**3. Empirical Method**

### *3.1. Setting up of Empirical Model*

According to the theoretical model, it can be known that the greater the government's short-term GDP incentives, the greater the difference in preferential subsidies between the two kinds of firms. Since most of the preferential subsidies are invisible, we use indirect methods to measure the biased intervention policies of the government. Specifically, we use the difference between the actual income tax rates in the two kinds of firms to reflect the difference in government intervention bias. The gap of actual income tax rate and the statutory tax rate, induced by taxation intensity, can reflect the degree of government intervention. The lower the actual income tax rate, the greater the government's preferential subsidy. Since the pre-tax profit is usually not the real profit of the enterprise, the proportion of the income tax in pre-tax profit does not accurately reflect the actual income tax rate of the enterprise. Some researchers use tax avoidance to measure the actual tax rate of the firms [41,42], because the larger the tax evasion equals the lower actual tax rate, which also indicates the smaller government

taxation intensity and the larger extent of the government intervention. We use the method of [41,42] to calculate the tax avoidance degree of the enterprise.

The idea of this method is like this. Although the reported profit is not the real profit of the enterprise, it is related to the real profit, and we can calculate the estimated profit, which is also not exactly the real profit, but related to it. Then there will be a large error if we use the difference between the estimated profit and the reported profit as the hidden profit of the enterprise. However, we can know that the estimated profit is related to the reported profit, and the greater the correlation, the smaller degree of the enterprise's tax avoidance. Thus, [41] measured the degree of tax avoidance of enterprises by calculating the sensitivity of estimated profit, which is based on the method of national income accounting, and the reported profit. Firstly, the estimated profit of the enterprise is highly correlated with the real profit π*it*. It is assumed that the relationship between the real profit and the estimated profit is expressed as:

$$
\pi\_{\rm it} = \eta\_{\rm it} + PRO\_{\rm it} + \theta\_{\rm it} \tag{29}
$$

here, the subscripts *i* and *t* represent the enterprise and the year, respectively. η*it* is a constant, θ*it* is a random error, and *PRO* is the estimated profit. According to the principle of national income accounting, the estimated profit can be expressed as:

$$PRO\_{it} = \frac{Y\_{it} - MED\_{it} - FC\_{it} - WAGE\_{it} - DEP\_{it} - VAT\_{it}}{TAS\_{it}},\tag{30}$$

here, *Y* represents the total industrial output value of the enterprise; *MED* represents the total industrial input; *FC* represents the financial expenses; *WAGE* represents the expenditure of wage expressed by the total payable wage; *DEP* is the depreciation this year; *VAT* is the amount of payable value added tax and *TAS* indicates the total assets of the enterprise.

Secondly, the industrial enterprise database discloses the pre-tax profit reported by the company, which is the reported profit of the enterprise, denoted by *RPRO*, and the reported profit of the enterprise is also related to the real profit π*it*, which can be expressed as:

$$RPRO\_{it} = d\_{it} \pi\_{it} + \varepsilon\_{it} + \mathcal{E}\_{it\prime} \tag{31}$$

here the reported profit *RPRO* is defined as the ratio of total profit and total assets; *eit* is the constant term; ξ*it* is the random disturbance term; *dit* is the sensitivity between the reported profit and the real profit, and the smaller value of *d* indicating the higher the degree of tax avoidance. According to the theoretical model, the government's GDP incentives will affect the difference between the actual tax burden of automobile manufacturing enterprises and automobile maintenance enterprises, which is the difference of sensitivity between the two kinds of firms. Therefore, we can express this impact as:

$$d\_{\rm it} = \beta\_0 + \beta\_1 V \text{EHM}\_{\rm il} + \beta\_2 GOV\_{\rm it} + \beta\_3 V \text{EHM}\_{\rm il} \times GOV\_{\rm it} + \chi X\_{\rm it} + \lambda\_t + \gamma\_j + \nu\_{\rm it} \tag{32}$$

here, *GOV* indicates the government's incentive; *VEHM* is a dummy variable which equals one if the firm belongs to the automobile manufacturing industry and zero otherwise; *X* indicates the firm level characteristic variables; λ*<sup>t</sup>* represents the year fixed effect, and γ*<sup>j</sup>* represents province fixed effect. β<sup>1</sup> presents the difference of sensitivity of reported profits to real profits between the manufacturing industry and the maintenance industry; β<sup>2</sup> indicates the influence of government incentives on the sensitivity of reported profits and real profits, and the coefficient β<sup>3</sup> of the interaction term *VEHM* × *GOV* indicates the difference of the impact of government's GDP incentives on sensitivity between automobile manufacturing firms and maintenance firms. Since the real profit of the enterprise cannot be observed, Equation (32) cannot be estimated directly. Therefore, we substitute the real profit represented by the estimated profit, which is Equation (29), into the expression of the reported profit, which is Equation (31) and then we can get

$$RPRO\_{it} = d\_{it}PRO\_{it} + d\_{it}
\eta\_{it} + 
\varepsilon\_{it} + 
\varepsilon\_{it} \tag{33}$$

here, ε*it* = ξ*it* + *dit*θ*it*. Then we take the expression of the sensitivity *dit* between the profit and the real profit, which is Equation (32), into the relationship between the estimated profit and the reported profit, which is Equation (33) and we finally get this expression:

$$\begin{aligned} \text{RPRO}\_{\text{it}} &= (\beta\_0 + \beta\_1 V \text{EHM}\_{\text{it}} + \beta\_2 \text{GOV}\_{\text{it}} + \beta\_3 V \text{EHM}\_{\text{it}} \times \text{GOV}\_{\text{it}} + \beta\_4 \text{X}\_{\text{it}} + \lambda\_{\text{I}} \\ &+ \gamma\_j \text{)} \times \text{PRO}\_{\text{it}} + a\_0 + \alpha\_1 V \text{EHM}\_{\text{it}} + \alpha\_2 \text{GOV}\_{\text{it}} + \alpha\_3 V \text{EHM}\_{\text{it}} \times \text{GOV}\_{\text{it}} \\ &+ a\_4 \text{X}\_{\text{it}} + \lambda\_{\text{I}} + \gamma\_j + \mu\_{\text{it}} .\end{aligned} \tag{34}$$

Thus, the coefficient β<sup>3</sup> of the triple interaction term *VEHM* × *GOV* × *PRO* indicates the difference of the impact of government's GDP incentives on sensitivity between automobile manufacturing firms and automobile maintenance firms. If β<sup>3</sup> is negative, it means that automobile manufacturing firms have been given more preferential support under government incentives, which lead to their larger tax avoidance compared with the automobile maintenance companies.

Referring to the relevant literature [41,42], we control other firm level variables, including the firm size (*SIZE*), which is expressed in terms of the natural logarithm of the company's total assets; the liability-asset ratio (*LEV*), which equals the ratio of total liabilities to total assets of an enterprise; the age of the firm (*AGE*), which is the logarithm of the difference between the establishment year and the sample year; the financial expense (*LOAN*), which is the ratio of interest expense to total assets; the proportion of exports (*EXPT*), which is the ratio of export delivery value to the total assets; the ratio of industrial sales to the total value of industrial output (*SALE*) and the dummy variable (*SOE*) that indicates whether the enterprise is a state-owned enterprise or not.
