Innovation of Family-Owned Enterprises and Government Subsidies: From A Policy-Oriented Perspective

Abstract

This paper investigates the influence effects of government subsidies on the innovation of family-owned enterprises in China through a panel data model and Heckman two-stage model, and explores the possible influence mechanisms of government subsidies on different innovation behaviors of family-owned enterprises through a mediation analysis method. It is found that government subsidies play a significant role in promoting innovation input, innovation quantity and innovation quality of family-owned enterprises. From the perspective of innovation quality, government subsidies are more beneficial to family-owned enterprises without “two jobs in one” or “2nd generation succession”. Compared with family-owned enterprises that have completed intergenerational inheritance, government subsidies are more conducive to enhancing the innovation quantity of family-owned enterprises that have not achieved “2nd generation succession”. We find also that government subsidies can indirectly improve the innovation quality of family-owned enterprises by increasing the proportion of state-owned shares and easing the financing constraints. By organically integrating two relatively independent research fields (effectiveness of government subsidy and innovation of family businesses), this paper opens up a new way of thinking for exploring the sustainability of family businesses.

1. Introduction

Family-owned enterprises (henceforth, FOEs) are the most dominant form of business organizations. In most countries, FOEs constitute more than 70 percent of the overall businesses and play a key role in economic growth and workforce employment. In China, for example, about 35 percent of the listed enterprises in China’s A-share market are family-owned [1] and contribute to 60 percent of the country’s GDP on average. According to PricewaterhouseCoopers’ (henceforth, PwC) “2018 China Family Business Research Report”, FOEs account for 55.7% of China’s non-state-owned enterprises, and have become the backbone of China’s economic development.

The “2019 Global Family Business Survey Report” points out that innovation is the key to the sustainable development of FOEs, and FOEs often need to innovate to avoid recession and death. However, according to the data about innovation in recent years, the average ratio of R&D investment to business income for FOEs is only 3.46%, far lower than the average ratio (4.17%) of non-family-owned enterprises in the same period [2]. The lack of R&D investment of FOEs will not only reduce the competitiveness and sustainable development ability of enterprises, but will also generate many serious problems that hinder economic development [3]. Thus, how to effectively encourage FOEs to increase innovation input and improve their innovation quantity and quality is an important research topic [4].

Since innovation has the characteristics of high costs, high risks and long cycles [5], enterprise innovation often needs to be promoted by the “supporting hand” of government. Theoretically, government subsidies should be able to effectively solve the market failure and stimulate the innovation of FOEs. However, in reality, there are some problems, such as asymmetric information between government and enterprises, which result in a poor incentive effect of subsidies on FOE innovation. Some FOEs have adopted “low-quality innovation” behavior in order to obtain the government’s innovation support, and even some extreme behaviors such as defrauding subsidies [6]. Moreover, the distinctive features of FOEs, such as highly centralized control, an excessive financing ratio and difficult succession for subsequent generations [7,8], often negatively affect the implementation of government subsidies. For example, only 30% of FOEs can successfully pass on to the second generation [9], and up to 85% of FOEs do not survive beyond the third generation [10]. Therefore, on the basis of the abovementioned features of FOEs, this study organically integrates the two relatively independent research fields, government subsidies and innovation behaviors of FOEs, and examines in-depth the effects and mechanisms of government subsidies on R&D investment, innovation quantity and quality of FOEs. To be specific, the following issues are discussed. First, does the innovation input or innovation output of family businesses stimulated by government subsidies increase? Does the quality of innovation output of FOEs improve? Second, are there any differences in the answers to the above questions among different groups of “intergenerational inheritance” and “two jobs in one” FOEs? Third, can government subsidies influence the innovation behavior of FOEs by alleviating financing constraints, reducing profit risk or increasing the proportion of state-owned shares in enterprise?

The marginal contributions of this paper are mainly manifested in three aspects. First, existing studies focus on the relationship between government subsidies and enterprise innovation. This study takes a step forward, focusing on the influence effects and mechanisms of government subsidies on innovation behaviors of FOEs. Second, the R&D input and innovation output of FOEs correspond to the relationship between process and result, which cannot be simply equated. This study investigates the actual effects of government subsidies on FOE innovation from the perspectives of innovation input, quantity and quality, which not only enriches the research on subsidy policies, but also helps to put forward more comprehensive policy suggestions. Third, the succession for subsequent generations, the ownership of control and the proportion of state-owned equity participation often have a profound impact on the future innovation and development direction of FOEs. This study incorporates all these distinctive features of FOEs into one framework, which not only makes the estimated results more accurate, but also provides the possibility to investigate the differences in the subsidy effects and mechanisms caused by the heterogeneity of family business.

The rest of the paper proceeds as follows. In Section 2, the literature review is described. The methodology is presented in Section 3. The data and variables are introduced in Section 4. The empirical analysis is conducted in Section 5. Finally, conclusions are drawn in Section 6.

2. Literature Review

2.1. Government Subsidies and Enterprise Innovation

The influence of government subsidies on enterprise innovation is the focus of academic circles, which can be roughly divided into two parts: “influence effect” and “influence mechanism”.

There are different perspectives regarding the “influence effect” of government subsidies on enterprise innovation. The first is the incentive view, which asserts that government subsidies can stimulate the innovation of enterprises [11,12,13], and this incentive effect is closely related to the scale of the subsidies received by enterprises [14]. Studies based on data from German [15], Italian [16] and Chinese enterprises [17] indicate that subsidized enterprises have a higher patent application rate compared with those that do not receive government subsidies. The second perspective is the inhibition view, which contends that rent-seeking behavior and incentive distortion under the economic-oriented promotion assessment system will lead to excessive investment and an unreasonable innovation structure [18]. The government cannot ensure that subsidies are allocated to innovation activities, and effective means to monitor subsidized enterprises’ innovation behavior are lacking, causing subsidies to inhibit innovation [19]. The third is the nonlinear view, which assumes that there is an inverted U-shaped relationship between government subsidies and enterprise innovation [20]. Moderate government subsidies can significantly stimulate enterprise innovation, whereas excessive government subsidies may inhibit the innovation of enterprises [21,22]. The fourth perspective is the irrelevance view, which argues that government subsidies may not have a significant incentive or inhibition effect on enterprise innovation due to the lax constraints of subsidies [23,24].

Concerning the “influence mechanism” of government subsidies on enterprise innovation, it can be organized into four mechanisms. First, alleviating the financing constraints of enterprises. Enterprises need long-term and sustained capital investment for innovation, and financing constraints tend to inhibit enterprises from investing in innovation [25], whereas government subsidies can enhance enterprises’ willingness to innovate by alleviating the financing constraints of enterprises [26]. Second, improving the risk-taking ability of enterprises. The higher an enterprise’s risk-taking ability, the stronger its willingness to innovate. Government subsidies can help innovative enterprises to share risks [27] and, to some extent, make up for the losses caused by the innovation failure [28], thus promoting enterprise innovation. Third, introducing the state-owned shares. Government subsidies help innovative enterprises to introduce state-owned shares, and thus, influence their innovation behavior. Especially for FOEs, the introduction of state-owned shares can effectively improve the willingness of FOEs to invest in R&D, and thus, promote the innovation activities of FOEs [2]. Fourth, strengthening the high-quality signal efficacy. Government subsidies are beneficial to convey the high-quality signal of enterprises to external investors [29], and thus, promote enterprise innovation [30].

2.2. Influencing Factors of FOE Innovation

The literature about the influencing factors of FOE innovation can be roughly sorted into two aspects: external environmental factors and internal control factors.

The external environmental factors mainly involve the horizontal competition environment [31], market operation environment and policy implementation environment faced by FOEs in the process of innovation. Usually, the horizontal competition environment can significantly adjust the performance and innovation spirit of FOEs. Under the precondition that the performance is fixed, the fiercer the competition in the same industry, the lower the willingness of FOEs to innovate [32]. The marketization degree is one of the important indexes to evaluate the market operation environment, and the difference in the marketization degree in different regions is often an important reason for the heterogeneity of innovation behavior in FOEs [33]. Especially when the marketization degree is at a high level, the heterogeneity of innovation behavior of FOEs will be more prominent [34]. The policy implementation environment also has an important influence on the innovation behavior of FOEs. The relatively fair and transparent policy implementation environment can often effectively improve the productivity and innovation ability of FOEs [35].

The internal control factors that affect the innovation of FOEs mainly involve family ownership and family management [36,37], and the impact of internal control factors on the innovation of FOEs is still inconclusive. First, from the perspective of family ownership, Chen, Tsao and Chen [38] confirm that the stronger the family’s control over enterprises, the more beneficial it is to encourage enterprises to increase innovation input and improve innovation output. However, some studies found that there is an “inverted U-shaped” relationship between the level of family ownership and the enterprise innovation, and a level of ownership that is too high or too low will reduce the willingness of FOEs to invest in R&D [39,40], and may hinder the innovation output [41]. Second, from the perspective of family management, a moderate concentration of management can ensure the efficient execution of FOEs and provide a strong guarantee for enterprises to carry out innovation activities [42]; excessively centralized management may lead to inefficient decision-making and further generate a negative impact on FOEs innovation [43,44], whereas excessively decentralized management may lead to decision-making conflicts [45,46], which in turn inhibits the innovation of FOEs [47]. Compared with family ownership, family management has a more obvious impact on enterprise innovation [48].

To sum up, the existing literature either focuses on the influence effects and mechanisms of government subsidies on the innovation of non-family-owned enterprises, or pays attention to the external environmental and internal control factors that affect the innovation of FOEs. Few studies explore the effects and mechanisms of government subsidies on FOE innovation. In addition, the existing literature mostly focuses on the impact of government subsidies on innovation input or innovation output of enterprises, and ignores the distinction of innovation “input and output” and that of innovation “quantity and quality”, resulting in the research conclusions having a weak pertinence of and a lack of policy connotation. Besides, the existing studies do not consider the heterogeneity of FOEs sufficiently, and neglect the distinctive features of FOEs such as “intergenerational inheritance”, “proportion of state-owned shares” and “proportion of controlling family shares” [49], thus covering up many important problems in the actual operation of FOEs.

3. Methodology

This study focuses on FOEs in China, and investigates the effectiveness of government subsidies on sustainable outcomes of FOEs. First, using the panel data model and Heckman two-stage model, we examine the impact of China’s government subsidies on the innovation of FOEs. Second, using the mediation analysis method, we analyze the mechanism of government subsidies on the innovation of FOEs.

3.1. Panel Data Model

Drawing lessons from Li and Zheng [50], we construct the following model to explore the influence effects of government subsidies on family business innovation.

$$Y_{it}=c+\beta X_{it}+\alpha Z_{it}+{\theta }_i+{\gamma }_t+{\epsilon }_{it}$$

(1)

The explained variable $Y$ in Equation (1) represents FOE innovation, which involves innovation input ($RDinput$), innovation output ($RDoutput$) and innovation quality ($RDquality$). The core explanatory variable $X$ represents the government subsidy. $Z$ is the independent variable or a series of FOE control variables, and $\alpha$ represents the corresponding coefficient. ${\theta }_i$ and ${\gamma }_t$ represent the individual fixed effect and the time fixed effect, respectively, and ${\epsilon }_{it}$ is a random disturbance term.

3.2. Heckman Two-Stage Model

Considering that not all FOEs in the sample can obtain government subsidies, the impact of government subsidies on their innovation behaviors cannot be observed for FOEs that do not obtain subsidies. To solve this potential sample selection problem [51], we use the Heckman two-stage method and check the results estimated by Equation (1). The precise form of the Heckman two-stage method is presented below, where Equation (2) is the selection equation and Equation (3) is the substantive equation of interest.

$$Y_2=\alpha Z+\delta$$

(2)

$$Y_1=B_0+B_{1}X+\sigma {\rho }_{\epsilon \delta }\lambda \left(T-\alpha Z\right)+{\sigma }^{\prime }{\epsilon }^{\prime }$$

(3)

In the selection equation (Equation (2)), $Y_2$ is the dichotomous dependent variable, and $\delta$ is the normally distributed error term. The selection equation (Equation (2)) is estimated using the probit model and the predicted values are retained as estimates of $T-\alpha Z$. In the regression equation (Equation (3)), the value of $Y_1$ is observed when $Y_2$ is greater than some threshold $T$, and it is censored (i.e., missing) if $Y_2\le T$. The regression equation is an ordinary least-squares regression with $X$ and the inverse Mills ratio included as regressors. Note that the inverse Mills ratio (Equation (4)) is estimated for each case by dividing the normal density function evaluated at $\varphi \left(T-\alpha Z\right)$ by one minus the normal cumulative distribution function estimated at $1-\Phi \left(T-\alpha Z\right)$.

$$\lambda \left(T-\alpha Z\right)=\frac{\varphi \left(T-\alpha Z\right)}{1-\Phi \left(T-\alpha Z\right)}$$

(4)

3.3. Mediation Analysis Method

Referring to the regression-based mediation analysis proposed by Wen and Ye [52], we construct the framework of the mediation analysis to test the possible channels of government subsidies affecting FOE innovation.

$$Me{d}_{it}=c_1+{\beta }_1{X}_{it}+{\alpha }_1{Z}_{it}+{\theta }_i+{\gamma }_t+{\epsilon }_{it}$$

(5)

$$Y_{it}=c_2+{\beta }_2{X}_{it}+{\delta }_{2}Me{d}_{it}+{\alpha }_2{Z}_{it}+{\theta }_i+{\gamma }_t+{\epsilon }_{it}$$

(6)

where $Med$ is a mediator variable. According to the panel data model (Equation (1)), the coefficient $\beta$ measures the total effect of government subsidies on FOE innovation; the coefficient ${\beta }_1$ in Equation (5) measures the effect of government subsidies on the mediator variable; the coefficient ${\beta }_2$ in Equation (6) reflects the direct effect of government subsidies on FOE innovation, whereas the coefficient ${\beta }_1{\delta }_2$, calculated by multiplying the two coefficients (${\beta }_1$ in Equation (5) and ${\delta }_2$ in Equation (6)), reflects the indirect effect. In general, there are two approaches to calculate the confidence interval (CI) of the indirect effect. The first one is the Sobel test, which is based on the product of two normally distributed values of coefficients. The second one is the bootstrap test, which does not require a prior assumption of the sampling distribution.

4. Data

This study examines the listed FOEs in China’s Shanghai and Shenzhen A-share markets. The listed enterprises that meet the following conditions are defined as listed FOEs: first, ultimate control can be attributed to a natural person or a family; second, the natural person or family has substantial control over the listed enterprise; and third, the ultimate controller is directly or indirectly the largest shareholder of the listed enterprise. The financial data, governance data and the registered place information of listed FOEs stem from the CSMAR database (http://cndata1.csmar.com (accessed on 15 December 2020)); the data about FOE innovation input and output stem from the Wind database. The sample is selected from 2009 to 2016, and the initial data is preprocessed according to the following steps: first, the enterprises whose ultimate controller changes are excluded; second, the enterprises that lack the calculation conditions of control powers are removed; third, listed enterprises in the financial and insurance industries are excluded; fourth, listed enterprises with an abnormal trading status, for example, ST (special treatment) and PT (particular transfer), are eliminated; and fifth, the samples of listed enterprises with serious data missing are removed. Finally, 4365 observation samples are obtained. The specific definitions of the main variables in this study are shown in

Table 1. Variable definition.

	Variable	Symbol	Definition
Explained variables
	Innovation input	$RDinput$	Natural logarithm of R&D expenditure.
	Innovation output	$RDoutput$	Natural logarithm of total patent application plus 1.
	Innovation quality	$RDquality$	Natural logarithm of invention patent application plus 1.
Core explanatory variable
	Government subsidy	$Subsidy$	Natural logarithm of the amount of government subsidy received by the FOE.
FOE grouping variables
	2nd generation succession	$Gene$	Refer to the practice of Hu and Wu [48]; if the family successor holds the post of director, the 2nd generation succession is defined as 1; otherwise, 0.
	Two jobs in one	$Dual$	The chairman and general manager of a FOE are combined, which is defined as 1; otherwise, 0.
FOE control variables
	Enterprise scale	$Size$	Natural logarithm of total assets.
	Enterprise debt	$Lever$	Sum of current liabilities and long-term liabilities divided by total assets.
	Enterprise profitability	$Roa$	Return on assets of enterprises.
	Operation capability	$Oper$	Ratio of total sales revenue to average total assets.
	Tobin Q	$Tobinq$	Ratio of enterprise market value to asset replacement cost.
	Enterprise growth	$Grow$	Growth rate of sales revenue of FOE.
	Enterprise market share	$Ms$	FOE’s market share is its sales measured as a percentage of an industry’s total revenues.
	Enterprise age	$Age$	Natural logarithm of enterprise age.
	Board size of enterprise	$Board$	Natural logarithm of number of board members.
	Enterprise independence	$Indep$	Proportion of independent directors in the board of directors.
	Family control	$Fhold$	Adjusted equity ratio of family members of actual controller.
	Family independence	$Fdir$	Proportion of family members of the actual controller to the total number on the board of directors.
	Family team	$Fman$	Proportion of the number of members controlled by family in the senior team of the enterprise.
Mediator variables
	Financing constraint	$Sa$	Refer to the method of Liu et al. [49] to construct the financing constraint index. The greater the value of the financing constraint index, the higher the degree of financing constraint enterprises face.
	Profit risk	$Irisk$	Profit fluctuation of FOE.
	State-owned participation	$Gsta$	Ratio between the number of shares held by state-owned enterprises and the number of shares held by the controlling family.

.

Following prior studies [53,54], the natural logarithm of R&D expenditure is taken to measure the innovation input, the natural logarithm of total patent applications plus 1 is chosen to measure the innovation output [55] and the natural logarithm of invention patent applications plus 1 is taken to measure the innovation quality [56]. Drawing lessons from Yuan [57] and Li et al. [58], we select some FOE control variables such as enterprise scale ($Size$), enterprise debt ($Lever$), enterprise profitability ($Roa$) and family control ($Fhold$). To further investigate the influence mechanism of government subsidies on FOE innovation, we refer to the practices of Liu et al. [49] and Costa et al. [59], construct a financing constraint index ($Sa$), and introduce profit risk ($Irisk$) and state-owned participation ($Gsta$). The statistical descriptions of the variables are shown in

Table 2. Descriptive statistics.

Symbol	Mean	Median	Variance	Min	Max	Observation
$RDinput$	14.508	17.158	6.524	0.000	20.227	4365
$RDoutput$	1.647	1.609	1.480	0.000	5.176	4365
$RDquality$	1.091	0.693	1.184	0.000	4.357	4365
$Subsidy$	8.052	12.285	7.951	0.000	21.022	4365
$Gene$	0.264	0.000	0.441	0.000	1.000	4365
$Dual$	0.220	0.000	0.414	0.000	1.000	4365
$Size$	21.659	21.577	0.991	19.503	24.570	4365
$Lever$	0.394	0.383	0.198	0.045	0.866	4365
$Roa$	0.048	0.043	0.053	−0.127	0.226	4365
$Oper$	1.124	0.939	0.782	0.101	4.880	4365
$Tobinq$	3.163	2.469	2.227	1.004	14.180	4365
$Grow$	0.209	0.133	0.460	−0.620	2.918	4365
$Ms$	0.004	0.001	0.010	0.000	0.073	4365
$Age$	1.896	1.946	0.747	0.000	3.135	4365
$Board$	2.213	2.213	0.126	1.792	2.565	4365
$Indep$	0.442	0.417	0.052	0.385	0.600	4365
$Fhold$	37.196	35.770	15.025	11.810	76.380	4365
$Fdir$	0.126	0.111	0.136	0.000	0.556	4365
$Fman$	0.091	0.000	0.141	0.000	0.667	4365
$Sa$	−3.416	−3.355	0.245	−3.951	−2.945	3464
$Irisk$	0.027	0.018	0.031	0.000	0.273	3954
$Gsta$	0.040	0.000	0.100	0.000	0.567	4365

.

5. Empirical Analysis

5.1. Impact of Government Subsidies on Innovation Behaviors of FOEs

Table 3. Estimated results of government subsidies affecting innovation behaviors of FOEs.

	(1)	(2)	(3)	(4)	(5)	(6)
	$\mathit{R}\mathit{D}\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{o}\mathit{u}\mathit{t}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{q}\mathit{u}\mathit{a}\mathit{l}\mathit{i}\mathit{t}\mathit{y}$	$\mathit{R}\mathit{D}\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{o}\mathit{u}\mathit{t}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{q}\mathit{u}\mathit{a}\mathit{l}\mathit{i}\mathit{t}\mathit{y}$
$Subsidy$	0.046 *** (5.038)	0.008 *** (3.015)	0.004 ** (2.023)
$L.Subsidy$				0.040 *** (3.885)	0.005 * (1.694)	0.003 (1.065)
$Size$	1.011 *** (8.401)	0.220 *** (7.348)	0.189 *** (7.557)	1.125 *** (8.312)	0.211 *** (6.037)	0.196 *** (6.712)
$Lever$	−1.290 *** (−2.481)	0.088 (0.722)	0.242 ** (2.403)	−1.051 * (−1.762)	0.179 (1.183)	0.343 *** (2.711)
$Roa$	9.334 *** (4.967)	3.536 *** (8.376)	3.364 *** (9.179)	7.816 *** (3.749)	4.086 *** (8.078)	3.967 *** (8.961)
$Oper$	−0.048 (−0.387)	0.016 (0.583)	−0.009 (−0.378)	0.221 * (1.649)	0.040 (1.223)	0.016 (0.559)
$Tobinq$	−0.133 *** (−2.873)	−0.038 *** (−3.560)	−0.012 (−1.268)	−0.058 (−1.102)	−0.028 ** (−2.092)	−0.002 (−0.193)
$Grow$	−0.144 (−0.751)	−0.167 *** (−3.987)	−0.138 *** (−4.072)	0.257 (1.242)	−0.184 *** (−3.536)	−0.178 *** (−4.088)
$Ms$	−47.445 *** (−2.934)	−8.103 *** (−3.386)	−5.776 *** (−3.084)	−55.137 *** (−2.965)	−9.299 *** (−3.415)	−7.190 *** (−3.318)
$Age$	−1.424 *** (−10.288)	−0.445 *** (−13.854)	−0.339 *** (−12.842)	−1.403 *** (−7.856)	−0.580 *** (−12.910)	−0.458 *** (−12.242)
$Board$	0.589 (0.885)	0.459 *** (2.632)	0.280 * (1.860)	0.504 (0.676)	0.270 (1.343)	0.079 (0.448)
$Indep$	−0.138 (−0.088)	0.443 (1.017)	0.525 (1.374)	−1.578 (−0.887)	0.249 (0.476)	0.224 (0.483)
$Fhold$	−0.008 (−1.307)	−0.003 ** (−2.056)	−0.004 *** (−3.042)	0.001 (0.094)	−0.004 ** (−2.320)	−0.005 *** (−3.458)
$Fdir$	−1.016 (−1.392)	0.258 (1.304)	−0.224 (−1.332)	−1.030 (−1.205)	0.379 (1.607)	−0.187 (−0.917)
$Fman$	0.509 (0.814)	−0.136 (−0.729)	−0.319 ** (−1.972)	0.509 (0.717)	−0.271 (−1.215)	−0.447 ** (−2.259)
Constant	−13.176 *** (−4.268)	−4.385 *** (−5.610)	−3.861 *** (−5.659)	−12.397 *** (−3.476)	−3.150 *** (−3.435)	−3.254 *** (−4.048)
Year	Yes	Yes	Yes	Yes	Yes	Yes
Industry	Yes	Yes	Yes	Yes	Yes	Yes
R2	0.5234	0.3317	0.2414	0.5286	0.3355	0.2444
Obs.	4365	4365	4365	3101	3101	3101

Note: ***, ** and * mean significance at the level of 1%, 5% and 10%, respectively; t-value in brackets.

reports the estimated results of the influence effects of government subsidies on innovation input ($RDinput$), innovation output ($RDoutput$) and innovation quality ($RDquality$) of FOEs. The results of columns (1)–(3) in Table 3 show that government subsidies can not only effectively improve the willingness of FOEs to invest in R&D, but also enhance the quantity and quality of FOE innovation. Besides, it is found that enterprise scale ($Size$) and profitability ($Roa$) are positively correlated with innovation input, innovation quantity and innovation quality of FOEs. The market share ($Ms$) and age ($Age$) of enterprises are negatively correlated with FOE innovation. The relationship between board size ($Board$) and innovation output of FOEs is significantly positive, whereas the family control ($Fhold$) has a significant negative correlation with the innovation output of FOEs.

5.2. Robustness Check

We use the following three ways to test the robustness of the estimated results: (1) replace the core explanatory variable; (2) change the estimation method; and (3) introduce the matching process.

5.2.1. Replace the Core Explanatory Variable

Government subsidies may be mutually causal with the decision-making of innovation behaviors of FOEs, which may cause endogenous problems. Therefore, we take the lag period of government subsidies ($L.Subsidy$) as the core explanatory variable, and re-examine the relationship between government subsidies and innovation behavior of FOEs. The results of columns (4)–(6) in Table 3 show that the lagging government subsidy still has a positive role in promoting the innovation of FOEs. In addition, the estimated results of the control variables are close to those shown in columns (1)–(3) of Table 3.

5.2.2. Change the Estimation Method

Consider that not all FOEs in the sample can obtain government subsidies; for FOEs without subsidies, the impact of government subsidies on their innovation cannot be observed. To solve this potential sample selection problem, we use the Heckman two-stage method to re-estimate. The results (

Table 4. Estimated results based on Heckman two-stage method.

	First Stage	Second Stage
	$\mathit{S}\mathit{u}\mathit{b}\mathit{s}\mathit{i}\mathit{d}\mathit{y}$	$\mathit{R}\mathit{D}\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{o}\mathit{u}\mathit{t}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{q}\mathit{u}\mathit{a}\mathit{l}\mathit{i}\mathit{t}\mathit{y}$
$Subsidy$		0.045 *** (4.956)	0.007 *** (2.894)	0.004 ** (2.013)
$Size$	−0.056 * (−1.732)	0.869 *** (4.425)	0.161 *** (3.864)	0.188 *** (5.270)
$Lever$	−0.036 (−0.256)	−1.350 ** (−2.551)	0.067 (0.543)	0.244 ** (2.402)
$Roa$	0.512 (1.078)	10.907 *** (4.435)	4.197 *** (8.024)	3.383 *** (7.438)
$Oper$	0.145 *** (4.896)	0.282 (0.730)	0.157 ** (2.006)	−0.007 (−0.095)
$Tobinq$	−0.062 *** (−4.609)	−0.296 (−1.587)	−0.107 *** (−3.024)	−0.013 (−0.418)
$Grow$	−0.082 * (−1.741)	−0.356 (−1.220)	−0.257 *** (−4.170)	−0.139 *** (−2.646)
$Ms$	9.182 *** (2.845)	−27.311 (−0.991)	0.267 (0.055)	−5.618 (−1.343)
$Age$	0.016 (0.458)	−1.385 *** (−9.610)	−0.429 *** (−12.971)	−0.340 *** (−12.434)
$Board$	0.404 ** (2.083)	1.514 (1.249)	0.855 *** (3.275)	0.287 (1.261)
$Indep$	0.235 (0.506)	0.434 (0.257)	0.676 (1.505)	0.526 (1.334)
$Fhold$	0.008 *** (4.811)	0.011 (0.497)	0.005 (1.154)	−0.004 (−1.003)
$Fdir$	−0.199 (−0.951)	−1.481 (−1.637)	0.058 (0.261)	−0.227 (−1.213)
$Fman$	0.793 *** (3.962)	2.229 (1.091)	0.618 (1.526)	−0.310 (−0.902)
Constant	0.082 (0.095)	−15.938 *** (−3.665)	−5.577 *** (−5.685)	−3.870 *** (−4.515)
Year	Yes	Yes	Yes	Yes
Industry	Yes	Yes	Yes	Yes
R2	—	0.5205	0.3309	0.2404
Obs.	—	4353	4353	4353

Note: ***, ** and * mean significance at the level of 1%, 5% and 10%, respectively; t-value in brackets.

) show that the main findings are still valid after changing the estimation method.

5.2.3. Introduce the Matching Process

Propensity score matching (PSM) is a commonly used statistical method to accomplish the removal of confounding bias from observational cohorts where the benefit of randomization is not possible. We use the PSM method to find matching samples for FOEs that receive government subsidies, and re-estimate the actual effect of government subsidies on innovation input, innovation quantity and innovation quality of FOEs based on the newly matched samples. The results in

Table 5. Balancing test.

		Mean		Bias	t-Test
	Unmatched Matched	Treatment	Control		t-Value	p-Value
$Size$	U	21.689	21.627	6.2	2.05	0.040 **
	M	21.677	21.667	1.0	0.31	0.760
$Lever$	U	0.392	0.397	−2.4	−0.79	0.430
	M	0.395	0.394	0.4	0.13	0.895
$Roa$	U	0.049	0.046	5.1	1.70	0.089 *
	M	0.048	0.047	0.4	0.13	0.898
$Oper$	U	1.208	1.037	22.1	7.29	0.000 ***
	M	1.063	1.079	−2.0	−0.67	0.505
$Tobinq$	U	2.931	3.404	−21.3	−7.06	0.000 ***
	M	3.069	3.141	−3.2	−1.04	0.299
$Grow$	U	0.195	0.222	−5.8	−1.93	0.053 *
	M	0.206	0.203	0.7	0.22	0.828
$Ms$	U	0.004	0.003	6.1	2.02	0.043 **
	M	0.003	0.003	−0.6	−0.18	0.858
$Age$	U	1.848	1.945	−12.9	−4.28	0.000 ***
	M	1.917	1.913	0.6	0.19	0.847
$Board$	U	2.219	2.207	9.0	2.98	0.003 ***
	M	2.211	2.213	−2.3	−0.72	0.470
$Indep$	U	0.441	0.443	−5.4	−1.77	0.077 *
	M	0.442	0.442	−0.1	−0.04	0.972
$Fhold$	U	38.726	35.599	20.9	6.91	0.000 ***
	M	36.010	36.532	−3.5	−1.08	0.279
$Fdir$	U	0.139	0.113	18.5	6.10	0.000 ***
	M	0.116	0.119	−2.1	−0.66	0.508
$Fman$	U	0.107	0.075	22.9	7.54	0.000 ***
	M	0.767	0.082	−3.8	−1.23	0.218

Note: ***, ** and * mean significance at the level of 1%, 5% and 10%, respectively; U stands for unmatched and M stands for matched.

show that the matched samples have good properties, and there is no significant difference in the mean values between the treatment group and the control group. The estimated results in

Table 6. Estimated results after matching.

	(1)	(2)	(3)
	$\mathit{R}\mathit{D}\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{o}\mathit{u}\mathit{t}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{q}\mathit{u}\mathit{a}\mathit{l}\mathit{i}\mathit{t}\mathit{y}$
$Subsidy$	0.054 *** (5.447)	0.010 *** (3.640)	0.007 *** (3.214)
$Size$	0.978 *** (7.327)	0.241 *** (7.311)	0.196 *** (7.076)
$Lever$	−1.092 * (−1.887)	0.074 (0.539)	0.236 ** (2.072)
$Roa$	8.179 *** (3.927)	3.416 *** (7.218)	3.303 *** (7.946)
$Oper$	0.069 (0.447)	0.030 (0.907)	0.022 (0.838)
$Tobinq$	−0.116 ** (−2.119)	−0.038 *** (−3.041)	−0.016 (−1.502)
$Grow$	−0.235 (−1.540)	−0.207 *** (−4.168)	−0.180 *** (−4.500)
$Ms$	−55.948 *** (−3.088)	−7.897 *** (−3.214)	−7.135 *** (−3.531)
$Age$	−1.434 *** (−9.244)	−0.481 *** (−13.490)	−0.352 *** (−11.946)
$Board$	0.156 (0.207)	0.477 ** (2.421)	0.283 * (1.660)
$Indep$	−1.373 (−0.784)	0.217 (0.457)	0.205 (0.491)
$Fhold$	−0.006 (−0.843)	−0.003 (−1.551)	−0.003 ** (−2.104)
$Fdir$	−1.118 (−1.374)	0.324 (1.468)	−0.241 (−1.299)
$Fman$	0.143 (0.189)	−0.061 (−0.274)	−0.016 (−0.084)
Constant	1.335 (0.044)	−12.398 * (−1.747)	−11.091 * (−1.841)
Year	Yes	Yes	Yes
Industry	Yes	Yes	Yes
R2	0.5258	0.3430	0.2497
Obs.	3614	3614	3614

Note: ***, ** and * mean significance at the level of 1%, 5% and 10%, respectively; t-value in brackets.

confirm that government subsidies can promote the innovation of FOEs, and the results are very robust.

5.3. Heterogeneity of FOEs

5.3.1. Intergenerational Inheritance of FOEs

The intergenerational inheritance of FOEs is not only a multidimensional phenomenon [60,61], but also a long-term socialization process [62]. The different characteristics of “pioneering generation” and “guarding generation” determine the future direction of FOEs [63].

According to

Table 7. Estimated results based on intergenerational inheritance of FOEs.

Group	Not Complete “2nd Generation Succession”			Complete “2nd Generation Succession”
	(1)	(2)	(3)	(4)	(5)	(6)
	$\mathit{R}\mathit{D}\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{o}\mathit{u}\mathit{t}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{q}\mathit{u}\mathit{a}\mathit{l}\mathit{i}\mathit{t}\mathit{y}$	$\mathit{R}\mathit{D}\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{o}\mathit{u}\mathit{t}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{q}\mathit{u}\mathit{a}\mathit{l}\mathit{i}\mathit{t}\mathit{y}$
$Subsidy$	0.045 *** (4.316)	0.010 *** (3.326)	0.008 *** (2.985)	0.048 *** (2.756)	0.002 (0.337)	−0.003 (−0.798)
Control	Yes	Yes	Yes	Yes	Yes	Yes
Year	Yes	Yes	Yes	Yes	Yes	Yes
Industry	Yes	Yes	Yes	Yes	Yes	Yes
R2	0.5576	0.3614	0.2654	0.4369	0.2722	0.2129
Obs.	3214	3214	3214	1151	1151	1151
Group differences	Insignificant	Significant	Significant	Insignificant	Significant	Significant

Note: *** means significance at the level of 1%; t-value in brackets.

, no matter whether the FOEs are succeeded by family successors or taken over by professional managers, government subsidies always encourage FOEs to increase innovation input. From the perspective of innovation quantity, government subsidies have a significant promoting effect on FOEs that have not achieved intergenerational inheritance, but have no significant effect on FOEs that have completed the “2nd generation succession”. Similarly, from the perspective of innovation quality, government subsidies have a positive and significant impact on FOEs that have not accomplished the “2nd generation succession”, but the impact on FOEs that have achieved intergenerational inheritance is not obvious or even negative.

Government subsidies cannot promote the innovation quantity and quality of FOEs that have completed the “2nd generation succession”; this may be related to the difference in knowledge resources between the “pioneering generation” and “guarding generation” [64]. The knowledge resources of FOEs are highly differentiated and difficult to emulate. The “pioneering generation” has rich experience in innovation and entrepreneurship, and accumulates enough knowledge resources that can guarantee the sustainable innovation of FOEs [65,66]. Although the “guarding generation” has a high willingness to invest in innovation, compared with the “pioneering generation”, their knowledge resources are seriously insufficient and they often fall into the embarrassing situation of “young master hard to convince everyone” [67]. This will greatly reduce the effectiveness of government subsidies and make it difficult to play the role of improving the innovation quantity and quality.

5.3.2. Chairman-Manager Combination of FOEs

Whether the chairman holds the position of general manager at the same time is an important feature of the corporate governance structure. The combination of two positions (two jobs in one) usually indicates that the power within the enterprise is highly centralized. The results in

Table 8. Estimated results based on chairman-manager combination of FOEs.

Group	“Two Jobs Separation”			“Two Jobs in One”
	(1)	(2)	(3)	(4)	(5)	(6)
	$\mathit{R}\mathit{D}\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{o}\mathit{u}\mathit{t}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{q}\mathit{u}\mathit{a}\mathit{l}\mathit{i}\mathit{t}\mathit{y}$	$\mathit{R}\mathit{D}\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{o}\mathit{u}\mathit{t}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{q}\mathit{u}\mathit{a}\mathit{l}\mathit{i}\mathit{t}\mathit{y}$
$Subsidy$	0.043 *** (4.001)	0.008 *** (2.842)	0.006 ** (2.295)	0.047 *** (2.844)	0.007 (1.242)	0.002 (0.355)
Control	Yes	Yes	Yes	Yes	Yes	Yes
Year	Yes	Yes	Yes	Yes	Yes	Yes
Industry	Yes	Yes	Yes	Yes	Yes	Yes
R2	0.5372	0.3289	0.2484	0.5483	0.3980	0.3116
Obs.	3404	3404	3404	961	961	961
Group differences	Insignificant	Insignificant	Significant	Insignificant	Insignificant	Significant

Note: *** and ** mean significance at the level of 1% and 5%, respectively t-value in brackets.

show that government subsidies can effectively promote the innovation input of FOEs, regardless of whether the FOEs are “two jobs in one”. From the perspective of innovation quantity, the influence effects of government subsidies on two groups of FOEs cannot be compared because of insignificant differences. From the perspective of innovation quality, government subsidy has a significant promoting effect on FOEs with “two jobs separation”, but no obvious effect on FOEs with “two jobs in one”. The reason may be that FOE leaders with “two jobs in one” are eager to have good performance [68], and such leaders usually have a strong willingness to innovate [69] and gain excess profits by developing new products; however, in the process of pursuing innovation input and innovation quantity, they neglect innovation quality.

5.4. Influence Mechanism

Combined with the possible paths of government subsidies affecting enterprise innovation summarized in the Literature Review section, we use the mediation analysis method to test the following mechanisms one by one: first, whether government subsidies can influence the innovation behavior of FOEs by alleviating financing constraints ($Sa$); second, whether government subsidies can influence the innovation behavior of FOEs by reducing profit risk ($Irisk$); and third, whether government subsidies can influence the innovation behavior of FOEs by increasing the proportion of state-owned shares in enterprise ($Gsta$).

5.4.1. Alleviate Financing Constraints

The results of

Table 9. Mediation analysis (alleviate financing constraints).

		$\mathit{R}\mathit{D}\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{o}\mathit{u}\mathit{t}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{q}\mathit{u}\mathit{a}\mathit{l}\mathit{i}\mathit{t}\mathit{y}$
Sobel test
	Sobel	Insignificant	Significant	Significant
	Indirect effect	0.003 (1.594)	0.001 * (1.909)	0.001 * (1.859)
	Direct effect	0.054 *** (3.876)	0.007 ** (1.973)	0.006 ** (2.154)
Bootstrap test
	Indirect effect	0.003 (1.380)	0.001 * (1.904)	0.001 (1.640)
	Direct effect	0.054 *** (4.150)	0.007 * (1.950)	0.006 ** (2.140)

Note: ***, ** and * mean significance at the level of 1%, 5% and 10%, respectively; z-value in brackets.

show that government subsidies cannot influence the innovation input of FOEs by alleviating financing constraints. Bank loans are the main financing channel for Chinese FOEs. Many commercial banks tend to favor state-owned enterprises, but give less support to private enterprises, especially FOEs. Although government subsidies can ease the financing constraints of enterprises and send a high-quality “signal” to the financial market [70], it is difficult for enterprises to invest their financing income in innovation because of possible problems such as an imperfect information disclosure system and inadequate supervision of funds. In addition, the results in Table 9 also confirm that government subsidies can significantly improve the innovation quantity and innovation quality of FOEs by alleviating the financing constraints of enterprises. The possible explanation is that by alleviating the financing constraints, government subsidies help the FOE to cooperate with universities or research institutes in R&D [71], thus improving the innovation quantity and quality of enterprises.

5.4.2. Reduce Profit Risk

The results of the Sobel test and bootstrap test in

Table 10. Mediation analysis (reduce profit risk).

		$\mathit{R}\mathit{D}\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{o}\mathit{u}\mathit{t}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{q}\mathit{u}\mathit{a}\mathit{l}\mathit{i}\mathit{t}\mathit{y}$
Sobel test
	Sobel	Significant	Insignificant	Insignificant
	Indirect effect	0.004 * (1.729)	0.000 (1.447)	0.000 (0.245)
	Direct effect	0.105 *** (9.264)	0.018 *** (6.643)	0.009 *** (4.215)
Bootstrap test
	Indirect effect	0.004 * (1.770)	0.000 (1.450)	0.000 (1.240)
	Direct effect	0.105 *** (10.120)	0.018 *** (6.230)	0.011 *** (5.130)

Note: *** and * mean significance at the level of 1% and 10%, respectively; z-value in brackets.

confirm that government subsidies can enhance the innovation input of FOEs by reducing the profit risk, but the impact on the innovation quantity and quality of FOEs is not significant. The reason may be that government subsidies are beneficial to FOEs for obtaining more detailed information on policy changes and improving the accuracy of a FOE’s judgment on future profit risks [72]. On the other hand, government subsidies provide a certain resource guarantee for the healthy development of enterprises, and reduce the profit risk by alleviating the impact of economic cycle fluctuations and unexpected events. The reduction in profit risk enables FOEs to invest in R&D activities with confidence and boldness. However, the amount of subsidy funds is limited, and it is difficult to support FOEs to engage in high-quality innovation. Therefore, it has no significant impact on the quantity and quality of innovation.

5.4.3. Increase the Proportion of State-Owned Shares in Enterprise

The results in

Table 11. Mediation analysis (increase the proportion of state-owned shares in enterprise).

		$\mathit{R}\mathit{D}\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{o}\mathit{u}\mathit{t}\mathit{p}\mathit{u}\mathit{t}$	$\mathit{R}\mathit{D}\mathit{q}\mathit{u}\mathit{a}\mathit{l}\mathit{i}\mathit{t}\mathit{y}$
Sobel test
	Sobel	Significant	Insignificant	Significant
	Indirect effect	0.002 * (1.856)	0.000 (1.355)	0.000 * (1.663)
	Direct effect	0.104 *** (9.137)	0.017 *** (6.586)	0.011 *** (4.946)
Bootstrap test
	Indirect effect	0.002 * (1.740)	0.000 (1.4250)	0.000 * (1.750)
	Direct effect	0.103 *** (8.990)	0.017 *** (6.110)	0.011 *** (5.050)

Note: *** and * mean significance at the level of 1% and 10%, respectively; z-value in brackets.

show that government subsidies can indirectly stimulate enterprises’ innovation input and improve the innovation quality by increasing the proportion of state-owned shares in FOEs, but this indirect effect on innovation quantity is not significant. The reason may be that government subsidies can change the investment confidence of state-owned capital in the family business and increase the willingness of state-owned capital to participate in FOEs. The participation or increase in state-owned shares is beneficial to expand the innovative resources of FOEs, and then, strengthen the innovation input of enterprises [73]. In addition, the state-owned shares in enterprises can establish the relationship between FOEs and government, which provides a certain guarantee for the enterprise’s invention patent application and authorization, and further improve the innovation quality of FOEs.

6. Conclusions

Existing studies focus on the relationship between government subsidies and enterprise innovation. In this paper, we investigate the influence effects of government subsidies on the innovation of FOEs from three different perspectives, innovation input, innovation quantity and innovation quality, and explore the possible influence mechanism of government subsidies on different innovation behaviors of FOEs. The succession for subsequent generations, the ownership of control and the proportion of state-owned equity participation often have a profound impact on the future innovation and development direction of FOEs. This study incorporates all these distinctive features of FOEs into one framework, which not only makes the estimated results more accurate, but also provides the possibility to investigate the differences in subsidy effects and mechanisms caused by the heterogeneity of family business. It is found that the government subsidy plays a significant role in promoting the innovation input, innovation quantity and innovation quality of FOEs. Compared with FOEs that have completed intergenerational inheritance, government subsidies are more conducive to enhancing the innovation quantity of FOEs that have not achieved “2nd generation succession”. From the perspective of innovation quality, government subsidies are more beneficial to FOEs without “two jobs in one” or “2nd generation succession”. Government subsidies can indirectly promote the increase in innovation quantity of FOEs by easing financing constraints. By increasing the proportion of state-owned shares and easing the financing constraints, government subsidies can indirectly improve the innovation quality of FOEs.

The findings of this study have strong policy implications. To enhance the positive role of government subsidies in promoting the innovation of FOEs, the relevant government departments should continuously improve the government subsidy system from three aspects: institutional environment, allocation structure, and guidance and training.

First, the government should create a transparent and fair subsidy system environment for enterprise innovation. Regardless of whether it is a FOE or a non-family business, as long as it meets the conditions and qualifications of subsidies, the relevant departments should grant subsidies to it without discrimination. This is not only conducive to fair competition among enterprises, but also conducive to effectively transmitting the government’s “certification” signal to the market, providing an excellent innovation environment for the subsidized FOEs, and thus, promoting their innovation input, innovation quantity and innovation quality.

Second, in terms of allocation structure, the relevant government departments should further strengthen “aimed subsidies”. Government subsidies have heterogeneous effects on FOEs with different operating and management conditions. For example, whether the “intergenerational inheritance” is completed and whether the “two jobs in one” strategy is adopted can influence the implementation effect of government subsidies to encourage the innovation of FOEs. Therefore, the relevant government departments should further improve the accuracy of subsidies, and strive to achieve an “enterprise-based policy”, so as to avoid FOEs’ inert thinking of “only relying on subsidies”.

Third, in terms of guidance and training, government subsidies should not only stimulate the innovation of FOEs, but also play the “educational function”. The “2nd generation succession” of the FOE affects the innovation behaviors and the decision-making of enterprise, and even concerns the fate of the enterprise. High-quality successors are the driving force for the innovation and development of FOEs. In the process of implementing subsidies, the relevant government departments should help FOEs cultivate successors and reduce the internal friction of intergenerational differences in enterprise innovation so that FOEs can maintain continuous innovation vitality in intergenerational inheritance.

There are still some limitations to this study, which can be expanded in the following aspects. First, based on the data of listed FOEs in China, the research results may have certain imperfections, and the abovementioned policy recommendations may not be suitable for developed countries such as European countries and the United States. The analysis of FOE innovation for youngsters starting family businesses [74] in some developed economies may be a perspective for future research directions. Second, this study pays little attention to the different subsidy tools, such as direct subsidies and tax incentives. In the future, the impacts of the joint or sequential use of different subsidy tools should be considered. Third, this study cannot identify whether the role of government subsidy in promoting FOE innovation depends on the external environment [75], for example, population concentration. Future research can construct an appropriate theoretical model and conduct proper empirical tests based on a novel setting to evaluate the role of government subsidy in promoting FOE innovation more accurately. Fourth, management innovation and marketing innovation of FOEs are also the results of innovation; however, this study focuses only on technological innovation. Future research can integrate the management innovation and the marketing innovation of FOEs into the research framework, in order that the findings are more general.