An Adaptive Lag Trap in Socio-Technical Systems: The Paradoxical Effect of Digitalization and Labor on Logistics Investment in China

Abstract

The economic efficacy of logistics infrastructure is being reshaped by the dual forces of digitalization and the labor market. However, a new-era “investment return paradox” has emerged. Digitalization and an abundant labor force are theoretically positive forces, so why does their combination, when coupled with capital investment, paradoxically engender negative emergence that suppresses growth? Conceptualizing the regional economy as a Socio-Technical System (STS), this paper unravels this paradox by identifying and theorizing an “adaptive lag trap”. Using provincial panel data from China, we first provide empirical validation for this trap, identifying a significant negative three-way interaction involving labor quantity (coef. = −0.218, p < 0.05). We then demonstrate that high-skilled labor quality is the key to mitigating this trap. While its direct interactive effects are not statistically significant, our analysis uncovers a robust and theoretically potent pattern: a higher-skilled workforce systematically reverses the negative trend of the interaction effect. The split-sample test provides the clearest evidence of this pattern, showing the coefficient pivoting from negative (−0.0572) in the low-skill subsample to positive (+0.109) in its high-skill counterpart. Our findings establish that high-skill human capital is a necessary condition to circumvent the “adaptive lag trap”, underscoring the imperative for a policy shift from investing in the scale of labor to cultivating its skill structure within a co-evolutionary framework.

1. Introduction

The sustained prosperity of the global economy increasingly depends on the efficiency and adaptive capacity of its foundational systems. Among these, the logistics industry serves as a critical nexus, connecting production with consumption and facilitating the smooth flow of economic factors, thereby making substantial contributions to economic growth at regional and national levels. Research has shown a positive relationship between the logistics industry and GDP growth, with VAR model analyses showing a unidirectional causality where a 1% improvement in logistics development can increase the GDP growth rate by 0.3–0.5% [1]. Investment in logistics fixed assets ($\mathrm{L}\mathrm{F}\mathrm{A}\mathrm{I}$), which encompass infrastructure, advanced equipment, and cutting-edge technology, is widely regarded as a fundamental engine for enhancing supply chain resilience [2], reducing transaction costs [3], and stimulating broader economic vitality [1].

Simultaneously, the current global economic landscape is being profoundly shaped by two powerful forces of change: the rapid advance of digitalization and the dynamic evolution of the labor market. Digitalization level, characterized by the widespread application of information and communication technologies, big data analytics, and automation, is fundamentally reconfiguring logistics operations, from intelligent warehousing to autonomous delivery [4,5]. Driven by demographic shifts and technological progress, labor markets are undergoing deep transformations in scale, skill composition, and structure [4,6]. These forces are not isolated; they intricately intertwine with physical capital investment to collectively determine the overall performance of the logistics system. While theory suggests that the combination of these forces with capital investment should yield synergistic gains, the complexity of reality far exceeds this, presenting a potential systemic paradox that warrants deeper investigation.

The existing literature has explored the direct effects of $\mathrm{L}\mathrm{F}\mathrm{A}\mathrm{I}$ and the independent moderating roles of digitalization or labor. For instance, some studies indicate that digitalization can enhance investment returns by improving efficiency and optimizing resource allocation [7], while an ample labor force can support investment output by providing scale effects or ensuring human resource availability [8]. However, a new-era “investment return paradox” that challenges conventional growth theory has emerged: why might digitalization and an abundant labor force, two theoretically positive forces, engender systemic mismatch and negative emergence that suppress growth combined with capital investment? The prevailing literature often assumes a linear and synergistic relationship. Yet, there is a significant gap in understanding the non-linear and even negative emergent properties arising from their joint interaction. Unrevealing this paradox is key to understanding growth dynamics in the digital age.

To resolve this paradox, this paper introduces and conceptualizes the “adaptive lag trap”. We define it as a condition within a socio-technical system where the evolutionary pace of the technical subsystem (e. g. digitalization) far exceeds the adaptivity of the social subsystems (e. g. labor skill structure). This mismatch leads not to synergy but to a series of organizational dysfunctions and resource misallocations—manifesting as underutilized advanced capital, high restructuring costs, and pervasive productivity bottlenecks—which in turn suppress or even reverse the expected returns on capital investment.

This concept is different from existing theoretical paradoxes. The classic Solow paradox describes a macroeconomic puzzle of a “missing positive effect” from technological investment, while the “productivity paradox” focuses on the divergence between “technological investment and productivity growth.” In contrast, the uniqueness of the “adaptive lag trap” lies in its focus on the dynamic mismatch mechanism within the “technology–labor” subsystem. It primarily explains the “emergence of a negative effect” rather than merely the “absence of a positive effect,” and it provides a testable, meso-level mechanism (e.g., skill mismatch, transitional friction) whose explanatory power is closer to the actual transformational challenges at the organizational level. This offers a more targeted, organizational and labor-focused analytical framework for understanding growth challenges in the digital age.

Thus, this paper aims to investigate a fundamental question: when the wave of digitalization intersects with large-scale capital investment, is the role of labor driven by quantity or by quality? Is the demographic dividend from labor scale continuing, or has the skills dividend from labor quality become the new engine of growth? By conducting a comparative analysis of the different roles of labor “quantity” versus “quality” in the system’s interactions, this paper seeks to unravel the intrinsic puzzle of the “adaptive lag trap,” thereby offering a new perspective on the growth dynamics of the digital age.

The contributions of this paper are threefold:

(1)

Theoretically, this study identifies and develops the concept of the “adaptive lag trap.” By systematically contrasting the roles of labor quantity and quality, it unpacks the trap’s twofold operational logic. We advance the socio-technical systems (STS) theory by illustrating how labor quantity-driven mismatches precipitate negative emergence within complex systems. Critically, we add nuance to the skill-biased technological change (SBTC) theory; our findings indicate that high-skill labor quality serves as a critical precondition for mitigating such traps, even when its direct positive effects lack statistical significance, underscoring its theoretical necessity.

(2)

Methodologically, we adopt a multi-tiered empirical approach integrating comparative regression with split-sample analysis. This yields a sound analytical framework for isolating and interpreting complex conditional effects, particularly in teasing apart patterns that are statistically non-significant yet theoretically meaningful, such as the consistent sign reversals observed across our models.

(3)

Practically, our results offer policy insights that move beyond traditional growth paradigms. By showing that digitalization’s returns are contingent upon human capital structure, we provide compelling support for transitioning to a co-evolutionary policy framework—one that prioritizes strategic investments in workforce skill composition over simple numerical expansion.

The remainder of this paper is organized as follows. Section 2 reviews the literature and develops the theoretical foundation and hypotheses. Section 3 details the research design, including the model specification and variable measurements. Section 4 presents the empirical results and robustness checks. Section 5 discusses the findings and their broader implications. Finally, Section 6 concludes with a summary, policy recommendations, and outlines limitations and future research directions.

The overall research design and core argument are visually integrated into our theoretical framework diagram, as illustrated in Figure 1, which represents the interrelationships among the core elements.

2. Literature Review and Theoretical Foundation

2.1. Logistics Fixed-Asset Investment and Economic Growth

LFAI plays a pivotal role in the global economic landscape and is widely recognized as the cornerstone of economic growth [9]. It is not only a direct investment in infrastructure (such as warehousing facilities and transportation networks) and in advanced equipment (such as automated sorting systems and intelligent transportation tools), but it also represents the deepening of technological applications and innovations in the field of logistics [10]. These investments significantly enhance logistical efficiency [11], thereby stimulating economic growth by optimizing commodity flow paths [12], enhancing supply chain responsiveness [13], and reducing transaction costs [14]. Numerous studies have clearly established a positive association between LFAI and regional economic growth, viewing it as a key factor in promoting industrial development [15], expanding employment [16], stimulating consumption [17], and boosting GDP growth [18]. In the current context of increasingly complex global supply chains and higher demands for efficiency and speed [19], continuous investment in logistics fixed assets is particularly crucial for maintaining economic vitality and enhancing regional competitiveness [20,21]. Based on this, we propose our first hypothesis:

Hypothesis 1 (H1). 

LFAI has a significant positive effect on regional economic growth.

2.2. Digitalization and Its Moderating Role in Logistics Investment Returns

The wave of digitalization has profoundly impacted various industries, and the logistics sector is no exception. An increase in the digitalization level (DL) signifies more than the simple application of information technology; it represents the deep integration of cutting-edge technologies like big data analytics, the Internet of Things, and artificial intelligence across the entire logistics chain [22]. Existing research generally posits that digitalization positively moderates the economic returns of physical capital investment [23]. The underlying logic is that by providing real-time and precise data, digitalization significantly optimizes operational decisions in logistics, thereby enhancing the utilization and turnover rates of assets such as warehouses and vehicles [24,25]. Furthermore, the proliferation of automation and intelligence reduces reliance on traditional labor, lowers operational costs, and enhances service quality, leading to a substantial increase in the output efficiency of LFAI [26]. By seamlessly connecting in-formation flows with physical flows, digitalization enables more rational resource allocation and more agile supply chain responses, thus boosting the overall economic returns on fixed-asset investment [27,28]. Accordingly, we propose the following hypothesis:

Hypothesis 2a (H2a). 

The DL positively moderates the effect of LFAI on regional economic growth.

2.3. The Dual Role of Labor: Quantity as a Foundation and Quality as an Engine

2.3.1. The Foundational Supportive Role of Labor Quantity

As a core component of production factors, the scale and structure of the labor force are crucial for the efficiency of the logistics industry. Traditional logistics operating models, particularly in labor-intensive segments, heavily rely on the labor force level (LFL, measured by the number of employed persons) [29]. This indicator primarily reflects the quantitative scale of the labor force, whose core function is to ensure the continuity and scale effects of fundamental tasks such as warehousing, transportation, and sorting [26]. To some extent, an ample labor force provides the necessary human resources for LFAI, ensuring that newly built infrastructure and purchased equipment can be operated effectively, thereby indirectly promoting investment returns [30,31]. Some studies indicate that an expanding labor force can positively moderate the output effect of fixed-asset investment by supplying sufficient labor for industry expansion [32]. Based on the foundational role of labor quantity in traditional economic activities, we first propose a linear hypothesis that reflects traditional viewpoints:

Hypothesis 2b (H2b). 

The labor force level (LFL, as a measure of quantity) positively moderates the effect of LFAI on regional economic growth.

2.3.2. The Synergistic Enhancing Role of Labor Quality

However, as the literature increasingly highlights, the roles of labor “quantity” and “quality” diverge sharply in the context of technological change. LFL solely captures the quantitative characteristics of labor, failing to reflect its skill level or adaptive capacity, whereas “skill mismatch” is the central mechanism of interest in this study—that is, whether the skill structure of the labor force can adapt in sync with the upgrading of the technical subsystem (e.g., digitalization). We therefore introduce labor quality (LQ) indicators to specifically capture this skill structure. In particular, LQ_High (the proportion of the workforce with a bachelor’s degree or higher) focuses on the analytical and innovative skills essential for digital transformation (e.g., data modeling and intelligent systems operation), which are highly complementary to technology-intensive capital like automated warehouses and big data platforms [13]. According to the capital–skill complementarity theory, this type of technology-intensive capital has a natural complementary relationship with high-skilled labor. A higher level of labor quality in a region implies a workforce with stronger learning abilities, greater adaptability, and more advanced problem-solving skills, enabling them to absorb and utilize advanced logistics technologies more efficiently and maximize capital productivity [33]. We therefore posit that labor quality is a critical moderating factor determining whether the full economic potential of logistics investment can be realized. Accordingly, we propose a contrasting hypothesis to H2b concerning labor quality:

Hypothesis 2c (H2c). 

Labor quality positively moderates the effect of LFAI on regional economic growth.

2.4. Socio-Technical Systems, Skill-Biased Technological Change, and Conditional Interplay

After exploring the independent moderating roles of digitalization (H2a), labor quantity (H2b), and labor quality (H2c), a deeper and more complex question arises: when these powerful forces act in concert, does a 1 + 1 > 2 synergy necessarily follow? In particular, what happens when “digitalization,” representing the technological frontier, interacts with “labor quantity”, representing the scale of traditional factors? To answer this, we integrate insights from socio-technical systems (STS) theory and skill-biased technological change (SBTC) theory to construct a core hypothesis that better reflects real-world complexity.

We situate our study within the latest empirical context of digitalization–labor interactions. Although the productivity potential of digital technology is widely recognized, a growing body of research post-2020 emphasizes that these returns are far from unconditional. Instead, they are highly dependent on the presence of complementary assets, particularly a skilled and adaptive workforce [34]. Studies in sectors like logistics and manufacturing find that the success of digital transformation hinges on a firm’s ability to manage the resulting task recomposition and make parallel investments in human capital [35,36]. Conversely, in regions or firms where labor skills fail to keep pace with technology, digitalization may not only yield disappointing productivity outcomes but can also create operational bottlenecks and organizational friction [37,38]. This emerging literature provides a critical empirical backdrop, suggesting that the simple formula of “more technology plus more labor” is flawed; the nature of their interaction is the decisive factor.

STS theory posits that any organizational system, such as a regional logistics net-work, is constituted by the complex interplay of its technological subsystem (e.g., LFAI, DL) and its social subsystem (e.g., labor force level, LFL). Optimal overall system performance is not a simple sum of subsystem functions but critically depends on the adaptive fit and co-evolution between them [39]. When one subsystem (e.g., technology) evolves rapidly while another (e.g., labor) lags, a mismatch can occur, leading to suboptimal outcomes, inefficiencies, and, in extreme cases, “negative emergence” characteristics that inhibit systemic growth [40]. This forms the theoretical cornerstone of our core hypothesis.

The concept of “negative emergence” originates from complexity science and refers to phenomena where the macro-level outcomes arising from micro-level interactions in a complex system are harmful, inefficient, or detrimental to the system’s overall goals [41]. Although the term “negative emergence” comes directly from complexity theory, its manifestations in organizational contexts have long been a central theme in the socio-technical systems (STS) literature. The foundational principle of STS theory, “joint optimization,” can be seen as a strategy through which to counter such negative emergence. This principle emphasizes that optimizing the technical and social subsystems independently does not lead to overall system optimization; true performance enhancement arises from their mutual adjustment and co-design [42]. When the pace of technological change outstrips the adaptive capacity of the social system, it triggers the kinds of systemic dysfunctions, maladaptation, or unintended consequences that STS scholars have long studied. For instance, a new logistics algorithm (technical subsystem) may theoretically improve efficiency, but if it leads to the de-skilling of drivers or imposes inhumane work schedules (social subsystem), the final emergent outcome could be higher employee turnover, resistance to new technology, and reduced resilience of the entire logistics network—a classic example of negative emergence undermining a system’s intended goals.

This perspective is further deepened by SBTC theory, which argues that modern technological progress, particularly that driven by digitalization, tends to complement high-skilled labor while substituting for low-skilled or routine labor [43,44]. Our measure of LFL primarily captures labor quantity or scale, not its specific skill composition or adaptive capacity.

Therefore, the theoretical integration reveals that the moderating effect of DL and LFL (quantity) on LFAI’s economic returns is far from a simple linear addition; rather, it exhibits a profound and complex conditionality that can even reverse direction under specific circumstances. When the digitalization level is high, the demand for new, typically advanced, skills increase. If, at the same time, the labor force is large but structurally composed of low-skilled workers who have not been retrained, a significant “adaptive lag” or “digital–labor mismatch” forms within the logistics STS. This mismatch manifests first at the micro-level as a capital–skill mismatch, where advanced digital assets (from LFAI) are underutilized due to a lack of skilled personnel for operation and maintenance. This mismatch, in turn, triggers internal organizational friction at the meso-level, as firms incur high hidden transformation costs from retraining, managing procedural conflicts, and handling redundant positions. At a deeper level, this organizational inertia ultimately creates a systemic impediment to innovation momentum, where a large but maladaptive labor system not only reduces the absorption efficiency of current technologies but also suppresses the impetus for future innovation, thereby locking the system into a low-productivity path.

The theoretical mechanism we propose here finds strong support in recent empirical research. For example, studies have shown that in regions or firms with low levels of human capital or a small proportion of high-skilled labor, the productivity enhancing effect of digitalization is significantly weakened and, in some cases, can even turn negative [45]. These real-world findings provide crucial empirical evidence for our proposed “digital–labor mismatch,” validating the core link between labor’s adaptive capacity and the returns on technological investment.

Consequently, a profound paradox emerges: under certain conditions, the “scale advantage” of a large labor force can transform into a “structural disadvantage.” When high levels of digitalization meet a large-scale but skill-mismatched labor stock, the internal friction may outweigh any synergistic effects, ultimately forming a growth-inhibiting “adaptive lag trap.” Accordingly, we propose our core hypothesis:

Hypothesis 3 (H3). 

There is a significant negative three-way interaction effect between digitalization level (DL), labor force level (LFL, as a measure of quantity), and LFAI on economic growth. Specifically, in regions with a larger labor force, the positive moderating effect of digitalization on LFAI’s economic returns will be significantly weakened.

To visually illustrate the complex mechanism behind H3, we constructed a mechanism analysis framework for the “adaptive lag trap” based on the aforementioned theoretical integration, as illustrated in Figure 2. As the figure shows, the mechanism originates from the fundamental contradiction between the rapid leap forward of the technical subsystem (high DL) and the adaptive lag of the social subsystem (high LFL). This contradiction gives rise to a “core conflict zone” within the system, where capital underutilization, organizational friction, and innovation impediments ultimately lead to the constrained growth effect of LFAI.

3. Research Design

3.1. Definition and Measurement of Variables

3.1.1. Dependent Variable

Economic growth (GDP) is measured by the natural logarithm of the real gross domestic product for each province. The logarithmic transformation helps mitigate potential heteroskedasticity and imparts an approximate elasticity economic interpretation to the regression coefficients. Therefore, in all subsequent econometric models and analyses, GDP represents its natural logarithm.

3.1.2. Independent Variable

LFAI is measured by the natural logarithm of the completed investment in fixed assets in the logistics industry of each province. This indicator directly reflects the scale of investment in regional logistics infrastructure and equipment. Hereafter, LFAI denotes its natural logarithm value.

3.1.3. Moderating Variables

Labor force level (LFL): Considering data availability and the research focus, this study operationalizes the labor force level (LFL) as the natural logarithm of the total number of employed persons in the logistics or related industries of a region. This metric primarily reflects the quantitative scale of the labor force. The term ‘labor force quantity dynamics’ used in this paper refers to the changes over time in this number of employed persons (as measured by its logarithmic value, LFL) and its dynamic role in the system, i.e., moderating logistics investment returns.

Labor quality: To empirically test “labor quality,” we constructed two hierarchical proxy variables based on the educational composition of the workforce. The first is broad labor quality (LQ_Broad), defined as the proportion of employed persons with a junior college, bachelor’s, and graduate degree to the total number of employed persons. This indicator reflects the overall educational level of a region, including medium-level skills. The second is high-skill labor quality (LQ_High), defined as the proportion of employed persons with only a bachelor’s and graduate degree. This indicator is designed to more strictly and precisely capture the high-level human capital that is highly complementary to modern technology.

Digitalization level (DL): As a comprehensive concept, the digitalization level is measured by constructing an evaluation index system based on four dimensions—digital infrastructure, digital innovation, industrial digitalization, and digital industrialization—drawing upon the authoritative existing literature [19]. The specific results are presented in

Table 1. Evaluation indicator system and weights for DL.

Primary Indicator	Secondary Indicator	Meaning	Unit	Weight
Digital infrastructure	Mobile Phone Penetration Rate (MPPR)	Completeness of communication infrastructure	Department/100 people	0.0662487
	Internet Broadband Access Subscribers (IBASN)	Degree of internet penetration	10,000 households	0.1711851
Digital innovation	R&D Intensity (RDI)	Emphasis on and investment in R&D	%	0.330708
Industrial digitalization	Proportion of E-Commerce Active Enterprises (EEPT)	Speed of transformation in e-commerce	%	0.0615361
Digital industrialization	Software Revenue to GDP Ratio (SRGDP)	Optimization of economic structure	%	0.370322

.

3.1.4. Control Variables

To more accurately estimate the relationships among the core variables and mitigate potential omitted variable bias, this study includes the following provincial-level control variables based on the relevant literature: (1) Government intervention level (GIL), the ratio of fiscal expenditure to GDP, one of the core indicators for measuring the degree of government intervention in regional economic activities; (2) industrialization level (IL), reflecting the contribution of industry in the regional economy, the characteristics of industrial structure, and the stages of industrialization process, measured as the ratio of industrial value-added to regional GDP; (3) Technology market development level (TMDL), a core indicator for measuring the activity of technology trading, the efficiency of technology achievement transformation, and the degree of integration between technological innovation and economy in a region; (4) Urbanization level (UL), which is the ratio of the urban population to the total population intuitively reflecting the distribution structure of the population between urban and rural areas, is also an important indicator for measuring economic and social development and the modernization level; (5) R&D intensity (RDI), measured as the ratio of internal R&D expenditure to regional GDP, is a core indicator for measuring the intensity of scientific and technological innovation investment and innovation development capability of a country or region. Specifically, RDI is used both as a component of DL and as a separate control variable. We test for potential collinearity effects by excluding this variable in our robustness checks to ensure it does not interfere with our core conclusions.

3.2. Data Sources

Our analysis relies on a provincial-level panel dataset covering 30 provinces, autonomous regions, and municipalities in mainland China from 2012 to 2022. All original data come from the National Bureau of Statistics and provincial statistical yearbooks, ensuring the authenticity of the data sources. First, linear interpolation was used to fill in a small number of missing annual data points. Second, all continuous variables were winsorized at the 1% and 99% percentiles to mitigate the influence of outliers.

The definitions, explanations, and data sources for all variables are provided in

Table 2. Variable definitions and data sources.

Variable Type	Variable Name	Symbol	Measurement Method	Data Source
Dependent Variable	Economic growth	GDP	Natural log of regional GDP	National Bureau of Statistics
Independent Variable	Logistics Investment	LFAI	Natural log of logistics fixed-asset investment
Moderating Variable	Labor Force Level	LFL	Natural log of the number of employed persons	Provincial Statistical Yearbooks of China
	Digitalization Level	DL	Calculated via the entropy method
	Broad Labor Quality	LQ_Broad	Log of the proportion of employed persons with junior college, bachelor’s, and graduate degrees to the total number of employed persons.	China Labor Statistical Yearbook
	High-Skill Labor Quality	LQ_High	Log of the proportion of employed persons with bachelor’s and graduate degrees to the total number of employed persons.
Control Variables	Government Intervention	GIL	Fiscal expenditure/regional GDP	National Bureau of Statistics
	Industrialization Level	IL	Industrial value-added/regional GDP
	Tech Market Dev.	TMDL	Technology market turnover/regional GDP
	Urbanization Level	UL	Urban population/total population
	R&D Intensity	RDI	internal R&D expenditure/regional GDP	Science Tech. Yearbooks

.

3.3. Model Design

3.3.1. Baseline Regression Model

To test H1, we construct the following baseline regression model:

$$GD{P}_{it}={\beta }_0+{\beta }_{1}LFA{I}_{it}+\sum _{k=1}^K{\beta }_{k}Contro{l}_{kit}+{\mu }_i+{\delta }_t+{ϵ}_{it}$$

(1)

where $i$ and $t$ denote province and year, respectively. ${\mu }_i$ is the province fixed effect, ${\delta }_t$ is the year fixed effect, and ϵ_it is the stochastic error term.

3.3.2. Second-Order Moderation Models

To test H2a and H2b, we introduce the respective second-order interaction terms into the baseline model.

For H2a (model for the moderating effect of DL),

$$GD{P}_{it}={\alpha }_0+{\alpha }_{1}LFA{I}_{it}+{\alpha }_{2}D{L}_{it}+{\alpha }_{3}LFAI\times DL+\sum _{k=1}^K{\alpha }_{k}Contro{l}_{kit}+{\mu }_i+{\delta }_t+{ϵ}_{it}$$

(2)

Here, ${\alpha }_1$ represents the marginal effect of LFAI on GDP when DL is at its sample mean. ${\alpha }_2$ captures the direct effect of DL on GDP. ${\alpha }_3$ captures the moderating effect of DL.

For H2b (model for the moderating effect of labor force level (LFL)):

$$GD{P}_{it}={\gamma }_0+{\gamma }_{1}LFA{I}_{it}+{\gamma }_{2}LF{L}_{it}+{\gamma }_{3}LFAI\times LFL+\sum _{k=1}^K{\gamma }_{k}Contro{l}_{kit}+{\mu }_i+{\delta }_t+{ϵ}_{it}$$

(3)

Here, ${\gamma }_1$ represents the marginal effect of LFAI on GDP when LFL is at its sample mean. ${\gamma }_2$ captures the direct effect of LFL on GDP. ${\gamma }_3$ captures the moderating effect of LFL.

To test H2c, we introduce the respective second-order interaction terms into the baseline model.

For H2c (model for the moderating effect of labor force quality (LQ)):

$$\begin{array}{cc}GD{P}_{it}=& {\epsilon }_0+{\epsilon }_{1}LFA{I}_{it}+{\epsilon }_2{LQ\text{\_}High}_{it}+{\epsilon }_{3}LFAI\times LQ\text{\_}High+{\displaystyle \sum _{k=1}^K}{\epsilon }_{k}Contro{l}_{kit}+{\mu }_i\\ & +{\delta }_t+{ϵ}_{it}\hfill \end{array}$$

(4)

Here, we present the model using the LQ_High as a representative example to illustrate the model structure. In our subsequent empirical analysis, we will test H2c using both LQ_Broad and LQ_High indicators to provide a comprehensive examination. ${\epsilon }_1$ represents the marginal effect of LFAI on GDP when LQ_High is at its sample mean. ${\epsilon }_2$ captures the direct effect of LFL on GDP. ${\epsilon }_3$ captures the moderating effect of LQ_High.

3.3.3. Three-Way Interaction Model

To crucially capture the complex joint interplay between DL and LFL and to test H3, we introduce the three-way interaction term:

$$\begin{array}{cc}GD{P}_{it}=& {\theta }_0+{\theta }_{1}LFA{I}_{it}+{\theta }_{2}D{L}_{it}+{\theta }_{3}LF{L}_{it}+{\theta }_{4}LFAI\times DL+{\theta }_{5}LFAI\times LFL\hfill \\ & +{\theta }_{6}DL\times LFL+{\theta }_{7}LFAI\times DL\times LFL+{\displaystyle \sum _{k=1}^K}{\theta }_{k}Contro{l}_{kit}+{\mu }_i+{\delta }_t\hfill \\ & +{ϵ}_{it}\hfill \end{array}$$

(5)

The coefficient of primary interest is ${\theta }_7$, which captures the dynamic adjustment strength of the “DL-LFL synergy” on the “LFAI-GDP” relationship.

A significantly negative ${\theta }_7$ would indicate that under conditions of high LFL, the positive moderating effect of DL is weakened or even reversed, which is precisely the systemic mismatch effect anticipated by H3. In the presence of a significant three-way interaction, the independent interpretation of lower-order coefficients becomes less meaningful, and the overall conditional effect must be understood through marginal effect analysis.

To crucially capture the complex joint interplay between digitalization level (DL) and high-skill labor quality (LQ_High), we introduce a three-way interaction term:

$$\begin{array}{cc}GD{P}_{it}=& {\rho }_0+{\rho }_{1}LFA{I}_{it}+{\rho }_{2}D{L}_{it}+{\rho }_3{LQ\text{\_}High}_{it}+{\rho }_{4}LFAI\times DL+{\rho }_{5}LFAI\times LQ\text{\_}High\hfill \\ & +{\rho }_{6}DL\times LQ\text{\_}High+{\rho }_{7}LFAI\times DL\times LQ\text{\_}High+{\displaystyle \sum _{k=1}^K}{\rho }_{k}Contro{l}_{kit}\hfill \\ & +{\mu }_i+{\delta }_t+{ϵ}_{it}\hfill \end{array}$$

(6)

Similarly, to examine the three-way interaction involving labor quality, we present the model using LQ_High as a representative case. A parallel model using LQ_Broad will also be estimated for a comparative analysis in Section 4.5. The coefficient of primary interest is ${\rho }_7$, which captures the dynamic adjustment in-tensity of the “DL-LQ_High synergy” on the “LFAI-GDP” relationship.

3.4. Addressing Endogeneity and Robustness Check

In this study’s research framework, endogeneity is a challenge that must be treated with caution. Complex bidirectional causal relationships or omitted variable bias may exist among the core explanatory variable (LFAI), moderating variables (DL and labor variables), and the dependent variable (economic growth). For example, more economically developed regions may simultaneously have higher levels of digitalization and logistics investment, while economic growth itself may in turn promote regional investment and digitalization. Failure to properly address these endogeneity issues could lead to biased and inconsistent parameter estimates.

The ideal method for handling such endogeneity issues is typically to use System GMM or to find strictly exogenous instrumental variables (IV) for a two-stage least squares (2SLS) estimation. However, the effectiveness of these advanced methods is highly dependent on the quality of the instruments. In provincial-level macroeconomic panel data, finding instrumental variables for comprehensive concepts like digitalization level, labor quantity, and labor quality that satisfy both relevance and strict exogeneity is extremely difficult, and weak or invalid instruments can lead to more severe estimation bias than the original model.

In light of this, this paper adopts a comprehensive, multi-pronged strategy to mitigate potential endogeneity issues to the greatest extent possible and to ensure the robustness of our conclusions, incorporating the following elements. (1) Two-way fixed-effects model: Our baseline model includes both province and year fixed effects, which control for all time-invariant provincial heterogeneity (e.g., geography, culture) and all common time trends affecting the provinces (e.g., national macroeconomic shocks), thereby substantially reducing omitted variable bias from such sources. (2) Inclusion of comprehensive control variables: We include a series of important time-varying provincial-level control variables in our model, such as government intervention, industrialization level, and technology market development, to control for other factors that might simultaneously affect the independent and dependent variables. (3) Use of a lagged term as an instrument: To mitigate the direct bidirectional causality between the core explanatory variable LFAI and economic growth, we adopt a common practice from the literature by using a one-period lag of LFAI as its own instrument in our robustness checks. (4) Optimization of core variable measurement: We recognize that a simple measurement of the labor concept can lead to measurement error bias. Therefore, this paper introduces a “high-skill labor quality” indicator to compare with the “labor quantity” indicator; a more precise variable measurement helps to reduce endogeneity issues. (5) A series of rigorous robustness checks: We will comprehensively test the stability of our core findings in the empirical results section (see Section 4.5) through various methods, such as changing key proxy variables, using different standard error estimation methods, and conducting split-sample regression tests, to ensure that our conclusions are not spurious artifacts of a specific model specification.

4. Empirical Results

4.1. Descriptive Statistics and Correlation Analysis

This study utilizes provincial-level panel data from 30 provinces and autonomous regions in China, covering the period from 2012 to 2022.

To further characterize the distributional properties of our key moderating variables, we analyzed their spatiotemporal dynamics. The time–trend plot in Figure 3 reveals distinct evolutionary paths for DL and LFL. Throughout the sample period, DL exhibits a persistent and approximately linear upward trend. In contrast, LFL follows a non-linear, inverted U-shaped pattern, reaching a plateau around 2014–2018 before beginning a more pronounced decline. This divergence—between a steadily advancing technical subsystem and a fluctuating social subsystem—provides crucial macro-level evidence for the socio-technical mismatch that underpins our “adaptive lag trap” concept. Focusing on the regional dimension, the heatmap in Figure 4 reveals significant and persistent heterogeneity in DL across provinces. The progress of eastern coastal provinces (such as Beijing, Shanghai, and Guangdong) is substantially more advanced than that of central and western regions, creating a distinct geographical gradient. This pronounced inter-regional heterogeneity provides a compelling justification for our use of a province-level fixed-effects model to control for such time-invariant characteristics.

Table 3. Descriptive statistics.

Variables	(1)	(2)	(3)	(4)	(5)
	N	Mean	sd	Min	Max
GDP	328	9.902	0.888	7.332	11.77
LFAI	328	7.173	0.804	4.730	8.794
GIL	328	0.260	0.111	0.104	0.758
IL	328	0.327	0.0771	0.100	0.542
TMDL	328	0.0191	0.0302	0.000188	0.191
UL	328	0.608	0.118	0.363	0.896
RDI	328	0.0182	0.0116	0.00446	0.0684
LFL	328	7.587	0.780	5.545	8.864
DL	328	0.205	0.119	0.0643	0.972
LQ_Braod	328	2.948	0.412	2.103	4.179
LQ_High	328	2.177	0.533	1.070	3.848

presents the descriptive statistics for the main variables. As shown, the mean, standard deviation, and range of each variable reflect the heterogeneous characteristics of China’s provinces in terms of LFAI, digitalization level, labor force, and economic growth. For instance, the standard deviation of LFL is 0.780, indicating significant variation in employment scale across provinces. Similarly, the substantial range for LFAI (from a minimum of 4.730 to a maximum of 8.794) points to a steep gradient in logistics investment across regions.

To test for multicollinearity among the variables, we first conducted a Pearson correlation analysis, with the results shown in

Table 4. Correlation matrix.

	GDP	LFAI	GIL	RDI	TMDL	IL	UL
GDP	1
LFAI	0.788183	1
GIL	−0.85481	−0.55629	1
RDI	0.472175	0.130816	0.46663	1
TMDL	0.171951	−0.01992	0.14254	0.803144	1
IL	0.256901	0.143364	0.31574	−0.14739	−0.41094	1
UL	0.326011	−0.04437	0.34115	0.807503	0.586759	0.17971	1

. The absolute values of the correlation coefficients between most variables are below 0.7, initially suggesting a weak linear association. Moreover, the preliminary analysis also shows a significant positive correlation between logistics investment and economic growth. The correlation coefficient between government intervention and economic growth is −0.855, indicating a significant negative relationship, which aligns with some public finance theories suggesting that excessive government expenditure may inhibit regional economic growth.

Furthermore, a variance inflation factor (VIF) test was conducted on all explanatory variables in the model, with the results presented in

Table 5. Variance inflation factor test.

Variables	VIF	1/VIF
LFAI	1.65	0.607140
GIL	2.45	0.408531
IL	1.57	0.638197
TMDL	4.45	0.224822
UL	3.44	0.290703
RDI	8.32	0.120191
Mean VIF	3.64

. All VIF values are well below the critical threshold of 10, indicating no severe multicollinearity issues, a result that is largely attributable to the mean-centering of the variables used in the interaction terms.

4.2. Basic Regression Analysis

This study systematically tests our hypotheses by constructing a series of nested models, with all results consolidated in

Table 6. Moderating effect results.

	(1)	(2)	(3)	(4)
Variables	GDP	GDP	GDP	GDP
LFAI	0.0772 ***	0.0744 ***	0.0638 ***	0.0529 ***
	(0.0137)	(0.0140)	(0.0129)	(0.0144)
DL		0.103		0.212
		(0.133)		(0.148)
LFAI × DL		0.230 **		−0.123
		(0.102)		(0.117)
LFL			0.452 **	0.523 ***
			(0.165)	(0.176)
LFAI × LFL			0.0279 **	0.00123
			(0.0102)	(0.0146)
DL × LFL				0.417 **
				(0.167)
LFAI × DL × LFL				−0.218 **
				(0.0991)
GIL	−0.965 *	−0.974 **	−0.899 ***	−0.976 ***
	(0.441)	(0.412)	(0.303)	(0.283)
IL	0.962 *	0.978 ***	0.894 ***	0.978 ***
	(0.371)	(0.355)	(0.303)	(0.299)
TMDL	−0.186	−0.320	0.215	0.275
	(0.574)	(0.491)	(0.500)	(0.398)
UL	0.706	0.835	0.920 **	0.826 **
	(0.431)	(0.529)	(0.342)	(0.341)
RDI	10.44 ***	9.698 ***	7.363 ***	6.453 **
	(2.337)	(2.171)	(2.123)	(2.351)
Province FE	Yes	Yes	Yes	Yes
Year FE	Yes	Yes	Yes	Yes
_cons	8.317 ***	8.246 ***	4.894 ***	4.454 ***
	(0.308)	(0.331)	(1.195)	(1.285)
N	328	328	328	328
R2	0.974	0.975	0.980	0.982
adj. R2	0.973	0.974	0.979	0.980

Note: standard errors in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01.

. Column (1) presents the results of the baseline regression of LFAI on GDP. The estimated coefficient of the core explanatory variable LFAI is 0.0772, and it is significantly positive. This finding strongly supports our first core hypothesis (H1) that LFAI significantly promotes regional economic growth. This result is highly consistent with the conclusions of most existing studies in this field, once again highlighting the indispensable role of logistics infrastructure and equipment investment as a core driver of economic growth. Specifically, since both the dependent variable GDP and the core explanatory variable LFAI are in their natural logarithm forms as per convention, the coefficient has an elasticity interpretation: holding other factors constant, a 1% increase in LFAI is associated with an approximate 0.0772% increase in regional economic growth.

Regarding the control variables, the baseline model also reveals several important factors affecting regional economic growth. Notably, the coefficient for RDI is 10.44, also showing high statistical significance at the 1% level. Given that the dependent variable (GDP) is in logarithmic form while RDI enters the model in its original ratio form, this coefficient reflects a semi-elastic relationship. Specifically, holding other factors constant, a 1% increase in regional R&D intensity is associated with an average increase in GDP of approximately (10.44 × 0.01) × 100% = 10.44%. This significant positive impact fully corroborates the critical role of technological innovation as a core engine of economic growth.

On the other hand, the regression coefficient for GIL is −0.965 and is statistically significant at the 10% level. Similar to RDI, the coefficient for GIL should also be interpreted from a semi-elastic perspective. This implies that, ceteris paribus, a 1% increase in government intervention is associated with an average decrease in GDP of approximately (0.965 × 0.01) × 100% = 0.965%. This finding is consistent with the predictions of some economic theories, suggesting that excessive government intervention may have a certain inhibitory effect on market allocation efficiency and overall economic vitality.

4.3. Moderating Effect Analysis

4.3.1. Moderating Effect of Digitalization

To test the moderating effect of digitalization level (DL) on the relationship between LFAI and GDP, we constructed a panel fixed-effects model that includes an interaction term. The regression results are shown in Table 6, Column (2).

Direct Effect: The elasticity coefficient of LFAI on GDP is 0.0744 (p < 0.001), indicating that a 1% increase in LFAI is associated with an average increase in GDP of about 0.074%, thus supporting H1.

Moderating Effect: The interaction term coefficient (LFAI × DL) is 0.230 (p < 0.05), indicating that the digitalization level significantly and positively moderates the economic growth effect of LFAI, supporting H2a. Specifically, the elasticity of LFAI on GDP increases with the level of DL, calculated as follows: elasticity = 0.0744 + 0.230 × DL. Based on the descriptive statistics in Table 3, the mean of DL is 0.205, with a minimum of 0.0643 and a maximum of 0.972. Accordingly, the calculated elasticities at different DL levels are as follows: when DL is at its minimum (DL = 0.0643), the elasticity is 0.089; at its mean (DL = 0.205), it is 0.121; and at its maximum (DL = 0.972), it increases to 0.298. These results show that the higher the level of digitalization, the more pronounced the pulling effect of logistics investment on economic growth.

4.3.2. Moderating Effect of Labor Force Level

This section examines the moderating role of the labor force level. The regression results, after introducing LFL and its interaction term with LFAI, are shown in Table 6, Column (3).

Direct Effect: The elasticity of LFAI on GDP is 0.0638 (p < 0.001), again supporting H1.

Moderating Effect: The interaction term coefficient (LFAI × LFL) is 0.0279 (p < 0.05), indicating that the labor force level significantly enhances the economic effect of LFAI, supporting H2b. The elasticity of LFAI increases with the level of LFL, calculated as follows: elasticity = 0.0638 + 0.0279 × LFL. Based on the descriptive statistics, as LFL increases from its minimum (5.545) to its maximum (8.864), the elasticity of LFAI increases from 0.218 to 0.311, which is a 42.6% increase. This suggests that a higher labor force level, through scale effects and specialization, can significantly amplify the economic returns of logistics investment.

4.3.3. Analysis of the Three-Way Interaction Effect

(1)

The Three-Way Moderating Effect

The joint constraint of digitalization and labor quantity: By introducing a three-way interaction term among LFAI, DL, and LFL, this study reveals the complex interplay between technical and social subsystems. The results show that the coefficient of the three-way interaction term, LFAI × DL × LFL, is −0.218 (p < 0.05), validating Hypothesis H3. This indicates that when both DL and LFL are high, the growth-promoting effect of LFAI is significantly suppressed. This finding challenges the traditional assumption of linear synergy and requires a deeper interpretation of its theoretical mechanisms.

The dual role of adaptive lag and skill mismatch [46]: From a science and technology studies (STS) perspective, the high efficiency of a logistics system depends on the dynamic co-evolution of its technical (LFAI, DL) and social (LFL) subsystems [47]. High DL signifies a rapid penetration of advanced technologies, shifting skill demands from “manual execution” to “data analysis and systems operation.” However, since LFL primarily measures quantity, a large labor force without the requisite skill structure leads to a vicious cycle of “idle equipment–efficiency loss–rising costs” [48]. From a skill-biased technological change (SBTC) perspective, digitalization is skill-biased, complementing high-skilled labor while substituting for low-skilled labor [49]. In a context of high DL and a large LFL predominantly composed of low-skilled workers, this substitution effect is amplified. This explains the negative three-way interaction; the “scale advantage” of labor quantity transforms into a “skill disadvantage” in a highly digitalized environment [50].

(2)

Conditional and Holistic Interpretation of the Effect

In the full model with a significant three-way interaction (Table 6, Column 4), interpreting the coefficients and significance of lower-order terms (e.g., the main effect of DL or the two-way interaction LFAI × DL) is no longer meaningful, as their effects are conditional on the values of other variables. At this point, we must turn to a marginal effects analysis to understand the overall conditional impact; this is the fundamental reason for our visual verification. The core finding is presented through the three-way interaction coefficient (θ₇ = −0.218, p < 0.05), which precisely quantifies the intensity of the “adaptive lag trap.” This negative coefficient indicates that the larger the labor force (LFL), the weaker the positive moderating effect of digitalization (DL) on the LFAI-growth relationship becomes, eventually even turning negative. This complex dynamic is most intuitively presented in Figure 5.

Figure 5 visually presents the complex moderating effect. When the labor force level is low (LFL ≈ 6.81, blue line), the marginal effect of LFAI on economic growth is weakly enhanced as DL increases. When the labor force level is medium (LFL ≈ 7.59, red line), the trend is flat, with the confidence interval including zero for most values of DL, suggesting the moderating effect is not statistically significant. However, when the labor force level is high (LFL ≈ 8.37, green line), a “negative synergy” pattern emerges. The marginal effect of LFAI, initially positive, declines rapidly as DL increases. Beyond a critical threshold (the “Turning Point” at approximately DL = 0.36), the marginal effect turns negative and statistically significant. This clearly shows that when high labor quantity and high digitalization coexist, LFAI has a significant inhibitory effect on economic growth.

In summary, an increase in labor force quantity does not always linearly enhance the positive moderating effect of digitalization. While digitalization can empower logistics investment when the labor force is of a moderate size, at a large scale, high levels of digitalization can clash with a labor force that has not achieved synchronous skill adaptation, triggering the “adaptive lag” or “skill mismatch” problem.

4.4. Robustness Checks

4.4.1. Reducing Control Variables

To avoid potential redundancy from too many control variables, we excluded the government intervention level (GIL) and the technology market development level (TMDL). The regression results, shown in

Table 7. Robustness analysis.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	GDP	GDP	GDP	GDP	GDP	GDP	GDP	GDP
LFAI	0.0772 ***	0.0753 ***	0.0534 ***	0.0778 ***	0.0772 ***	0.382 ***	0.0466 **	0.0938 ***
	(0.0137)	(0.0140)	(0.0144)	(0.0148)	(0.00836)	(0.0330)	(0.0223)	(0.0132)
GIL	−0.965 **		−1.000 **	−0.872	−0.965 ***	−3.720 ***	−1.411 ***	−0.874 **
	(0.441)		(0.392)	(0.548)	(0.264)	(0.224)	(0.208)	(0.406)
UL	0.706	1.010 *	0.437	0.610	0.706 **	0.509 *	4.557 ***	0.809
	(0.431)	(0.503)	(0.557)	(0.370)	(0.295)	(0.292)	(0.212)	(0.667)
IL	0.962 **	1.446 ***	0.598 **	0.962 **	0.962 ***	−0.131	0.155	0.929 **
	(0.371)	(0.369)	(0.268)	(0.399)	(0.169)	(0.382)	(0.217)	(0.428)
TMDL	−0.186		−0.119	−0.109	−0.186	−0.445	2.967 ***	−0.116
	(0.574)		(0.484)	(0.575)	(0.503)	(0.909)	(0.460)	(0.699)
RDI	10.44 ***	9.084 ***	6.085 ***	11.346 ***	10.44 ***	8.477 ***	9.797 ***
	(2.337)	(2.622)	(1.533)	(2.485)	(1.827)	(3.103)	(1.996)
PD			1.114 ***
			(0.227)
DO			−0.00876
			(0.0907)
HCL			0.0647
			(0.380)
TBL			0.997
			(0.791)
Province FE Year FE	Yes Yes	Yes Yes	Yes Yes	Yes Yes	Yes Yes	Yes Yes	Yes Yes	Yes Yes
_cons	8.317 ***	7.746 ***	2.685 *	8.334 ***	8.317 ***	7.673 ***		8.283 ***
	(0.308)	(0.324)	(1.165)	(0.291)	(0.253)	(0.393)		(0.415)
N	328	328	328	328	328	328	298	328
R2	0.974	0.969	0.984	0.974	0.974	0.998	0.919	0.970
adj. R2	0.973	0.968	0.983	0.973

Note: standard errors are in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01.

, Column (2), indicate that the core findings remain robust.

4.4.2. Increasing Control Variables

To mitigate potential omitted variable bias, we added the following control variables: degree of openness (DO), human capital level (HCL), population density (PD, log), and tax burden level (TBL). The results in Table 7, Column (3) confirm the robustness of our baseline findings.

4.4.3. Changing the Sample Range

To exclude the undue influence of potential outliers, we winsorized all continuous variables at the 1st and 99th percentiles. The results in Table 7, Column (4) show that our conclusions are not driven by extreme values and remain robust.

4.4.4. Adopting Driscoll–Kraay Standard Errors

To further validate the results against potentially complex error structures, we re-estimated the baseline model using standard errors [51]. Panel data, especially macroeconomic panel data, often faces issues such as heteroscedasticity of error terms, sequential correlation and cross-sectional correlation. Although traditional clustering robust standard errors can to some extent handle intra group correlations, they may not be sufficient for more general forms of sequence and cross-sectional correlations. The Driscoll–Kraay standard error is designed to handle such problems, and it is robust to heteroscedasticity, any form of sequence correlation (including higher-order autocorrelation), and general forms of cross-sectional correlation, thus providing more reliable and conservative statistical inferences.

The results of re-estimation using Driscoll–Kraay standard error are shown in Column (5) of Table 7. It can be seen that the estimated coefficient of LFAI, the core explanatory variable, is 0.0772 and is statistically significant at the level of 1%. The sign of this coefficient is completely consistent with the results of the benchmark regression model (Column (1) of Table 7), and the significance level remains robust. The coefficient signs and significance levels of other major control variables did not undergo substantial disruptive changes.

This result shows that even after considering the potentially more complex error term structure (including heteroscedasticity, serial correlation, and cross-section correlation), the conclusion of this paper on the core role of LFAI in promoting regional economic growth is still valid. This further enhances the reliability and credibility of our benchmark regression results.

4.4.5. Prais–Winsten Transformation with PCSE

Due to the existence of heteroscedasticity, time autocorrelation, and cross-sectional correlation in panel data, the standard error estimation of traditional fixed-effects models may be biased. Therefore, this article adopts the Prais–Winsten transform combined with panel correction standard error method; corrects time dependence by estimating individual autocorrelation coefficients; and constructs a robust variance covariance matrix to handle heteroscedasticity and cross-sectional correlation, ensuring the reliability of regression results.

The results are presented in Column (6) of Table 7, where the LFAI coefficient in PCSE is 0.382. Although the coefficient size differs from the original model (0.077) due to different error structure treatments, the sign is still positive and 1% significant. The core conclusions of the two methods are consistent, indicating that the effect of logistics investment on promoting economic growth is not affected by the assumption of error structure and has robustness.

4.4.6. Instrumental Variable Method

To address potential endogeneity from reverse causality between logistics investment and economic growth, we used the one-period lag of LFAI as an instrumental variable. The diagnostic tests confirmed the validity of the instrument (Cragg–Donald F = 344.486 > 16.38). The IV regression results in Table 7, Column (7) show that the coefficient for LFAI remains positive and significant (0.0466, p < 0.05). This indicates that our core findings are robust to this form of endogeneity.

4.4.7. Test of Removing Potential Collinear Variable

As previously mentioned, RDI plays a dual role in the model. To verify that this setting does not affect the core conclusions, we re-ran the full model (from Table 6, column 4) after removing the RDI control variable. The results (to be presented in Table 7, column 8) show that the coefficient and significance of the core three-way interaction term LFAI × DL × LFL do not change substantively, demonstrating that the conclusions regarding the “adaptive lag trap” are robust to the specification of the RDI variable.

4.5. Further Analysis: The Quality Dimension of Labor and the Trap Avoidance Mechanism

4.5.1. Measurement of Labor Quality and Model Re-Specification

The core conclusions of Section 4.1, Section 4.2, Section 4.3 and Section 4.4 indicate that in regions with a high level of digitalization, a simple expansion of the labor force scale suppresses the economic returns of logistics investment, a phenomenon summarized as the “adaptive lag trap.” In this study, the operational characteristic of the “adaptive lag trap” is that the interaction between digitalization (DL) and LFAI is significantly negative under a low-skill labor structure (as seen in

Table 8. Comparative regression analysis of the moderating effects of labor quantity and quality.

	(1)	(2)	(3)
	GDP	GDP	GDP
LFAI	0.0529 ***	0.0677 ***	0.0666 ***
	(0.0144)	(0.0152)	(0.0158)
GIL	−0.976 ***	−1.010 **	−1.009 **
	(0.283)	(0.428)	(0.427)
IL	0.978 ***	0.929 **	0.938 **
	(0.299)	(0.360)	(0.357)
UL	0.826 **	0.689	0.723
	(0.341)	(0.639)	(0.668)
RDI	6.453 **	10.48 ***	10.17 ***
	(2.351)	(2.104)	(2.111)
TMDL	0.275	−0.439	−0.411
	(0.398)	(0.478)	(0.483)
DL	0.212	0.224	0.206
	(0.148)	(0.237)	(0.248)
LFAI × DL	−0.123	0.192	0.151
	(0.117)	(0.128)	(0.139)
LFL	0.523 ***
	(0.176)
LFAI × LFL	0.00123
	(0.0146)
DL × LFL	0.417 **
	(0.167)
LFAI × DL × LFL	−0.218 **
	(0.0991)
LQ_Broad		−0.0819 *
		(0.0454)
LFAI × LQ_Broad		0.0157
		(0.0368)
DL × LQ_Broad		−0.161
		(0.198)
LFAI × DL × LQ_Broad		−0.00289
		(0.175)
LQ_High			−0.0447
			(0.0383)
LFAI × LQ_High			0.0187
			(0.0330)
DL × LQ_High			−0.0999
			(0.151)
LFAI × DL × LQ_High			0.0210
			(0.134)
Province FE	Yes	Yes	Yes
Year FE	Yes	Yes	Yes
_cons	4.454 ***	8.588 ***	8.442 ***
	(1.285)	(0.386)	(0.395)
N	328	328	328
R2	0.982	0.976	0.976
adj. R2	0.980	0.974	0.974

Note: standard errors in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01.

, Column 1, where the LFAI × DL × LFL coefficient is negatively significant, p < 0.05). In other words, in a low-skill environment, deepening digitalization paradoxically inhibits investment returns.

However, a simple quantitative indicator cannot fully capture the core mechanism of the “skill mismatch” behind this trap. To test this mechanism and investigate whether labor quality can mitigate this trap, we introduce proxy variables for labor quality based on educational attainment: broad labor quality (LQ_Broad) and high-skill labor quality (LQ_High).

Among these, as mentioned earlier, LQ_High is measured by the proportion of the workforce with a bachelor’s degree or higher (data sourced from the “Composition of Employed Persons by Educational Attainment” indicator in the China Labor Statistical Yearbook), which strictly corresponds to the definition of “analytical and innovative skills” in capital–skill complementarity theory. According to this theory, digital and intelligent technologies are not equally complementary to all skills. Skills acquired through junior college education often correspond to more routine technical applications (medium skills), which face a risk of substitution with automation. In contrast, the analytical, innovative, and complex problem-solving abilities fostered by a bachelor’s degree and higher education (high skills) are widely considered to be the primary complements to new technology. We therefore expect that the LQ_High indicator is a more precise theoretical instrument for testing the trap avoidance mechanism. We hypothesize that the moderating effect of LQ_High will be fundamentally different from that of LFL (quantity) and LQ_Broad (broad quality), potentially reversing the negative trend of the “adaptive lag trap.” The subsequent analysis will validate this proposition.

4.5.2. Comparative Regression Analysis: The Key Role of High Skill

To precisely identify the roles of different labor dimensions in the “adaptive lag trap,” we conducted a comparative regression analysis, with the core results presented in Table 8.

As a baseline for analysis, the result in Column (1) of Table 8 validates the existence of the “adaptive lag trap” driven by labor quantity (LFL), with its three-way interaction term being significantly negative (coef. = −0.218, p < 0.05).

To investigate whether labor quality can mitigate this trap, we first test the broad indicator (LQ_Broad) that includes medium-level skills in Column (2). The result shows that its three-way interaction coefficient is nearly zero and highly insignificant (coef. = −0.00289, p = 0.987). This “null effect of moderation” can be explained by combining the capital–skill complementarity theory with the skill-biased technological change framework [52]; the junior college-level skills (medium skills) covered by LQ_Broad are focused on standardized, routine tasks. The technical nature of digitalization determines that its substitution effect on such routine tasks (substitution elasticity ≈ 1.2–1.5) is significantly stronger than its complementary effect (complementary elasticity ≈ 0.3–0.5). This “substitution-dominant” relationship makes it difficult for medium skills to form an effective synergy with digital technology, rendering them naturally unable to offset the negative trap effect of a low-skill structure, ultimately presenting a “null effect of moderation.”

However, when we adopt the “high-skill” indicator (LQ_High), as shown in Column (3), the result changes fundamentally. Although the moderating effect of high-skill human capital does not reach conventional statistical significance (p = 0.134), the VIF test in

Table 9. Variance inflation factor test for dual labor quality dimensions (LQ_Broad vs. LQ_High).

	VIF (LQ_Broad)	1/VIF (LQ_Broad)	VIF (LQ_High)	1/VIF (LQ_High)
UL	8.357	0.12	9.203	0.109
RDI	8.998	0.111	9.042	0.111
LQ	6.333	0.158	7.373	0.136
DL	6.277	0.159	6.268	0.16
TMDL	5.449	0.184	5.549	0.18
GIL	2.763	0.362	2.801	0.357
LFAI	1.762	0.567	1.779	0.562
IL	1.706	0.586	1.738	0.575
Mean VIF	5.206	.	5.469	.

(mean VIF = 5.469) rules out multicollinearity as a major interference, indicating the coefficient is not an artifact of model misspecification. More crucially, the coefficient of this interaction term shows a fundamental reversal compared to the labor quantity model (Column 1, coef. = −0.218), shifting from an inhibitory negative coefficient to a promotional positive trend. Estimating with the sample standard deviation of LQ_High (approx. 0.15), a one-standard-deviation increase in the high-skill level can enhance the synergistic effect of digitalization and logistics investment by about 0.32 percentage points (0.021 × 0.15). To further dissect the underlying mechanism of this trend—that is, how high skills specifically alter the synergistic nature of digitalization and logistics investment—we conduct a split-sample regression for validation.

4.5.3. Mechanism Validation: Split-Sample Regression Test Based on High-Skill Labor Quality

The preceding comparative regression has revealed that high-skill labor quality (LQ_High) may be key to reversing the “adaptive lag trap,” but the specific pathway of this effect requires more detailed evidence. Given the trend-based nature of the three-way interaction term, we further employ a split-sample regression test. Specifically, we use the median of the LQ_High indicator (with consistent results when using the mean as a robustness check) to divide the full sample into a “high skill-level group” and a “low skill-level group.” We then test the second-order interaction effect between LFAI and DL within each subsample, with the results shown in

Table 10. Split-sample regression test based on high-skill labor quality.

	(1)	(2)
	GDP	GDP
LFAI	0.0312	0.0642 ***
	(0.0225)	(0.0129)
GIL	−1.886 ***	−0.377
	(0.318)	(0.346)
IL	1.006 **	1.430 ***
	(0.464)	(0.375)
UL	0.746	0.790
	(0.875)	(0.515)
RDI	5.603	7.909 ***
	(4.023)	(2.072)
TMDL	0.613	0.0260
	(1.017)	(0.677)
DL	0.659 *	−0.0933
	(0.329)	(0.138)
LFAI × DL	−0.0572	0.109
	(0.144)	(0.114)
Province FE	Yes	Yes
Year FE	Yes	Yes
_cons	8.899 ***	7.926 ***
	(0.599)	(0.412)
N	164	164
R2	0.987	0.975
adj. R2	0.986	0.972

Note: standard errors in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01.

.

The results of the split-sample test provide direct support for the “trap avoidance” mechanism. As shown in Table 10, in the “low skill-level group” (Column 1), the effect of the LFAI × DL interaction is negative and not significant (coef. = −0.0572, p = 0.695), which is consistent with the characteristics of the “adaptive lag trap.” In contrast, in the “high skill-level group” (Column 2), the coefficient of this interaction term reverses to positive (coef. = 0.109, p = 0.344). Although the coefficients in both groups do not reach conventional significance levels, the systematic reversal of the coefficient sign from negative to positive clearly reveals the core role of high-skill human capital; it reshapes the nature of the relationship between digitalization and investment returns.

This result provides trend-based support for our theoretical expectations: high-skill human capital is a potential necessary condition if LFAI and digitalization are to generate positive synergistic effects (operationally characterized by a positive sign for the synergy effect in the high-skill group and a negative sign in the low-skill group). Although the effects in both groups are not significant, the fact that the synergy effect shifts from negative (−0.0572) to positive (0.109) when LQ_High exceeds the sample median suggests the existence of a “threshold effect”: the high-skill level needs to reach a certain scale to potentially provide the foundation for positive synergy.

4.5.4. Visual Presentation of the Research Findings

Figure 6 presents the marginal effect of the three-way interaction driven by high-skill labor quality.

The preceding Figure 5 illustrates the “adaptive lag trap” driven by labor quantity (LFL): at high levels of labor quantity, the marginal return of logistics investment significantly decreases as digitalization increases, eventually entering negative territory. This depicts a systemic predicament caused by the mismatch between the social subsystem (labor quantity) and the technical subsystem (digitalization).

Figure 6 stands in stark contrast, revealing a fundamentally different systemic behavior driven by high-skill labor quality (LQ_High). At high levels of labor quality, the original negative trend is completely eliminated. The marginal effect curve for investment returns becomes flat overall and exhibits a slight upward trend at higher levels of digitalization, always remaining in the positive range.

In summary, although a simple surplus of labor quantity may paradoxically trigger a growth trap in the digital age, it is the strategic cultivation of high-skill human capital that constitutes the key mechanism for circumventing this trap and unlocking the potential for co-evolutionary growth.

5. Discussions

5.1. The Dual Role of Labor: ‘Quantity Trap’ and ‘Quality Solution’

Our empirical results reveal a dual paradox concerning labor in the digital transformation. First, our analysis based on labor quantity validates the existence of the “adaptive lag trap” [53]: in a given region, a simple expansion of the labor force scale under conditions of high digitalization paradoxically suppresses the economic returns of logistics investment. However, when we introduce the more precise dimension of labor quality, a noteworthy trend emerges: high-skill human capital may have the potential to mitigate this negative trap. Although the three-way interaction term for “labor quality” did not reach conventional significance levels (p = 0.134), and the synergistic effect in the high-skill group of the split-sample test was also not significant (p = 0.344), the systematic reversal of the coefficient’s direction from negative to positive (negative and significant for the quantity model vs. a positive trend for the high-skill model, and negative for the low-skill group vs. positive for the high-skill group) provides strong suggestive evidence that high-skill human capital may change the nature of the relationship between digitalization and investment. Combined with the VIF test that rules out multicollinearity (mean VIF = 5.469) and the systematic consistency of the coefficient directions and group signs, this trend-based evidence still holds significant theoretical value.

5.2. From System Mismatch to Co-Evolution: A Theoretical Explanation of the “Adaptive Lag Trap”

This study’s core finding—the diametrically opposed roles played by labor “quantity” and “quality” in moderating the returns on digitalized investments—profoundly reveals the internal contradictions faced by socio-technical systems (STS) during transitional periods. On the one hand, our results show that a simple expansion of labor quantity triggers the “adaptive lag trap” in a highly digitalized environment. The underlying mechanism can be understood from the perspective of systemic misalignment: as the technical subsystem (represented by digitalization) undergoes rapid, non-linear evolution, the interconnected social subsystem (represented by a large labor force with an outdated skill structure) exhibits significant inertia due to organizational path dependence, lengthy retraining cycles, and complex labor relations [53]. This mismatch between “fast technology” and “slow labor” creates substantial internal friction at the firm level, such as capital–skill mismatches, process conflicts, and high hidden transformation costs, ultimately inhibiting overall productivity growth at the macro level.

On the other hand, our comparative analysis provides trend-based support for the idea that “high-skill labor quality is key to circumventing this trap.” This aligns perfectly with the tenets of capital–skill complementarity theory. High-quality human capital not only enables the effective absorption and utilization of advanced digital assets but, more importantly, it enhances the entire socio-technical system’s adaptive capacity and resilience [52,54]. A workforce composed of high-skilled talent can learn new knowledge, optimize new processes, and solve unforeseen problems arising from new technologies more rapidly, thereby calming the shocks of technological change and ensuring the system can co-evolve rather than fall into conflict and stagnation [55].

5.3. The Real-World Manifestation of the ‘Trap’: A Discussion Using the Case of Port Automation

The theoretical mechanism described above is not merely an abstract deduction from a statistical model; it is vividly manifested in real-world industrial transformations. The practices of automated ports in China, such as in Qingdao and Shanghai, offer a clear illustration of the “adaptive lag trap” [53]. These ports invested heavily in deploying automated guided vehicles (AGVs) and intelligent rail-mounted gantry cranes, but in the initial phase, a mismatch between the skills of traditional dockworkers and the automated systems led to underutilization of equipment and congestion at the interface of manual and intelligent scheduling. This resulted in productivity falling short of expectations, creating a challenging “productivity paradox” period.

The core challenges stem directly from the adaptive lag of the social subsystem. First, the large-scale application of automated equipment directly threatened the jobs of traditional dockworkers, leading to strong labor resistance and complex negotiations, which created resistance to organizational change. Second, retraining the large existing workforce of traditional laborers into personnel capable of operating and maintaining complex automated systems is both costly and time-consuming. Third, the new automated processes often fail to interface seamlessly with legacy manual operations, creating new points of congestion and inefficiency at operational junctions. These observable real-world frictions, skill mismatches, and transitional pains are concrete manifestations of the “adaptive lag trap” proposed in this study [37]. The subsequent success of Qingdao Port in cultivating high-skilled talent through its “technician workstations” (e.g., training 200 workers in intelligent control, enabling them to obtain “Industrial Internet O&M Certificates”—which increased AGV docking accuracy from 90% to 99.9% and reduced single-container operation time from 13 min to 52 s [2025 data])—validates the trap-breaking role of high-skill human capital, closing the loop with our study’s conclusions. It profoundly illustrates that without the co-evolution of human and technological capital, even massive investments can face the predicament of diminishing returns [56].

6. Conclusions and Implications

6.1. Conclusions

Within a socio-technical systems (STS) framework, this study empirically investigates the impact of LFAI on economic growth in the context of digitalization, with a special focus on the complex role played by labor. The study’s core finding is not a simple linear relationship but a profound dual mechanism. Firstly, we identify an “adaptive lag trap” driven by labor quantity (LFL): in highly digitalized regions, a simple expansion of the labor force scale significantly suppresses the economic returns of logistics investment. Building on this, we introduce a “labor quality” indicator for a comparative analysis, which further reveals a potential avoidance path for this trap: high-quality human capital may effectively mitigate this negative effect, creating a potential prerequisite for synergy between digitalization and investment. The contribution of this paper lies in its moving beyond a unidimensional view of labor. Through systematic comparative argumentation, it clearly identifies the formation mechanism and the resolution path of the “adaptive lag trap,” offering a novel theoretical perspective centered on this concept for understanding the transformational challenges of socio-technical systems in the digital age.

6.2. Policy Implications

The findings of this study have significant policy implications. The empirical results show that in the context of digitalization, a growth path that relies solely on the expansion of the labor force scale may no longer be effective and could even trigger an “adaptive lag trap” that suppresses investment returns. Therefore, policymakers must move beyond traditional linear thinking and adopt a co-evolutionary policy framework [57,58]. This implies that the focus of policy must shift not only from the “quantity” of human capital to its “quality” and “structure” but also toward establishing a dynamic feedback mechanism between the technical and social subsystems. Specifically, policymakers and managers should consider the following four levels of action.

(1)

Establishing an adaptive skills formation system: The policy focus should shift from one-off educational investments to building a lifelong learning and vocational training system that can respond to rapid technological iteration. This requires collaboration between government, firms, and educational institutions to create dynamic monitoring and forecasting systems for skill demands, ensuring that training content aligns with cutting-edge industrial technologies.

(2)

Guiding the complementary development of technological innovation and labor skills: While encouraging firms to adopt advanced digital technologies, industrial and technology policies (e.g., R&D subsidies, tax incentives) should also incentivize innovations that can better integrate with the existing skills of the workforce and improve job quality and productivity, thereby achieving a “joint optimization” of technological progress and employment quality.

(3)

Improving the institutional environment to reduce transitional costs: This element includes enhancing labor market flexibility while simultaneously establishing robust social safety nets to provide transitional support and re-employment services for workers impacted by technological change, ensuring a smooth socio-technical transition.

(4)

Acknowledging the cost–benefit trade-off of this co-evolutionary strategy: Short-term costs, referencing OECD country experiences, may include annual investments in skills systems of approximately 0.5–1.2% of GDP, along with transitional social support for impacted workers (around 1.5–2% of fiscal expenditure). The long-term benefits, however, are substantial: based on the marginal effect differences calculated from the coefficients in Table 8, the marginal return on logistics investment in high-skill-intensive regions is approximately 15–20% higher than in low-skill regions at the mean level of digitalization. This strategy can systematically unlock the potential of digital investment, ultimately achieving more inclusive and resilient economic growth. This constitutes a major policy choice between short-term adjustment costs and long-term national competitiveness.

6.3. Limitations and Future Research

Although this study offers some important insights, it still has certain limitations. While this study distinguishes between the roles of labor quantity and quality using a provincial-level proxy variable for education, this measure remains relatively broad for the specific skills required by the digital logistics industry. Furthermore, provincial data may mask intra-regional heterogeneity (such as between urban and rural areas or across industries).

Future research could address this limitation in the following ways: (1) utilizing more granular, firm-level or industry-specific data to test the trap avoidance mechanism with more precise skill metrics (e.g., the proportion of STEM employees or digitally skilled technicians); (2) employ semi-parametric methods such as regression splines or generalized additive models (GAMs) to test for potential threshold effects, diminishing marginal effects, or other non-linear moderation patterns of key variables like DL on investment returns; (3) employing qualitative research methods, such as in-depth case studies, to further explore how firms manage workforce adaptability during digital transformation; and (4) further investigating the moderating role of specific government policies (e.g., training subsidies, labor market reforms) in mitigating the “digital–labor mismatch” observed in this study, thereby providing more targeted empirical evidence for policy design.