Subject service is the main way of university libraries to serve and integrate the construction of ‘first-class subjects’, and the key to first-class subject service lies in the subject service team. The subject service team mainly provides services for administrative decision-making departments, scientific researchers, key laboratories through subject dynamic analysis, subject resource promotion, information retrieval and document delivery. Subject librarians are proficient not only in a variety of databases and analysis tools but also in using them to sort, analyse, predict and evaluate data, so as to provide comprehensive, timely objective decision support for the subject construction in universities. Therefore, the subject service team is not only closely related to the construction of first-class subjects in universities but also vital to it. However, outstanding problems such as ‘insufficient incentives’ and ‘ineffective incentives’ faced by the subject service team have caused subject librarians to encounter problems such as lack of competitiveness, insufficient ability, insufficient innovation, low work enthusiasm, negative attitudes and serious brain drain. As a result, subject service quality and efficiency are low, which severely restricts the construction of ‘first-class subjects’ in universities. Therefore, the incentive mechanism of the subject service team is a key issue to accelerate, promote and ensure the construction of ‘first-class subjects’ and the sustainable and healthy development of subject service teams. How to construct a scientific and effective incentive mechanism for discipline service teams is worthy to further research.
Subject librarians are very important in the university library and cannot be replaced by experts [1]. Based on the perspective of management, many scholars have summarised the incentive factors and measures to motivate subject librarians through experience judgement and analysis. For examples, they found that salary incentive is one of the most effective incentive methods. Subject librarians with longer work service are more likely to strive for higher pay, and the number of male subject librarians involved in the fight for higher pay tends to be higher than the number of women; satisfied and stable income guarantee can effectively motivate librarians to work hard [2, 3]. Many researchers have found that the compensation level, office conditions, fair chance, justice, professional promotion, emotion, learning training, faculty status and tenure, and organisational socialisation factors have a significant effect on librarian satisfaction. By implementing the above factors, the passion and enthusiasm of subject librarians can be significantly improved. High income has a vigorous effect in promoting the work efficiency of subject librarians and providing quality service to customers [4, 5, 6, 7, 8, 9, 10]. The existing research mainly summarises the incentive factors and measures of subject librarians from the perspective of management, which is not only lack of solid theoretical support but also lack of empirical test based on data.
Principal-agent theory is an important economic incentive theory. ‘Principal-agent theory’, and vigorously advocated the separation of management right and ownership, the owner has the residual claim, and then transferred the management right. The principal-agent relationship begins with the existence of ‘specialisation’. Once ‘specialisation’ exists, the principal-agent relationship may appear. In this principal-agent relationship, the agent acts on behalf of the principal due to his own comparative advantages. Principal-agent theory studies the principal-agent relationship within and among enterprises from the perspective of general microeconomics, which is better than traditional microeconomics while explaining some organisational phenomena. Its core task is how the principal should construct the best contract to incentive the agent under the condition of private information and interest conflict. Holmstrom and Milgrom [11, 12] established the basic traditional principal-agent model. Subsequently, they extended a single task to multiple tasks and established their theoretical analysis framework. In addition, the principal-agent theory has been widely used in various fields.
There exists typical principal-agent relationship between the academic managers and subject librarians. In view of this, we adopt the economic incentive theory, that is, multi-task principal-agent analysis framework, to discuss the incentive problem of subject librarians. The main contributions of this paper are as follows: ① Construct an optimisation model of subject librarian compensation incentives with inter-task correlation. ② Design the best compensation incentive contract. ③ Analyse the characteristics of the best incentive contract. ④ Establish an empirical model based on data and empirically test the theoretical model and relevant theoretical conclusions.
Let
If
If
If
This hypothesis shows that as the level of effort of the subject librarian on the two tasks continues to increase, the cost of the two tasks increases and the cost increases at an increasing rate.
Based on Hypotheses 3 and 4, we can get the expected net utility of the principal as follows:
Based on Hypotheses 2 and 4, we can obtain the expected net return of the agent (subject librarian) as follows:
The certainty equivalent income, namely CE, can directly describe the agent's expected utility or income, and CE is equal to the difference between the agent's expected utility and the cost of risk. Then, CE can be obtained as follows:
Then, under the inter-task dependence, the best incentive model can be expressed as follows:
Under the inter-task dependence and information asymmetry, managers cannot fully monitor the efforts made by the agent. Subject librarians will choose rational behaviours that maximise their own interests, instead of satisfying the demand of the academic managers. Therefore, under the inter-task dependence, the best incentive contract is the solution of the following incentive optimisation model:
The first-order conditions of effort levels Therefore, Eq. (1) can be restated as follows:
From the incentive compatibility constraint in Eq. (2), the following equation can be obtained:
When the participation constraint is equal, the subject librarian gets the reserved salary, which is expressed as follows:
Substituting Eqs (3)–(5) into the objective function in Eq. (2), the following equations are obtained:
And then the simplified optimisation problem is obtained as follows:
The first-order conditions of the share proportion Through simultaneous simplification, it can be obtained that under the inter-task dependence, the share proportion for the two tasks is, respectively, given as follows:
Substituting Eqs (7) and (8) into Eqs (3) and (4), the efforts made by the subject librarian are denoted as follows:
Substituting Eqs (7) and (8) into Eq. (5), the fixed compensation can be obtained as follows:
In fact, in the expression of
And because
Then, Similarly, it can be proved that
First, by Eq. (7) and the chain guide rule, the following equation is obtained:
Second, by Eq. (8) and the chain guide rule, the following equation is obtained:
From Proposition 1, the best effort level is differentiated with respect to the best incentive intensities
When
And when
The best effort level is differentiated with respect to the optimal incentive intensities
When
And when
Based on the Proposition 1 and Corollaries 1–4, the following empirical model is established. And the correlation analysis between incentive intensity and main variables is as follows in Table 1.
Correlation regression analysis of main core variables
0.1073 (0.54) | −1.0254 (−0.51) | 2.5067 (0.20) | 3.5464 (0.28) | 11.1197 (0.98) | 9.7586 (0.86) | |
( |
0.2858 (0.56) | −1.5639 (−0.24) | −2.0848 (−0.32) | −5.9094 (−1.00) | −5.3936 (−0.91) | |
( |
0.3174 (0.29) | 0.4044 (0.36) | 1.0522 (1.04) | 0.9937 (0.98) | ||
0.3899*** (4.92) | 0.3919*** (4.93) | 0.3912*** (4.92) | 0.3922*** (4.93) | 0.4475*** (6.00) | 0.4468*** (6.00) | |
−0.253*** (−4.33) | −0.2565*** (−4.35) | −0.2552*** (−4.32) | −0.2569*** (−4.34) | −0.2725*** (−4.91) | −0.2715*** (−4.90) | |
0.0137 (1.17) | −0.0136 (−1.26) | −0.0267** (−2.03) | ||||
0.6614*** (2.95) | 0.5993*** (2.65) | |||||
0.7104*** (2.97) | 0.7746*** (3.21) | |||||
0.0018* (1.69) | ||||||
0.0805 | 0.0804 | 0.0821 | 0.0829 | 0.1930 | 0.1912 | |
0.1324 | 0.1448 | 0.1355 | 0.1341 | 0.3361 | 0.3584 | |
0.0905 | 0.0845 | 0.0803 | 0.0913 | 0.2597 | 0.3059 | |
315 | 315 | 315 | 315 | 315 | 315 |
indicate that the correlation coefficient is significant at the level of 1%, 5% and 10%, respectively.
In reality, tasks are not independent of each other but interdependent. When the tasks are interchangeable, it means that the completion of one task will increase the difficulty of the other task. When the tasks are mutually complementary, it means that the completion of one task is more conducive to the other task. Based on the Holmstrom and Milgrom [11, 12] traditional model, we introduce the correlation coefficient between tasks, and the best compensation incentive model is constructed under the inter-task cost function. The best compensation incentive contract is constructed by solving the incentive model, and the incentive characteristics are analysed. The results show that the best incentive intensity decreases as the subject service selectivity increases. The higher incentive intensity of university managers for specific tasks, the lower efforts of subject librarians for another specific task. Moreover, when the tasks are substituted for each other, the profit-sharing ratios corresponding to different tasks are complementary. Finally, we establish the econometric empirical models to test these results.