t}$ , IBTC > 1 indicates that technological progress favors use x₂, and savings x₁: IBTC < 1 indicates that technological progress favors use x₁, and savings x₂. When $x_{2}^{t + 1} / x_{1}^{t + 1} < x_{2}^{t} / x_{1}^{t}$ , IBTC > 1 indicates that technological progress favors use x₁, and savings x₂: IBTC < l indicates that technological progress favors use x₂, and savings x₁.

2.2

Logistic regression

2.2.1

Basic concepts

Logistic regression [26] a generalized linear regression analysis model, and multiple linear regression has a lot in common, compared with multiple linear regression added Logistic distribution, for the binary classification problem is more commonly used, indicating the likelihood of the occurrence of an event.

There is a random variable Y with random variable X, where Y ∈ {0, 1}, X ∈ Rⁿ, P(Y|X) denotes the probability of Y occurring given X that for a given example dataset $D = {(y_{i}, x_{i}^{k})}$ , denotes the i th sample, k denotes the k th random variable X, and assuming that there y_i = 1 are positive effectors $y_{i}^{+} = f (x_{i})$ and negative effectors $y_{i}^{-} = g (x_{i})$ , such that $z_{i} = y_{i}^{+} - y_{i}^{-}$ , then: (13) $y_{i} = {\begin{matrix} 1, z_{i} > 0 \\ 0, z_{i} \leq 0 \end{matrix}$

can be envisioned based on the linear model: (14) $\begin{matrix} y_{i}^{+} = X_{i} φ + δ_{i} \\ y_{i}^{-} = X_{i} γ + τ_{i} \end{matrix}$

where x_i denotes the vector of the ind sample independent variables, φ, γ denotes the parameter vector of the model, and δ_i, τ_i denotes the error terms and are independent of each other obeying a normal distribution with: (15) $\begin{matrix} β = φ - γ \\ ε_{i} = δ_{i} + τ_{i} \end{matrix}$

Then it is obtained according to Eqs. (13) and (14): (16) $z_{i} = X_{i} β + ε_{i}$ (17) $P (y_{i} = 1) = 1 - F_{ε} (- X_{i} β)$

Where F_ε is the cumulative distribution function of the random variable error term ε, ε obeys a normal distribution with expectation of μ and variance of σ², then its standard normal cumulative distribution function, since there is no analytical expression for the cumulative distribution function of the normal distribution, according to the high degree of similarity between the logistic distribution and the normal distribution, the logistic distribution function is used to approximate it.

2.2.2

Model form

If x is a continuous random variable and obeys a Logistic distribution, the graph of its distribution is a S-shaped curve with a logistic distribution function expression: (18) $F (x) = \frac{1}{1 + e^{-^{(x - μ)} / γ}}$

Where, μ is the position parameter and γ > 0 is the shape parameter, which is obtained by substituting (18) according to Eq. (17): (19) $P (y_{i} = 1) = 1 - F_{ε} (- X_{i} β) = 1 - \frac{1}{1 + e^{X_{i} β}}$ (20) $P (y_{i} = 1) = \frac{1}{1 + e^{- X_{i} β}}$ (21) $P (y_{i} = 0) = \frac{1}{1 + e^{X_{i} β}}$

2.2.3

Parameter estimation

Unlike linear regression, logistic regression dependent variable is non-continuous, so its parameter estimation no longer uses the least squares method, but the great likelihood estimation, by maximizing the product of the estimated probabilities of each sample point to estimate the β parameter vector, for the y_i ∈ {0, 1} binary classification its likelihood function is expressed in the form: (22) $f_{i} = X_{i} β$ (23) ${\hat{y}}_{i} = g_{i} (f_{i}) = \frac{1}{1 + e^{- f_{i}}}$ (24) $L = \prod_{i = 1}^{n} g_{i} {(f_{i})}^{y_{i}} {(1 - g_{i} (f_{i}))}^{1 - y_{i}}$

For arithmetic convenience, the natural log-likelihood is simplified by taking the natural log-likelihood and changed from extremely large to extremely small to obtain: .(25) $L L = - l n (L) = \sum_{i = 1}^{n} - y_{i} \ln (g_{i} (f_{i})) - (1 - y_{i}) l n (1 - g_{i} (f_{i}))$

In finding the best estimate $\hat{β}$ of the parameter vector β, L is equivalent to LL, which follows from the chain rule for partial derivatives: (26) $\frac{\partial L L}{\partial β} = \sum_{i = 1}^{n} \frac{\partial L L}{\partial g_{i}} \cdot \frac{\partial g_{i}}{\partial f_{i}} \cdot \frac{\partial f_{i}}{\partial β}$

where the respective partial derivative functions [27] are: (27) $\frac{\partial L L}{\partial g_{i}} = - \frac{y_{i}}{g_{i} (f_{i})} + \frac{1 - y_{i}}{1 - g_{i} (f_{i})} = - \frac{y_{i}}{{\hat{y}}_{i}} + \frac{1 - y_{i}}{1 - {\hat{y}}_{i}}$ (28) $\frac{\partial g_{i}}{\partial f_{i}} = g_{i} (f_{i}) \cdot (1 - g_{i} (f_{i})) = {\hat{y}}_{i} \cdot (1 - {\hat{y}}_{i})$

The above equation is substituted into Eq. (27) to obtain the vector of partial derivatives of the parameter vector β: (29) $\frac{\partial L L}{\partial β} = \sum_{i = 1}^{n} ({\hat{y}}_{i} - y_{i}) X_{i}$

Combined with the 2-1-2 gradient descent method described above, the estimate β of the parameter vector β can be found.

2.2.4

Regression coefficient tests

Based on the measurement theory of great likelihood estimation, the distribution of the great likelihood estimators approximates a normal distribution with no or little bias when in the case of large samples. By implication, the variance and covariance of the set of great likelihood estimates can be obtained from the second order partial derivatives of the log-likelihood function of the model parameters estimated at the great likelihood estimate, and then the test statistic can be constructed with reference to the form of the t statistic, a test known as the wald test.

This test is called the wald test. Let G denote the p*p matrix of the second-order partial derivatives of the log-likelihood function, and p denote the number of dimensions, i.e: (30) $G_{i j} = \frac{\partial^{2} L (β)}{\partial β_{i} \partial β_{j}} (i, j = 0, 1, \dots, p)$

G is called the Hessian matrix. If the elements of the Hessian matrix are estimated at the great likelihood estimator $β = \hat{β}$ , then the large sample covariance of the regression coefficients is approximated as: (31) $V a r (\hat{β}) = - G {(\hat{β})}^{- 1} = {(X^{T} V X)}^{- 1}$

The square root of the diagonal elements of this covariance matrix is the large sample standard error of the regression coefficient. In the above equation, matrix X^T represents the transpose of matrix X, matrix (X^TVX)⁻¹ represents the inverse of matrix X^TVX, matrix V is the diagonal matrix of n*n, and n is the number of samples. The main diagonal is the variance estimate for each observation, i.e., the i th diagonal element of v is: (32) $V_{i i} = {\hat{y}}_{i} (1 - {\hat{y}}_{i})$

So set the null hypothesis to: (33) $H_{0} : β_{j} = 0, H_{1} : β_{j} \neq 0$

Its test statistic is: (34) $Z_{0} = \frac{{\hat{β}}_{j}}{s e (β_{j})}$

This statistic is tested with reference to the standard normal distribution, and also with reference to squaring 1 and comparing it to a chi-square distribution with Z₀ degree of freedom.

3

Regression results and safeguards for university budgeting

3.1

Results and Analysis of Budget Performance Evaluation of Higher Education Institutions

3.1.1

Input-output indicators of university budget performance

This paper takes colleges and universities in 10 provinces, cities and autonomous regions in China (A, B, C, D, E, F, G, H, I, J) as research samples, and analyzes the performance of education expenditure of the sample colleges and universities from 2014 to 2023, taking into account the human, financial and material inputs of the colleges and universities, and from the five basic functions of the 10 colleges and universities. Educational funding performance is analyzed. That is, full-time teachers at colleges and universities are selected as human input, general public budget education funding as financial input, and fixed assets at colleges and universities as material input. The five basic functions of colleges and universities are talent cultivation, scientific research, social service, cultural heritage and innovation, and international exchange and cooperation. Therefore, the total number of graduates is selected as the indicator of talent cultivation, published scientific and technical papers as the indicator of scientific research results, income from technology transfer of scientific and technical results as the indicator of output of social services of colleges and universities, the percentage of top 100 colleges and universities in alumni associations as the indicator of cultural inheritance and innovation, and collaborative research of colleges and universities as the indicator of international exchanges and cooperation. The input and output indicator system for university performance evaluation is constructed as follows, and the input and output indicators for university budget performance are shown in Table 1.

Table 1.

The performance of the university budget performance is the output index

Primary indicator	Secondary indicator	Tertiary index
Input index	Manpower	Special teacher number (person)
	Financial resources	General public budget education funding (yuan)
	Resources	Fixed asset investment (10,000 yuan)
Output indicator	Talent culture	Total number of graduates (10,000)
	Scientific research	Publish science and technology papers
	Social services	Technology transfer income (1000 yuan)
	Cultural heritage and innovation	The alumni association of the top 100 universities
	International exchanges and cooperation	Cooperative research (dispatch)

3.1.2

Comparative analysis of the efficiency of budget performance evaluation in higher education institutions

The input and output indicators of university education funding selected in this paper are analyzed in terms of efficiency by using deap software under the model to analyze the input and output indicators of colleges and universities in China’s provinces and cities. Comprehensive efficiency indicates that the decision-making unit with the best efficiency is selected as the evaluation standard, and the input level should be increased when the output level of the decision-making unit remains unchanged. Technical efficiency indicates the optimal output that can be achieved by each decision-making unit when the input is certain. Scale efficiency indicates the appropriateness of the size of the decision unit. The product of technical efficiency and scale efficiency is equal to the comprehensive efficiency (retaining 4 effective digits).The results of the comparative analysis of the efficiency of budget performance evaluation of universities in provinces and cities in 2014 and 2023 are shown in Table 2. As can be seen from the table, in 2023, the average value of the comprehensive efficiency of China’s educational resource allocation in colleges and universities was 0.9991, and the average values of scale efficiency and technical efficiency were 0.9999 and 0.9992, respectively.The average values of the comprehensive efficiency, scale efficiency and technical efficiency of the budgets of colleges and universities in each province in 2023, compared with that of 2014 (the three indicators were 0.9846, 0.9987 and 0.9860, respectively), were all There is a significant increase, and the average value of the overall comprehensive efficiency is higher. It indicates that the input-output status of education expenditure in Chinese universities in all provinces and cities is relatively effective, and that universities have strengthened the learning of budget management capacity, so that the existing technical level of budget performance management has been upgraded.

Table 2.

Evaluation efficiency of university budget performance

Year	City name	Integrated efficiency	Scale efficiency	Technical efficiency	Scale benefit
2014	A	0.9987	1	0.9987	Drs
	B	0.8993	1	0.8993	Irs
	C	1	1	1	-
	D	0.9983	0.9989	0.9994	Drs
	E	1	1	1	-
	F	0.9913	0.9986	0.9927	Drs
	G	1	1	1	-
	H	0.9800	0.9988	0.9812	Irs
	I	0.9907	0.9923	0.9984	Irs
	J	0.9880	0.9982	0.9898	Drs
2023	A	1	1	1	-
	B	0.996	1	0.996	Drs
	C	0.9989	0.9995	0.9994	Drs
	D	1	1	1	-
	E	1	1	1	-
	F	1	1	1	-
	G	0.9960	0.9997	0.9963	Irs
	H	1	1	1	-
	I	1	1	1	-
	J	1	1	1	-

3.1.3

Dynamic efficiency analysis of the Malmquist Index

In order to better determine the changes in the utilization efficiency of educational funding inputs and outputs over time in Chinese universities in various provinces and cities, this paper further adopts the Malmquist index to determine the dynamic changes of each decision-making unit in terms of comprehensive efficiency and technical efficiency. Table 3 shows the results of MALMQUIST decomposition of colleges and universities in each region. From the table, it can be seen that in 2014-2023, the average values of the technical efficiency change index, technical progress index, pure technical efficiency change index and scale efficiency change index are 1, 0.9829, 0.9996 and 0.9995, respectively, indicating that the resource allocation efficiency of colleges and universities is constantly optimized. And the average value of the total factor productivity change index of universities is 0.9805 < 1. In this decade, the total factor productivity change index of Chinese universities shows a fluctuating upward trend in 2020-2023, and the total factor productivity change index is 0.8306 in 2019-2020, which is mainly caused by the reduction of technological progress the index of total factor productivity change in Chinese universities in 2019-2023 shows a fluctuating upward trend. The reason for this is that 2019-2020 is in the period of epidemic prevention and control, and the closed management of colleges and universities has led to the problems of budgeting and actual inconsistency and budget implementation difficulties, which seriously affects the internal budget performance management of the university. This also shows that strengthening the technical level of internal budget management in colleges and universities is a key point to improve the efficiency of higher education expenditure.

Table 3.

The results of a resolution of MALMQUIST in various districts

Year	Technical efficiency index(effch)	Technological improvement index(techch)	Pure technology efficiency index(pech)	Scale efficiency index(sech)	Total factor productivity index(tfpch)
2014-2015	1.0008	0.9958	1.0014	0.9967	1.0002
2015-2016	1.0006	1.0017	1.0008	1.0027	0.997
2016-2017	0.9986	0.9999	0.9997	0.9989	0.9993
2017-2018	0.9982	1.0011	1.0004	0.9984	0.9998
2018-2019	1.0007	0.9998	0.9995	1.0013	0.999
2019-2020	0.9972	0.8489	0.9984	0.9948	0.8306
2020-2021	1.003	1.0004	0.9972	1.0046	0.9983
2021-2022	1.0014	0.9999	1	0.9994	0.9998
2022-2023	1.0001	0.9982	0.9988	0.9991	1.0002
Mean value	1	0.9829	0.9996	0.9995	0.9805

Figure 1 shows the results of the analysis of the MALMQUIST index of colleges and universities in each province and city from 2014 to 2023. It can be seen that in 2014-2023, the average value of technical efficiency, scale efficiency and pure technical efficiency index of Chinese universities is close to 1, which indicates that higher education is moving from epitaxial development to connotative and high-quality development path, and that under the existing technological level, the elements of the development environment of colleges and universities, the management system, the transformation of achievements, incentive mechanisms and other elements are coordinated with each other, and can fully utilize the university’s input resources. Overall, the total factor productivity in each decision-making unit during 2014-2023 showed large fluctuations, which were observed to be caused by fluctuations in the technological progress index. Among the 10 provinces and cities in China, the technical progress index of province and city A is lower than 0.9. It indicates that the current level of budget performance management of higher education institutions, with the same input of resources, does not result in more outputs for basic functions of higher education institutions. It also shows that China’s higher education budget performance has a problem of pursuing inputs but neglecting performance management. Therefore, in the case that the proportion of human, financial and material resources input in colleges and universities remains unchanged, the study of the concept of budget performance in colleges and universities as well as the training of new budget performance management techniques should be strengthened to significantly enhance the technological progress of budget performance management and to promote the improvement of the internal management level of the utilization of resources in colleges and universities.

3.2

Analysis of logistic regression results of comprehensive budgeting in higher education institutions

3.2.1

Data Acquisition and Sample Basics

The sample data comes from the sub-project of “Input-Output Indicators of Budget Performance of Universities”, which is a joint research project of 10 universities in 10 provinces in China in August 2023, which uses simple sampling method to conduct a survey through the excellent budget management of universities that have invested their budgets. The survey was conducted using a simple sampling method, and it was conducted through the excellent budget management of colleges and universities that have already invested in the budget. A total of 2950 questionnaires were distributed. Actually, 2745 valid questionnaires were returned, with a recovery rate of 93.05%. The data was organized and excluded. The basic findings of the sample are shown in Table 4. The frequency of the three budgeted and unbudgeted financial inputs, human, financial, and material, ranged from 28.63%-38.21% and 25.09%-45.69%, respectively. In the actual output, there is a big difference between the proportion of budgeted and unbudgeted in the five aspects of “talent training, scientific research, social service, cultural inheritance and innovation, and international exchange and cooperation”, which are between 0.19%-47.36% and 0.45%-34.60%, respectively. It can be seen that the presence or absence of budget is very important for the proportion of input and output in overall budget performance management.

Table 4.

The basic situation of the sample is investigated

Primary indicator	Secondary indicator	Budget		No budget
Primary indicator	Secondary indicator	Frequency	Percentage(%)	Frequency	Percentage(%)
Financial input	Manpower	350	38.21	658	45.69
	Financial resources	303	33.15	361	25.09
	Resources	262	28.63	421	29.21
	Total	915	100.00	1440	100.00
Actual output	Talent culture	413	47.36	564	31.99
	Scientific research	183	20.99	610	34.60
	Social services	203	18.35	527	26.09
	Cultural heritage and innovation	114	13.11	121	6.84
	International exchanges and cooperation	2	0.19	8	0.45
	Total	872	100.00	1763	99.98

3.2.2

Model regression results

On the basis of preliminary statistical results, irrelevant variables and variables with multiple covariates are eliminated, the 1st categorical variable is fitted as a reference system, and iteration is carried out through the stepwise regression method to finally establish a logistic integrated model of budgeting with the influence of multiple factors such as school budgeting characteristic variables, information channels, comprehensive budgeting and performance management, etc. The logistic results Regression results As shown in Table 5. The logarithmic value of the maximum likelihood squared of the integrated model -2log(likelihood)=1528.953, which is greater than the chi-square critical value of 35.74, Cox and snell R²=0.3452, Nagelkerke R²=0.4758, which indicates that the fitting effect is good. The predictive accuracy of the model reached 88.43% and 90.34% in the budgeted samples of 915 and 872 for actual inputs and outputs. The predictive accuracy of the model is 87.42% in the unbudgeted samples of 1440 and 1763 of actual inputs and outputs, which has strong explanatory power, making the results of the regression model credible.

Table 5.

Logistic results regression

Budget	The name of the budget	B	SE	Wals	df	Sig.	Exp(B)
Financial input	Manpower	0.903	0.174	17.364	1	0.000	3.037
	Financial resources	1.182	0.196	24.307	1	0.000	3.851
	Resources	1.307	0.254	20.648	1	0.000	4.399
Actual output	Talent culture	0.835	0.187	20.548	1	0.000	0.135
	Scientific research	0.459	0.146	7.724	1	0.004	0.094
	Social services	1.035	0.287	13.268	1	0.000	0.235
	Cultural heritage and innovation	1.479	0.201	50.889	1	0.000	0.149
	International exchanges and cooperation	1.352	0.213	38.243	1	0.000	0.161

3.3

Safeguards for budgeting and management in higher education institutions

3.3.1

Improvement of staff quality

More business training activities, for the new online budget system, as soon as possible to train specialized budget managers, familiar with the operation process; at the same time to strengthen the interoperability of information from various departments, so that departments, departments to grasp the work of the dynamics in a timely manner; in addition, to increase the encouragement of personnel for the enhancement of their own capabilities, the current assets of the Financial Services Department of the intermediate level of four accountants, the leadership of the College to encourage personnel to participate actively in the examination of certificates as well as scientific research, and to enhance the overall level of the team. Enhance the overall level of the team.

3.3.2

Increased level of budgeting

Departments and departments should strengthen their budgeting power, identify specialists closely combined with departmental responsibilities and development planning, to set the budget by department and promote budget development. To clarify the person responsible for the implementation of the project budget, who executes who compiles, so as to facilitate the implementation of the executor according to the initial preparation of the idea of implementation, on how to implement is with the overall planning ideas.

3.3.3

Enhanced data accuracy

In accordance with the unified statement format, relevant quota standards and preparation methods issued by the Assets and Financial Services Branch, the calculation is carried out strictly through the prescribed system, and the authenticity of the data is carefully verified, so as to avoid, as far as possible, the situation in which an understatement or an overstatement is found after the submission of the budget declaration form. As far as possible, the budget data are accurate, reliable and truthful, so as to ensure the quality of budgeting in practice.

3.3.4

Implementation of whole-process budget performance management

1)

The budgeting process is performance-oriented. Carry out ex ante performance evaluation, such as capital investment to fully consider the financial capacity.

2)

Strengthen performance monitoring in the budget execution process. In accordance with the principle of “who spends, who is responsible for”, the progress of budget implementation, as well as the degree of achievement of performance objectives, both implement a two-pronged monitoring model.

3)

Full implementation of performance evaluation in the final accounts.

4)

Promote the disclosure of performance information.

5)

Improve the system and indicator system.

4

Conclusion

Budget performance management, which plays a crucial role in enhancing the efficiency of financial funds, has been a concern for colleges and universities regarding whether they can achieve the maximum budget performance output within the established resource inputs. This paper measures college budgeting through data envelopment analysis and the Malmquist model. Afterwards, it analyzes the influencing factors for the input and output efficiency of university budgeting using a logistic regression model, and then optimizes budgeting. 1)

The existing technical level of budget performance management of 10 colleges and universities in 10 provinces and cities has been improved, and the mean values of comprehensive efficiency, scale efficiency and technical efficiency of educational resource allocation in colleges and universities have increased by 0.9991, 0.9999 and 0.9992 in 2023 compared with that in 2014.During the period of 2014-2023, the efficiency of resource allocation in colleges and universities has been optimized. The average values of its technical efficiency change index, technical progress index, pure technical efficiency change index and scale efficiency change index are above 0.98. However, the total factor productivity change index in 2019-2020 is low (0.8306), which shows that strengthening the technical level of internal budget management in colleges and universities is a key point to improve the efficiency of higher education expenditure.

2)

The existence of budget has a great impact on the proportion of input and output of overall budget performance management of universities, especially in the actual output, the five aspects of “talent training, scientific research, social service, cultural inheritance and innovation, and international exchange and cooperation” account for 0.19%-47.36% and 0.45%-34.60% respectively in the case of budget preparation and non-budget preparation.

3)

In the performance evaluation system, the indicators are designed according to the university’s own situation, and four safeguards are proposed, namely, “improving staff quality, improving budgeting level, enhancing data accuracy, and implementing whole-process budget performance management”, so that the program can be well applied to the next year’s budget.

Language:: English

Publication timeframe:: 1 times per year
Journal Subjects:: Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other

Journal RSS Feed

An analysis of the optimization algorithm of comprehensive budget performance management for budgeting in higher education institutions

Wei Cao

Published Online: Mar 21, 2025

Received: Nov 09, 2024

Accepted: Feb 24, 2025

DOI: https://doi.org/10.2478/amns-2025-0591

KeywordsEnvelopment Analysis, Comprehensive Budget Performance Management, Malmquist Index Model, Logistic Logistic Regression

© 2025 Wei Cao, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Envelopment Analysis, Comprehensive Budget Performance Management, Malmquist Index Model, Logistic Logistic Regression