Evaluation of Family Firm Value and Its Spatial Evolution Towards Sustainable Development in China

Abstract

This study develops a four-dimensional value-assessment framework encompassing economic, innovation, social, and cultural dimensions to evaluate the multidimensional performance of family firms in China. Drawing on the entropy weighting method, we construct a composite value index for 251 A-share listed family firms from 2014 to 2023 and apply spatial statistical techniques—including Dagum Gini coefficients, Theil indices, and coefficients of variation—to examine temporal evolution and regional disparities. We further estimate explanatory panel models with firm and year fixed effects (Hausman test favoring FE) to identify the firm-level determinants of composite value. Leverage exhibits a significantly negative association with value, while firm size and innovation capacity are positively related; no significant moderating effect of technology-intensive industry is found. A robustness check using equal weights (0.25 for each dimension) yields an almost perfect correlation (0.9999) with the entropy-weighted index, confirming that the dominance of the innovation dimension in the weighting scheme does not materially affect the overall conclusions. The results highlight the importance of integrating multidimensional value perspectives into both academic research and policy design to promote balanced, inclusive, and sustainable development trajectories for family enterprises.

1. Introduction

Over the past four decades, family firms have emerged as a dominant organizational form within China’s private sector, playing a pivotal role in industrial upgrading, capital accumulation, and the stabilization of regional economies. Characterized by intertwined ownership and control, intergenerational continuity, and strong path dependencies, these firms embody a distinctive logic of governance that both supports long-term vision and imposes structural inertia. Nevertheless, significant disparities persist in the development and performance of family firms across different regions in China, driven by heterogeneous access to resources, market conditions, and policy environments.

At the global level, the sustainable development of family businesses has become a pressing concern in academic and policy discussions. Institutions such as the OECD, IFERA, and the UN Sustainable Development Goals (SDGs) have called for broader frameworks that go beyond short-term financial metrics to incorporate innovation, social responsibility, and cultural continuity. These developments underscore the necessity of adopting multidimensional and spatially-aware perspectives when evaluating family firm value, particularly in emerging economies undergoing rapid structural transformation.

Despite growing attention, the existing literature reveals several limitations. (1) Many studies continue to prioritize financial outcomes while underrepresenting intangible forms of value, such as innovation capacity, social legitimacy, and cultural resilience. (2) Common evaluation methods suffer from temporal inconsistency, as dynamic or subjective weighting schemes hinder cross-period comparability. (3) The spatial dimension remains insufficiently theorized, especially in the context of China’s uneven institutional development and regionally differentiated policy regimes, which significantly shape firm behavior and outcomes.

To address these shortcomings, this study develops a four-dimensional value-assessment framework encompassing economic, innovation, social, and cultural dimensions. Drawing on entropy-based weighting methods, a composite value index is constructed for 251 A-share listed family firms from 2014 to 2023. Spatial statistical techniques—including Gini coefficients, Theil indices, and measures of variation—are employed to analyze regional disparities and patterns of temporal evolution.

The following research questions guide the empirical investigation:

(1)

How has the value of family firms in China evolved across time and space?

(2)

What spatial patterns and regional disparities characterize the distribution of family firm value?

(3)

How do the four value dimensions interact and contribute to divergence or convergence trends?

This study contributes to the literature by offering a theoretically grounded and empirically robust framework for understanding the spatial and multidimensional evolution of family firm value in China. It highlights the structural drivers of regional inequality and provides actionable insights for policymakers aiming to promote balanced, inclusive, and sustainable development trajectories for family enterprises.

Sustainability in family enterprises should be understood as a dynamic balance among multiple forms of value rather than a single growth objective. Economic value underpins resource-allocation efficiency and capital returns; innovation value drives the accumulation of knowledge and technological renewal; social value builds legitimacy and trust; and cultural value preserves identity, governance philosophy, and intergenerational continuity. These four dimensions form an integrated architecture in which the absence or imbalance of any element can weaken resilience to external shocks and internal transformations.

Existing research acknowledges the importance of such multidimensional value but often remains conceptually fragmented and methodologically narrow, dominated by financially oriented assessments. Few studies offer a systematic model linking economic, innovation, social, and cultural dimensions or integrate spatial heterogeneity into the analysis. In China’s highly uneven regional landscape, differences in institutional quality, marketization, and cultural context exert path-dependent effects on value structures. Incorporating a spatial perspective is thus essential for uncovering how multidimensional value connects to sustainable development.

Research Hypotheses

Building on the theoretical framework and research questions, this study proposes the following testable hypotheses:

H1. 

Regional institutional quality has a positive and significant effect on the comprehensive value of family enterprises. Stronger institutions facilitate resource allocation, innovation absorption, and stakeholder trust, thereby enhancing multidimensional value creation.

H2. 

Higher levels of marketization are associated with a more balanced distribution across economic, innovation, social, and cultural value dimensions. Market-oriented environments provide greater incentives and resources for firms to pursue diverse value-creation strategies rather than focusing narrowly on innovation or economic returns.

H3. 

The industry type moderates the relationship between innovation value and overall firm value, with the effect being stronger in technology-intensive industries. In such industries, innovation outputs are more directly translated into competitive advantages and long-term sustainability.

These hypotheses allow for empirical testing of the causal mechanisms underlying regional disparities and value composition differences. The explanatory analysis complements the descriptive spatial statistics by identifying structural drivers of variation, thereby advancing both the theoretical understanding and policy relevance.

2. Theoretical Foundations

2.1. Paradigm Evolution and Scholarly Progress in Family Business Research

Research on family firm value has undergone significant evolution over the past decades, transitioning from a narrow focus on financial performance to a broader multidimensional perspective encompassing economic, innovation, social, and cultural value dimensions. Early studies predominantly adopted a financial-centric paradigm, evaluating family firm performance through return on assets (ROA), Tobin’s Q, or market capitalization metrics (Anderson & Reeb, 2003) [1]. However, this approach was soon challenged for its inability to capture the distinctive governance mechanisms, value systems, and non-economic goals embedded within family-controlled enterprises.

In response, scholars began to adopt the socioemotional wealth (SEW) perspective, which posits that family firms prioritize the preservation of non-financial utilities such as identity, legacy, and social legitimacy (Gómez-Mejía et al., 2007 [2]; Berrone et al., 2012) [3]. This shift opened space for integrating softer dimensions into value evaluation, including stakeholder engagement, intergenerational trust, and cultural resilience (Debicki et al., 2016) [4]. Concurrently, the resource-based view (RBV) emphasized firm-specific capabilities—such as tacit knowledge, reputation capital, and relational networks—as key drivers of long-term value in family firms (Habbershon & Williams, 1999; Chrisman et al., 2005) [5,6].

More recently, institutional and behavioral theories have enriched this discussion by foregrounding the role of external environments and managerial cognition. For example, Wang Defa (2022) [7] empirically demonstrated that institutional embeddedness significantly moderates the impact of family-related social responsibility and cultural orientation on firm value, thereby emphasizing the context-dependent nature of non-financial performance. Similarly, Zhou (2021) [8] highlighted that region-specific policy incentives interact with internal governance structures—particularly in second-generation family firms—to produce divergent sustainability trajectories. These insights reinforce the need to situate family firm value within both internal dynamics and macro-environmental contexts.

In addition to firm-level and institutional perspectives, regional development and spatial evolution theories offer a critical lens for analyzing the uneven trajectories of family firms across China. Krugman’s (1991) [9] core–periphery model explains how economic activities tend to cluster in regions with stronger agglomeration forces, generating persistent spatial inequality. Storper (1997) [10] further highlighted the role of “relational assets” and “institutional thickness” in fostering localized industrial advantages, which are particularly relevant for family enterprises embedded in specific socio-cultural milieus. Coe et al. (2007) [11] advanced the notion of geographical embeddedness by demonstrating how firms’ strategic choices are conditioned by regional institutional arrangements, cultural norms, and network structures. These spatially aware perspectives are crucial for understanding the divergent development paths of family firms in China’s highly heterogeneous regional landscape.

Taken together, the evolution of research perspectives reveals a clear trend: the value of family firms cannot be fully understood without accounting for their multidimensional nature and their embeddedness in both institutional and spatial contexts. This study builds upon this body of work by proposing a composite framework that incorporates these theoretical advancements into an integrated value assessment approach.

2.2. Theoretical Foundations and Multi-Perspective Frameworks in Family Firm Value Research

The evaluation of family firm value requires a robust theoretical foundation that captures both firm-specific characteristics and contextual heterogeneity. Existing literature provides multiple theoretical perspectives that illuminate different dimensions of value creation in family firms. This section synthesizes the dominant approaches—including the socioemotional wealth framework, the resource-based view, institutional theory, and spatial embeddedness theory—to construct a multidimensional interpretive framework.

The socioemotional wealth (SEW) perspective offers a foundational lens for understanding the non-financial goals of family firms. It suggests that family owners prioritize preserving family control, identity, and reputation, often at the expense of short-term financial returns (Gómez-Mejía et al., 2007) [2]. These priorities manifest in long-term investment horizons, aversion to external equity dilution, and sustained commitments to social capital and local communities (Berrone et al., 2012) [3]. As such, SEW provides theoretical justification for incorporating social legitimacy, stakeholder trust, and cultural continuity into value assessment.

Complementing SEW, the resource-based view (RBV) emphasizes the internal resources and capabilities that distinguish family firms from non-family counterparts. These include tacit knowledge transmitted across generations, founder influence on corporate culture, and high levels of trust and relational capital within management teams (Habbershon & Williams, 1999 [5];. Studies show that such idiosyncratic resources contribute to innovation persistence, risk resilience, and intergenerational adaptability (Chrisman et al., 2005) [6], which are critical indicators of long-term value.

Institutional theory further enriches the analysis by situating family firm behavior within broader regulatory, normative, and cognitive environments. In the Chinese context, informal institutions such as guanxi networks, regional cultures, and family-based trust systems interact dynamically with formal regulations and market mechanisms. Huang, Lyu, and Zhu (2019) [12] demonstrated that second-generation involvement significantly enhances the innovation capacity of family firms, particularly through increased patent output, thereby strengthening their long-term competitiveness and sustainability. Likewise, Hui (2021) [13] examined the evolution of relational governance mechanisms in Chinese family firms during intergenerational succession, highlighting how institutional and relational contexts shape governance structures and contribute to firm resilience in periods of uncertainty. These insights underscore the importance of integrating institutional asymmetry into evaluation frameworks.

Most critically for this study, spatial embeddedness theory highlights how the value trajectories of family firms are shaped by the characteristics of the regions in which they operate. Krugman’s (1991) [9] new economic geography emphasizes spatial agglomeration and cumulative causation, while Storper (1997) [10] stresses the importance of localized institutional thickness and untraded interdependencies. Applying these concepts to family firms, regional disparities in innovation ecosystems, access to capital, and human capital mobility become explanatory factors for spatial divergence in firm value. Coe et al. (2007) [11] further argue that firms are socially embedded within specific locales, where institutional practices, trust mechanisms, and cultural norms co-evolve with firm strategies.

Incorporating these diverse theoretical streams allows for the construction of a value evaluation system that accounts for both the endogenous characteristics of family firms and their exogenous operating environments. The integration of SEW, RBV, and spatial–institutional perspectives forms the basis of a four-dimensional framework of family firm value—economic, innovation, social, and cultural—which is further operationalized in the next section through an analytical model.

2.3. Analytical Framework and Theoretical Linkages in Family Firm Value Research

Building on the above research gap, this study develops a family enterprise value-evaluation framework centered on four core dimensions—economic, innovation, social, and cultural—and incorporates spatial heterogeneity within the same analytical system. The theoretical premise of this framework is that sustainability is not a linear extension of a single objective, but a dynamic equilibrium among multiple values. Regional institutions and market environments influence resource acquisition, innovation absorption, and the production of social legitimacy, thereby reshaping value structures in spatial terms. Accordingly, the four-dimensional framework is designed not only to measure the long-term capabilities and responsibility orientations of enterprises, but also to examine the mechanisms of value differentiation across diverse regional contexts. By integrating multidimensional indicators and spatial statistical methods within a unified system, the analysis can capture both the temporal evolution and spatial distribution of structural characteristics, while providing a robust measurement basis for subsequent explanatory testing. This design addresses gaps in the existing literature by advancing both the theoretical integration of multiple value dimensions and the methodological incorporation of spatial factors.

Building on the theoretical foundations discussed above, this study constructs a multidimensional analytical framework for evaluating the value of family firms in China. The framework integrates endogenous characteristics—such as governance structure, intergenerational succession, and strategic orientation—with exogenous environmental conditions, particularly institutional and spatial heterogeneity across regions.

To account for the complexity and richness of family firm value, the framework adopts four interrelated dimensions:

(1)

Economic Value: Captures traditional financial performance metrics, including profitability, operating efficiency, and market competitiveness. It reflects the firm’s ability to generate stable returns and allocate resources effectively.

(2)

Innovation Value: Reflects the firm’s capacity for technological development, knowledge accumulation, and adaptation. Metrics include R&D investment, patent activity, and the presence of dedicated innovation personnel, indicating the firm’s orientation toward long-term strategic renewal.

(3)

Social Value: Refers to the firm’s contribution to employment stability, social trust, and stakeholder engagement. It reflects how family firms leverage their embeddedness in local communities and their relational governance practices to build legitimacy and social capital.

(4)

Cultural Value: Represents the firm’s role in preserving family heritage, promoting organizational identity, and transmitting value systems across generations. This dimension is particularly salient in family firms, where legacy and continuity often supersede short-term profit motives.

Each of these value dimensions is operationalized through a set of measurable indicators and aggregated using an entropy-based weighting system. This approach allows for objectivity in determining the relative importance of indicators and facilitates temporal comparability across firms and regions. The resulting composite index serves as the empirical foundation for further spatial and longitudinal analysis.

What distinguishes this framework from prior studies is its explicit integration of spatial dynamics into the evaluation of family firm value. By incorporating regional development theories and spatial embeddedness perspectives, the framework acknowledges that family firms do not operate in isolation but are deeply embedded in heterogeneous institutional environments. Variations in infrastructure, market access, innovation ecosystems, and regulatory regimes across regions can significantly affect firms’ capacity to generate and sustain value over time.

Accordingly, this study incorporates spatial analysis techniques—including heat maps and regional divergence measures—to examine how institutional asymmetry and regional development patterns influence the value trajectories of family firms. These tools allow for an enriched understanding of both spatial structure and temporal evolution.

This multidimensional and spatially sensitive framework integrates internal firm characteristics, value system construction, and regional heterogeneity, providing a comprehensive foundation for the empirical analysis that follows.

3. Empirical Analysis

3.1. Sample Selection and Data Sources

To ensure representativeness and data quality, this study selects A-share listed companies in China from 2014 to 2023 as the research sample. Family firms are identified based on multiple criteria, including shareholding structure, board composition, and family involvement in management, following the operational definitions proposed by prior literature. Specifically, a firm is classified as a family business if it meets the following conditions: (1) the ultimate controlling shareholder is a natural person or a group of relatives with blood ties or marriage relationships; (2) the founder or family members hold key positions such as chairman or CEO; and (3) the family maintains substantial control over corporate strategic decisions. These criteria are widely adopted in studies such as Zhao (2019) [14] and Huang (2019) [12].

After excluding ST and *ST companies, firms with significant missing values, and those without complete textual disclosures, the final sample consists of 251 family firms, with an unbalanced panel structure. Financial indicators and R&D data are obtained from the CSMAR and Wind databases, while governance and family information are manually collected from company announcements and board reports. Textual data, including CSR disclosures and cultural keywords, are extracted from annual reports using Python 3.7 based textual mining algorithms. Spatial variables such as regional location and provincial policy intensity are cross-referenced with the National Bureau of Statisbsaed tics and local government policy bulletins.

Importantly, this research emphasizes the need to integrate spatial dimensions into family firm analysis. Traditional firm-level assessments often overlook the contextual variability introduced by geographic and institutional heterogeneity. However, following the theoretical insights of Krugman (1991) [9] on economic geography and Storper (1997) [10] on regional production systems, firm behavior and value generation are profoundly shaped by location-specific conditions. Family firms, in particular, exhibit strong ties to their home regions due to localized networks, path dependency, and region-specific institutional familiarity. These features necessitate the incorporation of spatial analytical perspectives in evaluating firm value, especially in a country like China where economic development, regulatory regimes, and cultural norms vary considerably across provinces. By embedding spatial heterogeneity into the empirical design, this study aims to provide a more nuanced understanding of the trajectories and disparities in family firm value across China. This spatialized approach allows researchers to move beyond firm-level idiosyncrasies and uncover structural patterns that are otherwise obscured in non-spatial analyses.

3.2. Variable Descriptions

In order to construct a comprehensive evaluation framework that captures the multidimensional nature of family firm value, this study establishes a four-dimensional index system, encompassing economic, innovation, social, and cultural dimensions. Each dimension is composed of several secondary indicators derived from both quantitative data and textual disclosures. The selection and operationalization of variables are grounded in existing literature and adapted to the institutional context of China.

(1)

Economic Value

The economic value dimension reflects the firm’s profitability and operational efficiency. This dimension includes indicators such as the Return on Assets (ROA), Return on Equity (ROE), and Operating Profit Margin. These metrics are widely recognized as standard measures of financial performance and are particularly relevant for assessing family firms operating under the institutional and market constraints of emerging economies. By capturing both profitability and resource utilization efficiency, they provide a solid foundation for evaluating the economic sustainability of family enterprises.

(2)

Innovation Value

Innovation value captures a firm’s commitment to technological advancement and knowledge generation. Following the research of Zhao (2019) [14], who demonstrated that family control and second-generation involvement significantly shape innovation strategy choices, this study incorporates R&D expenditure, the number of R&D personnel, and annual patent applications as core indicators. These variables capture both input-based and output-based innovation activities, reflecting the dual channels through which family firms pursue long-term competitiveness. These variables reflect both input-based and output-based innovation activities.

(3)

Social Value

Social value refers to a firm’s fulfillment of stakeholder responsibilities and contributions to societal well-being. According to Wang Defa (2021) [7], family firms embedded in stronger institutional environments tend to exhibit higher sensitivity to social legitimacy and stakeholder perception, thus enhancing their non-market value. Therefore, this study extracts relevant content from corporate social responsibility (CSR) reports using a keyword-based textual analysis. Key phrases include “community engagement,” “charitable donations,” and “employee welfare,” which are aggregated into annual frequency indices. The frequency count serves as a proxy for the firm’s emphasis on social responsibility over time.

(4)

Cultural Value

Cultural value encompasses the degree to which firms integrate and express traditional or family-based cultural elements in their strategic narratives and governance ethos. Zhou (2021) [8] found that the expression of family legacy and cultural continuity in corporate disclosures enhances stakeholder trust and internal cohesion. This study constructs a cultural value index based on the frequency of culture-related terms in annual reports, such as “tradition,” “family spirit,” “founder philosophy,” and “long-term inheritance.” Python-based text mining tools are used to extract these terms from publicly available disclosures, and annual frequencies are normalized across the sample.

Each indicator is normalized using the min–max method and aggregated using entropy-based weights to reduce subjectivity and reflect data-driven heterogeneity in indicator importance. The entropy method captures the degree of variation across firms and years, assigning higher weights to more informative indicators. This composite index thus serves as a robust measure of firm value that is sensitive to both time-series dynamics and cross-sectional differences.

Table 1. Evaluation index system for family firm value in China.

Primary Indicator	Secondary Indicator	Calculation Method
Economic Value	Revenue Growth Rate	Ratio of current-period revenue increase to prior-period revenue
	Return on Net Assets	Net profit after tax/Net assets
	Tobin’s Q	Market value of total assets/Book value of total assets
	Debt-to-Asset Ratio	Year-end total liabilities/Year-end total assets
	Firm Size	Natural logarithm of total assets
Innovation Value	Number of Patents	Natural logarithm of total patent count
	R&D Investment Ratio	R&D expenditures/Operating income
	Number of R&D Personnel	Natural logarithm of R&D staff count
Social Value	Frequency of Social–Ecological Keywords	Logarithm of keyword count + 1
Cultural Value	Frequency of Corporate Culture Keywords	Logarithm of keyword count + 1

below summarizes the four-dimensional value framework and its corresponding indicators:

By integrating financial, innovation-oriented, social, and cultural components, the index system provides a multidimensional lens for assessing the evolution and spatial divergence of family firm value in China.

3.3. Research Methods

This study employs the entropy weight method to construct a composite index of family firm value and integrates spatial analytical tools—including the Dagum Gini coefficient, coefficient of variation (CV), and Theil index—to systematically examine the spatial distribution and evolution characteristics of such value over time.

At the conceptual level, family firm value is regarded as a multidimensional construct composed of four dimensions: economic, innovation, social, and cultural value. This framework is rooted in the sustainability-oriented perspective of firm performance, which emphasizes not only financial outcomes but also the firm’s innovation capacity, societal contributions, and cultural legacy. These dimensions collectively reflect the long-term competitiveness and systemic importance of family firms in the regional economy.

At the operational level, ten specific indicators were selected to capture the above dimensions, based on prior literature, data availability, and relevance to the Chinese institutional context. These indicators were integrated into a four-dimensional evaluation framework. To determine indicator weights, the entropy method was adopted due to its data-driven, objective nature. Recognizing the potential inconsistency of time-varying weights in panel data contexts, this study adopts a fixed-weight strategy, wherein the arithmetic mean of each indicator’s yearly weight over the 2014–2023 period serves as its final coefficient. This design enhances temporal comparability and ensures analytical robustness.

Step-by-Step Procedure:

(1)

Standardization of Raw Data

All indicators were standardized using SPSS Statistics 29.0.2 (64-bit) to eliminate the effects of differing units and scales. Positive and negative attributes were also normalized to ensure directional consistency. Detailed formulas and procedures are omitted here for brevity, as they were introduced earlier.

(2)

Normalization of Proportions

For each observation $i$ and indicator $j$, the proportion of indicator value was calculated:

$$p_{ij}={\displaystyle \frac{x_{ij}}{{\sum }_{i=1}^n{x}_{ij}}}$$

(1)

(3)

Calculation of Entropy Value $e_j$

$$e_j=-k{{\displaystyle \sum }}_{i=1}^n{p}_{ij}\cdot \mathit{ln}\left(p_{ij}\right),\mathrm{where}k={\displaystyle \frac{1}{\mathit{ln}\left(n\right)}}$$

(2)

(4)

Calculation of Entropy Weight $w_j$

$$w_j={\displaystyle \frac{1-e_j}{{\sum }_{j=1}^m\left(1-e_j\right)}}$$

(3)

(5)

Computation of Composite Value Score $S_i$

$$S_i={\displaystyle \sum }_{j=1}^m{w}_j\cdot x_{ij}’$$

(4)

where $x_{ij}’$ is the standardized value of indicator j for firm $i$.

(6)

Spatial Analysis Methods

To capture spatial evolution characteristics, the study incorporates geospatial tools based on firm registration coordinates. Heatmaps and spatial density visualizations are generated to depict clustering phenomena. Furthermore, to quantitatively assess spatial polarization and regional disparity, three statistical measures are employed, as summarized in

Table 2. Models for spatial evolution analysis.

Method	Formula (Simplified)	Key Feature
Dagum Gini Coefficient	$\begin{array}{c}G=Gw+Gb+Gt\end{array}$	More sensitive to concentration in top-value regions; emphasizes overall gap
Coefficient of Variation	$CV=\frac{\sqrt{\frac{1}{n}{\sum }_{i=1}^n{\left(Y_{i,t}-{\overline{Y}}_t\right)}^2}}{{\overline{Y}}_t}$	Reflects total dispersion; does not distinguish between head and tail effects
Theil Index	$T={\Sigma }_{i=1}^n{y}_i\cdot ln\left({\displaystyle \frac{y_1}{p_i}}\right)$	Focuses on dynamic decomposition between groups; sensitive to extremes

:

Dagum Gini Coefficient: This decomposition-based Gini measure accounts for intra-regional, inter-regional, and transvariation inequality, making it particularly suitable for heterogeneous distributions.

Coefficient of Variation (CV): Captures the dispersion of firm value across space relative to the mean, offering a straightforward interpretation of spatial volatility.

Theil Index: Enables additive decomposition into within-region and between-region inequality components, highlighting structural asymmetries.

Where $Y_{\left\{i,t\right\}}$ denotes the value score of region $i$ at time $t$;${\overline{Y}}_t$ represents the average family firm value score across all regions in period $t$; $n$ is the number of regions (a constant); $CV$ is the coefficient of variation to be estimated; $GW$, $Gb$, and $Gt$ refer to the within-group Gini coefficient, between-group Gini coefficient, and transvariation (overlapping) Gini coefficient, respectively;$p_i$ is the proportion of the total value contributed by region $i$; and $q_i$ is the hypothetical equal-share proportion for each region.

This methodological framework offers a comprehensive, data-driven approach to evaluating the spatiotemporal evolution of family firm value, bridging firm-level microfoundations with macro-level geographic patterns, and laying the groundwork for the causal mechanism analysis developed in subsequent chapters.

As an objective weighting method, entropy weighting assigns larger weights to indicators with greater variability. This may result in disproportionate weights for certain dimensions if their indicators exhibit higher dispersion. This potential imbalance is addressed in the results discussion and robustness checks.

3.4. Explanatory Panel Data Analysis

To test the research hypotheses, the composite value index and its four sub-dimensions—economic, innovation, social, and cultural value—are employed as dependent variables in panel regression models. The key explanatory variables include the following:

Regional institutional quality: capturing the overall level of formal and informal institutional environments;

Marketization index: reflecting the degree of market orientation and openness in each region;

Industry type: distinguishing technology-intensive industries from non-technology-intensive ones;

Firm age: calculated as the difference between the observation year and the year of establishment.

Control variables comprise the firm size (log of total assets), leverage ratio, and return on assets (ROA) to account for scale effects, capital structure, and profitability.

The general form of the model is as follows:

$$Valu{e}_{it}=\alpha +{\beta }_{1}InstQua{l}_{it}+{\beta }_{2}Marke{t}_{it}+{\beta }_{3}Industr{y}_i+{\beta }_{4}FirmAg{e}_{it}+\gamma Control{s}_{it}+{\mu }_i+{\lambda }_t+{\epsilon }_{it}$$

(5)

where $i$ denotes firms, $t$ denotes years, ${\mu }_i$ represents firm fixed effects, and ${\lambda }_t$ represents year effects. SEs are clustered at the provincial level.

Both fixed-effects (FE) and random-effects (RE) estimations are conducted, and the Hausman test is used to select the preferred specification. Robust standard errors are clustered at the regional level to address potential heteroskedasticity and serial correlation.

3.5. Data Sources and Processing

Firm-level financial, innovation, and disclosure indicators are primarily obtained from the CSMAR database and cross-checked against annual reports of A-share listed family enterprises. Social and cultural value indicators are derived from keyword frequency counts in annual report texts, with keyword selection guided by prior research and sustainability-related policy documents, and, where possible, validated against third-party CSR ratings such as Rankins CSR Ratings (RKS) to improve measurement validity. Regional institutional quality and marketization data are sourced from the China Provincial Marketization Index Report (latest edition) compiled by Fan Gang and colleagues, which covers dimensions such as government–market relations, non-state sector development, product and factor market maturity, market intermediary organizations, and the legal environment. Industry classification follows the official CSRC taxonomy, with a distinction between technology-intensive and non-technology-intensive sectors. Firm age is calculated from the year of incorporation reported in annual filings.

This explanatory analysis complements the descriptive spatial statistics by identifying the structural factors—institutional, market, and industry—that drive regional disparities and shape value composition. By linking the multidimensional value framework to observable regional and firm-level characteristics, the approach provides deeper insights into the causal mechanisms underlying divergence or convergence trends in family firm value and offers empirical support for theoretical refinement and policy formulation.

Given current data availability, province-level institutional-quality and marketization measures are not yet included; time-invariant regional heterogeneity and common time shocks are absorbed by firm and year fixed effects, respectively. Direct tests of H1–H2 will be conducted once these indices are integrated.

4. Empirical Results and Analysis

4.1. Calculation Results

To accurately portray the multidimensional value composition of Chinese family firms and its temporal evolution characteristics, this study employs the entropy weight method to calculate fixed weights for the four dimensions—economic value, innovation value, social value, and cultural value—based on panel data from 2014 to 2023. The resulting weights, derived from the full-period dataset, are presented in

Table 3. Entropy and weights of evaluation indicators for family firm value.

Primary Indicator	Secondary Indicator	Entropy ej	Weight wj	Rank	Total Weight	Primary Rank
Economic Value	Revenue Growth Rate	0.9977	0.0044	8	0.1167	2
	Return on Net Assets	0.9992	0.0015	9
	Tobin’s Q	0.9591	0.0775	4
	Debt-to-Asset Ratio	0.9924	0.0144	7
	Firm Size	0.9901	0.0188	5
Innovation Value	Number of Patents	0.7743	0.4281	1	0.8648	1
	R&D Investment Ratio	0.8407	0.3022	2
	Number of R&D Personnel	0.9291	0.1346	3
Social Value	Frequency of Social–Ecological Keywords	0.9905	0.0181	6	0.0181	3
Cultural Value	Frequency of Corporate Culture Keywords	0.9998	0.0004	10	0.0004	4

.

The weight of innovation value reaches 0.8648, significantly exceeding that of economic value (0.1167), social value (0.0181), and cultural value (0.0004). This indicates that innovation indicators—such as patent applications, R&D investment, and the number of R&D personnel—exhibit high levels of inter-firm variability and time-series fluctuation. According to the principles of entropy weighting, indicators with greater dispersion and information entropy are assigned higher weights, as they carry stronger explanatory power for distinguishing differences among firms. In contrast, the weight of economic value, though the second highest, is substantially lower than that of innovation value, suggesting that traditional financial and scale indicators have reached a saturation point in their explanatory capacity, exhibiting relatively limited marginal contribution. The social and cultural dimensions, both constructed from text-mined annual report data, are assigned extremely low weights due to their relatively weak variability and limited structural discrimination in the current dataset. However, these two dimensions remain theoretically indispensable for assessing long-term sustainability. Future refinements to the index system may consider incorporating more valid proxies such as third-party CSR ratings, pollution data, or records of philanthropic activities to better capture the substantive aspects of social and cultural value.

Based on the above weighting scheme, composite scores for each family firm in each year are calculated, and annual average scores across all firms are obtained to reveal temporal trends.

Table 4. Indicator scores of family firm value evaluation (2014–2023).

	Revenue Growth Rate	Return on Total Assets	Tobin’s Q	Debt-to-Asset Ratio	Firm Size	Number of Patents	R&D Investment	R&D Personnel	Social Value	Cultural Value
2014	0.1369	0.2260	1.9522	2.2878	1.3745	0.9704	0.5432	0.8220	2.4146	0.0895
2015	0.1428	0.2226	3.2224	2.2541	1.4847	1.0002	0.6280	0.8905	2.3633	0.0905
2016	0.1422	0.2219	2.2682	2.2474	1.6007	1.2796	0.7389	0.9590	2.3624	0.0915
2017	0.1405	0.2231	1.6285	2.1443	1.7102	1.4914	0.9562	1.0567	2.2463	0.0926
2018	0.1362	0.2204	0.9738	2.0890	1.7630	1.0744	1.1852	1.1436	2.2375	0.0929
2019	0.1349	0.2205	1.2915	2.0624	1.8045	1.0783	1.3859	1.2328	2.0706	0.0963
2020	0.1351	0.2193	1.5255	2.0442	1.8760	0.9028	1.5665	1.3440	1.8910	0.0958
2021	0.1352	0.2193	1.5293	1.9607	1.9537	1.4202	1.9292	1.4468	1.8251	0.0971
2022	0.1320	0.2176	1.1322	1.9683	2.0080	1.0856	2.2087	1.5745	1.8007	0.0974
2023	0.1307	0.2136	1.0590	1.9435	2.0402	1.0296	2.2758	1.6645	1.9707	0.0984

presents the average annual composite value and sub-dimensional scores for family firms from 2014 to 2023.

The results reveal a relatively stable trajectory of economic value over time, with slight fluctuations around 0.25, indicating that the overall financial performance and operating scale of listed family firms have maintained a consistent level. The innovation value dimension shows a sustained upward trend, rising from 0.1661 in 2014 to 0.3129 in 2023. This growth aligns with the increasing policy emphasis on technological self-reliance and the rising internal incentives for innovation among family firms, thereby reinforcing their role as a core engine of value enhancement. In contrast, the social and cultural value dimensions exhibit relatively lower and more fluctuating scores. The decline in social value between 2020 and 2022 may be attributed to the impact of the COVID-19 pandemic, which disrupted firms’ capacity for community engagement and social responsibility initiatives. The cultural value score remains low but stable, reflecting the long-term nature of cultural construction and the lag in its external representation.

Overall, the temporal evolution of family firm value demonstrates a transition from scale-driven growth to innovation-driven development. While the weight and score of innovation value have significantly increased, economic value has become relatively saturated, and the role of social and cultural value remains insufficiently activated. This imbalance reveals that, despite the inclusion of multiple dimensions, current value generation in family firms is still dominated by technological indicators. In the long run, sustainable development requires a more balanced structure, where non-financial performance and stakeholder value are systematically integrated into the core logic of firm governance and strategy.

The dominance of the innovation value dimension in the entropy weighting results reflects the high variability of innovation-related indicators during the study period rather than a normative prioritization. To verify that the main findings are not solely driven by the high weight of the innovation dimension in the entropy weighting scheme, a robustness check was conducted by recalculating the composite index using equal weights (0.25 for each dimension). The equal-weighted index exhibited an almost perfect correlation (0.9999) with the entropy-weighted index, and the temporal trends were virtually identical (see

Table A1. Annual average scores under entropy and equal weighting.

Year	Entropy_Weighted_Avg	Equal_Weighted_Avg
2014	0.04309557	0.010773893
2015	0.049000524	0.012250131
2016	0.047457431	0.011864358
2017	0.046572911	0.011643228
2018	0.043489879	0.01087247
2019	0.045329285	0.011332321
2020	0.04621588	0.01155397
2021	0.049866436	0.012466609
2022	0.04870479	0.012176198
2023	0.049506033	0.012376508

and Figure A1 in Appendix A). This indicates that the dominance of the innovation dimension in the weighting scheme does not materially affect the overall conclusions.

4.2. Analysis of Overall Family Firm Value Evaluation

From a temporal perspective, the overall value of Chinese family firms has shown a clear upward trend over the past decade, with some fluctuations observed between 2020 and 2022. This evolution reflects not only the continuous optimization of firm-level resource allocation but also the impact of external macroeconomic factors and policy stimuli. Based on a multidimensional evaluation framework encompassing economic, innovation, social, and cultural dimensions, this section provides a detailed analysis of the temporal dynamics across these four value components and explores the underlying mechanisms behind their evolution.

The economic value of family firms, as the foundational dimension of enterprise development, has generally maintained steady growth throughout the observation period. This growth is closely related to the overall improvement in China’s economic climate, the upgrading of industrial structures, and the continued enhancement of market efficiency. As illustrated in

Table 5. Composite scores of family firm value evaluation (2014–2023).

Year	Economic Value	Innovation Value	Social Value	Cultural Value	Composite Score
2014	5.9773	2.3356	2.4146	0.0895	10.8170
2015	7.3267	2.5186	2.3633	0.0905	12.2991
2016	6.4804	2.9775	2.3624	0.0915	11.9118
2017	5.8466	3.5043	2.2463	0.0926	11.6898
2018	5.1825	3.4032	2.2375	0.0929	10.9160
2019	5.5138	3.6970	2.0706	0.0963	11.3777
2020	5.8000	3.8133	1.8910	0.0958	11.6002
2021	5.7981	4.7962	1.8251	0.0971	12.5165
2022	5.4581	4.8687	1.8007	0.0974	12.2249
2023	5.3870	4.9699	1.9707	0.0984	12.4260

, the economic value score rose steadily from 2014 to 2019, peaking in 2015. However, in 2020, the score experienced a slight decline due to the impact of the COVID-19 pandemic on production and demand. It subsequently rebounded rapidly in 2021 and 2022, driven by recovery policies, and remained stable thereafter. This indicates that family firms possess strong endogenous resilience and financial adaptability, enabling them to absorb external shocks in the short term and quickly return to stable growth.

In contrast, the innovation value of family firms demonstrated the most pronounced growth trajectory. As shown in

Table 6. Coefficient of variation for innovation value dimension (2014–2023).

Year	Coefficient of Variation (CV)
2014	/
2015	5.33%
2016	12.39%
2017	18.51%
2018	17.53%
2019	18.30%
2020	18.76%
2021	23.14%
2022	24.74%
2023	25.72%

2014 CV is not computed due to baseline limitations.

, the innovation dimension surged significantly after 2018, primarily due to increased R&D investment and the improvement of intellectual-property-protection policies. Moreover, innovation value became the dominant component in the comprehensive value calculation, with its weight reaching 0.8648 according to the entropy weight method. Although this has raised concerns about value dimension imbalance, it also reflects the transformation of Chinese family firms from traditional, resource-driven growth models to innovation-oriented development pathways. The rise in innovation value aligns closely with national strategies such as “Made in China 2025” and various regional innovation initiatives.

The evolution of social value exhibits a more complex pattern. Between 2014 and 2018, family firms increasingly engaged in social responsibility practices, with annual reports demonstrating a rising frequency of related keywords. However, from 2020 to 2022, social value declined noticeably, as indicated in Table 5. This decline can be partially attributed to pandemic-induced operational pressure, which led firms to prioritize financial stability over community engagement. Moreover, the validity of text-based frequency as a proxy for social value is limited, since it may capture symbolic communication rather than substantive action. To address this limitation, future studies could incorporate third-party CSR ratings or data on environmental and philanthropic performance for better triangulation.

The temporal pattern of cultural value remained relatively stable but showed signs of marginal fluctuation. Table 5 illustrates a moderate upward trend between 2015 and 2019, driven by increased cultural emphasis on corporate narratives and the institutionalization of family governance mechanisms. Nevertheless, the cultural value score exhibited minimal variation post-2020, suggesting that cultural investment by family firms tends to lag behind economic and innovation priorities. Moreover, the weight assigned to cultural value in the entropy framework is notably low (0.0004), which may further obscure its role in the composite score. Future enhancements to the evaluation system could explore alternative measurement approaches, such as family ownership continuity, internal culture audits, or external reputation indices.

In summary, the temporal evolution of family firm value is characterized by a strong upward trend in innovation-driven performance, modest but stable growth in economic fundamentals, and variable trajectories for social and cultural dimensions. These temporal trends are further illustrated in Figure 1, which plots the comprehensive evolution of family firm value and its four dimensions from 2014 to 2023.

This pattern reflects both internal transformation dynamics and external policy influences. Table 5 synthesizes the average scores of the four dimensions across years, highlighting the growing divergence among them. The dominance of innovation value raises concerns about potential overdependence, while the decline in social value suggests that achieving sustainable development in family firms requires more balanced attention to non-financial dimensions. Future policy support should therefore not only incentivize innovation but also strengthen social and cultural value creation capacities within family business ecosystems.

4.3. Regional Distribution Characteristics

From a spatial perspective, the comprehensive value of family firms in China exhibits pronounced regional disparities. Based on the entropy-weighted composite scores from 2014 to 2023,

Table 7. Regional family firm value scores in China (2014–2023).

Region	Northeast China	North China	East China	South China	Central China	Northwest China	Southwest China
2014	0.1729	1.1036	5.3149	2.7929	0.8650	0.0817	0.4859
2015	0.2060	1.2471	6.0125	3.1354	1.0750	0.0810	0.5423
2016	0.1959	1.1336	5.7536	3.0519	1.1696	0.0786	0.5285
2017	0.1805	1.0378	5.5489	3.0808	1.2627	0.0752	0.5039
2018	0.2140	1.0266	5.2127	3.0133	0.9164	0.0661	0.4668
2019	0.2119	1.2154	5.3124	2.9800	1.1044	0.0735	0.4801
2020	0.2192	1.2236	5.4154	3.1681	0.9773	0.0757	0.5209
2021	0.2187	1.2796	5.6628	3.3852	1.3575	0.0695	0.5431
2022	0.2122	1.2956	5.5569	3.5034	1.0696	0.0654	0.5218
2023	0.2316	1.2578	5.6472	3.6390	1.0342	0.0689	0.5473

presents the annual average value across seven major geographic regions. Figure 2 illustrates the temporal evolution of regional value trends, while Figure 3 visualizes the spatial concentration of high-value firms via heatmaps.In the heatmap, the color gradient (blue–green–yellow–red) represents the intensity of family firm concentration, with blue indicating low density and red indicating the highest density.

Overall, the spatial structure of family firm value demonstrates a distinct pattern of “higher in the east, lower in the west; stronger in the south, weaker in the north.” The East China region consistently leads in firm value, with a 2023 score of 5.6472—well above the national average. This dominance stems from the agglomeration of high-performing urban clusters such as the Yangtze River Delta, Shandong Peninsula, and Western Taiwan Straits Economic Zone. The synergy of supportive policies, robust infrastructure, and industrial clusters has created a favorable ecosystem for sustained value generation. Meanwhile, South China exhibits strong catch-up dynamics, rising to second place nationally by 2023. This upward trend reflects the ongoing investment in innovation and institutional improvement across the Pearl River Delta.

In contrast, the Central and North China regions show more volatile value trajectories and substantial internal heterogeneity. Central China experienced a phase of rapid growth from 2014 to 2019, followed by stagnation in recent years. Uneven development across provinces remains a major constraint. North China displays signs of value contraction, especially after 2020, driven by slow industrial upgrading and demographic pressures. These patterns suggest that the region’s governance capacity and market institutional quality may be insufficient to support high-value firm development.

Western regions consistently remain at the lower end of the value spectrum. Although some improvements are observed in the Southwest and Northwest, the overall value levels remain significantly below those in coastal areas. The sparse distribution of firms in the heatmap reinforces this point. High costs associated with factor mobility—such as transportation, information, capital, and talent—combined with limited local market scale and weak intergenerational succession foundations, hinder sustainable value growth. The Northeast region, in particular, lags behind due to sluggish economic restructuring and institutional disadvantages, struggling to integrate into the national value chain.

Structurally, the concentration of high-value firms has continued to intensify in eastern regions, while low-value areas face path dependence and stagnation, reflecting a classic Matthew Effect in spatial dynamics. On one hand, eastern regions consolidate their leading position through innovation, resource integration, and institutional refinement, forming a virtuous cycle of value accumulation and regional upgrading. On the other hand, central, western, and northeastern regions struggle to escape low-value traps due to endogenous capability gaps and exogenous resource constraints, further exacerbating interregional disparities.

This spatial gradient highlights not only the inherent characteristics of family firm development but also the underlying influence of institutional arrangements, market capacity, and resource endowments. In light of China’s national strategy for coordinated regional development, breaking the “lock-in” of value agglomeration through targeted policy mechanisms is critical. Doing so would unleash the latent potential of family firms in inland and peripheral regions and promote a more balanced and sustainable spatial distribution of enterprise value.

4.4. Spatial Evolution Characteristics

Building upon the structural patterns observed in spatial distribution maps, this section provides a more comprehensive analysis of the spatial stratification and dynamic inequality associated with family firm value across Chinese regions. Instead of limiting the discussion to static clustering, the analysis further explores the underlying mechanisms of spatial lock-in and the emergence of a regional Matthew effect.

Figure 4 illustrates the density distribution and tiered stratification of registered family firms across China. High-value firms are predominantly concentrated in the southeastern coastal provinces—particularly within the Yangtze River Delta and Pearl River Delta regions—where advanced market institutions, infrastructure, and financial ecosystems prevail. In contrast, low- and mid-value firms are scattered across central and western hinterlands, indicating insufficient resource endowments and weaker innovation ecosystems. The rigid boundaries observed between different value tiers suggest a persistent spatial hierarchy in firm performance. This spatial fixity implies a strong path dependence, whereby low-value regions are locked into a “low-level equilibrium trap,” unable to break into higher-value segments of the economy due to institutional and structural inertia.

Figure 5 visualizes the spatial trajectory of high-value firm centers from 2014 to 2023. While minor annual shifts are noted, the center of gravity remains firmly anchored in the southeastern coastal corridor throughout the decade. The absence of significant inland diffusion underscores a lack of value spillover, reflecting the limited capacity of leading regions to disseminate innovation and capital toward peripheral zones. This concentration aligns with the theory of regional cumulative causation, wherein initial advantages in institutional capacity, skilled labor, and industrial agglomeration lead to self-reinforcing cycles of value creation and capital absorption. Consequently, this locked-in spatial pattern has policy implications for cross-regional coordination and incentive realignment.

Quantitatively,

Table 8. Dagum Gini coefficient and its decomposition for family firm value across the decade.

Year	Gini Coefficient				Contribution Rate (%)
	Overall	Within-Group Gini Coefficient (Gw)	Between-Group Gini Coefficient (Gb)	Transvariation Gini Coefficient (Gt)	Contribution of Within-Group Gini (Gw) (%)	Contribution of Between-Group Gini (Gb) (%)	Contribution of Transvariation Gini (Gt) (%)
2014	0.569	0	0.569	0	0.00%	100.00%	0.00%
2015	0.566	0	0.566	0	0.00%	100.00%	0.00%
2016	0.561	0	0.561	0	0.00%	100.00%	0.00%
2017	0.562	0	0.562	0	0.00%	100.00%	0.00%
2018	0.565	0	0.565	0	0.00%	100.00%	0.00%
2019	0.552	0	0.552	0	0.00%	100.00%	0.00%
2020	0.557	0	0.557	0	0.00%	100.00%	0.00%
2021	0.546	0	0.546	0	0.00%	100.00%	0.00%
2022	0.557	0	0.557	0	0.00%	100.00%	0.00%
2023	0.558	0	0.558	0	0.00%	100.00%	0.00%

presents the Dagum Gini coefficient and its decomposition for interregional inequality. The overall Gini coefficient consistently exceeds 0.55 across the decade, surpassing the international warning threshold of 0.4 and confirming the structural severity of spatial inequality. Notably, the decomposition reveals that the between-group Gini component (Gb) accounts for 100% of the disparity, while the within-group (Gw) and transvariation (Gt) components remain negligible. This suggests that value inequality is primarily driven by systematic institutional and structural differences among regions, rather than intra-regional dispersion or cross-border firm mobility.

Table 9. Theil index and coefficient of variation for family firm value (2014–2023).

Year	Between-Group Theil Index	Within-Group Theil Index	Total Theil Index	Coefficient of Variation (CV)
2014	0.2273	0.3481	0.5754	1.2271
2015	0.224	0.3547	0.5787	1.2168
2016	0.2129	0.3465	0.5594	1.2025
2017	0.2104	0.3438	0.5542	1.1907
2018	0.2314	0.3343	0.5657	1.2108
2019	0.2206	0.3057	0.5263	1.1670
2020	0.2241	0.3221	0.5462	1.1793
2021	0.2116	0.3131	0.5247	1.1410
2022	0.2287	0.316	0.5447	1.1676
2023	0.2304	0.3186	0.549	1.1746

reports the Theil index and coefficient of variation (CV) over time. The between-group Theil index shows a slight upward trend, indicating a modest increase in spatial divergence among macro-regions. Conversely, the within-group Theil index and CV exhibit a downward trend, reflecting intra-regional convergence and greater internal cohesion in value creation. Together, these patterns reflect a dual process: while regional block disparities are persistent or even rising slightly, internal integration within regions—especially within coastal clusters—is improving. This internal convergence, juxtaposed with interregional polarization, constitutes a hybrid form of the Matthew effect, where leading regions not only maintain their advantage but also consolidate internal structures, widening the gap vis-à-vis lagging territories.

Beyond statistical observations, these results point toward deep-rooted institutional mechanisms. The dominance of coastal regions in value creation correlates with higher levels of market liberalization, advanced industrial infrastructure, and regional innovation policies. Inland regions, particularly in the west and northeast, often face challenges such as capital outflow, talent drain, and underdeveloped service sectors. The lack of upward mobility among low-value regions reflects a failure in policy diffusion and fiscal equalization, demanding regionally targeted industrial upgrading strategies, infrastructural investments, and governance reforms to enable functional spillovers.

In sum, the spatial evolution of family firm value in China illustrates a locked-in hierarchical structure with limited vertical mobility. While some indicators suggest marginal improvement in intra-regional equality, the persistence of high interregional disparities calls for a rethinking of spatial economic governance. Future research should explore how specific variables—such as provincial innovation incentives, transportation connectivity, digital infrastructure, and informal institutional trust—mediate value mobility across space.

4.5. Explanatory Regression Results

Table 10. Fixed-effects panel regression results with composite value index as the dependent variable.

	coef(se)
Age_z	0.0005 (0.0020)
Lev_z	−0.0048 (0.0009) ***
ROA_z	0.0008 (0.0007)
ln_Size_z	0.0120 (0.0045) ***
ln_Patent_z	0.0041 (0.0008) ***
TechInd	0.0006 (0.0044)

Firm FE and year FE included; SE clustered at the provincial level. *** denote significance at 1% levels. Reported coefficients are standardized for continuous regressors.

reports panel regression estimates using the composite value index as the dependent variable. The preferred specification adopts firm fixed effects and year fixed effects with standard errors clustered at the provincial level. Leverage exhibits a significantly negative association with composite value (p < 0.01), suggesting that higher financial pressure impairs multidimensional value creation in family firms. Firm size is positively associated with composite value (p < 0.01), and patent intensity also shows a robust positive relationship (p < 0.01), indicating that innovation contributes meaningfully to long-term multidimensional value. By contrast, firm age and ROA are not statistically significant.

To assess whether the innovation–value link is stronger in technology-intensive industries, we include an interaction between a technology-intensive industry indicator and the log of patents. The interaction term is not statistically significant, implying that the marginal contribution of innovation does not differ systematically across industry groups in the current sample (H3 not supported). A Hausman test comparing fixed-effects and random-effects specifications favors the fixed-effects model (χ² = 35.24, df = 6, p < 0.001), and we therefore rely on the fixed-effects estimates for interpretation.

Due to data availability at this stage, province-level institutional-quality and marketization measures are not directly included. Time-invariant regional heterogeneity and common time shocks are absorbed by firm and year fixed effects, respectively. Once the regional indices are incorporated, we will directly test H1 and H2.

5. Conclusions and Policy Recommendations

5.1. Conclusions

This study, grounded in the theoretical context of sustainable development, constructs a four-dimensional value evaluation system for family firms—covering economic, innovation, social, and cultural dimensions. Based on panel data of 251 listed Chinese family firms from 2014 to 2023, a multi-level entropy weighting method was applied to compute comprehensive value scores. Spatial analysis tools such as heat maps, Gini coefficients, and Theil indices were then used to reveal spatiotemporal evolution characteristics. The main findings are as follows:

(1)

From a longitudinal perspective, the overall value of family firms has shown a sustained upward trend during the study period, with innovation emerging as the primary driver of growth. Since the launch of the 14th Five-Year Plan, substantial increases in R&D investment and patent output have significantly improved innovation scores. In contrast, economic, and social value remain at moderate levels with some fluctuations, while cultural value remains low and relatively stagnant. These results indicate a shift from traditional stable operations to innovation-oriented strategies, reflecting a path-dependent model of “innovation-led” sustainable development.

(2)

From a spatial perspective, there exists a marked imbalance between eastern and western regions. High-value clusters are concentrated in coastal areas, while inland regions show weaker value creation capacity and limited growth momentum. In particular, regions such as the Yangtze River Delta and Pearl River Delta consistently lead in both economic and innovation value, forming national value hubs. In contrast, the northwest and northeast face structural bottlenecks such as low firm density and limited R&D input. These disparities suggest that institutional quality, factor accessibility, and market maturity significantly influence the value evolution trajectories of family firms.

(3)

Despite persistent regional disparities, certain signs of convergence can be observed. While the Gini coefficient remains above the international warning threshold of 0.4, it has gradually declined over the study period, indicating that interregional gaps have not widened further. Within-region Theil indices and coefficients of variation have also decreased, suggesting a trend toward internal equilibrium—what may be interpreted as a reverse Matthew effect. However, the coefficient of variation for innovation value has increased steadily, pointing to a growing polarization: high-value firms are concentrating innovation resources, while low-value firms risk marginalization.

(4)

From a theoretical standpoint, the four-dimensional value structure provides a meaningful framework for assessing the sustainable development of family firms. Economic and innovation value represent core “hard” capabilities, while social and cultural value reflect “soft” strength and responsibility orientation. Firms lacking cultural value accumulation are more prone to short-termism and less likely to develop long-term resilience. This highlights the need to strengthen non-financial value dimensions within enterprise strategy. Achieving a balanced, multi-dimensional value system is key to the long-term sustainable development of family firms.

(5)

Despite building a relatively comprehensive evaluation framework and employing spatial analysis models, the study faces several limitations: (i) social and cultural value are measured via keyword frequency in annual reports, an indirect metric lacking validation through third-party data; (ii) the weight assigned to innovation value is disproportionately high, potentially skewing the composite scores; (iii) the sample is limited to listed firms, excluding smaller or unlisted family businesses.

While explanatory panel models are estimated, the absence of province-level measures precludes direct tests of H1–H2; future work will incorporate institutional-quality and marketization indices and, where appropriate, structural modeling.

5.2. Policy Recommendations

To promote the balanced and sustainable development of family firms nationwide, the following recommendations are proposed:

To promote the coordinated and sustainable development of family firm value in China—particularly in addressing regional imbalance and structural polarization—this study proposes differentiated policy interventions in the following four areas, with attention to their practical feasibility and implementation challenges:

(1)

Promote governance transformation and strengthen innovation-driven mechanisms

Target Regions: Eastern and innovation-intensive regions

Core Measures: Encourage high-value family firms to undertake governance reforms, institutionalize R&D processes, and adopt professional management. Fiscal incentives should be directed toward firms with high innovation output to promote synergy between innovation and industrial chains.

Implementation Challenges: Founders may exhibit path dependence and lack willingness to reform; internal resistance to governance restructuring is common within family-controlled firms.

(2)

Improve financing support systems and alleviate capital constraints on growth

Target Regions: Central and western regions with underdeveloped financial ecosystems

Core Measures: Local governments should establish special funds or risk-compensation mechanisms to support family firms in accessing diversified financing channels, such as equity, bonds, or supply chain finance. Policy banks should increase the share of long-term lending to these firms.

Implementation Challenges: Financial infrastructure is weaker in inland regions; limited transparency and creditworthiness hinder effective financing.

(3)

Build university–industry collaboration mechanisms to enhance regional innovation ecosystems

Target Regions: Regions with strong academic resources but weak commercialization capabilities (e.g., parts of the southwest and northeast)

Core Measures: Local governments should facilitate long-term collaboration between family firms and universities/research institutes through joint labs, industrial alliances, and technology transfer platforms. Incentive mechanisms should reward successful commercialization.

Implementation Challenges: Many family firms lack absorptive capacity for external R&D; intellectual property rights and benefit-sharing mechanisms remain ambiguous.

(4)

Implement regionally differentiated incentive policies to optimize spatial resource allocation

Target Regions: Low-value or slow-growth regions (e.g., northwest, northeast)

Core Measures: Central authorities should implement region-specific incentives such as tax breaks, talent subsidies, and targeted infrastructure investment. National-level industrial parks and resource allocations should prioritize inland deployment to guide spatial upgrading.

Implementation Challenges: Institutional quality and policy implementation capacity vary widely across regions, reducing the effectiveness of top-down incentives.