*3.2. Variable Definition of Government Incentive*

Literature on political promotion tournaments, fiscal decentralization, fiscal revenue incentives and GDP growth [34,36] all mentioned that fiscal decentralization leads to GDP and fiscal incentives of the local government. In addition, stronger fiscal autonomy is most directly related to GDP incentives compared with other policies that can be used by local governments. Since China introduced to reform and opening policies, economic growth has been the main task of the government. When the promotion of officials depends more on the performance of economic growth under the horizontal competition among regions, the GDP incentive of local governments through fiscal approach becomes stronger [34,35]. Therefore, fiscal decentralization is the best measure of GDP incentive of local governments. It can be considered that the fiscal decentralization is a measure of autonomy of local governments on fiscal revenue and expenditure, and the larger the degree of fiscal decentralization, the stronger the fiscal autonomy of local governments because of the higher financial autonomy and the higher resource utilization capacity.

The fiscal decentralization system reflects the division of fiscal power and administrative power between the central and local governments, especially the revenue and expenditure power delegated by the central government to local ones. So the fiscal decentralization index should reflect the degree of local governments' control over fiscal power and administrative power. Oates firstly adopted three indicators of fiscal revenue and expenditure to represent the degree of fiscal decentralization [58]. Zhang and Gong [35] defined a group of indicators that represent the ratio of local government's income, or expenditure to the central government ability to measure fiscal decentralization. Lv et al. [42] used the tax decentralization index to measure the tax sharing incentives of local government. Since fiscal revenue, especially tax revenue, can represent a large part of the government's financial power, thus, tax sharing incentive is consistent with fiscal decentralization. So we use the following three tax sharing indicators to define the government's GDP incentive referring to Lv et al. [42].

