**1. Introduction**

The economic development process of various countries in the world shows that vehicle ownership gradually increases with the development of economy, especially GDP per capita [1]. Although the automobile manufacturing industry increased rapidly in China, automobile maintenance industry less developed compared with developed countries and has not received enough attention [2]. The auto care industry is developing quickly in the United States in recent years. According to the data of Auto Care Association, the number of people employed in the auto care industry is 4.6 million, and the number of automobiles in operation is 278.6 million in early 2018, and the average annual sales value of auto care industry is now 381 billion. Chain operation mode, which has been developed rapidly in 30 years, was adopted in automobile after-sales service companies in the United States [3]. The supply chain not only includes the automobile manufacturer, but also the after-sales service market of auto parts supply and an integrated maintenance service provider [4]. This pattern not only makes the price of service more transparent, but also can integrate the auto parts resources of each brand and break the vertical monopoly [5].

The situation of auto care is less encouraging in China. According to the China Automotive Aftermarket Blue Book (2013–2017) [6], the average annual growth rate of China's automotive aftermarket will exceed 30% in the future, and the market size is expected to exceed one trillion Yuan after 2018. According to the news of research and markets [7], Chinese automotive aftermarket revenue is expected to record a compound annual growth rate of 7.7%, increasing from \$290.44 billion in 2017 to \$523.80 billion in 2025. During this period, the vehicles in operation for Chinese passenger vehicles are expected to grow from 185 million units to 401.7 million units. However, the development of automotive aftermarket is not sufficient to satisfy the increasing demand for automobile maintenance service in China. 4S stores (store for automobile sale, spare parts, service, and survey) is the leading form of after-sales service market in China [8], and it needs a large investment to develop well. However, many of them with limited sales in the market are unable to cover their costs with intense competition and the gradual increase of investment [6]. The development of domestic automobile maintenance enterprises in the initial stage will also be impacted by the external competitive environment because foreign enterprises bring more new technologies and new business models when they enter the market.

The ignorance of maintenance and service will have a negative impact on the automobile industry, which is not conducive to the sustainable development of the automobile industry. Firstly, the quality and development of auto maintenance industry will affect customer loyalty, which has been paid attention by the American automobile industry [9,10]. There are a large number of single stores and brand chains providing high-quality maintenance and customer service in the United States, and automobile service is insurance of financial and strategic advantages to help the company survive in this highly competitive industry [11,12]. Secondly, from the perspective of market sustainability, automobile maintenance will satisfy and promote the development of new kinds of vehicles. The market share of shared vehicles, electric vehicles and autonomous driving is increasing, and maintenance process of these kinds of vehicles is different with the conventional ones, for example, the annual maintenance cost of vehicles will increase as the annual mileage of shared cars increases. In addition, customers' expectations and requirements on the automotive maintenance industry are also constantly rising with the development of economy, science and technology. So it is necessary for the automotive service industry to constantly improve its development mode and introduce new technologies, which presents challenges and opportunities for the whole industry. Thirdly, lack of attention to maintenance will make China's maintenance industry lag behind in the Internet era. Nowadays, the popularization of the internet brought business opportunities for shopping and O2O (Online to Offline) service industry [13,14], and the automobile maintenance industry should also grasp the opportunities of the internet era and realize the transition of traditional industries. Finally, from the perspective of sustainable regional growth, the diversity of aftermarket growth in different regions reflects the market maturity to a large extent. The growth rate of emerging markets will exceed that of mature markets, and the rapid growth of China's vehicle ownership will drive the share of Asia in the global aftermarket. According to the experience of North American and European markets, the more developed the post-market is, the higher the degree of integration in the transaction level of the industry is. Therefore, it is of great significance to understand the reasons of the slow development of the automobile maintenance industry in China and to make the automobile maintenance and automobile manufacturing industry develop and integrate in a balanced way. What's more, automobile maintenance industry is an important part of the service industry, which is critical to national competitiveness and industrial structure [15,16]. The appropriate industrial structure adjustment will promote economic growth because of the "structure bonus" brought by the movement of production factors in different sectors [17,18], especially for developing countries [19,20]. Although it's right to

develop the automobile manufacturing industry more than the automobile maintenance industry in the initial phase of the development of the automotive industry, China should pay more attention to the balanced development of the two industries after passing this first phase.

As an important part of the service industry, there are some reasons why China's automobile maintenance industry has not developed enough. Firstly, the imperfect investment and financing environment lead to the fact that most maintenance firms lack external financial support and the investment is far away from enough for development. Secondly, China is still in early stage of vehicle ownership development process, and the ratio of vehicle ownership per thousand people is only 172 according to the data of World Road Statistics dataset (WRS) [21]. This number is far away from saturation level, 807, according to Dargay and Sommer [22], and there is still a lot of space for the automobile industry to develop. Thirdly, some researchers believe customer recognition is the most serious barrier at present in the external environment [9,10]. Most of China's automobile maintenance businesses do not pay sufficient attention to information resources, and they have not yet formed a unique business model that is closely connected with the market [6]. What's more, some market factors that affect industrial structures, such as the change of demand, technology improvement, endowment and trade [23–26], can affect the automobile maintenance industry as well. According to the theory of development economics, industrial structure changes with economic development; however, the industrial structure varies in countries that share similar development stages. Although the economy grows rapidly, industry accounts for the largest share of GDP for years until 2015 in China, and the ratio of the service industry is still far away from that of developed countries, even some developing countries. According to the data of Statistical Yearbook of the World [27], service sector accounts 70.9% on average all over the world, 74.3% in the high-income countries in 2010, and 55.6% in middle income countries, 55.5% in low income countries, while, it is only 44.6% in China. So, are there any other reasons that can explain these facts?

Since the marketization degree in China is not very high, and the government plays a great role in the economy, we think that government intervention is another important factor that can affect industry structure in China. Some researchers proposed that in early stage of economic development, industrial policies may accelerate the industrial structural change and improve resource allocation [28,29]. It is also found that the industrial policy can enhance competition among enterprises and promote the growth of enterprises [30]. Local governments are important participants in promoting China's economic development in the process of China's industrial transformation. Therefore, in addition to the natural evolution of market behavior, the industrial structure is also subject to government intervention. We try to explain the problem from the perspective of government incentives and provide a logical framework for analyzing the industrial structure. Some researchers proposed incentives for self-interest and for electoral success in public choice theory [31,32]. Some researchers believe that local governments have fiscal revenues, GDP and promotion incentives under the centralized political and decentralized fiscal institute in China [33]. Thus, many stimulus measures are adopted to boost economies [34,35] and then affected industrial structure [36]. However, the mechanism of the process has not been systematically studied because existing researches pay more attention to the evaluation of policy effects. Therefore, we try to explain the mechanism of the impact of the government incentives on automobile industrial structure.

The government can use different kinds of interventions, which take many forms, including explicit subsidies and bonus, such as research and development subsidies [37–39], but more of them are invisible, such as granting loan guarantees and loan preferences to enterprises to reduce their capital costs and financing constraints [40]. Another example is effective tax rates, which can be affected by tax preference and taxation intensity so that a firm's tax burden can be affected as well, although the tax rate is legal [41,42]. This kind of intervention changes with government incentives and varies in different enterprises.

We found both theoretically and empirically that the governments' GDP incentive induced the biased intervention policy on automobile manufacturing and maintenance industries. In the theoretical model, the government's GDP incentive leads to the more patience of the government than the consumer. The government doesn't care about current consumption, but care about whether enough investment and capital can be generated to promote economic growth. Thus, the enterprises of different industries that have different contributions to investment and capital accumulation will inevitably be subject to different government intervention. More preferential subsidies are given to automobile manufacturing firm whose production serve as intermediate goods and capital. Moreover, the greater the government's GDP incentive, the more biased the intervention will be. Then we test the differential impacts of GDP incentive on tax avoidance of the two kinds of firms empirically. The empirical results show that the government GDP incentive induced more preferential treatment to automobile manufacturing enterprises, and thus, increased their tax evasion compared with automobile maintenance firms.

Our study makes several contributions to the existing literature. First, we explained why China's automobile manufacturing and maintenance industry is unbalanced from the perspective of government intervention and incentives. Some researchers analyzed government intervention instruments and their effects on economic variables, such as resource misallocation, total factor productivity and costs [43,44], but little literature involves the motivation of government policies. The literature on optimal policy [30–32], which adds government policy in the general equilibrium model are more about the fiscal policy, monetary policy or tax policy on consumption or capital; little is about industrial policy in different sectors. Therefore, we investigated the impact of government incentive on industrial policy and industry structure, and provide a framework to study the interaction of government and the market, which also applies to other countries. Second, the growth rate of GDP is converging from the perspective of the development economics [45], and since automobile industry has always been a pillar industry and in China, how to promote the automobile industry to develop in a balanced way is crucial to the sustainable development of the automobile industry and even the whole economy in the future. Although some researchers focus on sustainable district development [46], balanced development of industry structure is also important. Finally, the research about China's automobile industry mainly focus on the manufacturing industry currently, such as the prediction of vehicle ownership [1,47,48], study on life cycle cost of electric vehicle [49–52], the bottleneck in the development of electric vehicles [53–55], and research on the development and market scale of ride-hailing [56,57]. There is little literature on automobile maintenance industry; however, we need to fully understand the development of the automobile industry, including the maintenance industry to promote sustainable development.

The remainder of the paper is organized as follows. Section 2 presents the theoretical model and the development of the empirical hypothesis. Section 3 introduces the empirical model, variable definitions and data resources. Section 4 provides the empirical evidence. Section 5 provides several robustness checks to make sure our results are robust. Section 5 concludes and presents policy implications.

### **2. Theoretical Model and Empirical Hypothesis**

We build a general equilibrium model with government incentive to investigate the effect of government intervention on the automobile industry. The general equilibrium model is widely used in modern economic research, especially the macroeconomic research about economic growth and industry structure [15,17,18,23–25]. Furthermore, the method of adding government policy in the general equilibrium model is usually used in the literature of optimal policy [30–32]. However, the literature is more about the fiscal policy, monetary policy or tax policy on consumption or capital, little is about industrial policy in different sectors. Thus, we also investigate the impact of government intervention on the automobile industry structure and its mechanism in this framework.

#### *2.1. Theoretical Model*

We assume that there are four participants in the economy: A representative consumer, two representative producers (i.e., one is an automobile manufacturing firm and the other is automobile maintenance firm) and a government. The market is completely competitive. The products of automobile manufacturing firm produce the finished automobile and auto parts, which can be formed capital in the economy, while the products or service of automobile maintenance firm can be consumed. Thus, the automobile manufacturing firm is more likely to be the upstream firm, and while the automobile maintenance firm is a downstream firm in the input-output production connections. Both of the two firms use capital and labor as input in the production process. We use subsidies as tools of government intervention and omit other intervention methods, such as tax rate. The subsidy rate for the automobile maintenance firm is denoted as *s*1, and the subsidy rate for the automobile manufacture firm is denoted as *s*2. The subsidy rates can be explained as the degree of government preferential, such as the relaxation of taxation [42]. The representative consumer is the providers of capital and labor. He provides capital and labor to producers and obtains rents and wage at the same time. Then the consumer uses the income to consume maintenance service to maximize utility for all periods of time. The utility maximization problem of the representative consumer can be expressed as:

$$\max\_{c\_t, K\_{t+1}} u = \sum\_{\mathbf{t}=0}^{\infty} \beta^t u(c\_t), \tag{1}$$

$$r\_t + p\_t(K\_{t+1} - K\_t + \delta K\_t) \le r\_t K\_t + w\_t L - T\_{t\prime} \tag{2}$$

here, *u* is the utility of the consumer, and *u*(·) is the utility function; *ct* is the consumption of the consumer at time *t*; *Kt* is the capital stock at time *t*; *L* is the fixed labor supply per period; β is the discount rate, and δ is the depreciation rate of capital. Since there are only two products in the economy, we might as well set the price of the automobile maintenance service as one and the price of the automobile manufacturing production as *pt*. The wages of the labor and the rent of capital are *wt* and *rt*, respectively. *Tt* is the lump-sum tax on consumer's income. We list the definition of each parameter in Table 1. If we set the Lagrangian multiplier of each period is λ*t*, then the first-order condition of the consumer problem is:

$$
\mu'(\mathbf{c}\_t) = \lambda\_{t\prime} \tag{3}
$$

$$
\lambda\_t p\_t = \beta \lambda\_{t+1} (p\_{t+1} + r\_{t+1} - \delta p\_{t+1}).\tag{4}
$$

Thus, the Euler Equation is obtained from Equations (3) and (4):

$$\frac{p\_t}{r\_{t+1} + (1 - \delta)p\_{t+1}} = \frac{\beta u'(c\_{t+1})}{u'(c\_t)}.\tag{5}$$

We assume that the production function of the automobile maintenance firm is *F*1(*K*1*t*, *L*1*t*) and the production function of the automobile manufacturing firm is *F*2(*K*2*t*, *L*2*t*). The production functions satisfy *FiK* > 0, *FiL* > 0, *FiKK* < 0, *FiLL*< 0, *FiKL* >0, *i* = 1, 2. The producers in each sector maximize the profits of each period:

$$\max\_{K\_{1t}, L\_{1t}} \pi\_1 = (1 + s\_{1t}) F\_1(K\_{1t}, L\_{1t}) - w\_t L\_{1t} - r\_t K\_{1t} \tag{6}$$

$$\max\_{K\_{2t}, L\_{2t}} \pi\_2 = p\_t (1 + s\_{2t}) F\_2(K\_{2t}, L\_{2t}) - w\_t L\_{2t} - r\_t K\_{2t} \tag{7}$$

here, π<sup>1</sup> and π<sup>2</sup> represent the profit of automobile maintenance and manufacturing firms, respectively. Then the first-order conditions for the capital of the automobile maintenance firm and automobile manufacture firm are:

$$(1 + s\_{1t})F\_{1K} = r\_{t\prime} \tag{8}$$

$$r\_l p\_l (1 + s\_{2t}) F\_{2K} = r\_{t\prime} \tag{9}$$

here, we omit the subscript of time *t* of the production functions for briefness. The first-order conditions for labor of the automobile maintenance firm and automobile manufacture firm are:

$$(1 + s\_{1t})F\_{1L} = w\_{t\prime} \tag{10}$$

$$
\hbar p\_t (1 + s\_{2t}) F\_{2L} = \mathfrak{w}\_t. \tag{11}
$$

We can know from Equations (8)–(11) that the government can influence the marginal production of labor and capital and then the production decisions of the firms, and then determine the capital flows between the two sectors by setting different subsidy rates. The government's subsidy expenditure comes from the lump-sum tax *Tt* imposed on consumers. Thus, the government's budget constraint is

$$T\_t = s\_{1t} F\_1(K\_{1t}, L\_{1t}) + s\_{2t} p\_{2t} F\_2(K\_{2t}, L\_{2t}).\tag{12}$$

As a social planner, the government's goal is certainly to maximize social welfare. However, the local governments have the promotion pressure in their career under the decentralization institute in China, so their goal is not entirely social welfare maximization, but the short-term GDP in their tenure. This incentive makes the government's time preference different from the consumer's in the market. The government is more willing to spend in the future and save currently to promote short-term growth of GDP. We set the government's short-term GDP incentive intensity to be *a*, which satisfies 1 < *a* < 1/β. Then the discount rate of government is *a*β, and the larger the value of *a*, the greater the GDP incentive the government has. Therefore, the government's objective function is:

$$\max \mu\_{\mathcal{S}} = \sum\_{t=1}^{\infty} (a\beta)^t \mu(c\_t) \,\tag{13}$$

here, *ug* is the utility of the government. Given the subsidy rates *s*1*<sup>t</sup>* and *s*2*<sup>t</sup>* for the automobile maintenance firm and automobile manufacturing firm, the equilibrium of market can be determined by Equations (2), (5), (8)–(11) and the market clear conditions of the products of the two sectors, capital and labor, which is the Equations (14)–(17) below. The market clear condition for automobile maintenance service market is:

$$F\_1(K\_{1t}, L\_{1t}) = c\_t. \tag{14}$$

The market clear condition for automobile manufacturing market is:

$$F\_2(K\_{2t}, L\_{2t}) = K\_{1, t+1} + K\_{2, t+1} - (1 - \delta)(K\_{1t} + K\_{2t}).\tag{15}$$

The market clear condition for capital is:

$$K\_{1t} + K\_{2t} = K\_t.\tag{16}$$

The market clear condition for labor is:

$$L\_{1t} + L\_{2t} = L.\tag{17}$$

This system expressed the dynamic equilibrium relationships for variables {*ct*,*K*1*t*,*K*2*t*,*Kt*, *L*1*t*, *L*2*t*, *pt*,*rt*, *wt*, *Tt* . Then the government will choose the optimal subsidy rates *s*1*<sup>t</sup>* and *s*2*<sup>t</sup>* constrained by the market equilibrium conditions. We solve this problem with the steps below. Firstly, using the Euler Equation, which is Equation (5) and budget constraint, which is Equation (2), we change the consumer's budget constraint, which is Equation (2), of each period into budget constraint of all periods (please see the detail calculation in Appendix A part), which is:

$$\sum\_{t=0}^{\infty} \beta^t \ u'(c\_t) (c\_t - w\_t L + T\_t) = \mu'(c\_0) [r\_0 K\_0 + p\_0 (1 - \delta) K\_0]. \tag{18}$$

*Sustainability* **2019**, *11*, 4721

We denote the right hand of Equation (18) as *A* = *u* (*c*0)[*r*0*K*<sup>0</sup> + *p*0(1 − δ)*K*0], which is constant. Then the government will optimize Equation (13) conditioning on Equations (14)–(18), and choose the optimal value of variables {*ct*,*K*1*t*,*K*2*t*, *L*1*t*, *L*2*t*}. The Lagrange function of this problem is:

$$\begin{aligned} \Gamma &= \sum\_{t=0}^{\infty} \begin{aligned} & \left\{ \begin{aligned} u(c\_{l}) &+ \eta\_{1t} [F\_{1}(K\_{1t}, L\_{1t}) - c\_{l}] \\ &+ \eta\_{2t} [F\_{2}(K\_{2t}, L\_{2t}) - K\_{1t+1} - K\_{2t+1} + (1 - \delta)(K\_{1t} + K\_{2t})] \end{aligned} \right\} \\ &+ \sum\_{t=0}^{\infty} \left[ \beta^{t} \phi u'(c\_{l}) (c\_{t} - w\_{l}L + T\_{l}) \right] - \phi A \end{aligned} \end{aligned} \tag{19}$$

here, the parameters η1*t*, η2*t*, η3*t*, φ are Lagrange multipliers for the constraints. We can get the dynamic equilibrium system for {*ct*,*K*1*t*,*K*2*t*, *L*1*t*, *L*2*t*, η1*t*, η2*t*, η3*t*,φ} using the first order conditions of variables *ct*, *K*1, *<sup>t</sup>*+1,*K*2,*t*+1, *L*1*t*, *L*2*<sup>t</sup>* of Equation (19) and constraints, which is Equations (14), (15) and (17). Specially, according to the analysis of the first order conditions at steady state we can get this conclusion below.

**Proposition 1.** *When a* > 1*, we have s*<sup>2</sup> > 0*; the greater the government's GDP incentives, the larger the subsidy s*<sup>2</sup> *to the automobile manufacturing sector, and the greater the gap of government's preferential support for automobile manufacturing sector and that for automobile maintenance sector.*

**Proof.** We only focus on the first order conditions of variables *K*1, *<sup>t</sup>*+1, *K*2,*t*+<sup>1</sup> and *ct*, at the steady state, which means we can omit the subscript of time, and they can be expressed as:

$$
\eta\_2 = a\beta [\eta\_1 F\_{1K} + (1 - \delta)\eta\_2],
\tag{20}
$$

$$
\eta\_2 = a\beta [\eta\_2 F\_{2\mathcal{K}} + (1 - \delta)\eta\_2],
\tag{21}
$$

$$
\eta\_1 = u'(c) + \frac{\phi u''(c)(c - wL) + u'(c)}{a^t}.\tag{22}
$$

From the steady state of Euler Equation, which is Equation (5), we can get:

$$\frac{1}{\beta} = 1 - \delta + \frac{r}{p}.\tag{23}$$

From the first order condition of the automobile maintenance sector, which is Equation (8), at the steady state, we can get:

$$F\_{1K} = r/(1+s\_1).\tag{24}$$

From the first order condition of the automobile manufacturing sector, which is Equation (9), at the steady state, we can get:

$$pF\_{2K} = r/(1+s\_2). \tag{25}$$

Substituting the conditions of Equations (8) and (23) into Equation (20), we can get:

$$\frac{1}{a\beta} - \frac{1}{\beta} + \frac{r}{p} = \frac{\eta\_1 r}{\eta\_2 (1 + s\_1)},\tag{26}$$

and substituting the conditions of Equations (9) and (23) into Equation (21), we can get:

$$\frac{1}{n\beta} - \frac{1}{\beta} + \frac{r}{p} = \frac{r}{p(1+s\_2)}.\tag{27}$$

Then from Equation (27), since we assume as *a* > 1, the subsidy rate for the automobile manufacturing sector *s*<sup>2</sup> > 0, and *s*<sup>2</sup> increases with the increasing of *a*, which means the government indeed give subsidy to the automobile manufacturing firm, and the subsidy increases with the increasing of short term GDP incentive.

Then we will analyze the subsidy to the automobile maintenance firms. Dividing Equation (27) by Equation (26), we can get:

$$\frac{1+s\_1}{1+s\_2} = \frac{p\eta\_1}{\eta\_2}.\tag{28}$$

We can know that η<sup>1</sup> decreases with parameter *a*, while η<sup>2</sup> does not change with parameter *a* according to Equation (22) assuming *u*(*c*) is small enough, and the term φ*u*(*c*)(*c* − *wL*) + *u* (*c*) is positive. This means the shadow value of automobile maintenance service decrease when the government' GDP incentive is large. So <sup>1</sup>+*s*<sup>1</sup> <sup>1</sup>+*s*<sup>2</sup> will decrease with *a*, which means the gap of government's preferential support for automobile manufacturing sector and automobile maintenance sector increases with government's GDP incentive. -

These results can be interpreted as that the government pays more attention to future consumption and production, due to short-term GDP incentives and the limited tenure, which means the government utility is different with the consumer's because the consumer prefers the current consumption. Then the government subsidizes the firms in the automobile manufacturing sector that can be formed as capital and then more capital will produce more product and GDP because the capital is the necessity of the production process and has the multiplier effect in the process. Moreover, the larger the short-term GDP incentives, the larger the subsidies on the automobile manufacturing sector, and the larger gap between the subsidy given to the automobile manufacturing firm and the subsidy given to the automobile maintenance firm. That's why the government with short-term GDP incentive will intervene differently in the different sectors.

In the empirical part in Section 3, we will test the positive correlation of the government's short-term GDP incentives on the biased subsidy between the firms of automobile manufacture sector and firms of automobile maintenance sector. So we firstly propose the empirical hypothesis in Section 2.2 before the empirical research design.
