1. Introduction
In view of the increasingly serious problem of environmental pollution, the problem of environmental protection is paid more and more attention. The central government of China has repeatedly called for the enhancement of environmental protection, and the public’s concern about environmental quality has also been increasing. In this background, local governments, which have important responsibility for environmental quality in their jurisdictions, are under increasing pressure.
Traditional command-and-control and market-incentive environmental regulation tools emphasize the punishment of environmental illegal enterprises, but punishing, shutting down or relocating the enterprises, etc., often causes local governments to face difficulties in finance, employment, staff resettlement, and it also has a negative impact on local economic development. As a result, when an environmental incident occurs, both the illegal enterprises and the local governments are willing to resolve the problem in a way that is less costly and more acceptable to both parties; for example, the enterprise continues to produce after paying a “symbolic fine”, the result of which is that the environmental pollution problem is not solved.
The coordination between regional economic development and environmental protection should be fundamentally implemented on two aspects, economic benefits and pollution reduction. From the perspective of principal–agent, enterprises, as the agents of the local government, should not only complete the tasks of increasing economic benefits and promoting economic development, but also complete the tasks of pollution reduction and improving environmental quality. Therefore, it will be the effective means to realize the coordinated development of regional economy and environment for local governments to guide and motivate enterprises reasonably through mechanism design, so as to promote enterprises to complete the tasks of economic benefits and pollution reduction.
In recent years research on environmental governance based on principal–agent theory has been increasing, while the core problem in the process of environmental governance is to design and optimize the reasonable incentive models and mechanism. For example, incentive model for third-party remediation of legacy contamination sites left by closed enterprises from the perspective of fully linked accountability [
1]; evolutionary game model of the environmental pollution third-party governance considering reward and punishment distribution incentive mechanism [
2]; and the information communication model of key pollution source monitoring [
3], etc. The design and optimization of reasonable incentive mechanism can effectively solve the problem of information asymmetry in the process of environmental governance, so as to reduce pollution emissions and improve environmental quality. Especially in the context of enterprises undertaking multiple tasks, it is of more theoretical and practical significance to consider introducing multi-task principal–agent theory to analyze environmental governance problems.
2. Literature Review
In order to improve the effect of environmental pollution control, many scholars at home and abroad conducted research on the design of pollution control mechanisms. Under the condition of incomplete information, Dasgupta et al. demonstrated that the use of mechanism design can lead to a Pareto optimal level of pollution control [
4]. Xepapadeas proposed a mechanism design to combine fines and subsidies [
5]. Huang et al. proposed a monitoring contract that combines supervision, report and fines to supervise and constrain the pollution discharging [
6]. Chen and Jiang took the risk attitude characteristics of different enterprises into account, and accordingly established different contractual mechanisms to deal with the enterprises’ lazy behaviour in the process of pollution control [
7]. Wang and Meng designed the optimal incentive contract for environmental regulation under adverse selection and limited liability of agents [
8].
In recent years, limited research has been conducted under the framework of multitask principal–agent; for example: the design of formal and relational contracts for the outsourcing of applied services; the institutional reform of food safety regulation [
9,
10]; the financing factor of bank in multi-task principal–agent to study the incentive mechanism between the manufacturer and the supplier [
11]; the note on organizational structure and environmental liability [
12]; the research on compensation incentive mechanism of doctors in public hospitals [
13]; and the chain multitask incentive model for complex weapon equipment delivery based on accountability mechanism [
14]. The research covers many aspects of social life.
Moreover, scholars have more often used the relatively complex principal–agent model for their research. For example, Li and Zhang analyzed the optimal environmental regulation of local governments and its fluctuations under the perspective of the optimal incentive contract design, and discussed the role of a third party [
15]. By constructing a double-layer principal–agent model, Chen et al. analyzed the adverse selection of enterprises to hide their own pollution information in environmental regulation and the moral hazard by conspiring of local governments [
16]. Taking the implementation of the negative list system for industry access in key ecological functional zones as an example, Xu et al. analyzed the theoretical mechanism of policy implementation deviation caused by multi-task conflict, and summarized the local practical experience of correcting policy implementation deviation by adjusting the principal–agent mode [
17]. The H&M multi-tasking principal–agent model is adopted to investigate the motivation behind the two tasks of business performance and compliance governance [
18]. The multi-task and multi-agent principal–agent model and auction model are used to construct the university budget performance management model under the information asymmetry, and through the theoretical analysis of the model the mathematical expression describing the optimal state relationship of the system is obtained [
19]. Using the multi-task principal–agent model, Xi and Han analyzed the effect of Chinese decentralization and industrial policy implementation [
20].
By reviewing the existing research we can see that there is not much literature on environmental issues under the principal–agent perspective. Although relevant studies constructed more complex principal–agent models and attempted to introduce more subjects and layers into the models in recent years, they only considered the case of agents engaging in one kind activity, so the studies always limited to design mechanism for environmental regulation and advocated increasing the supervision and punishment of enterprises, ignoring the mutually constraining relationship between environmental governance and economic development. In fact, the production management process of an enterprise has obvious multitask characteristics, so the use of the multitask principal–agent model will be more suitable for analyzing problems and closer to reality. There is still a lack of research applying multitask principal–agent theory to environmental governance.
Accordingly, on the basis of previous studies a multitask principal–agent model between local governments and pollution reduction enterprises is developed, the design of incentive mechanism under the tasks of economic benefit and pollution reduction is examined, the influence of various factors on the optimal incentive contract is focused on in this paper; the more operational incentive mechanism is proposed, theoretical reference for promoting the harmonious development of economy and environment is provided.
4. Influencing Factors Analysis of Optimal Incentive Contracts
According to H3, the cost function
is a strictly increasing convex function and therefore the function satisfies the sufficient conditions of the lower convex function [
23]:
In which, , , , and from this it can be seen that .
In Formula (6), , so we get , and according to H2 the incentive intensity and are positive, so we get , .
According to Formula (6), the optimal economic benefit incentive intensity and the optimal pollution reduction incentive intensity are determined by parameters , , , , , , and . We analyze the influence of a single factor change on the optimal incentive contract while keeping other influential factors stable in the following. In the multitasking principal–agent model, the economic and environmental optimal incentive contracts are affected by many factors, but the enterprise-related factors are the main factors affecting the establishment of optimal incentive contracts by local governments. Therefore, based on Stackelberg Model the enterprise in the multitask principal–agent model can be regarded as a “Stackelberg Leader”, so the inverse derivation method is used to analyze the influencing factors of the optimal incentive contract.
4.1. Influencing Factors Analysis of the Optimal Economic Benefit Incentive Intensity
According to Formula (7), it is clear that the optimal economic benefit incentive intensity is an increasing function of
. As the influence coefficient of enterprise economic benefit on local government income increases, the optimal economic benefit incentive intensity also increases.
According to Formula (8), when
,
, the optimal economic benefit incentive intensity is a decreasing function of
. As the environmental index weight in the performance evaluation system increases, the optimal economic benefit incentive intensity decreases. When
,
, the optimal economic benefit incentive intensity is an increasing function of
. As the environmental index weight in the performance evaluation system increases, the optimal economic benefit incentive intensity increases.
According to Formula (9), when
, that is when
,
, the optimal economic benefit incentive intensity is a increasing function of
. As the absolute risk-averse degree of enterprises increases, the optimal economic benefit incentive intensity will gradually increase. When
, that is when
,
, the optimal economic benefit incentive intensity is a decreasing function of
. As the absolute risk-averse degree of enterprises increases, the optimal economic benefit incentive intensity will gradually decrease.
According to Formula (10), the optimal economic benefit incentive intensity is a decreasing function of
. As the variance in economic benefit increases, the optimal economic benefit incentive intensity will gradually decrease.
According to Formula (11), when
,
, the optimal economic benefit incentive intensity is a decreasing function of
. As the variance in emission reduction increases, the optimal economic benefit incentive intensity will gradually decrease. When
,
, the optimal economic benefit incentive intensity is an increasing function of
. As the variance in emission reduction increases, the optimal economic benefit incentive intensity will gradually increase.
According to Formula (12), the optimal economic benefit incentive intensity is a decreasing function of
. As the ability of economic benefit of enterprises decreases (
↑), the optimal economic benefit incentive intensity will gradually decrease.
According to Formula (13), when
,
, the optimal economic benefit incentive intensity is an increasing function of
. As the direct cost of pollution control for enterprises increases, the optimal economic benefit incentive intensity will gradually increase. When
,
, the optimal economic benefit incentive intensity is a decreasing function of
. As the direct cost of pollution control for enterprises increases, the optimal economic benefit incentive intensity will gradually decrease.
According to Formula (14), when , if , that is when , , the optimal economic benefit incentive intensity is an increasing function of . As the economic cost of pollution control for enterprises increases, the optimal economic benefit incentive intensity will gradually increase. If , that is when , , the optimal economic benefit incentive intensity is a decreasing function of . As the economic cost of pollution control for enterprises increases, the optimal economic benefit incentive intensity will gradually decrease.
When , , the optimal economic benefit incentive intensity is a decreasing function of . As the economic income of pollution control for enterprises increases (↑), the optimal economic benefit incentive intensity will gradually decrease.
4.2. Influencing Factors Analysis of the Optimal Pollution Reduction Incentive Intensity
According to Formula (15), when
,
, the optimal pollution reduction incentive intensity is a decreasing function of
. As the influence coefficient of enterprise economic benefit on local government income increases, the optimal pollution reduction incentive intensity will gradually decrease. When
,
, the optimal pollution reduction incentive intensity is an increasing function of
. As the influence coefficient of enterprise economic benefit on local government income increases, the optimal pollution reduction incentive intensity will gradually increase.
According to Formula (16), the optimal pollution reduction incentive intensity is an increasing function of
. As the environmental index weight increases in the performance appraisal system, the optimal pollution reduction incentive intensity will gradually increase.
According to Formula (17), when
, that is when
,
, the optimal pollution reduction incentive intensity is an increasing function of
. As the absolute risk-averse degree of enterprises increases, the optimal pollution reduction incentive intensity will gradually increase. When
, that is when
,
, the optimal pollution reduction incentive intensity is a decreasing function of
. As the absolute risk-averse degree of enterprises increases, the optimal pollution reduction incentive intensity will gradually decrease.
According to Formula (18), when
,
, the optimal pollution reduction incentive intensity is a decreasing function of
. As the variance in economic benefit increases, the optimal pollution reduction incentive intensity will gradually decrease. When
,
, the optimal pollution reduction incentive intensity is an increasing function of
. As the variance in economic benefit increases, the optimal pollution reduction incentive intensity will gradually increase.
According to Formula (19), the optimal pollution reduction incentive intensity is a decreasing function of
. As the variance in emission reduction increases, the optimal pollution reduction incentive intensity will gradually decrease.
According to Formula (20), when
,
, the optimal pollution reduction incentive intensity is an increasing function of
. As the ability of economic benefit of enterprises decreases (
increases), the optimal pollution reduction incentive intensity will gradually increase. When
,
, the optimal pollution reduction incentive intensity is a decreasing function of
. As the ability of economic benefit of the enterprise decreases (
increases), the optimal pollution reduction incentive intensity will gradually decrease.
According to Formula (21), the optimal pollution reduction incentive intensity is a decreasing function of
. As the direct cost of pollution control for enterprises increases, the optimal pollution reduction incentive intensity will gradually decrease.
According to Formula (22), when , if , that is when , , the optimal pollution reduction incentive intensity is an increasing function of . As the economic cost of pollution control for enterprises increases, the optimal pollution reduction incentive intensity will gradually increase. If , that is when , , the optimal pollution reduction incentive intensity is a decreasing function of . As the economic cost of pollution control for enterprises increases, the optimal pollution reduction incentive intensity will gradually decrease.
When , , the optimal pollution reduction incentive intensity is a decreasing function of . As the economic income of pollution control for enterprises decreases (↑), the optimal pollution reduction incentive intensity will gradually decrease.
5. Discussion of the Results
Influencing factors of the optimal incentive contracts include the influence coefficient of enterprise economic benefit on local government income
, the environmental index weight in the performance appraisal system
, the absolute risk-averse degree of enterprises
, the variance in economic benefit
, the variance in pollution control
, the ability of economic benefit of enterprises
, the direct cost of pollution control for enterprises
and the economic cost of pollution control for enterprises
. According to Hypothesis 4,
and
, respectively, reflect the importance that local governments attach to the economic
of enterprises and pollution reduction. For easier discussion, the economic meaning of
is given as the relative importance that local governments attach to the economic benefit of enterprises; the economic meaning of
is the relative importance that local governments attach to pollution reduction by enterprises.
Table 1 shows the impact of these factors on the optimal incentive contract. It can be seen that local governments should differentiate between types of enterprises, examine their attributes, and design and adjust the optimal incentive contract by combining institutional factors.
When the influence coefficient of the economic benefit of enterprises on local government income increases, the incentive intensity of the economic benefit of enterprises can be increased, prompting them to actively improve their economic benefit. For traditional enterprises, local governments should reduce the incentive intensity of pollution reduction for enterprises, resulting in weakening the incentive for pollution reduction tasks. For innovative enterprises, local governments should increase the incentive intensity of pollution reduction for enterprises, resulting in strengthening the incentive for pollution reduction tasks.
When the environmental index weight in the performance appraisal system increases, the incentive intensity for enterprises to reduce pollution can be increased, prompting enterprises to actively reduce pollution. For traditional enterprises, local governments should reduce the incentive intensity of economic benefit for enterprises, resulting in weakening the incentive for economic benefit tasks. For innovative enterprises, local governments should increase the incentive intensity of economic benefit for enterprises, resulting in strengthening the incentive for economic benefit tasks.
All in all, in order to increase overall benefits local governments should guide traditional enterprises to increase their efforts in two ways: increase the incentive intensity of the task directly; and reduce the opportunity cost of the task. For innovative companies, local governments can increase the incentive intensity of any work task.
If considering the risk preference of enterprise, the local government should combine the institutional factors with the characteristics of enterprise to examine and adjust the incentive contract. For enterprises with high risk aversion, if the relative importance attached by local governments to economic benefit is larger than the threshold value , the incentive intensity of economic benefit for enterprises should be increased, and if is smaller than , the incentive intensity of economic benefit for enterprises should be decreased; if attached by local governments to pollution control is larger than the threshold value , the incentive intensity of pollution control for enterprises should be increased, and if is smaller than , the incentive intensity of pollution control for enterprises should be decreased.
For enterprises with low risk aversion, the completely opposite incentive strategy can be adopted. The implied economic implication is that for enterprises with high risk aversion at this time, if the relative importance attached by local governments to economic benefit is larger than the threshold value the incentive intensity of economic benefit for enterprises should be increased, and if the relative importance attached by local governments to pollution control is larger than the threshold value the incentive intensity of pollution control for enterprises should be increased; otherwise, more conservative enterprises will be more inclined not to engage in economic benefits or pollution reduction tasks, or to reduce their efforts and investment in the tasks. On the contrary, if the relative importance attached by local governments to economic benefit is smaller than the threshold value or the relative importance attached by local governments to pollution control is smaller than the threshold value, then the incentive to increase economic benefit or reduce pollution reduction can be weakened accordingly.
For the factors of the variance in economic benefit, the variance in pollution reduction, the ability of economic benefit and the direct cost of pollution control, local governments can ignore the institutional factors and the importance it determines for the task, and establish or adjust the incentive contract according to the specifics of these factors and the type of enterprises. For enterprises where the variance in economic benefit is large, whether they are traditional or innovative, local governments should reduce the incentive intensity of their economic benefits. This is because a large variance in economic benefit means that the correlation between the economic benefit efforts of enterprises and the level of economic benefit is not high, and the good or bad of enterprise benefit is more determined by random factors other than enterprise effort (such as business environment, market demand, policy changes, etc.), rather than reflecting the true level of enterprise effort, and thus the level of enterprise benefit tends to show characteristics such as instability and volatility. In this case, intensifying the incentive for enterprises on economic benefit tasks will not achieve the effect of making them work hard. For traditional enterprises, the incentive intensity of pollution reduction should also be reduced to prevent the opportunity cost of economic benefit tasks increasing and further reducing the effort level of the enterprise on economic benefit tasks. For innovative enterprises, the incentive intensity can be increased proportionally to strengthen the incentive for the task of pollution reduction. Conversely, for enterprises with low variance in economic benefit the opposite incentive strategy can be adopted.
For enterprises whose variance in pollution reduction is large, whether traditional or innovative, local governments should reduce the incentive intensity of their pollution reduction. This is because a large variance in pollution reduction implies that the correlation between an enterprise’s efforts to reduce pollution and the amount of pollution reduction is not high, the amount of pollution reduction is more determined by random factors other than enterprise’s efforts (such as geographical factors, climatic factors, other human factors, and so on), and it does not reflect the true level of an enterprises’ effort. In this situation, strengthening the incentive for the task of pollution reduction for enterprises will not achieve the effect of making them work hard. For traditional enterprises, the incentive intensity for economic benefit should also be reduced to prevent the opportunity cost of the pollution reduction task increasing and further reducing the effort level of enterprises on the pollution reduction task. On the other hand, for innovative enterprises the incentive intensity for the economic benefit of enterprises can be increased proportionally to strengthen the incentive for the economic benefit task. Conversely, for enterprises with small variance in pollution reduction, the opposite incentive strategy can be adopted.
For enterprises whose economic benefit capacity is relatively strong, whether traditional and or innovative, local governments should increase the incentive intensity for economic benefit. This is because if enterprises are more capable of economic benefit, such as carrying out production with advanced concepts and methods, abundant knowledge and experience, and a higher level of management, enterprises should further develop their strengths in this area and strengthen incentives for their economic benefit tasks, so as to induce them to devote more time and energy to increasing economic benefit and thereby improving the efficiency of economic output and optimizing resource allocation. For traditional enterprises, the incentive intensity for enterprises to cut pollution can also be reduced to lower the opportunity cost of economic benefit tasks. For innovative enterprises, the incentive intensity for enterprises to reduce pollution can be increased accordingly to strengthen the incentive for the task of pollution reduction. Conversely, for enterprises with relatively poor economic benefit ability the opposite incentive strategy can be adopted.
For enterprises whose direct cost of pollution control is relatively high, whether traditional and or innovative, local governments should reduce the incentive intensity of pollution reduction for enterprises. This is because if the direct cost of pollution control is relatively high, for example, in order to achieve emission reduction targets, enterprises need to directly invest more human, material and financial resources, and the incentive for pollution reduction tasks should be weakened to avoid inefficient use of resources. For traditional enterprises, the incentive intensity for economic benefits can also be increased to raise the opportunity cost of pollution reduction tasks. For innovative enterprises, the incentive intensity for economic benefit can be reduced accordingly to weaken the incentive for economic benefit tasks. Conversely, for enterprises with relatively low direct costs of pollution control, the opposite incentive strategy can be adopted.
For the economic costs of abatement in traditional enterprises, local governments should also combine institutional factors and the importance they determine to the task with the specific economic costs of pollution control, in order to make adjustments to the incentive contract through a comprehensive examination.
For enterprises with a high economic cost of pollution control, if the relative importance attached by local governments to economic benefit is larger than the threshold value the incentive intensity of economic benefit for enterprises should be increased, and if is smaller than the incentive intensity of economic benefit for enterprises should be decreased; if the relative importance attached by local governments to pollution control is larger than the threshold value the incentive intensity of pollution control for enterprises should be increased, and if is smaller than the incentive intensity of pollution control for enterprises should be decreased. The implied economic meaning is that for enterprises with relatively high economic costs of pollution control, such as those that are mainly industrial in their production and development methods and more dependent on environmental resource exploitation in their use of resources, or those that are more sensitive to changes in the intensity of pollution reduction and those where the negative impact of investment in pollution reduction on economic benefit is greater, at this time, if the relative importance that local governments attach to the economic benefits of enterprises is higher than the threshold value, the incentive intensity for the economic benefits of enterprises should be strengthened, and if the relative importance that local governments attach to the pollution reduction in enterprises is higher than the threshold value, the incentive intensity for the pollution reduction in enterprises should be strengthened.
Once local governments start to pay attention to environmental issues, if they increase the incentive intensity for enterprises to reduce pollution and induce them to treat and reduce emissions, they can also obtain significant improvements in environmental quality at the cost of abandoning economic benefits. Therefore, adjusting the incentive contract based on the relative importance local governments attach to the task can significantly increase the total utility of local governments. Conversely, if the relative importance that local governments attach to the economic benefits of enterprises is below the threshold value, or the relative importance that they attach to pollution reduction in enterprises is below the threshold value, the incentives for the economic benefits task or the pollution reduction task can be weakened accordingly. As for enterprises with relatively low economic costs of pollution control, such as those whose sources of economic benefits are less dependent on environmental resources, whose production and development methods are dominated by agriculture or service industries with smaller pollution, and who are less affected by the pressure to reduce pollution, at this time the incentive for the task of increasing economic benefits should be weakened if the relative importance that local governments attach to the economic benefits of the enterprises is higher than the threshold value, and the incentive for the task of reducing pollution should be weakened if the relative importance that local governments attach to the pollution reduction in the enterprises is higher than the threshold value. For such enterprises whose constraints between economic efficiency and pollution abatement are weak, the output effect of either strengthening incentives for the economic benefit task or for the pollution reduction task is not particularly significant. Therefore, the more importance local governments attach to either economic efficiency or pollution reduction, the weaker the incentives for both tasks should be so that the total utility of local governments can be increased instead. Conversely, if the relative importance that local governments attach to the economic benefit of enterprises is lower than the threshold value, or the relative importance that they attach to the pollution reduction in enterprises is lower than the threshold value, then the incentives for the economic benefit task or the pollution reduction task can be strengthened correspondingly.
For the economic benefit of pollution control for innovative enterprises, local governments can ignore the institutional factors and the importance they determine for the task. The higher the economic benefit of pollution control, the stronger the incentive for economic benefit or pollution control; the lower the economic benefit of pollution control, the lower the incentive for economic benefit or pollution control. This is because for such enterprises, there are different levels of synergy between the two tasks, with higher economic benefit of pollution control indicating this synergy is stronger and therefore local government incentives for either task will increase the output level of the work task.
Previous studies often emphasized incentives to enterprises on control pollution and punishments for illegal emissions, and most of the policy suggestions that have been put forward were single-dimensional, ignoring the restrictive relationship between economic development and environmental protection. Compared with earlier studies the differences in this study are: based on the multitask principal–agent model, this paper comprehensively examines economic development and environmental protection, and introduces the three influencing factors of institutional characteristics, enterprise types and enterprise attributes. It not only examines the influence of a single factor on the optimal incentive contract, but also comprehensively analyzes the interaction of multiple factors, so as to put forward more operational policy suggestions: the establishment of optimal incentive contract cannot simply rely on rewarding or punishing enterprises, but should consider various factors, adjustable policies and measures flexibly.