Assessing the Effect of Factor Misallocation on Grain Green Production Capacity: A Case Study of Prefecture-Level Cities in Heilongjiang Province

Abstract

Improving the efficiency of factor allocation in food production is the foundation for accelerating the formation of new quality productivity and achieving an agricultural green transformation. However, there has been no scholarly focus on their mechanisms and the interactions involved. This exploration is an important reference for enhancing the green production capacity of major grain-producing areas. In this study, 13 prefecture-level cities in Heilongjiang Province, China’s largest grain production base, were selected as the research samples. A model for identifying factor misallocation and grain green total factor productivity (A_GGTFP) was constructed to identify the spatiotemporal differences in factor misallocation and green total factor productivity. A fixed effects model was used to explore the impact of single-factor misallocation and the interaction of dual-factor misallocation with A_GGTFP. The results show that from 2004 to 2022, the A_GGTFP in 13 prefecture-level cities in Heilongjiang Province has shown a slow growth trend. The inhibitory effects of single-factor misallocation of land, labor, and capital on green total factor productivity are sequentially enhanced. The interaction effects of capital misallocation and labor misallocation and labor misallocation and land misallocation strengthen the inhibitory effects of misallocation on the A_GGTFP. Therefore, it is necessary to further promote the optimization of production factors and improve the green production capacity for grain.

1. Introduction

Improving the efficiency of the factors of production in food systems is the foundation for accelerating the formation of new quality productivity and achieving a green transformation of agriculture. Heilongjiang Province, as a major agricultural province, plays a crucial role in safeguarding national security. Its grain output has ranked first nationwide for 13 consecutive years, making it the largest commodity grain production base in China. However, due to relatively low interests in production [1] and the transition from old to new drivers of regional economic development [2], issues such as black soil degradation, aging and feminization of the labor force, and fragmented capital have emerged within the factors of food production [3]. The endowment advantage of labor-intensive agriculture in China and the sustained growth capacity of grain production are facing severe challenges. The weak quality, basic nature, and semi-public goods attributes of grain production determine its market failure, which leads to distorted factor markets and factor misallocation [4].

From the perspective of sustainable agriculture through low-carbon production practices, the impact of misaligned factors on the capacity of green grain production mainly manifests in influencing input costs and distorting grain production prices. First, from the angle of resource allocation efficiency, misallocation leads to inefficient resource allocation and waste [5]. In agricultural production, ineffective and irrational allocation of land, labor, and capital reduces the utilization efficiency of these resources, failing to fully unleash their production potential. Consequently, energy consumption and emissions in the agricultural production process may increase, thereby reducing green grain production capacity. Second, misallocation suppresses the diffusion effects of technological advancement [6]. When the input factors in grain production are misaligned, agricultural producers may lack the impetus to introduce and adopt new technologies, which typically require matched input factors. As a result, the potential of technological progress to enhance agricultural production efficiency and reduce its environmental impact cannot be fully realized, directly inhibiting the enhancement of green grain production capacity. Moreover, misallocation exacerbates environmental pressures [7]. Given the dependence of grain production on the environment [8], excessive use of petrochemical elements such as fertilizers and pesticides negatively impacts the environment, reduces the soil organic content, increases agricultural carbon loads, raises greenhouse gas emissions, disrupts ecological balance, and diminishes agricultural sustainability [9]. Lastly, misallocation distorts factor market prices, rendering market mechanisms ineffective in allocation [10]. This distortion not only lowers resource allocation efficiency but also hinders the effective deployment of new productive forces such as technological innovation, thus restraining the improvement of green grain production capacity [10,11]. Scholars, drawing on neoclassical economic theory, have explained the distortion of agricultural production factors by describing deviations from Pareto optimal states caused by market failures or frictions in factor allocation, focusing on the marginal output per unit of production factor. Prominent scholars such as these include Harberger [12], Balassa [13], Bergsman [14], and Mundlak [15]. Drawing on the characteristics of agricultural production in China, Cai [16] used rural survey data to examine the “resource reallocation effect”; Gong et al. [17] explored the identification and formation of misallocation in China’s agricultural factor markets; Shi et al. [18] studied the causes of misallocation in land factors and methods for its identification; and Yang et al. [19] analyzed the causes of misallocation and its impacts on agricultural technology resources. Total factor green productivity represents agricultural green capacity, and a consensus has been reached on this indicator in the academic community [20]. However, there is still contention regarding how factor misallocation affects agricultural total factor productivity. Scholars often draw on the static analysis framework from Hsieh and Klenow [21] and the dynamic analysis framework from Aoki [22], combined with the characteristics of agricultural production, to construct agricultural production functions and analyze the process of factor misallocation’s influence on total factor productivity, measure the distortion elasticity coefficient of factor misallocation, estimate the loss of production efficiency and output caused by factor misallocation, further study the causes of factor misallocation, and propose corrective measures. Kirwan et al. [23] and Adamopoulos and Restuccia [24], respectively, chose different agricultural products to study the causes of factor misallocation in American agriculture. Dower and Markevich [25] analyzed the role and impact of Russian agricultural institutions on agricultural factor misallocation from the perspective of institutional change. Zhu et al. [26] adjusted and expanded the HK model based on the characteristics of Chinese households, constructed a static agricultural factor misallocation model, and measured the loss of agricultural TFP due to factor misallocation. Li et al. [27] constructed a factor misallocation model, estimating the impact of misaligned labor, capital, and land factors on the yield in different regions of China’s agricultural production. Zhang et al. [28] and Shi et al. [29] researched the influence of misallocation according to single factors such as water resources and land on agricultural output, while Qin et al. [8] analyzed the impact of misallocation on the high-quality development of grain-producing areas in response to industrial structure upgrading and technological progress.

Based on practical observations and a review of the domestic and international literature, it has been found that correcting factor misallocation to enhance agricultural efficiency has become a new perspective for improving agricultural green capacity [30,31,32]. However, grain is not a typical commodity, and its production has multiple attributes which distinguish the standards for identifying factor market distortions for grain from those for general agricultural products. Based on the uniqueness of grain production, the principles for identifying factor misallocation are key and challenging issues that the academic community needs to address. Exploring how new productive forces can drive high-quality development in grain production will be an urgent research topic for both academia and practical sectors. This paper considers grain green total factor productivity as the core indicator of grain green production capacity [33], with factor misallocation being determined by the characteristics of green grain production. Identifying the temporal and spatial differences in factor misallocation and green total factor productivity which arise from green grain production is an important means to correct factor misallocation to enhance green grain production capacity. Accordingly, the factors of grain production studied in this article refer to a series of resources and their effective combinations that are necessary in the process of grain production, including capital, labor, and land. These factors together constitute the material and technological basis of grain production, and their effectiveness, technological content, and contribution to grain production efficiency should be emphasized. This article constructs an identification model for factor misallocation and the green grain production capacity, examines the temporal and spatial differences in factor misallocation and grain green total factor productivity across 13 regions in Heilongjiang Province from 2004 to 2022, and explores the direction and degree of and trend in the impact of single-factor misallocation and interactive factor misallocation on the overall factor efficiency of green grain production. This study aims to provide theoretical support and policy suggestions for correcting factor misallocation and enhancing the green production capacity in grain production.

2. Methodology

2.1. Heilongjiang Province—An Overview

Heilongjiang Province is located in the northeastern part of the Chinese mainland, with a temperate continental monsoon climate. It has unique natural resources, a wide area of arable land, fertile soil, and rich black land resources. Heilongjiang Province has a high degree of agricultural intensification, producing high-quality grain crops such as rice, wheat, corn, and soybeans, and has favorable conditions for developing green and efficient agriculture. This article takes 13 cities in Heilongjiang Province as the research samples, with a sample period from 2004 to 2022. The original data for each city come from the “Heilongjiang Statistical Yearbook”, “Summary of Rural Economic and Social Statistics in Heilongjiang County (City)”, and “Compilation of National Agricultural Product Cost Benefit Data”, as well as statistical yearbooks and bulletins of various cities. Due to the fact that the statistical analysis of input factors such as pesticides, irrigation, and machinery in relevant yearbooks did not separate the use of grain production from agriculture, this article uses the weight coefficient method to separate the relevant factors of grain production. The specific calculation formula is grain-related factors = agriculture-related factors × (grain-sowing area/crop-sowing area) or grain-related factors = primary-industry-related factors × (agricultural output value/primary industry output value) × (grain-sowing area/crop-sowing area). Individual missing data can be reasonably inferred and supplemented based on the indicator characteristics and time series data trends.

2.2. The Calculation Model and Variable Selection for a Factor Misallocation Index for Grain Production

This study focuses on grain, using a classical production function to assume that the input factors in production include capital, labor, and land, with output elasticities α, β, and γ, respectively. It is also assumed there is a constant returns to scale and the representative farmer has the same output elasticity for factor production. The Cobb–Douglas function represents the production function:

$$Y_i=A_i{K}_i^{{\alpha }_i}{L}_i^{{\beta }_i}{E}_i^{{\gamma }_i}, \alpha +\beta +\gamma =1$$

(1)

where Y represents output, A represents technological progress, K represents capital, L represents labor, and E represents land.

The relative distortion coefficient of the input factors in region i at time t can be expressed as follows:

$${\rho }_{K_{it}}=\left[{\displaystyle \frac{K_{it}}{K_t}}\right]/\left[{\displaystyle \frac{s_{it}{\alpha }_{it}}{{\displaystyle {\sum }_i{s}_{it}{\alpha }_{it}}}}\right],{\rho }_{L_{it}}=\left[{\displaystyle \frac{L_{it}}{L_t}}\right]/\left[{\displaystyle \frac{s_{it}{\beta }_{it}}{{\displaystyle {\sum }_i{s}_{it}{\beta }_{it}}}}\right],{\rho }_{E_{it}}=\left[{\displaystyle \frac{E_{it}}{E_t}}\right]/\left[{\displaystyle \frac{s_{it}{\gamma }_{it}}{{\displaystyle {\sum }_i{s}_{it}{\gamma }_{it}}}}\right]$$

(2)

The distortion coefficient may have negative values. To facilitate comparison and interpretation based on Chen’s [34] research, the degree of factor misallocation represented by the distance between the reciprocal of the relative distortion coefficient and 1 serves as an index for measuring factor misallocation in grain production according to the following formula:

$${\tau }_{K_{it}}=\left|{\displaystyle \frac{1}{{\rho }_{K_{it}}}}-1\right|,{\tau }_{L_{it}}=\left|{\displaystyle \frac{1}{{\rho }_{L_{it}}}}-1\right|,{\tau }_{E_{it}}=\left|{\displaystyle \frac{1}{{\rho }_{E_{it}}}}-1\right|$$

(3)

Taking the capital element as example, ${\displaystyle \frac{K_{it}}{K_t}}$ indicates the actual proportion of capital used by region i at time t under factor misallocation compared to the capital input in the entire economy. $s_{it}$ represents the proportion of the total grain output value of region i to the total grain output value of the entire economy. ${\displaystyle \frac{s_{it}{\alpha }_{it}}{{\displaystyle {\sum }_i{s}_{it}{\alpha }_{it}}}}$ represents the weighted capital elasticity for region i at time t. For example, if ${\rho }_{Kit}>0$, this means that region i has relatively low capital input during period t, which leads to excessive investment in capital; conversely, if ${\rho }_{Kit}<0$, this means region i has higher than average capital input costs during period t, resulting in insufficient investment in capital. The value of ${\tau }_{K_{it}}$ remains positive throughout, and a larger value indicates a higher degree of capital misallocation for i at time t.

Accurately measuring agricultural output and factor inputs is a prerequisite for calculating the factor mismatch index, and the main variables selected in the calculation are shown in

Table 1. Index of grain production factors.

Variable	Symbol	Indicator	Unit
Agricultural total output	Y	grain production	10,000 tons
Capital input	K	capital stock of the grain industry	hundred million yuan
Labor input	L	the number of people employed in grain production	100,000 people
Land input	E	grain sown area	100,000 hectares

. Agricultural total output (Y) is represented by grain production, with a unit of 10,000 tons. This refers to the narrow definition of material capital stock, excluding human capital, land capital, etc. Capital input (K) is represented by the capital stock of the grain industry in various regions and cities, with a unit of hundred million yuan. Refer to Li et al. [35] for the formula for calculating the agricultural capital stock, $K_{it}=I_{it}/P_{it}+\left(1-{\delta }_t\right)K_{it-1}$, where K_it represents the current grain production capital stock of region i, K_it−1 represents the previous period’s grain production capital stock for region i, I_it represents the current fixed capital investment, P_it represents the price index of agricultural production materials; and ${\delta }_t=5.42\%$ represents the depreciation rate of capital. Labor input (L) is represented by the number of people employed in grain production, with a unit of 100,000 people. Land input (E) is represented by the grain sown area, with a unit of 100,000 hectares.

In order to avoid reliance on cross-sectional data that may cause certain indicators to exhibit abnormal fluctuations in empirical research, and in combination with the characteristics of grain production, a geographically and temporally weighted regression model with spatial lag terms and a space–time weighting function based on the Gaussian function method is established. This integrates temporal and spatial information, constructing a geographically weighted regression model containing explanatory variable spatial lag terms. The space–time geographically weighted regression model (GTWR) is as follows:

$$y_i={\beta }_0\left(u_i,v_i,t_i\right)+{\displaystyle \sum _{k=1}^p{\beta }_k\left(u_i,v_i,t_i\right)}{x}_{ik}+{\epsilon }_i$$

(4)

Among these terms, $(u_i,v_i,t_i)$ represents the three-dimensional spatiotemporal coordinates of the i-th sample point, which, respectively, represent the spatial position (longitude, latitude) and time. ${\beta }_0(u_i,v_i,t_i)$ is an intercept term and also a function of the spatiotemporal coordinates. ${\beta }_k(u_i,v_i,t_i)$ is the regression coefficient of the k-th independent variable at the i-th sample point, which is also a function of the spatiotemporal coordinates and reflects the spatial and temporal heterogeneity of the independent variable’s influence on the dependent variable. ${\epsilon }_i$ is a random error term for the i-th sample point, usually assumed to follow a normal distribution and be independent of the others.

2.3. The Calculation Model and Variable Selection for Grain Green Production Capacity

Assuming there are n decision-making units, denoted as DMU_i (j = 1, 2,…, n), each decision-making unit has m₁ inputs and m₂ outputs. Let x_ij (i = 1, 2,…, n; j = 1, 2,…, m₁) represent the j-th input of the i-th decision-making unit, and y_ij (i = 1, 2,…, n; j = 1, 2,…, m₂) represent the j-th output of the i-th decision-making unit. Let u = (u_m, u₂,…, u_u) and v = (v_m, v₂,…, v_u) denote weight vectors for inputs and outputs, respectively. The efficiency evaluation index of decision-making unit k is expressed in Formula (5):

$$e_k={\displaystyle \frac{u^T{X}_k}{v^T{Y}_k}},(k=1,2,\dots ,n)$$

(5)

The DEA–Malmquist index uses distance functions to calculate the changes in the input–output efficiency from period t to t + 1. Fare [36] decomposes the obtained total factor productivity index into the technical efficiency change index (EFFCH) and the technological progress index (TECHCH), where the former can be further decomposed into the pure technical efficiency change index (PECH) and the scale efficiency change index (SECH), as shown in Formula (6):

$$\begin{array}{c}TFPCH\left(x_{t+1},y_{t+1};x_t,y_t\right)=EFFCH(x_{t+1},y_{t+1};x_t,y_t)\times TECHCH(x_{t+1},y_{t+1};x_t,y_t)\\ =PECH\times SECH\times TECHCH\end{array}$$

(6)

This study focuses on 13 cities in Heilongjiang Province. Based on existing research [27], grain yield and carbon emissions are selected as the output indicators, while capital, labor, and land are selected as the input indicators. The index system for calculating the grain green total factor productivity growth index is constructed as shown in

Table 2. Index system of grain green total factor productivity growth index.

Variable	Symbol	Index	Unit
Grain output	Y	Total grain production	10,000 tons
Carbon emissions	C	Carbon emission coefficient × carbon sources from grains [37]	10,000 tons
Capital investment	K	Grain capital stock (detailed formula can be found in Section 2.2)	10,000 yuan
Labor input	L	Number of agricultural, forestry, animal husbandry, and fishery workers × (grain output value/total output value of agricultural, forestry, animal husbandry, and fishery)	10,000 people
Land input	E	Grain sown area	10,000 hm2

.

2.4. Econometric Models and Variable Selection for Empirical Analysis

Due to the independence and interaction of agricultural production factors, this article analyzes the influence of the misallocation of factors on the efficiency of green grain production from the perspective of both single-factor misallocation and interaction effects.

Considering that the misallocation of factors and the TFP of green grain production have spatial differentiation characteristics, this study intends to estimate a fixed-effects model, as follows:

$$A_{G}GTF{P}_{it}={\alpha }_1+{\beta }_{1}Misallocatio{n}_{it}+{\gamma }_1{X}_{it}+{\phi }_i+{\theta }_t+{\mu }_{it}$$

(7)

In the equation, i represents the city, t represents the year, X represents the control variables, φ_i represents the fixed effect of the city, θ_t represents the fixed effect of the year, and µ_it represents the random disturbance term.

$$A_{G}GTF{P}_{it}={\alpha }_1+{\beta }_{1}Misallocatio{n}_{it}+{\beta }_{2}Misallocatio{n}_{it}\times Z_{it}+{\gamma }_1{X}_{it}+{\phi }_i+{\theta }_t+{\mu }_{it}$$

(8)

Based on Equation (7), Equation (8) introduces the interaction term for the factor misallocation index and mechanism variables. If the coefficient of the interaction term, 2, is significantly greater than zero, this indicates that the enhancement of the mechanism variable can significantly counteract the hindrance to the growth of grain green total factor productivity caused by factor misallocation.

Based on Equation (7), Equations (9)–(14) introduce cross-terms for the core explanatory variables. This article examines the interaction of factor mismatch by introducing interaction terms for capital mismatch, labor mismatch, and land mismatch. The formula is as follows:

$$A_{G}GTF{P}_{it}={\alpha }_1+{\beta }_{1}Mis{K}_{it}+{\beta }_{2}Mis{K}_{it}\times Mis{L}_{it}+{\gamma }_1{X}_{it}+{\phi }_i+{\theta }_t+{\mu }_{it}$$

(9)

$$A_{G}GTF{P}_{it}={\alpha }_1+{\beta }_{1}Mis{L}_{it}+{\beta }_{2}Mis{K}_{it}\times Mis{L}_{it}+{\gamma }_1{X}_{it}+{\phi }_i+{\theta }_t+{\mu }_{it}$$

(10)

$$A_{G}GTF{P}_{it}={\alpha }_1+{\beta }_{1}Mis{K}_{it}+{\beta }_{2}Mis{K}_{it}\times Mis{E}_{it}+{\gamma }_1{X}_{it}+{\phi }_i+{\theta }_t+{\mu }_{it}$$

(11)

$$A_{G}GTF{P}_{it}={\alpha }_1+{\beta }_{1}Mis{E}_{it}+{\beta }_{2}Mis{K}_{it}\times Mis{E}_{it}+{\gamma }_1{X}_{it}+{\phi }_i+{\theta }_t+{\mu }_{it}$$

(12)

$$A_{G}GTF{P}_{it}={\alpha }_1+{\beta }_{1}Mis{L}_{it}+{\beta }_{2}Mis{L}_{it}\times Mis{E}_{it}+{\gamma }_1{X}_{it}+{\phi }_i+{\theta }_t+{\mu }_{it}$$

(13)

$$A_{G}GTF{P}_{it}={\alpha }_1+{\beta }_{1}Mis{E}_{it}+{\beta }_{2}Mis{L}_{it}\times Mis{E}_{it}+{\gamma }_1{X}_{it}+{\phi }_i+{\theta }_t+{\mu }_{it}$$

(14)

where i represents provinces, t represents years, X denotes control variables, φ_i denotes provincial fixed effects, θ_t represents year fixed effects, and µ_it stands for random disturbance terms. If the coefficient β₂ of the interaction term is significantly less than zero, this indicates that the interaction of factor misallocation exacerbates the negative effects caused by single-factor misallocation.

Dependent variable: Green total factor productivity in grain production (A_GGTFP).

Independent variables: Factor misallocation index (MisK, MisL, MisE).

Control variables: Based on the previous literature [38,39,40], this study includes other factors that may affect A_GGTFP as control variables. These include (1) agricultural fiscal expenditure level (Money), the ratio of agricultural and water affairs expenditure to the total fiscal expenditure in Heilongjiang Province; (2) agricultural machinery level (Machine), the total power of agricultural machinery; (3) the agricultural technology expenditure level (Technology); (4) the water and soil erosion control level (Gov), the ratio of the drained area to the irrigated area; (5) the per capita water resource level (Water), the ratio of road mileage to provincial area; (6) fertilizer application rate per unit output (Fertilizer), the ratio of fertilizer application volume to grain production.

Mechanism variables: According to the mechanism analysis, this study divides the control variables into two groups. Variables (1), (2), and (3) are considered mechanism variables affecting A_GGTFP through capital misallocation and labor misallocation, while variables (4), (5), and (6) are considered mechanism variables affecting A_GGTFP through land misallocation. Descriptive statistics of the control variables are shown in

Table 3. Descriptive statistics of main variables.

Variable Name	Control Variable Explanation	Mean	ST.	Min	Max
Money	Agricultural fiscal expenditure level	0.077	0.058	0.016	0.227
Machine	Total power of agricultural machinery	0.029	0.024	0.003	0.096
Technology	Level of agricultural technology expenditure	1.199	2.481	0.019	15.631
Gov	Level of water and soil erosion control	0.145	0.270	0.003	3.207
Water	Per capita water resource level	0.781	2.186	0.017	26.400
Fertilizer	Fertilizer application rate per unit output	0.083	0.124	0.002	0.654

.

3. Results

3.1. Identification of Spatial–Temporal Heterogeneity in Factor Misallocation of Grain Production in Heilongjiang Province

3.1.1. Descriptive Statistics of Factor Output Elasticity and the Misallocation Index

Based on the constructed model, the relevant data on grain production in various regions and cities in Heilongjiang Province were used to calculate the output elasticity and the misallocation index (

Table 4. Mean grain production factor output elasticity and the misallocation index.

Province	Factor Output Elasticity			Mean Factor Misallocation Index (2004—2022)
	Capital	Labor	Land	Capital	Labor	Land
Harbin	0.041	−0.965	4.653	0.923	0.866	0.387
Qiqihar	−0.898	−3.350	6.001	0.906	2.207	0.353
Jixi	−0.397	−0.424	4.237	3.898	0.542	0.241
Hegang	−0.407	−0.915	4.633	4.755	0.532	0.197
Shuangyashan	0.084	−0.492	3.906	1.587	0.613	0.181
Daqing	−0.220	0.443	2.617	2.347	4.142	0.160
Yichun	−1.215	−0.306	4.744	1.537	1.213	0.401
Jiamusi	−0.110	−0.616	4.161	1.921	0.361	0.144
Qitaihe	−0.210	−0.417	4.056	2.125	0.453	0.073
Mudanjiang	−0.499	−0.489	4.456	1.437	0.549	0.053
Heihe	0.227	1.955	3.692	2.964	6.937	0.653
Suihua	0.010	−0.782	4.664	1.714	0.328	0.374
Daxing’anling	−1.291	4.990	3.440	0.820	1.528	0.808

). The output elasticity for capital and labor is mostly negative, while the output elasticity for land is consistently positive and relatively large, ranging from 2.617 to 6.001. This indicates that most cities have excessive capital and labor investment, while land investment may be insufficient. The negative elasticity of capital output may be due to unreasonable investment directions, investment decision-making errors, improper capital allocation, and failure to synchronize capital investment with technological progress; the reason for the positive and significant elasticity of land output may be due to the abundant and high-quality land resources in Heilongjiang Province. With the promotion and application of modern agricultural technology, scientific planting management, reasonable fertilization, and irrigation measures can improve land use efficiency. However, there is also a risk of insufficient land input; the negative elasticity of labor output is derived from the assumption of constant returns to scale. Compared to capital and land, this may be due to the serious aging of the population, low skill levels, and problems with labor mobility and allocation in Heilongjiang Province. Compared to capital and land, labor does not contribute much to grain production in Heilongjiang Province.

Based on the average misallocation index of the factors from nearly 2004 to 2022 in each region and city, the misallocation index for capital and labor factors is higher than that for the land factor. There is a significant difference in the misallocation for labor, with 60% of cities having an index less than 1 and 40% of cities ranging from 1.528 to 6.937. Hegang, Jixi, and Heihe show obvious capital misallocation, while Heihe, Daqing, and Qiqihaer show noticeable labor misallocation. Daxing’anling and Heihe demonstrate relatively significant land misallocation. Mudanjiang and Qitaihe exhibit a minor degree of land misallocation below 0.1. Harbin performs relatively well in all indicators. These empirical findings validate the implementation of differentiated strategic positioning in grain production among different regions and cities in Heilongjiang Province.

3.1.2. Spatial–Temporal Analysis of Capital Misallocation

Using the centroid standard deviation ellipsoid method, the spatial distribution range, shape, and direction of capital misallocation in 13 cities in Heilongjiang Province were analyzed, as shown in Figure 1. The spatial and temporal distribution range of the capital mismatch in the prefecture-level cities remains relatively stable, showing a horizontal distribution from southeast to northwest, and the center of gravity of the ellipse continuously moves towards the northeast over time. From 2004 to 2013, the degree of capital misallocation in Heilongjiang Province worsened, but there was a trend of mitigation from 2014 to 2022. Capital misallocation in the southwest direction of the cities has been alleviated, indicating that Heilongjiang Province has corrected the degree of capital misallocation by investing more in high-standard farmland construction, upgrading agricultural modernization, and increasing agricultural machinery inputs.

3.1.3. Spatial–Temporal Analysis of Labor Misallocation

Using the centroid–standard deviation ellipsoid method, the spatial distribution range, shape, and direction of labor misallocation in 13 cities in Heilongjiang Province were analyzed, as shown in Figure 2. The spatial distribution range of labor misallocation in different cities in Heilongjiang Province is unstable, but it narrowed during the study period, which is directly related to the rural labor outflow in various cities of Heilongjiang Province.

3.1.4. Spatial–Temporal Analysis of Land Misallocation

Using the centroid–standard deviation ellipsoid method, the spatial distribution range, shape, and direction of land misallocation in 13 cities in Heilongjiang Province were analyzed, as shown in Figure 3. The spatial distribution range of land misallocation in Heilongjiang Province is relatively stable, indicating significant achievements in ensuring the quantity and quality of arable land.

3.2. Descriptive Statistics and Trend Analysis in Grain Green Total Factor Productivity in Heilongjiang Province

From a longitudinal perspective, the growth rate of grain green total factor productivity, the technological efficiency variation index, and the technological progress index in Heilongjiang Province from 2004 to 2022 fluctuates around 1, as shown in

Table 5. Growth index of total factor productivity of grain green production in Heilongjiang Province from 2004 to 2022.

Year	Effch	Techch	Pech	Sech	Tfpch
2004–2005	1.460	0.705	1.252	1.166	1.030
2005–2006	1.058	1.040	1.006	1.051	1.100
2006–2007	0.881	1.050	0.951	0.926	0.925
2007–2008	1.045	1.237	0.998	1.046	1.292
2008–2009	0.918	0.921	1.002	0.916	0.845
2009–2010	1.066	1.122	1.022	1.043	1.196
2010–2011	1.062	1.078	1.020	1.041	1.145
2011–2012	1.027	1.078	1.026	1.001	1.108
2012–2013	0.960	0.817	1.006	0.955	0.784
2013–2014	1.044	0.987	1.000	1.044	1.030
2014–2015	1.022	0.962	0.999	1.023	0.983
2015–2016	0.989	0.934	1.000	0.989	0.925
2016–2017	1.054	0.874	1.041	1.012	0.921
2017–2018	1.042	0.969	1.011	1.031	1.010
2018–2019	0.920	1.300	0.989	0.930	1.196
2019–2020	1.045	0.928	1.045	1.000	0.969
2020–2021	0.980	1.059	0.988	0.992	1.038
2021–2022	1.003	0.964	1.000	1.003	0.967

. The growth rate of total factor productivity shows a slow downward trend. The direction of change in the growth index and the technological progress index is generally similar and is roughly opposite to the direction of change in the technological efficiency variation index. One possible reason for this is that there is a time lag in the impact of technological efficiency variation on total factor productivity. Another reason is that over the past 19 years, the technological transformation of grain production in China has gradually occurred, with the growth of total factor productivity relying more on technological progress in grain production. This also reflects the emerging economies of scale effect of land in Heilongjiang Province.

From a horizontal perspective, as shown in Figure 4 and

Table 6. Growth index of grain green total factor productivity in 13 cities in Heilongjiang Province from 2004 to 2022.

Num.	Firm	Effch	Techch	Pech	Sech	Tfpch
1	Harbin City	1.017	0.984	1.000	1.017	1.001
2	Qiqihar City	1.051	0.987	1.041	1.010	1.038
3	Mudanjiang City	1.030	0.993	1.025	1.005	1.023
4	Jiamusi City	1.000	1.012	1.000	1.000	1.012
5	Jixi City	1.047	1.017	1.047	1.000	1.065
6	Hegang City	1.042	0.990	1.030	1.011	1.031
7	Shuangyashan City	1.019	0.986	1.000	1.019	1.005
8	Qitaihe City	1.051	0.995	1.028	1.023	1.045
9	Heihe City	1.033	0.995	1.000	1.033	1.028
10	Yichun City	1.030	0.985	1.032	0.999	1.015
11	Daqing City	1.063	1.007	1.051	1.011	1.071
12	Suihua City	0.999	0.979	1.000	0.999	0.978
13	Daxing’anling	0.981	0.988	1.000	0.981	0.969

, the A_GGTFP in most cities in Heilongjiang Province is greater than 1 from 2004 to 2022. The kernel density peak of the technological progress efficiency index is closest to 1, and the amplitudes of the total factor productivity and the technological efficiency variation index are similar, indicating that the technological efficiency variation index has a greater impact on total factor productivity. The technological progress index in Jiamusi, Jixi, and Daqing is greater than 1, while for the rest of the cities, it is less than 1, indicating that the achievements of technological transformation in grain production in Heilongjiang Province have been relatively mediocre over the past 19 years. The technological efficiency variation index in Suihua and Daxing’anling is less than 1, while the rest of the cities are greater than 1, indicating that Heilongjiang Province has paid great attention to the coordination of resource elements in the past 19 years, using limited resources to maximize the production potential.

This article sets the total factor productivity in the reference year of 2004 to 1 and calculates the A_GGTFP for the other years according to the base year, as shown in Figure 5. Most provinces experienced a peak in A_GGTFP between 2010 and 2015. After this peak, the TFP of grain in the Suihua and Daxing’anling areas showed a continuous downward trend, while the A_GGTFP in the Harbin, Daqing, and Yichun areas remained relatively stable, gradually returning to 1. The remaining cities exhibited a more obvious fluctuating upward trend.

3.3. Impact of Single-Factor Misallocation on Grain Green Production Capacity in Heilongjiang Province

3.3.1. Impact of Capital Misallocation on Grain Green Production Capacity

(1)

Baseline Regression Results

This study conducted Pearson’s correlation tests before regression to preliminarily determine the correlation between the research variables. Overall, there is significant correlation at the 5% level between the explanatory variables and the dependent variable in the model, which preliminarily demonstrates the effectiveness of the research model. The absolute values of the correlation coefficients between the variables do not exceed 0.6, preliminarily ruling out the issue of multicollinearity among the variables. After the VIF test, the VIF values of each variable do not exceed 1.79, excluding the problem of multicollinearity between the variables. It can be observed that the factor misallocation in grain production in Heilongjiang Province significantly negatively affects the A_GGTFP.

The baseline regression results are shown in

Table 7. Empirical results on the impact of capital misallocation on the grain green total factor productivity in Heilongjiang Province.

	OLS	RE	FE	FE
MisK	−0.004 (−0.35)	−0.015 * (−1.77)	−0.015 * (−1.79)	−0.020 ** (−2.41)
money	−1.505 * (−1.73)	1.823 (1.21)	6.637 *** (3.24)	5.194 *** (3.16)
machine	1.290 (0.62)	2.064 (0.94)	1.840 (0.83)	14.150 *** (5.08)
technology	−0.011 (−0.64)	0.045 ** (2.19)	0.073 *** (3.34)	0.041 ** (2.19)
gov	−0.009 (−0.08)	−0.083 (−0.93)	−0.089 (−1.01)	−0.146 * (−1.74)
water	0.001 (0.08)	−0.007 (−0.60)	−0.003 (−0.28)	0.012 (1.24)
fertilizer	−2.384 *** (−7.43)	−1.910 *** (−3.81)	−1.950 *** (−3.57)	−1.756 *** (−3.81)
constant	1.681 *** (19.96)	1.274 *** (6.99)	0.877 *** (4.90)	0.876 *** (5.57)
observations	247	247	247	247
R-squared	0.235	0.165	0.185	0.528
area FE			YES	YES
year FE				YES

Note: *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively; values in parentheses are t-statistics; the same applies below.

, with columns (1)–(4) representing the results of ordinary least squares regression, random effects regression, fixed effects regression, and double fixed effects regression, respectively. From column (4), it can be seen that capital misallocation in grain production has a significant negative impact on A_GGTFP at the 5% level. In terms of the control variables, the level of agricultural fiscal expenditure, the total power of agricultural machinery, and the level of agricultural technology expenditure have a significant positive promoting effect on A_GGTFP, indicating that increasing agricultural investment, adopting mechanical production, and promoting the application of technological innovation can promote the efficiency growth of green grain production in various regions. Additionally, the level of water and soil erosion control and the fertilizer application rate per unit output have a significant negative impact on the efficiency of green grain production, while the per capita water resources do not have a significant impact on A_GGTFP.

(2)

The Robustness Test

Following the research approach of Zhuang et al. [41], this study conducted a regression analysis using the lagged term of capital misallocation as an instrumental variable, and the results are shown in

Table 8. Empirical results of robustness test and mechanism test.

	GMM-SYS	IV	EC	TC	AGGTFP	AGGTFP	AGGTFP
MisK	−0.030 *	−0.032 **	−0.018 **	−0.015 ***	−0.028 *	−0.021	−0.032 ***
	(−2.07)	(−2.23)	(−2.24)	(−2.87)	(−1.87)	(−1.49)	(−2.92)
L.AGGTFP	−0.065
	(−0.42)
MisK × Money					0.155
					(0.65)
MisK × Machine						0.051
						(0.16)
MisK × Technology							0.015 **
							(1.97)
Constant	0.890	−0.730	0.866 ***	0.921 ***	0.872 ***	0.874 ***	0.828 ***
	(0.73)	(−0.73)	(6.32)	(5.41)	(5.54)	(5.53)	(5.20)
Observations	234	234	247	247	247	247	247
R-squared		0.371	0.514	0.497	0.529	0.528	0.535
Control Variables	YES	YES	YES	YES	YES	YES	YES
Area FE	YES	YES	YES	YES	YES	YES	YES
Year FE	YES	YES	YES	YES	YES	YES	YES
AR(2)	0.402
Sargan	0.230	0.654
First-Stage F		1408.79 ***
5% Wald Test		55.67 > 16.38

Note: *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively; values in parentheses are t-statistics; the same applies below.

, column (1).

The results show that the Sargan Test for the model is not significant, rejecting the null hypothesis of the Sargan Test and proving the effectiveness of the instrumental variable selection. Furthermore, the result for AR(2) is also not significant, indicating the absence of second-order autocorrelation in the residuals, demonstrating the reliability and accuracy of the model specification. The regression coefficient for capital misallocation is −0.030, and it is statistically significant at the 10% level.

To further examine the reasonableness of the above results, this study used the “Bartik instrument” method, where the lagged term of the endogenous variable was employed as an instrumental variable to address endogeneity issues. After introducing the “Bartik instrument” instrumental variable, the regression coefficient for capital misallocation is −0.032, and it is statistically significant at the 5% level.

Substituting the dependent variable, the grain green total factor productivity (A_GGTFP), with measures of technical efficiency change (EC) and technological progress (TC) in a similar context, the regression results in columns (3) and (4) indicate that the regression coefficients for capital misallocation are −0.018 and −0.015, and they are each statistically significant at the 5% and 1% levels, respectively, indicating robust results.

(3)

The Mechanism Test

Based on Equation (8), the regression results for capital misallocation and its interaction terms with the level of agricultural fiscal expenditure, the total power of agricultural machinery, and the cross-term with agricultural technology expenditure for A_GGTFP are presented in Table 8, columns (5)–(7). It can be observed that only the estimation coefficient for the interaction term between capital misallocation and agricultural technology expenditure is significantly positive, indicating that increasing agricultural technology expenditure can effectively mitigate the adverse impact of capital misallocation on the growth of A_GGTFP.

3.3.2. Impact of Labor Misallocation on Grain Green Production Capacity

(1)

Baseline Regression Results

From

Table 9. Empirical results on the impact of labor misallocation on the grain green total factor productivity in Heilongjiang Province.

	OLS	RE	FE	FE
MisL	−0.052 *** (−6.18)	−0.045 *** (−6.17)	−0.040 *** (−5.47)	−0.041 *** (−6.48)
money	−1.706 ** (−2.18)	−0.019 (−0.01)	3.853 * (1.93)	2.231 (1.42)
machine	0.767 (0.41)	1.209 (0.59)	1.081 (0.52)	−11.774 *** (−4.56)
technology	−0.003 (−0.18)	0.043 ** (2.30)	0.066 *** (3.23)	0.028 (1.61)
gov	0.012 (0.11)	−0.069 (−0.83)	−0.077 (−0.93)	−0.148 * (−1.92)
water	0.003 (−0.22)	−0.008 (−0.76)	−0.005 (−0.50)	0.008 (0.86)
fertilizer	−2.313 *** (−7.94)	−2.039 *** (−4.48)	−2.062 *** (−4.08)	−1.794 *** (−4.36)
constant	1.603 *** (22.91)	1.414 *** (8.87)	1.100 *** (6.48)	1.049 *** (7.32)
observations	247	247	247	247
R-squared	0.345	0.260	0.274	0.599
area FE			YES	YES
year FE				YES

Note: *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively; values in parentheses are t-statistics; the same applies below.

, it can be observed that labor misallocation has a significant negative impact on A_GGTFP at the 1% level. Comparing the regression coefficients, it is found that labor misallocation < capital misallocation, indicating that labor misallocation has a stronger inhibitory effect on the A_GGTFP of Heilongjiang Province.

(2)

The Robustness Test

From

Table 10. Empirical results of robustness test and mechanism test.

	GMM-SYS	IV	EC	TC	AGGTFP	AGGTFP	AGGTFP
MisL	−0.057 *	−0.053 ***	−0.041 ***	−0.045 ***	−0.030	−0.012	−0.014
	(−2.03)	(−9.04)	(−6.35)	(−6.89)	(−1.37)	(−0.78)	(−1.23)
MisL × Money					0.101
					(0.55)
MisL × Machine						0.830 **
						(2.15)
MisL × Technology							0.017 ***
							(2.75)
Constant	3.226	0.202	1.181 ***	1.074 ***	1.083 ***	1.182 ***	1.100 ***
	(1.73)	(0.34)	(6.96)	(7.99)	(6.91)	(7.63)	(7.74)
Observations	234	234	247	247	247	247	247
R-squared		0.864	0.589	0.565	0.600	0.608	0.614
Control variables	YES	YES	YES	YES	YES	YES	YES
Area FE	YES	YES	YES	YES	YES	YES	YES
Year FE	YES	YES	YES	YES	YES	YES	YES
AR(2)	0.589
Sargan	0.288	0.356
First-stage F		176.492 ***
5% Wald Test		760.378 > 16.38

Note: *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively; values in pa-rentheses are t-statistics; the same applies below.

, it can be seen that the Sargan Test result for the model in column (1) is not significant, indicating the effectiveness of the instrumental variable. Additionally, the result for AR(2) is also not significant, demonstrating the absence of second-order autocorrelation in the residuals, suggesting that the model specification is reliable and accurate. The regression coefficient for labor misallocation is −0.057, and it is statistically significant at the 10% level. In Model 2, both the first-stage F-value and the 5% Wald Test results are statistically significant, confirming a strong correlation between the instrumental variable and the endogenous variable. The Sargan Test results are not significant in the model, and the regression coefficient for labor misallocation is −0.053, being statistically significant at the 1% level. Substituting the dependent variable yields the regression results in columns (3) and (4), where the regression coefficients for labor misallocation are −0.041 and −0.045, respectively, both statistically significant at the 1% level, indicating robust results.

(3)

The Mechanism Test

Based on columns (5)–(7) in Table 10, the regression results of labor misallocation and its interactions with the levels of agricultural fiscal expenditure, the total power of agricultural machinery, and the cross-term with agricultural technology expenditure for A_GGTFP are presented. It can be observed that the estimated coefficient of the interaction term between labor misallocation and the total power of agricultural machinery is positive at the 5% significance level, while the estimated coefficient of the interaction term with agricultural technology expenditure is positive at the 1% significance level, indicating that increasing agricultural technology expenditure can effectively mitigate the adverse impact of labor misallocation on the growth of A_GGTFP. Furthermore, the estimated coefficient for the interaction term between labor misallocation and the total power of agricultural machinery is 0.830, which is greater than 0.017, suggesting that compared to agricultural technology expenditure, the increase in the total power of agricultural machinery has a larger effect.

3.3.3. Impact of Land Misallocation on Grain Green Production Capacity

(1)

Baseline Regression Results

The baseline regression results are presented in

Table 11. Empirical results on the impact of land misallocation on the grain green total factor productivity in Heilongjiang Province.

	OLS	RE	FE	FE
MisE	−0.277 * (−1.75)	−0.279 (−1.45)	−0.365 * (−1.80)	−0.367 ** (−2.21)
money	−2.038 ** (−2.25)	1.053 (0.72)	6.444 *** (3.14)	4.948 *** (3.00)
machine	1.628 (0.80)	3.203 (1.42)	3.290 (1.44)	−12.250 *** (−4.27)
technology	−0.011 (−0.65)	0.036 * (1.79)	0.067 *** (3.09)	0.033 * (1.78)
gov	−0.006 (−0.05)	−0.094 (−1.05)	−0.101 (−1.15)	−0.159 * (−1.89)
water	0.002 (0.13)	−0.008 (−0.66)	−0.003 (−0.28)	0.012 (1.20)
fertilizer	−2.740 *** (−7.21)	−2.143 *** (−4.35)	−2.102 *** (−3.92)	−2.005 *** (−4.50)
constant	1.647 *** (21.89)	1.277 *** (7.07)	0.790 *** (4.11)	0.782 *** (4.55)
observations	247	247	247	247
R-squared	0.244	0.158	0.185	0.526
area FE			YES	YES
year FE				YES

Note: *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively; values in parentheses are t-statistics; the same applies below.

, where columns (1)–(4) depict the ordinary least squares regression, random effects regression, fixed effects regression, and two-way fixed effects regression, respectively. As per the previous analysis, each variable is significantly influenced by time and space. Therefore, controlling for time and location renders the regression results more reliable. It can be observed from column (4) that land misallocation has a significantly negative impact on A_GGTFP at the 5% level. Comparing the regression coefficients, it is found that land misallocation << labor misallocation, indicating that land misallocation is the primary factor inhibiting the A_GGTFP of Heilongjiang Province.

(2)

The Robustness Test

Following the previous approach, based on

Table 12. Empirical results of robustness test and mechanism test.

	GMM-SYS	IV	EC	TC	AGGTFP	AGGTFP	AGGTFP
MisE	−0.555 *	−0.704 *	−0.344 ***	−0.315 ***	−0.605 ***	−0.378 **	−0.197
	(−1.97)	(−1.84)	(−2.95)	(−3.77)	(−3.36)	(−2.22)	(−0.99)
MisE × Gov					1.107 ***
					(3.09)
MisE × Water						0.042
						(0.32)
MisE × Fertilizer							1.838
							(1.55)
Constant	1.260 *	−0.946	0.681 ***	0.741 ***	0.803 ***	0.789 ***	0.868 ***
	(2.10)	(−0.97)	(5.16)	(4.74)	(4.77)	(4.55)	(4.82)
Observations	234	234	247	247	247	247	247
R-Squared		0.880	0.535	0.558	0.548	0.526	0.531
Control Variables	YES	YES	YES	YES	YES	YES	YES
Area FE	YES	YES	YES	YES	YES	YES	YES
Year FE	YES	YES	YES	YES	YES	YES	YES
AR(2)	0.315
Sargan	0.924	0.372
First-Stage F		6.733 **
5% Wald Test		36.659 > 16.38

Note: *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively; values in parentheses are t-statistics; the same applies below.

, it can be observed that the Sargan Test result for the model in column (1) is not significant, indicating the effectiveness of the instrumental variable. Additionally, the result for AR(2) is also not significant, demonstrating the absence of second-order autocorrelation in the residuals, thus confirming the reliability and accuracy of the model specification. The regression coefficient for labor misallocation is −0.555, and it is statistically significant at the 10% level. In Model 2, both the first-stage F-value and the 5% Wald Test results are statistically significant, confirming a strong correlation between the instrumental variable and the endogenous variable. The Sargan Test results are not significant in the model, and the regression coefficient for labor misallocation is −0.704, being statistically significant at the 10% level. Substituting the dependent variable yields the regression results in columns (3) and (4), where the regression coefficients for labor misallocation are −0.344 and −0.315, respectively, both statistically significant at the 1% level, indicating robust results.

(3)

The Mechanism Test

Columns (5)–(7) in Table 12 report the regression results of land misallocation and its interactions with the levels of soil erosion control, per capita water resources, and the cross-term with fertilizer application per unit output for A_GGTFP. It can be seen that only the estimated coefficient of the interaction term between land misallocation and the level of soil erosion control is significantly positive, indicating that strengthening soil erosion control can effectively mitigate the adverse impact of land misallocation on the growth of A_GGTFP.

3.4. The Impact of Interactions of Factor Misallocations on Grain Green Production Capacity in Heilongjiang Province

(1)

Baseline Regression Results

Table 13. Empirical results on the impact of factor misallocation interaction on Heilongjiang Province’s grain green total factor productivity.

	AGGTFP	AGGTFP	AGGTFP	AGGTFP	AGGTFP	AGGTFP
MisK	−0.067 ***	−0.039 ***
	(−8.07)	(−4.02)
MisL			−0.023 **	−0.003
			(−2.60)	(0.16)
MisE					−0.413 **	−0.236
					(−2.05)	(1.56)
MisK × MisL	−0.018 ***		−0.012 ***
	(−6.07)		(−2.78)
MisK × MisE		−0.028			0.008
		(−1.27)			(0.40)
MisL × MisE				−0.074 ***		−0.759 ***
				(−2.69)		(−6.89)
Constant	0.982 ***	1.170 ***	1.041 ***	1.066 ***	0.780 ***	0.957 ***
	(7.09)	(8.17)	(7.39)	(7.55)	(4.35)	(6.11)
Observations	247	247	247	247	247	247
R-squared	0.603	0.644	0.614	0.614	0.526	0.618
Control variables	YES	YES	YES	YES	YES	YES
Area FE	YES	YES	YES	YES	YES	YES
Year FE	YES	YES	YES	YES	YES	YES

Note: **, and *** indicate significance at the 5%, and 1% levels, respectively; values in parentheses are t-statistics; the same applies below.

reports the impact of the interaction between capital, labor, and land misallocation on Heilongjiang Province’s A_GGTFP. It shows that the estimated coefficients of the interaction terms for capital misallocation and labor misallocation are −0.018 and −0.012, respectively, both significant at the 1% confidence level. Similarly, the interaction coefficients for labor misallocation and land misallocation are −0.074 and −0.759, respectively, also significant at the 1% confidence level. However, the interaction term coefficient between capital misallocation and land misallocation is not significant. This suggests that the interactions between capital misallocation and labor misallocation, as well as between labor misallocation and land misallocation, strengthen the inhibitory effects of misallocation on the A_GGTFP. One possible reason is that labor plays the most important role in the process of grain production in Heilongjiang Province, and the degree of labor mismatch varies greatly among different cities. Compared with the other two factors of mismatch, the situation is more complex and severe. The mobility of labor is closely related to China’s promotion of urbanization. In November 2012, the 18th National Congress of the Communist Party of China officially proposed the concept of “new urbanization”. In December 2014, the National Development and Reform Commission and 11 other departments jointly issued the “Notice on Carrying out the Comprehensive Pilot Work of National New Urbanization”. Around 2013, there was a large scale of labor mobility within the province. However, in the third batch of national comprehensive pilot areas for new urbanization in 2016, Heihe City showed significant regional differences due to policy delays. Second, capital misallocation may limit investment in technological innovation, while labor misallocation may reduce the supply of highly skilled labor capable of driving technological innovation. Technological innovation is crucial for enhancing A_GGTFP; thus, exacerbating this interaction further suppresses green production growth. Third, land misallocation may lead to the underutilization of high-quality land resources or the overexploitation of inefficient land. Meanwhile, labor misallocation may result in insufficient labor input for some land or an excessive concentration of labor on inefficient land. This interaction reduces the land utilization efficiency, thereby affecting A_GGTFP. Fourth, labor and land misallocation may also exacerbate ecological environmental issues. For instance, excessive use of fertilizers and pesticides due to labor shortages can lead to soil and water pollution. Moreover, improper land use practices may disrupt ecological balance, further hindering green production growth in grain.

(2)

The Robustness Test

A robustness Test for models (9)–(14) was conducted in this study using the method of replacing the explained variables. The results obtained by substituting technical efficiency change (EC) for green total factor productivity are shown in

Table 14. Empirical results of robustness test.

	EC	EC	EC	EC	EC	EC
MisK	−0.061 **	−0.045 **
	(−3.87)	(−4.21)
MisL			−0.028	−0.003
			(0.22)	(−0.46)
MisE					−0.521 ***	−0.673
					(−8.22)	(−0.59)
MisK × MisL	−0.018 ***		−0.023 **
	(−6.56)		(−3.24)
MisK × MisK		−0.017			−0.018
		(−0.87)			(−1.12)
MisE × MisL				−0.071 ***		−0.074 ***
				(−6.63)		(−7.37)
Constant	1.018 ***	0.992 ***	1.112 ***	1.439 ***	1.106 ***	0.979 ***
	(6.67)	(7.02)	(5.36)	(6.02)	(7.25)	(7.11)
Observations	247	247	247	247	247	247
R-squared	0.591	0.556	0.624	0.598	0.602	0.634
Control variables	YES	YES	YES	YES	YES	YES
Area FE	YES	YES	YES	YES	YES	YES
Year FE	YES	YES	YES	YES	YES	YES

Note: **, and *** indicate significance at the 5%, and 1% levels, respectively; values in parentheses are t-statistics; the same applies below.

. The obtained results are generally consistent with the baseline regression results, indicating a relatively stable model.

4. Discussion

Firstly, the output elasticity of capital and labor in various cities in Heilongjiang Province is mostly negative, while the output elasticity of land is positive and relatively large; the mismatch index of capital and labor factors in various cities is greater than that of land factors, and the regional differences in labor factor mismatch are significant. This, to some extent, confirms Lei’s [42] viewpoint, and this article supplements the mismatch index with the regional characteristics of Heilongjiang. From 2004 to 2022, the total factor productivity growth index, the technical efficiency change index, and the technological progress index for grain in Heilongjiang Province fluctuated around 1, and most cities maintained a positive growth trend in grain green total factor productivity. This, to some extent, confirms Yu’s [43] viewpoint.

Secondly, the inhibitory effects of land mismatch, labor mismatch, and capital mismatch on green grain production capacity become stronger in sequence, which is consistent with Lei’s [44] research conclusion.

Thirdly, increasing agricultural technology expenditure can effectively suppress the adverse effects of capital mismatch on green grain production capacity, strengthening the overall power of agricultural machinery can effectively suppress the adverse effects of labor mismatch on green grain production capacity, and strengthening soil erosion control can effectively suppress the adverse effects of land mismatch on green grain production capacity. This is more consistent with the views of Yang [19] and Qin [45]. However, Zhang’s [46] research found that the coupling and coordinated development trend between the benefits of regional soil erosion control and the level of ecological agriculture development is slow. Strengthening the capacity of soil erosion control to correct land mismatch may be the role of black soil protection policies in the Heilongjiang region.

Fourthly, the interaction between capital mismatch and labor mismatch, as well as labor and land mismatch, will strengthen the inhibitory effect of mismatch on green grain production capacity. Unlike the existing research [44,47,48], this article provides a more systematic and comprehensive analysis of the negative impacts of factor mismatch interactions, providing empirical evidence for proposing more targeted and practical measures.

5. Conclusions

Factor mismatch is a prominent issue in agricultural production capacity, and many studies have focused on the impact of industrial factor mismatch on productivity, usually targeting the national market. This effective method can provide useful and targeted information about industrial provinces. However, we demonstrate that a more suitable approach to agriculture is possible and can yield interesting results.

The advantages of our method include the following: the research area is more focused, based on panel data from 2004 to 2022, combined with the actual situation of the endowment structure of grain production factors in Heilongjiang Province, it has sufficient representativeness and typicality, and it is a key area for grain production problems; using the GTWR method for index calculation has significant advantages compared to other methods; not only did we empirically explore the impact of three mismatched factors on green grain production capacity but we also studied the effects of their interactions; finally, we provide countermeasures and suggestions for optimizing the allocation of grain production factors and improving the green production capacity in major grain-producing provinces.

Based on the above, we propose some countermeasures and suggestions.

Firstly, we suggest guiding the flow of funds towards improving the quality of the labor force. The government can establish a dedicated funding pool to support labor quality improvement projects, such as education and training, skill enhancement courses, etc. These funds can be allocated and managed through fiscal budgets or special funds. The government can also provide tax incentives to encourage businesses and individuals to invest in the field of improving labor quality: for example, providing tax reductions or credits to enterprises participating in vocational training and deducting pretax expenses for individuals participating in vocational training. Financial institutions can develop financial products aimed at improving labor quality, such as education loans, skill enhancement loans, etc. They can also expand their credit scale in the field of labor quality improvement and provide more financial support for related projects. At the same time, by lowering loan interest rates and guarantee requirements, the financing threshold for labor is lowered.

Secondly, we emphasize the land use concept of “human–land symbiosis”. Ecological protection of land is an important guarantee for improving the grain green total factor productivity. Strict land protection policies should be implemented, ecological protection areas should be designated, and activities that damage the ecological environment should be prohibited within the protection areas. At the same time, we suggest promoting green production methods such as ecological agriculture and organic agriculture to reduce pollution and damage to land. For damaged land, efforts should be made to increase ecological restoration, using various methods such as biological restoration and physical restoration to restore the ecological functions of the land. In addition, implementing a land fallow rotation system allows the land to receive sufficient rest and restoration and improves the sustainable utilization capacity of the land.

Thirdly, we suggest improving the policy support system and developing and improving fiscal, tax, and financial policies and measures for grain production, providing a stable policy environment for the grain industry: for example, increasing financial subsidies, providing certain financial subsidies to eligible grain producers to reduce production costs and improve production enthusiasm; implementing preferential tax policies, implementing tax reductions and exemption policies for enterprises related to grain production, reducing their burden, and encouraging them to increase investment; and establishing a policy implementation supervision mechanism, establishing a specialized supervision agency responsible for conducting regular inspections and evaluations of policy implementations to ensure the effective implementation of policies.

Fourthly, we suggest enhancing international cooperation and exchange, actively engaging in international cooperation in food production and trade, introducing advanced agricultural production technology and management experience from abroad, and enhancing the international competitiveness of Heilongjiang Province’s grain industry: for example, expanding international grain markets by strengthening connections with foreign grain markets, extending grain exports, and actively introducing high-quality grain varieties and advanced technology from overseas; hosting international agricultural exchange and cooperation events by regularly organizing international agricultural expos, seminars, and other activities to provide a platform for domestic and foreign agricultural enterprises and research institutions to engage in collaboration; strengthening alignment with international agricultural policies by enhancing coordination and communication with foreign agricultural policies; and learning from advanced agricultural management experiences and practices from abroad to promote the internationalization of Heilongjiang Province’s grain industry.