“Scale Effect” and “Crowding Effect”: A New Perspective of Agglomeration Externalities Based on China’s Forestry Green Total Factor Productivity

Abstract

Industrial agglomeration (IA) is an important factor in promoting forestry development, which has a notable impact on green total factor productivity (GTFP). IA can generate a “scale effect”, but excessive agglomeration may also bring a “crowding effect”, ultimately leading to an inverted U-shaped impact of IA on GTFP. How do these two effects work? From the perspective of agglomeration externalities, this study explores the intermediate role of labor pooling, input sharing, and knowledge spillover to clarify the mechanism between IA and GTFP. This study calculates forestry GTFP of Chinese provinces from 2004 to 2021 and empirically tests the inverted U-shaped relationship between IA and GTFP. It further examines the mediating and moderating effects of agglomeration externalities. The findings reveal that most provinces are still in the “scale effect” stage, but as IA intensifies, the “crowding effect” gradually becomes increasingly evident. Additionally, “crowding effect” is most significant in the eastern region and forestry industrialization areas. Therefore, this study proposes policy measures based on regional differences to promote the green development of the forestry sector.

1. Introduction

As China advances its ecological civilization, forestry functions as a foundational pillar. To attain high-quality forestry development, it is essential to continuously enhance the new qualitative productive forces, with green total factor productivity (GTFP) at the core. Although forestry output in China has been steadily increasing, issues related to high input and pollution in the industry have become more prominent. Forestry GTFP has attracted increasing academic attention. Regional industrial agglomeration (IA) has become prominent in forestry development, driving regional economies and drawing attention for its role in promoting GTFP. However, as research on IA deepens, scholars have found that its impact on GTFP is not simply positive; it can also exert inhibitory effects, exhibiting nonlinear characteristics. Advancing the high-quality development within the forestry industry is not merely about concentrating resources within a region, but rather about the rational allocation of these resources. Therefore, understanding how IA affects GTFP and analyzing its mechanisms in depth is of considerable practical importance for optimizing the allocation of forestry resources, promoting high-quality development, and advancing ecological civilization. The underlying mechanisms behind the nonlinear impact of IA on GTFP remain to be further explored.

Total factor productivity is generally defined as the “residual” of total output that cannot be explained by input factors, reflecting the essence of productivity as an economic concept [1]. In the forestry sector, TFP is used to measure the production efficiency and technological progress of the industry, while GTFP considers energy inputs and environmental pollution as undesirable outputs [2,3], making it a more comprehensive indicator of sustainable forestry development. In the measurement of GTFP, previous studies have mainly employed methods such as Stochastic Frontier Analysis (SFA) [4,5], Data Envelopment Analysis (DEA) [6], and the super efficiency SBM model [7]. SFA is a parametric method, which needs to make assumptions about the function model and the random error distribution in advance. Chen et al. [8] employed this method to evaluate forestry production efficiency across China. DEA and SBM are non-parametric methods that do not require the setting of functional forms and are applicable to multi-input and multi-output frontier production functions [9], thus becoming more widely used TFP measurement methods [10,11,12]. In order to consider the production system with multiple polluting outputs, the super-efficiency SBM model provides a more accurate measurement of the actual level of GTFP [13].

Existing studies on the determinants of forestry GTFP primarily concentrate on natural and social conditions [14,15], emerging technology development [16], policy implementation [17], and other aspects. With the development of regional characteristic industries, forestry IA has also received attention. The “scale effect” and “crowding effect” of IA on GTFP have been widely discussed. IA in different regions and industries has been widely studied, with some scholars showing that factors such as foreign direct investment [18], improvements in transportation infrastructure [19], and high-speed rail construction [20] can influence IA. Various methods for measuring IA include the locational entropy index [21], DO index [22], and EG indices [23], etc. The locational entropy index effectively eliminates endogeneity problems arising from regional scale differences and provides a more accurate description of agglomeration distribution [24]; thus, it is widely used. Moreover, existing research has found that IA has an inverted U-shaped relationship with ecological efficiency [25], carbon productivity [26], energy efficiency [27], and TFP [28]. Yu et al. [29] and Xie et al. [30] also verify that the influence of IA has obvious spatial correlation. Some studies suggest that IA can promote the knowledge flow and the dissemination of technology, thereby accelerating the movement and sharing of production factors [31,32]. However, there are also studies showing that IA can lead to the excessive agglomeration phenomenon [33], resulting in negative externalities such as environmental pollution and traffic congestion [34]. These nonlinear effects are attributed to “scale effect” and “crowding effect” [35].The impact of IA largely arises from the externalities it generates. The study of agglomeration externalities can be traced back to Marshall [36], who pioneered the definition of three sources of agglomeration externalities: labor pooling, input sharing, and knowledge spillover. In addition, there are studies that analyze the labor market [37], knowledge flows [38], production networks [39], and collaborative innovation [40] on Marshallian agglomeration externalities. Most research on agglomeration externalities has focused on the manufacturing [41,42], service [43], and agricultural sectors [44]. As forestry in China develops rapidly, the agglomeration characteristics arising from the increase in forestry enterprises have become more evident, yet research on agglomeration externalities in the forestry sector remains scarce.

An examination of prior studies demonstrates that most studies have empirically validated the nonlinear impact of IA on forestry GTFP, but few have analyzed its underlying mechanisms. Furthermore, research on GTFP in forestry is limited. Considering environmental factors, the “crowding effect” generated by IA may exert external environmental impacts closely linked to GTFP, which integrates environmental considerations into productivity assessments. This study endeavors to elucidate the underlying mechanisms through which IA exerts a nonlinear influence on GTFP through the lens of agglomeration externalities theory, considering the labor pooling of labor agglomeration, the input sharing of transportation infrastructure, and the knowledge spillover of knowledge innovation reflected by agglomeration externalities in the mediating and moderating effects of IA on GTFP. Therefore, this study utilizes the theory of agglomeration externalities to examine the mechanisms by which IA impacts forestry GTFP, with the hope of providing new theoretical perspectives and practical solutions for high-quality forestry development and the promotion of ecological civilization.

2. Theoretical Analysis and Research Hypotheses

IA refers to the process by which resources and markets of a certain industry agglomerate within a specific region. The positive impact of IA is known as the “scale effect”, while its negative impact is referred to as the “crowding effect”. These two effects coexist, with the final “net effect” depending on their relative magnitudes. As a result, the effect of IA on GTFP is nonlinear and varies across different stages of agglomeration.

The “scale effect” generated by IA helps achieve increasing returns to scale, reduce factor costs, and promote information exchange. It leads to a reduction in the average unit production cost [45], and through the scaling up of production and specialization, production efficiency improves. As the number of forestry enterprises within a region increases, upstream and downstream linkages gradually form, and refine the division of labor in raw materials, processing, and trade industries, which is conducive to enhancing collaborative innovation and promoting the growth of GTFP. However, excessive agglomeration creates a “crowding effect” that exacerbates negative externalities. The excessive concentration of low-efficiency enterprises that cannot exit results in diminishing returns to scale and a lack of innovation momentum. The “crowding effect” increases the cost of environmental governance, and the presence of high-pollution enterprises diminishes overall GTFP. Building upon the preceding analysis, the hypotheses are proposed:

Hypothesis 1.

IA exerts a nonlinear impact on forestry GTFP, exhibiting an inverted U-shaped relationship.

According to Marshall’s externality theory, industrial specialization agglomeration can form labor pooling (LP), input sharing (IS), and knowledge spillover (KS). Agglomeration can accumulate human capital, concentrate resource factors, and save on research and development costs, thereby creating a “scale effect” [46]. However, labor agglomeration can also increase management costs, excessive concentration of resources can lead to pollution concentration, and reliance on external knowledge may reduce innovation incentives. These effects generated by excessive agglomeration [33] lead to a “crowding effect”. In the forestry sector, the concentration of factors and shared knowledge can generate a “scale effect”, while pollution control and rising costs in production can generate a “crowding effect” (Figure 1).

The development of the forestry industry generates greater demand for specialized labor. From the “scale effect” perspective, technological progress in forestry raises demand for skilled labor, enhancing human capital. IA facilitates the accumulation of such human capital [47] and the formation of a specialized, high-quality labor force, which in turn boosts LP and promotes GTFP growth. From the “crowding effect” perspective, the agglomeration of labor may raise management costs [28]. Furthermore, labor concentration may increase resource consumption and environmental burdens, generating negative externalities that hinder GTFP improvement.

The production process requires a lot of intermediate inputs, and IS is influenced by the industrial chain and infrastructure. From the “scale effect” perspective, agglomerated firms collaborate efficiently across sectors, lowering marginal costs, while infrastructure development reduces transportation and transaction costs [48]. Resource concentration reduces acquisition costs, improves infrastructure efficiency, and supports resource recycling and pollution control cost reduction [49], thereby enhancing industrial structure and promoting GTFP. From the “crowding effect” perspective, excessive agglomeration can intensify competition within the industry, leading to inefficient resource allocation. In scenarios where output efficiency does not obviously increase, the capacity expansion associated with agglomeration may lead to overconsumption of resources, while unhealthy competition among concentrated firms exacerbates negative externalities [50]. Resource scarcity further raises factor costs, and heavier production burdens increase pollution control costs, thereby suppressing GTFP growth.

Knowledge exhibits positive externalities, and agglomeration can better leverage KS. From the “scale effect” perspective, innovation generated by agglomeration aligns stakeholder incentives, encourages collaborative upgrading, and improves overall industry efficiency [23]. KS promotes green technology adoption and reduces resource waste from redundant R&D, ultimately fostering GTFP growth. From the “crowding effect” perspective, due to the substantial capital investment made by enterprises in the early stages, some traditional non-green technology enterprises with low technical efficiency and poor management find it difficult to exit the industry [51]. These inefficient enterprises not only occupy limited resources but also further hinder the advancement of green technology through pollution and resource waste, ultimately leading to a decrease in overall GTFP level. Moreover, excessive reliance on external knowledge may dampen firms’ innovation incentives, slowing the pace of technological progress and efficiency improvements. Without sufficient motivation, firms may remain in inefficient production modes, lacking self-innovation and unable to meet the demands of environmental protection and green development, thus inhibiting GTFP growth. Building upon the preceding analysis, the following hypotheses are proposed:

Hypothesis 2.

IA influences forestry GTFP through the intermediate effects of labor pooling, input sharing, and knowledge spillover.

3. Materials and Methods

3.1. Model Selection

3.1.1. Super Efficiency SBM Model

The measurement of GTFP is conducted using the super efficiency SBM model. Compared to the general SBM model, the super SBM model allows for further differentiation of efficient Decision Making Units (DMUs) that are on the frontier. Following the approach of Tone [7], the model is formulated as follows:

$$Min\delta ={\displaystyle \frac{1}{m}}\sum _{i=1}^m\left({\displaystyle \frac{\overline{x}}{x_{ik}}}\right)/{\displaystyle \frac{1}{r_1+r_2}}\left(\sum _{s=1}^{r_1}{\displaystyle \frac{\overline{y^d}}{y_{sk}^d}}+\sum _{q=1}^{r_2}{\displaystyle \frac{\overline{y^u}}{y_{qk}^u}}\right)$$

(1)

$$s.t.\left\{\begin{array}{c}\overline{x}\ge {\displaystyle \sum _{j=1,\ne k}^n}{x}_{ij}{\lambda }_j;\overline{y^d}\le {\displaystyle \sum _{j=1,\ne k}^n}{y}_{sj}^d{\lambda }_j;\overline{y^d}\ge {\displaystyle \sum _{j=1,\ne k}^n}{y}_{qj}^d{\lambda }_j;\\ \overline{x}\ge x_k;\overline{y^d}\le y_k^d;\overline{y^u}\ge y_k^u;\\ {\lambda }_j\ge 0,1,2,\dots ,m;\\ j=1,2,\dots ,n,j\ne 0;\\ s=1,2,\dots ,r_1;\\ q=1,2,\dots ,r_2;\end{array}\right.$$

(2)

In the equation, there are n DMUs, each consisting of $m$ inputs, $r_1$ desirable outputs, and $r_2$ undesirable outputs. $x$ represent elements in corresponding input, $y^d$ represent desirable output, $y^u$ represent undesirable output. $\delta$ denotes the ecological efficiency value.

3.1.2. Spatial Durbin Model

Existing research has shown that both IA and forestry GTFP exhibit spatial correlation and are therefore suitable for spatial econometric models. To explore spatial correlation, this study employs a Spatial Durbin Model (SDM):

$$\begin{gathered} {\mathrm{GTFP}}_{\mathrm{it}}=\mathsf{\alpha }+{\rho }_0\sum _{i=1}^{n}W{\mathrm{GTFP}}_{\mathrm{it}}+{\mathsf{\beta }}_1{\mathrm{IA}}_{\mathrm{it}}+{\rho }_1\sum _{i=1}^{n}W{\mathrm{IA}}_{\mathrm{it}} \\ {+\mathsf{\beta }}_2{\mathrm{IA}}_{\mathrm{it}}^2+{\rho }_2\sum _{i=1}^{n}W{\mathrm{IA}}_{\mathrm{it}}^2+\mathsf{\gamma }\sum {\mathrm{X}}_{\mathrm{it}}+{\rho }_3\sum _{i=1}^{n}W{\mathrm{X}}_{\mathrm{it}}+u_i+v_t+{\mathsf{\epsilon }}_{\mathrm{it}} \end{gathered}$$

(3)

where $i$ and $t$ represent regions and years, ${\mathrm{IA}}_{\mathrm{it}}^2$ is the square term of forestry IA level, and ${\mathrm{X}}_{\mathrm{it}}$ represents control variables. $\mathsf{\alpha }$ is a constant term, $W$ is the spatial weight matrix, $\rho$, $\mathsf{\beta }$ are the spatial autoregressive coefficient and regression coefficient for ${\mathrm{IA}}_{\mathrm{it}}$, $u_i$, $v_t,$ are fixed effect terms, ${\mathsf{\epsilon }}_{\mathrm{it}}$ is a random error term.

According to Tobler’s First Law of Geography [52], spatial weight matrices can reflect the strength of connections between regions. This study adopts three types of spatial weight matrices for spatial econometric analysis: geographic distance matrix, spatial adjacency matrix, and economic distance matrix. Our main regression used the geographic distance matrix, with its specific representation shown in Equation (4):

$$W_{ij}={\displaystyle \frac{1}{d_{ij}}}$$

(4)

The inverse-distance geographic weight matrix has the advantage that a smaller distance $d_{ij}$ between locations i and j yields a larger weight $W_{ij}$, indicating stronger spatial linkages between closer regions. This matrix effectively captures spatial interactions based on geographical proximity, which aligns with most real-world activity patterns. For robustness, we also employ a spatial adjacency matrix and an economic distance matrix in the SDM regression, as defined in Equations (5) and (6):

$$D_{ij}=\left\{\begin{array}{c}1ifi,jareadjacent\\ 0otherwise\end{array}\right.$$

(5)

$$E_{ij}={\displaystyle \frac{1}{\left|\overline{Y_i}-\overline{Y_j}\right|}}$$

(6)

Equation (5) defines the spatial adjacency matrix, where a connection exists only between adjacent regions, ignoring both the strength of connections and potential interactions between non-adjacent areas. Equation (6) defines the economic distance matrix based on the average per capita GDP difference between regions, where greater similarity in economic development implies stronger spatial linkage. However, this matrix captures connectivity only from a single economic dimension, neglecting other relevant factors. As these matrices only partially capture interregional connections, they are used for robustness testing.

3.1.3. Mechanism Testing Model

When testing the mechanism of how IA affects GTFP, it is necessary to verify whether the primary explanatory variable influences the intermediate variables. Then, the mechanism can be tested by introducing the intermediate variables and their interaction terms with the core variable. Since the relationship between IA and GTFP follows an inverted U-shape, the nonlinear effects must be considered when testing the mechanism. Referring to the mechanism tests of the inverted U-shaped relationship by Wen [53] and Edwards [54], this study adopts a Spatial Durbin Model for stepwise regression. The model specification for testing the mechanism is as follows:

$$M={\beta }_0^{\prime }+{\beta }_1^{\prime }X+{\beta }_2^{\prime }{X}^2+e^{\prime }$$

(7)

$$Y={\beta }_0+{\beta }_{1}X+{\beta }_2{X}^2+{\beta }_3\mathrm{M}+{\beta }_{4}XM+e$$

(8)

In the equation, M represents the agglomeration externalities mediating variables, including LP, IS, and KS. X is the key explanatory variable IA, X2 is the square term of IA, and XM represents the interaction term between the independent variable and the intermediate variable. Equation (7) is used to test the nonlinear relationship between IA and agglomeration externalities, while Equation (8) is used to verify the inverted U-shaped relationship, as well as the intermediate role of agglomeration externalities in this process.

3.2. Variable Description

3.2.1. Dependent Variable

The dependent variable is GTFP, calculated using the super-efficiency SBM model. When incorporating undesirable outputs, the traditional radial DEA method may overlook certain aspects of inputs or outputs, leading to biases in efficiency measurement results. The non-radial SBM method addresses these issues [55]. In this model, the input variables include labor, capital, land, and energy. The desirable output variables include economic output and ecological output, while the undesirable output refers to “industrial three wastes”, waste gas, waste water, and solid waste.

Table 1. Forestry GTFP measurement index system.

Indicator Type	Indicator Name	Indicator Representation
Inputs	Labor input	Number of forestry employees at the end of the year
	Capital input	Completed investment in fixed forestry assets
	Land input	Area of forestry land
	Energy input	Regional total energy consumption × Forestry total output value/Regional GDP
Desirable Outputs	Economic output	Regional forestry GDP
	Ecological output	Regional afforestation area
Undesirable Outputs	Forestry industrial SO2 emissions	Regional industrial SO2 emissions × Forestry secondary industry output/Regional industrial GDP
	Forestry industrial wastewater discharge	Regional COD in industrial wastewater × Forestry secondary industry output/Regional industrial GDP
	Forestry industrial solid waste generation	Regional industrial solid waste generation × Forestry secondary industry output/Regional industrial GDP

presents the detailed GTFP measurement index system.

Since there is no specific data available for forestry energy input, it is indirectly calculated by using the formula [56]: total regional energy consumption × regional forestry total output/regional GDP, to represent forestry’s energy input. The forestry industrial pollutant emissions data is also obtained through indirect measurement [16]. The forestry industrial pollutant emissions are calculated as regional industrial pollutant generation × regional forestry secondary industry output/regional industrial GDP. This includes the emissions of SO₂, wastewater discharge, and solid waste generation. The spatial distribution of forestry GTFP across the provinces is shown in Figure 2. It can be observed that over time, the GTFP levels in the eastern and central areas have obviously improved. Although the western area has declined, the overall GTFP level is constantly improving.

3.2.2. Key Explanatory Variable

The key explanatory variable is the level of forestry IA. The level of IA is represented by the location entropy index. The calculation is as follows:

$${IA}_{it}={\displaystyle \frac{{FGDP}_{it}/{FGDP}_t}{{GDP}_{it}/{GDP}_t}}$$

(9)

where ${IA}_{it}$ represents the forestry industrial agglomeration measured by the location entropy, ${FGDP}_{it}$ is the regional forestry production value, ${FGDP}_t$ is the national forestry production value, ${GDP}_{it}$ is the GDP of the province, and ${GDP}_t$ is the national GDP. Since the impact of IA on GTFP is nonlinear, the square term of forestry IA level is added to represent the quadratic relationship. The spatial distribution of the national forestry IA level is shown in Figure 3. It can be found that the overall IA level is declining, especially in the Northeast, while the IA level in some southern provinces is increasing.

3.2.3. Intermediate Variables

LP refers to the inflow of labor in IA, reflecting the availability and matching of labor. We measure LP using the location entropy index method based on the year-end number of forestry employees and the total number of employed individuals in the region. IS refers to the spatial concentration of upstream and downstream enterprises, where shared intermediate product factors form economies of scale. It is mainly manifested as cost savings in transport and transaction processes [57]. In the forestry production process, IS also manifests in the agglomeration of upstream and downstream enterprises, which can be reflected by transportation costs. We measure IS as the ratio of the total highway length in the region to the area of the province. KS refers to the accessibility of knowledge among different enterprises within the agglomeration area. Forestry knowledge innovation can enhance the level of KS, and increased innovation allows knowledge to spread within the region at a lower cost, so innovation capacity is also used to measure KS. We measure KS using the location entropy index method based on regional forestry patents and regional patent authorizations.

3.2.4. Control Variables

Control variables selected are economic development level (EDL), proxied by the natural logarithm of regional per capita GDP; urbanization rate (UR), proxied by the ratio of urban residents to the total population; industrialization level (IL), proxied by the ratio of the secondary forestry industry’s output value to total forestry output value; financial support (FIS), represented by the cumulative forestry investment amount in each region, with its logarithm taken; forest stock (FS), represented by the regional forest stock volume; forest fire (FF), represented by the area affected by forest fires, with 1 added to the value and then the logarithm taken; forest pests and diseases (FPD), represented by the logarithm of the area affected by pests and diseases.

Table 2. Descriptive statistics of variables.

Variable	Variable Name	Mean	Standard Deviation	Minimum	Maximum
Dependent Variable	Forestry Green Total Factor Productivity (GTFP)	0.492	0.206	0.181	1.056
Key Explanatory Variable	Forestry Industrial Agglomeration (IA)	1.045	0.757	0.017	4.450
Intermediate Variables	Labor Pooling (LP)	1.433	2.087	0.044	12.220
	Input Sharing (IS)	0.846	0.498	0.039	2.245
	Knowledge Spillovers (KS)	1.647	1.094	0.387	8.327
Control Variables	Economic Development Level (EDL)	10.436	0.706	8.353	12.142
	Urbanization Rate (UR)	0.552	0.143	0.254	0.896
	Industrialization Level (IL)	0.347	0.238	0.000	2.372
	Financial Support (FIS)	11.428	1.678	4.190	16.047
	Forest Stock (FS)	4.377	5.257	0.010	19.730
	Forest Fire (FF)	4.845	2.468	0.000	12.695
	Forest Pests and Diseases (FPD)	3.222	1.127	−0.821	5.304

presents the descriptive statistics for each variable.

3.2.5. Data Sources

This study utilizes data sourced from the China Forestry and Grassland Statistical Yearbook, China Environmental Statistical Yearbook, China Energy Statistical Yearbook, and China Statistical Yearbook. The forestry patent data comes from the China Forestry Information Network (http://lygc.lknet.ac.cn). Due to data availability, this study adopts a provincial-level balanced panel, with data selected for the period from 2004 to 2021, totaling 18 years of data. Due to the missing data, this study focuses on relevant data from the other 30 provinces. Missing values were supplemented through linear interpolation, and some data are deflated using 2004 as the base year.

4. Results and Discussion

4.1. Results Description

4.1.1. Analysis of Forestry GTFP Calculation Results

This study uses the super efficiency SBM model to calculate GTFP of 30 provinces, covering the period from 2004 to 2021. The evolution trend of GTFP is shown in Figure 4. The figure includes the regional average GTFP trends for Eastern, Central, and Western and the national average. From Figure 4, it can be observed that the overall level of GTFP fluctuates and increases over time. GTFP in the east is the highest of all regions and above the national average, which could stem from the Eastern region’s superior economic development. GTFP in the Central region remains under the national average, yet its upward movement indicates consistent forestry development. GTFP in the western region fluctuates greatly; forestry development is unstable and is gradually falling below the national level.

4.1.2. Analysis of Forestry IA Measurement Results

The average IA levels of each province from 2004 to 2021 are shown in Figure 5. As can be seen, IA levels vary notably across provinces, with the southern and northeastern regions exhibiting higher degrees of agglomeration. This is largely due to their favorable natural resource endowments, which have supported forestry development and made it a pillar industry. In contrast, coastal provinces show lower IA levels, as their comparative advantages favor other industries, resulting in relatively limited forestry development. The natural resource conditions in the arid western regions limit the development of forestry, resulting in the lowest IA levels.

4.1.3. Estimating the Relationship Between IA and GTFP

Before examining how IA affects GTFP, this study first fits their relationship, as shown in Figure 6. The effect of IA exhibits a clear inverted U-shaped pattern, where IA initially promotes the growth of GTFP before reaching a turning point, reflecting the characteristics of the “scale effect”. However, after IA reaches the turning point, it starts to suppress the growth of GTFP, showing the characteristics of the “crowding effect.”

4.2. Results Analysis

4.2.1. Estimation and Results of SDM

To identify the most suitable form of spatial model, this study applies the LM test, Hausman test, LR test, and Wald test.

Table 3. Spatial econometric model test results.

Spatial Econometric Model Test	Spatial Econometric Model Test
Moran’s I	6.747 ***
LM(lag)test	9.796 ***
Robust LM(lag)test	29.584 ***
LM(error)test	38.708 ***
Robust LM(error)test	58.496 ***
LR test spatial lag	43.75 ***
Wald test spatial lag	41.04 ***
LR test spatial error	41.55 ***
Wald test spatial error	34.05 ***
Hausman test	66.99 ***
Individual LR test	60.74 ***
Time LR test	320.16 ***

Note: *** represent significance at the 1% confidence levels.

reports detailed test results. Moran’s I indicates a spatial correlation between IA and GTFP, confirming the appropriateness of spatial econometric models for examining their relationship. The LM test results show the null hypothesis is rejected at the 1% level by both SAR and SEM, indicating that SDM is applicable. The Hausman test shows fixed effects should be accounted for, and the SDM’s estimation results are compared under both time and spatial fixed effects. LR test results indicate that individual and time fixed effects are significant at the 1% level, making the dual fixed effects model optimal. LR and Wald tests further examine whether SDM can degrade into SAR or SEM. The results are significant at the 1% level, confirming that SDM is suitable for this study.

4.2.2. Benchmark Regression

In this section, the model includes the linear term of IA

Table 4. Benchmark regression results.

Variable	(1) Fixed Effects Model		(2) Spatial Durbin Model
IA	0.072 ***	0.197 ***	0.059 ***	0.238 ***
	(3.701)	(3.713)	(3.055)	(4.457)
IA2		−0.027 **		−0.044 ***
		(−2.529)		(−3.709)
Constant	0.328	0.488
	(0.554)	(0.824)
ρ			−14.194 **	−15.600 ***
			(−2.479)	(−2.669)
R2	0.3103	0.3192	0.1749	0.2232
Control Variables	yes	yes	yes	yes
Turning Point		3.648		2.705
Sample Size	540	540	540	540

Note: ***, ** represent significance at the 1% and 5% confidence levels.

displays the regression results for the fixed effects model alongside the spatial Durbin model. In Model (1), IA’s coefficient is significant, suggesting that IA affects GTFP. When considering the quadratic relationship, with a significantly positive coefficient for IA and a significantly negative coefficient for IA², the results show that the relationship between IA and GTFP is a clear inverted U-shape. The turning point is 3.648. Before reaching this point, the “scale effect” allows the improvement in IA levels to promote GTFP growth. However, as IA levels continue to rise, the “crowding effect” starts to emerge, and IA levels inhibit GTFP growth. Model (2) incorporates spatial correlation by including a spatial lag term. In this model, the IA coefficient is also significant, indicating that IA has a notable effect on GTFP, even when spatial correlation is considered. When considering the quadratic relationship, the IA coefficient is 0.238, and the IA² coefficient is −0.044, both are 1% significant. An inverted U-shaped relationship is empirically supported, and the turning point for IA is found to be 2.705, which confirms Hypothesis 1.

4.2.3. Robustness Test

This study conducts robustness tests by modifying the dependent variable and adjusting the spatial weight matrix.

Table 5. Robustness test results.

Variable	(1) Change in Dependent Variable	(2) Change in Matrix W1	(3) Change in Matrix W2
IA	0.428 ***	0.194 ***	0.190 ***
	(4.192)	(3.917)	(3.791)
IA2	−0.078 ***	−0.032 ***	−0.026 **
	(−3.401)	(−3.200)	(−2.516)
ρ	−16.969 ***	−0.089	0.300
	(−2.708)	(−1.501)	(.)
R2	0.2242	0.1572	0.1218
Control Variables	Yes	Yes	Yes
Sample Size	540	540	540

Note: ***, ** represent significance at the 1% and 5% confidence levels.

reports estimated results. To change the dependent variable, the super SBM-Malmquist model is used to recalculate GTFP. To change the spatial weight matrix, the spatial adjacency weight matrix (W1) and economic distance weight matrix (W2) replace the geographic distance spatial weight matrix. Following the substitution, SDM is employed to perform robustness checks. Based on these three robustness tests, the conclusions drawn after replacing the dependent variable and changing the weight matrix align with the findings of the benchmark regression. Furthermore, after these modifications, IA still exhibits an inverted U-shaped relationship with GTFP, further confirming Hypothesis 1.

4.2.4. Mechanism Test

Grounded in the theoretical analysis outlined above, IA has a nonlinear impact on GTFP. So, how does this nonlinear impact arise, and under what conditions does it occur? A thorough analysis of the mechanism is needed to clarify the relationship between IA and GTFP. According to the theoretical mechanism in section two, IA affects GTFP through the formation of agglomeration externalities. To test this, this study selects proxy variables based on Marshallian agglomeration externality theory, treating agglomeration externalities as an intermediate variable for mechanism testing. The intermediate variables for the mechanism test are agglomeration externalities, including LP, IS, and KS.

The results for testing the mechanisms of LP, IS, and KS are provided in

Table 6. Mechanism test results.

Variable	(1) LP	(2) GTFP	(3) IS	(4) GTFP	(5) KS	(6) GTFP
IA	0.442 ***	0.319 ***	0.086 *	0.086	0.994 ***	0.239 ***
	(2.706)	(5.723)	(1.919)	(1.286)	(3.970)	(4.305)
IA2	−0.108 ***	−0.049 ***	−0.013	−0.030 **	−0.210 ***	−0.034 ***
	(−2.940)	(−4.164)	(−1.321)	(−2.442)	(−3.726)	(−2.755)
LP		0.004
		(0.245)
IA × LP		−0.042 ***
		(−3.595)
IS				−0.137 **
				(−2.062)
IA × IS				0.126 ***
				(3.154)
KS						0.052 ***
						(3.154)
IA × KS						−0.016 **
						(−2.286)
ρ	−1.490	−14.548 **	4.483	−18.955 ***	−13.742 **	−17.785 ***
	(−0.305)	(−2.512)	(0.788)	(−3.172)	(−2.368)	(−3.006)
R2	0.0013	0.2562	0.6916	0.2486	0.0212	0.2540
Control Variables	Yes		Yes		Yes
Sample Size	540	540	540	540	540	540

Note: ***, **, * represent significance at the 1%, 5%, and 10% confidence levels.

, with Columns (1), (3), and (5) corresponding to the first-step tests. In column (1), the significantly positive coefficient of IA and the significantly negative coefficient of IA² suggest a nonlinear impact of IA on LP, exhibiting an inverted U-shaped relationship. In column (3), although the IA coefficient passes the 10% significance test, the IA² coefficient does not, suggesting an uncertain impact of IA on IS. In column (5), the positive and significant IA coefficient, along with the negative and significant IA² coefficient, validates that IA has an inverted U-shaped effect on KS. These regression results verify the first-step mechanism test, proving that intermediate variables are influenced by the independent variable and that the effect of IA on LP and KS is nonlinear.

Columns (2), (4), and (6) represent the second-step test for the mechanism. In column (2), the mediating effect test of LP shows that the LP coefficient is positive but not significant, while the interaction term between LP and IA is negative and significant, indicating that LP has a negative moderating effect on IA. In column (4), after introducing the IS term and the interaction term of IS, the IA coefficient becomes insignificant; this results in an unstable inverted U-shaped relationship. However, from the IA and IS interaction term, IS has a positive moderating effect on IA. In column (6), with a significantly positive KS coefficient and a significantly negative interaction term, the results suggest that KS has a positive impact on GTFP and a negative moderating effect on IA.

The results from the mechanism test show that IA significantly affects LP and KS and follows a nonlinear inverted U-shaped pattern. While IA has a positive effect on IS, the relationship is not significant; this may be due to the smaller marginal impact of IA on IS. In terms of the intermediate effect, LP only has a negative moderating effect, which suggests that the aggregation of labor does not directly promote GTFP growth but weakens the effect of IA on GTFP. This may be because the forestry labor market is not perfectly competitive, and labor cannot move freely. Thus, an increase in LP does not necessarily lead to an increase in human capital, which in turn cannot clearly promote GTFP growth. Additionally, as LP increases, it may lead to higher management costs and environmental externalities caused by crowding, which suppresses the effect of IA on GTFP. Introducing the intermediate variable IS actually making the effect of IA on GTFP less stable. However, IS has a positive moderating effect on IA, which indicates that the improvement of IS can enhance the effect of agglomeration; this enhances the impact of IA on GTFP in regions with superior transportation infrastructure. KS exerts a positive direct impact on GTFP, while its moderating effect on IA is negative, meaning that KS improvement benefits the region’s green technology advancement, promoting GTFP growth. On the other hand, technology spillovers lead firms to acquire new technologies through purchasing rather than R&D, reducing their innovation incentives and thus decreasing the innovative behavior of agglomerated firms, which suppresses the effect of IA on GTFP.

The analysis above shows that agglomeration externalities have an intermediate effect. IA influences GTFP through the moderating effect of LP and IS and the partial mediating and moderating effects of KS, which generates both scale and the “crowding effect”. This leads to the nonlinear impact of IA on GTFP, thus confirming Hypothesis 2.

4.2.5. Heterogeneity Analysis

Natural and socio-economic factors contribute to the regional disparities in the distribution of forestry in China. The level of forestry development varies across regions, and each faces distinct constraints. Therefore, the impact of IA on GTFP may exhibit considerable regional heterogeneity. This study categorizes the 30 provinces into three regions: East, Central, and West, and applies SDM to conduct regression estimates for each region.

Table 7. Heterogeneity analysis.

Variable	(1) East		(2) Central		(3) West
IA	0.148 ***	0.525 ***	0.126 ***	0.075	0.054 *	0.025
	(4.907)	(6.773)	(2.692)	(0.300)	(1.856)	(0.283)
IA2		−0.082 ***		0.017		0.005
		(−5.216)		(0.216)		(0.250)
ρ	−25.737 **	−28.754 ***	−36.616 **	−36.027 **	−72.853 ***	−77.543 ***
	(−2.494)	(−2.790)	(−2.294)	(−2.249)	(−4.936)	(−5.196)
R2	0.4981	0.5880	0.3837	0.3779	0.0056	0.0453
Control Variables	yes	yes	yes	yes	yes	yes
Turning Point		3.201		2.206		2.5
Sample Size	198	198	144	144	198	198

Note: ***, **, * represent significance at the 1%, 5%, and 10% confidence levels.

displays the test results. For the Eastern region in model (1), the linear model reveals a significant and positive effect of IA. In the nonlinear model, both the IA and IA² coefficients are 1% significant; the turning point for IA is 3.201. This indicates that IA positively affects GTFP in the Eastern region, but once IA exceeds the turning point, its effect becomes negative. In the Central region in model (2), there is a positive effect of IA, and the coefficient in the linear model is significant. In contrast, the nonlinear model shows that neither coefficient passes the significance test, suggesting a positive impact of IA on GTFP in the Central region without a clear inverted U-shaped relationship. The regression for the Western region in model (3) shows that the coefficient for IA in the linear model only passes the 10% significance test, indicating a relatively weak impact. The coefficients in the nonlinear model are not significant, suggesting that the relationship between IA and GTFP in the Western region is ambiguous. The possible reasons for these results are: In the Eastern region, advanced infrastructure and strong innovation capacity enhance agglomeration externalities. The GTFP is also higher than the national level, having reached the “crowding effect” stage of agglomeration, which obstructs the enhancement of GTFP. In contrast, the Central region has a lower level of technology and production efficiency compared to the East, but it has rich natural resources and more room for growth. It is more likely to be in the “scale effect” stage, thus promoting GTFP growth. The Western region has weaker agglomeration effects, and its impact on GTFP is unclear.

Due to variations in resource endowment, technological levels, and market conditions, the impact of IA on GTFP may differ across different stages of development. In this study, the differentiation of industrial structure among different provinces is used to classify regions into industrialized and non-industrialized stages. To distinguish these stages, the ratio of the secondary and tertiary industries to the primary industry is employed, with a ratio greater than 1 indicating an industrialized stage and a ratio less than or equal to 1 indicating a non-industrialized stage. As the forestry industry structure fluctuated in earlier years but became stable after 2016, the forestry industry structure of 2016 is used as the criterion for determining industrialization [58]. As shown in

Table 8. Heterogeneity test.

Variable	(4) Industrialization Stage		(5) Non-Industrialization Stage
IA	0.065 **	0.272 ***	−0.038	−0.084
	(2.537)	(3.573)	(−1.527)	(−1.229)
IA2		−0.046 ***		0.004
		(−2.798)		(0.244)
ρ	−31.326 ***	−30.067 ***	−21.290 *	−22.508 *
	(−3.500)	(−3.335)	(−1.738)	(−1.844)
R2	0.2617	0.2417	0.0113	0.0322
Control Variables	yes	yes	yes	yes
Turning Point		2.957		10.5
Sample Size	342	342	198	198

Note: ***, **, * represent significance at the 1%, 5%, and 10% confidence levels.

, there are 19 industrialized provinces and 11 non-industrialized provinces in the sample. The results for industrialized regions in model (4) show that both the linear and non-linear models have significant IA coefficients, with an IA turning point of 2.957. In industrialized regions, both “scale effect” and “crowding effect” coexist, and the inverted U-shaped relationship is evident. For non-industrialized regions in model (5), the coefficients are not statistically significant at the 10% level, indicating that the effect of IA on GTFP is ambiguous. This can be attributed to the fact that in industrialized regions, the strong development of secondary and tertiary industries fosters growth of forestry enterprises and the emergence of significant agglomeration effects, thereby promoting GTFP growth. However, in the primary industry, there is less investment in resources and technology, fewer enterprises, and weaker agglomeration effects, making it difficult for GTFP to experience considerable improvements.

5. Discussion

This study focuses on the inverted U-shaped relationship between IA and GTFP and employs the theory of agglomeration externalities to analyze the “scale effects” and “crowding effects” behind the inverted U-shaped relationship in forestry agglomeration. In the study of forestry IA, some scholars believe that China’s forestry IA is still in the “scale effect” stage, with room for improvement in agglomeration [59,60]. Some scholars also argue that the impact of IA on forestry total factor productivity presents an inverted U-shaped feature, indicating that the “crowding effect” has already appeared [61]. In the study of other sectors, for example, Ye et al. [62] believe that IA has an inverted U-shaped impact on agricultural environmental efficiency, Huang et al. [63] believe that tourism is not conducive to reducing carbon emissions when it is over-agglomerated, and Zhang et al. [64] believe that IA can promote industrial carbon productivity, but excessive agglomeration hinders its increase. According to many previous studies, with the increase of agglomeration, the “crowding effect” tends to emerge, leading to reduced efficiency and increased negative environmental externalities. For forestry GTFP, the impact of IA is an inverted U-shaped relationship of first promotion and then inhibition. It is appropriate to explain the nonlinear impact of IA from the perspective of “scale effect” and “crowding effect”, and the introduction of the theory of agglomeration externalities to explain these two effects can help us better understand the causes of nonlinear effects and implement reasonable policies to alleviate the “crowding effect”. Previous studies on agglomeration externalities have mainly focused on industrial manufacturing and service industries [41,42,43], while our study introduces this theory into the forestry sector and empirically verifies the mediating role of LP, IS, and KS in forestry. This study first uses a spatial econometric model to verify that the impact of IA on GTFP has an inverted U-shaped relationship of first promoting and then inhibiting, which is consistent with the conclusion of Wei and Zhang [61]. By adding the square term of IA to the regression model, its coefficient is significantly negative. We continue to use the mediation and moderation test models to verify the role of forestry agglomeration externalities, while Wu et al. [42] also used a similar method to test the mediating role of the agglomeration effect in the impact of IA on ecological efficiency.

Looking back at agglomeration itself, the “crowding effect” brought about by agglomeration is not ideal, so it is unreasonable to promote IA as a policy goal for industrial development [65]. Introducing the theory of agglomeration externalities to explain the impact mechanism of forestry IA on GTFP can clarify why the agglomeration process produces the “scale effect” and “crowding effect”, as well as how to guide and utilize the “scale effect” in forestry development and limit the “crowding effect” caused by excessive agglomeration. Therefore, in actual policymaking, we can start from LP, IS, and KS to more accurately regulate industrial development, optimize factor allocation, and achieve high-quality development.

In addition, the level of forestry agglomeration externalities varies across regions. The endowment conditions of different regions, such as the richness of forestry resources, the level of human capital, and the level of technology, determine the agglomeration externalities of forestry in each region. Among Chinese provinces, there are large differences in agglomeration. The IA level in the eastern region is not high, but it has the highest GTFP level. A common feature of these regions is a high level of forestry industrialization, which is consistent with the findings of Chen et al. [66]. From the perspective of agglomeration externalities, the LP level in the eastern region is low, forestry processing and manufacturing industries are developed, and there is a tendency for capital to replace labor, thus achieving optimal factor allocation. The IS level is also high, and strong infrastructure facilitates the flow of resource factors. These factors together contribute to the eastern region’s high GTFP level. The current status of forestry development also varies among provinces in the central region. For example, provinces with strong forestry agglomeration, such as Guangxi, Jiangxi, and Hunan, have low GTFP levels and high LP levels. However, further analysis shows that a high LP level does not necessarily reflect higher human capital. These major timber-exporting regions [66] rely on ordinary labor that is easily replaceable. Excess labor has intensified competition, and since China’s forestry marketization remains incomplete [67], this has raised management costs. In other provinces that have not yet reached the crowded stage, the “scale effect” of agglomeration externalities has not yet fully materialized. Steadily expanding agglomeration can increase LP, enhance human capital, and better utilize the “latecomer advantage” to improve KS. Forestry development in the western region mainly depends on local forest and grass resources, and IA characteristics are not prominent. Industrial development is still in its early stage, and the industrial structure requires further upgrading. After integrating local endowment resources, it is necessary to define the future development path and leverage the “scale effect” of agglomeration in key industries.

However, this study also has some limitations. When employing econometric models to assess the impact of IA on GTFP, the results may not fully reflect the development status of China’s forestry sector due to the limited sample size of the available data. Future research could incorporate larger datasets to improve the precision of the estimates. Moreover, in selecting variables to represent forestry agglomeration externalities, data limitations hindered the use of more accurate measures for labor pooling, input sharing, and knowledge spillovers. This may have introduced bias into the results. As more suitable data become available in the future, these externalities can be measured more accurately, thereby providing more robust evidence to inform policy formulation.

6. Conclusions and Implications

By constructing a spatial econometric model, this study assesses the nonlinear impact of IA on GTFP using provincial panel data from China. The results have passed robustness tests, and the mechanism of agglomeration externalities has been analyzed. Furthermore, the effects under different types of heterogeneity have also been examined. Based on these analyses, the study yields the following findings: (1) The nonlinear effect of IA on GTFP is inverted U-shaped, and the turning point of IA is 2.705. At the initial stages of agglomeration, GTFP increases, but excessive agglomeration of the forestry industry leads to crowding and suppresses further GTFP growth. This conclusion holds even after robustness tests. (2) After introducing LP, IS, and KS as mediating variables to test the mechanism, the results reveal that IA has an inverted U-shaped relationship with LP and KS and a positive but weak impact on IS. LP has a significant negative moderating effect, IS exhibits a positive moderating effect, and KS has both a positive direct effect and a negative moderating effect on GTFP. These results suggest agglomeration externalities play a crucial mediating role between IA and GTFP. (3) The inverted U-shaped relationship remains significant in the east, with the turning point at 3.201. In the central region, IA only exhibits a positive effect, while in the western region, the impact is weak. In industrialized regions, the relationship follows a significant inverted U-shape, with the turning point at 2.957. However, in non-industrialized areas, the impact is unclear.

This study empirically examines the impact of IA on GTFP, emphasizing the role of agglomeration externalities and their contribution to the sustainable development of the forestry sector. Based on the conclusions drawn, the following policy recommendations are proposed to promote green development in China’s forestry sector:

Firstly, the impact of IA on GTFP presents an inverted U-shaped relationship, so the “crowding effect” caused by excessive agglomeration must be avoided. Facing future forestry development, different regions should plan and layout in advance, identify their own strengths and weaknesses, and promote development through rational resource allocation and industrial structure optimization. Forestry-related departments should set IA thresholds based on their environmental carrying capacity and avoid blindly expanding agglomeration. When the “crowding effect” begins to emerge, the government should adopt appropriate measures to curb excessive IA development. For example, it can provide tax incentives or subsidize technology transfer to encourage green innovation and promote high-quality rather than high-quantity growth. In addition, it can guide the transformation of the forestry industry structure by reallocating certain factor resources from the primary or secondary sectors to more advanced ones, thereby supporting the development of the tertiary forestry industry.

Secondly, the role of agglomeration externalities in the impact of IA on GTFP should be reasonably utilized. Strengthening professional training and enhancing human capital can help accumulate skilled talent, promote the reform of the forestry factor market, and guide labor toward advanced sectors, thereby enhancing the positive effect of LP. Improving infrastructure and public services can enhance IS, for example, by upgrading road conditions in forest areas, applying forestry remote sensing technology, and increasing the efficiency of public services in forestry-related government departments. For KS, technological innovation and knowledge exchange can be promoted through policy subsidies and the enhancement of intellectual property protection regulations.

Thirdly, regions should develop differentiated policies based on their respective development conditions. In the eastern region, where economic development and forestry GTFP are relatively high and forestry is not the main driver of economic growth, the focus should be on reducing resource input and enhancing green efficiency. Promoting forest tourism and service industries can help advance the forestry tertiary sector. In the central region, provinces such as Guangxi, Jiangxi, Jilin, and Hunan still rely on forestry for economic gains and have higher levels of IA. For these regions, it is crucial to control the level of IA and mitigate the “crowding effect”, as GTFP still has substantial room for improvement. They should dispose of resource-dependent development models, promote technological innovation, and prioritize quality growth over quantity growth. Although some central provinces have not yet reached the crowding stage, proactive planning is necessary to avoid potential negative environmental externalities. In the western region, where some provinces are rich in forest and grassland resources but forestry industry development remains limited, leveraging the “scale effect” of IA can help expand the sector and achieve both economic and ecological benefits.

Fourthly, regions in the forestry industrialization stage have developed more downstream industries, which has generated greater economic benefits but also intensified the “crowding effect”. Due to early industrial development, many inefficient enterprises remain in the market, consuming substantial resources with low output and causing environmental pollution. Therefore, it is necessary to control the scale of forestry processing and manufacturing and gradually phase out inefficient and polluting enterprises by increasing emission taxes.