Farmland Scale and Technical Efficiency in Chinese Agriculture: A Land Transfer Cost Perspective

Abstract

This study investigates the relationship between farmland scale and technical efficiency. Using a household-level dataset from 10 provinces in China, we employed a flexible Stochastic Frontier Analysis (SFA) model to simultaneously estimate technical efficiency and evaluate its relationship with farmland scale. The results show that the average technical efficiency scores for the full sample, wheat, rice, and maize are 0.677, 0.708, 0.733, and 0.669, respectively, indicating substantial potential for improving China’s agricultural production efficiency. Furthermore, an inverted U-shaped relationship exists between farmland scale and technical efficiency; technical efficiency initially rises and subsequently declines as farmland scale increases. Additional analysis reveals that this inverted U-shaped relationship is moderated by the marginal cost of land transfer. Specifically, a lower marginal cost of land transfer corresponds to a larger optimal farmland scale. The marginal cost of land transfer was captured by proxy variables, including the relief degree of land surface, the slope degree of land surface, and the development level of the village-level land rental market. We conclude that flatter terrain and a better-developed land rental market lead to a larger optimal farmland scale for rural households.

1. Introduction

Since the reform and opening-up, China’s agricultural productivity has increased significantly [1,2,3]. Cereal yield rose from 4659 kg/ha in 1995 to 6272 kg/ha in 2019. Per capita grain output has exceeded the internationally recognized security line of 400 kg for 13 consecutive years. Concurrently, the agricultural labor force has continuously migrated to cities, driving the urbanization rate from 17.9% in 1978 to 60.6% in 2019. This spatial population restructuring and labor transfer are deeply shaped by national macro-policies, including the hukou system reform, regional development strategies, and new urbanization plans [4]. As rural labor has massively shifted to non-agricultural sectors, farmers’ land-use behaviors have changed. The growing prevalence of off-farm employment has significantly increased farmers’ willingness to transfer (lease out) their land [5]. To address the risk of land abandonment caused by labor outflow and to optimize resource allocation, the Chinese government has introduced macro-policies to promote rural land transfer. A notable example is the comprehensive implementation of the “Three Rights Separation” system, which eliminates transfer barriers at the property rights level [6]. Driven by institutional reforms and labor transfer, China’s land transfer rate rose rapidly from 12.0% in 2009 to 37.0% in 2017 (National Bureau of Statistics of China). However, following this rapid expansion, the pace of land transfer has recently stagnated. Recent studies confirm that the transfer rate has fallen back and stabilized at around 36%, indicating a significant slowdown in the expansion of farmland scale [7,8].

The plateau in land transfer has sparked ongoing academic debates regarding the driving forces and actual effects of farmland scale expansion. One central controversy is whether farmland scale expansion inevitably improves production efficiency [9,10]. No consensus has been reached on this issue due to two main reasons. First, factor endowments and natural conditions vary significantly across countries, leading to different cultivated land characteristics in research samples. Second, the indicators used to measure production efficiency vary widely. These indicators include yield [10], labor productivity [11], technical efficiency [12], and total factor productivity [13]. Existing literature provides a rich foundation for understanding agricultural production characteristics. However, most studies focus solely on the direct impact of farmland scale on production efficiency. Few studies incorporate the marginal cost of land transfer into their analytical frameworks to explore its dynamic constraints on the optimal farmland scale.

In China’s agricultural practice, land fragmentation [14] and underdeveloped land rental markets [15,16] are the primary constraints driving up land transfer costs. On the one hand, due to the egalitarian land distribution system in the early stages of reform, farmers’ cultivated land exhibits persistent fragmentation, which hinders spatial consolidation. On the other hand, the current land rental market remains highly informal. Transactions frequently lack written contracts (67.4%) or definite lease terms (65.2%), relying heavily on acquaintance networks, which results in a lack of formal institutional guarantees for these transfers (China Rural Revitalization Survey, 2020). This physical fragmentation and institutional market friction jointly inflate the transaction costs of land transfer. When farmers attempt to expand their operations, the increasing number of rented plots escalates the difficulties in information searching, negotiation, and contract enforcement, which manifests as increasing marginal transaction costs for land transfer. According to microeconomic production theory, farmers will stop expanding when the marginal cost equals marginal revenue, restricting the spontaneous expansion of farmland at the micro level.

Against this backdrop, this study aims to explore the intrinsic relationship between farmland scale and technical efficiency under the practical constraints of land fragmentation and an underdeveloped land rental market. Specifically, this paper empirically tests two core hypotheses: (1) whether an inverted U-shaped relationship exists between farmland scale and technical efficiency, and thus the existence of a theoretical optimal scale maximizing efficiency; and (2) whether the marginal cost of land transfer dynamically moderates and significantly shifts this optimal turning point.

The contributions of this study are threefold. First, theoretically, we incorporate the physical characteristics of land fragmentation and the market frictions of informal land rental into a transaction cost framework. By analyzing the objective constraints of an increasing marginal cost on farmland scale expansion, this study provides a micro-level explanation for the current slowdown in the land transfer process. Second, empirically, we employ a Stochastic Frontier Analysis (SFA) model. By introducing a quadratic term for farmland scale into the technical inefficiency equation, we calculate the optimal scale that maximizes the technical efficiency of the sampled farmers. Furthermore, using a constrained interaction model and grouped regressions, we examine the quantitative shifts in this optimal turning point under different natural endowments and market development levels. Third, in terms of measurement, using micro-level household survey data from 10 provinces, we introduce the relief degree of land surface (RDLS), the slope degree, and the village-level land transfer rate as objective proxy variables for physical resistance and institutional friction. This empirically operationalizes and tests the inherently unobservable marginal cost of land transfer, providing empirical evidence for related theoretical discussions.

The remainder of this paper is structured as follows: Section 2 systematically reviews the literature and underlying theoretical mechanisms regarding the relationship between farmland scale and production efficiency. Section 3 constructs an analytical framework from the perspective of marginal transaction costs of land transfer. Section 4 and Section 5 describe the empirical model specification and data sources, respectively. Section 6 reports the baseline estimation results. Section 7 uses grouped and interaction models to test the moderating effect of marginal costs on the optimal farmland scale. Finally, Section 8 presents the research conclusions and policy implications.

2. Literature Review

2.1. The Relationship Between Farmland Scale and Production Efficiency

Although the relationship between farmland scale and agricultural production efficiency is one of the most classic topics in agricultural economics, empirical consensus remains elusive. Due to differences in agricultural factor endowments across countries, combined with variations in empirical methods and productivity indicators (such as land productivity, labor productivity, technical efficiency, or total factor productivity), existing studies present mixed findings. Based on a systematic review of the literature, the relationship between farmland scale and production efficiency can be broadly categorized into four patterns: negative, positive, U-shaped, and inverted U-shaped.

A substantial body of research supports an inverse relationship (IR) between farmland scale and production efficiency, often summarized by the assertion that “small is beautiful” [17]. This phenomenon is particularly prevalent in agricultural production across developing countries. Empirical evidence from India [18,19,20], Madagascar [9,21], Burundi [22], Rwanda [23], Uganda [24], and China [10] confirms that, under specific conditions, smallholder farmers can achieve higher yields per unit area or greater production efficiency than large farms.

However, other empirical studies report contrasting results, suggesting that large-scale farms exhibit higher production efficiency [13,25,26,27]. This positive relationship is primarily observed in agriculturally developed countries or highly modernized agricultural regions. With the transformation of agricultural production systems, land-intensive and capital-intensive farming practices have become increasingly prevalent. Some studies have observed that traditional small farms are progressively losing their competitive advantage in efficiency [28].

Beyond simple linear relationships, some scholars have identified more complex, nonlinear relationships—primarily U-shaped [12,29,30,31,32] and inverted U-shaped [1,33,34,35]—between farmland scale and production efficiency. Muyanga and Jayne noted that earlier literature often reported linear relationships partly because it evaluated a narrow range of farmland scale (e.g., mostly under 10 hectares) [32]. When expanding the analysis to a broader size range (e.g., 0 to 113 hectares), production efficiency exhibits an inverse relationship among small farms, but a significantly positive relationship among large farms [32]. Furthermore, differences in measurement levels can also affect the shape of these nonlinear relationships. For example, an empirical study in Zambia found a positive correlation when using overall farmland scale, but a U-shaped relationship when the measurement was disaggregated to the plot level [36]. A summary of the aforementioned literature regarding these patterns is presented in

Table 1. Summary of literature on the relationship between farmland scale and productivity.

Authors	Indicators of Farmland Scale	Indicators of Productivity	Countries
Panel A: Farmland scale has a positive relationship with productivity
Fan and Chan-Kang [13]	Household	Labor productivity, Land productivity, Total factor productivity	China, India, Thailand, Japan, Korea
Foster and Rosenzweig [26]	Household	Profits per acre	India
Dorward [25]	Crop level	Net output per ha	Malawi
Sheng and Chancellor [27]	Dry sheep equivalent (DSE) 1	Total factor productivity	Australia
Panel B: Farmland scale has a negative relationship with productivity
Bardhan [19]	Net sown area	Value of crop production	India
Carter [20]	Household	Value of total production	India
Barrett et al. [9]	Plot level	Yield per plot	Madagascar
Ali and Deininger [23]	Plot level	Value of output per plot	Rwanda
Bevis and Barrett [24]	Household and plot level	Revenue per hectare	Uganda
Sheng et al. [10]	Crop level	Maize yield per crop	China
Sen [37]	Household	Gross output per acre	India
Verschelde et al. [22] (2013)	Household	Agricultural output; market value of output	Burundi
Panel C: Farmland scale has a U-shaped relationship with productivity
Carter and Wiebe [30]	Household	Output and net returns per acre	Kenya
Heltberg [29]	Household	Value-added per acre	Pakistan
Helfand and Levine [31]	Household	Technical efficiency (DEA 2)	Brazil
Bhatt and Bhat [12]	Household	Technical efficiency (DEA 2)	India
Muyanga and Jayne [32]	Household	The gross value per hectare; The net value per hectare; Total factor productivity	Kenya
Panel D: Farmland scale has an inverted U-shaped relationship with productivity
Wang et al. [1]	Cultivated plot area	Output per unit area	China and India
Desiere and Jolliffe [34]	Plot level	Crop cuts and self-reported production	Ethiopia
Byiringiro and Reardon [33]	Household	Average value products (AVPs) and marginal value products (MVPs) of land and labor	Rwanda
Subbarao [35]	Household	Total output of all crops per hectare	India

Notes: ¹ This variable is essentially a measure of farmland carrying capacity and is frequently used as a unit of quality-adjusted land size in Australian cropping and grazing analysis (Sheng and Chancellor, 2019 [27]). ² Data Envelopment Analysis (DEA) is used to calculate technical efficiency.

.

2.2. Theoretical Mechanisms of Scale Efficiency Differences

The aforementioned empirical controversy arises from differences in the microeconomic mechanisms governing agricultural production under various factor endowments and stages of agricultural development. Based on existing theoretical frameworks, the underlying mechanisms driving the diverse relationships between farmland scale and efficiency can be categorized into the following three dimensions.

2.2.1. Factor Allocation Mechanism

Literature exploring the negative correlation between farmland scale and production efficiency primarily analyzes this issue from the perspective of factor market frictions. Imperfect factor markets cause farmers to face systematic variations in shadow prices [37]. For instance, because the performance of hired labor is heavily dependent on family supervision, this supervision constraint systematically affects the relationship between yield and farmland scale [38]. In this context, empirical studies confirm a significant negative correlation between farmland scale and both productivity and technical efficiency [39]. Specifically, smallholder farmers apply more fertilizer and pesticides per unit of land [18]. Their yield advantage stems mainly from allocative efficiency (i.e., optimized proportions of factor inputs) rather than advanced production technology itself [40].

The allocation differences caused by factor market frictions fundamentally represent the broader issue of “factor misallocation.” Cross-country studies indicate that policy and institutional arrangements driving resource misallocation are crucial to explaining differences in farmland scale and productivity across nations [41]. At the micro level, information asymmetry in credit markets creates non-price constraints, rendering farmers’ productivity highly dependent on their initial endowments [42]. In Chinese agricultural practice, the substitution of capital for land also faces misallocation risks; specifically, expanding farmland scale can further exacerbate distortions in capital investment [43]. Farmers’ input choices between labor and capital can attenuate the nonlinear relationship between scale and output. If policies only subsidize land rental without helping farmers upgrade their equipment, resources may be diverted to large farms that rely on inefficient, labor-intensive technologies [10].

However, with factor market development and institutional adjustments, these allocation distortions can be partially mitigated. China’s rural land property rights reform formalized rental rights, promoting the reallocation of land to more productive farmers, thereby increasing aggregate output and total productivity [44]. Concurrently, the transition of rural labor to non-agricultural employment has changed the structure of agricultural labor input. A U-shaped relationship exists between non-agricultural employment and land productivity, indicating that the substitution effect of capital and technology for labor shifts from weak to strong [45].

2.2.2. Technological Intensification Mechanism

Literature reporting a positive correlation between farmland scale and efficiency focuses primarily on the application of technology-intensive factors, such as agricultural machinery. As wage rates rise, labor-saving and mechanized production methods become more efficient [46]. Given the complementarity between machinery and land, coupled with the partial indivisibility of machines, large-scale mechanized farms become more efficient, thereby weakening the inverse relationship between farmland scale and productivity [46]. The increase in machine capacity alongside farmland scale drives the globally observed phenomenon of productivity rising with scale [47]. Empirical evidence from Chinese agriculture also shows that rising non-agricultural wages lead to an expansion of owner-operated farmland, suggesting that economies of scale are emerging alongside mechanization and active land rental markets [48].

To cope with rising labor costs, farmers outsource certain production stages to professional service providers. Such outsourcing services enable smallholder farmers to maintain agricultural production [49]. Capital outsourcing can narrow the productivity gap between large and small farms, as the productivity advantage of large farms diminishes when they substitute owned capital with outsourced services [27]. Micro-level surveys also reveal that medium-sized farms are more likely than small and large farms to adopt agricultural mechanization services, achieving greater productivity gains as a result [50]. Nevertheless, mechanization and its outsourced services still exhibit scale bias and capital thresholds. Larger farms achieve more significant improvements in labor and land productivity from semi-mechanized and fully mechanized agriculture [51]. Meanwhile, mechanization services have a smaller positive impact on farms lacking their own capital equipment [52]. Further research indicates that mechanization services positively influence farm efficiency primarily by optimizing factor allocation channels, such as agricultural investment and planting structures [53].

The scale bias of mechanization further drives farmers’ inclination to expand their farmland scale. Research confirms that as ownership of household-owned agricultural machinery increases, or as more mechanization services are purchased, farmers are more likely to lease in land and less likely to lease it out [54]. Furthermore, the physical size of plots exerts a significant positive impact on the development of agricultural mechanization services; an increase in plot size can substantially reduce service costs and improve efficiency [55].

2.2.3. Transaction Cost Mechanism

The aforementioned mechanisms of factor allocation and technological intensification can partially explain the relationship between farmland scale and efficiency; however, these traditional perspectives often presuppose a perfectly competitive land market with zero transaction costs. In practice, farmland scale expansion is not a frictionless process. A growing body of literature suggests that the high transaction costs stemming from physical land fragmentation and institutional market informality represent key endogenous variables constraining farmers from achieving the theoretical optimal farmland scale.

First, the physical characteristics of land fragmentation directly escalate the spatial integration costs and management difficulties of land transfer, thereby offsetting the gains from economies of scale. Land fragmentation is not only an inherent characteristic of agricultural production but also affects labor use by reducing the marginal productivity of agricultural labor [56]. In China, driven by factors such as household size, land fragmentation remains severe [57]. When farmers attempt to expand their farmland scale, this spatial dispersion increases the input costs of materials and labor, while simultaneously reducing the efficiency of purchasing mechanization services and mechanized operations [14]. Empirical studies in France and Bangladesh similarly confirm that fragmentation increases production costs, exerting a significant negative impact on farm productivity, revenue, and efficiency [58,59]. In the case of Japanese rice farmers, the increased production costs caused by land fragmentation not only offset the advantages of economies of scale, but this adverse effect also intensifies as farmland scale expands [60]. This implies that when farmers attempt to expand their farmland scale through land transfer, they must overcome the spatial frictions that drive up marginal costs caused by fragmentation. In contrast, an increase in plot size can substantially reduce mechanization service costs and improve efficiency [55], further confirming the spatial frictions induced by fragmentation.

Second, the underdeveloped nature and high informality of the current rural land rental market further exacerbate the institutional frictions during the transfer process. In China’s acquaintance-based social networks, land transfers among farmers rely heavily on informal verbal agreements. Micro-survey evidence shows that, across heterogeneous transfer participants, farmers’ contract choices are deeply constrained by the “differential mode of association”. Under strong relational governance, farmers tend to choose verbal or informal contracts; in contrast, under weak relational governance, as transaction costs rise, farmers are more inclined to adopt formal written contracts [61]. Although good personal reputation, as a form of relational governance, facilitates the self-enforcement of informal contracts, this reputational penalty effect relies heavily on tight social networks and the trust foundation of close-knit rural communities. Once farmers attempt to extend beyond these localized networks to expand their farmland scale externally, the conditions for maintaining the self-enforcement of informal contracts are undermined [62]. In the currently underdeveloped rental market, existing informal contracts face frequent disputes and defaults, while formal contracts often impose higher transaction costs on dispersed smallholders [62]. Furthermore, due to the immaturity of China’s farmland rental market, transfers between relatives establish a bilateral governance mechanism to cope with opportunistic behavior from both parties [63], indirectly highlighting the market frictions encountered when transferring land to outsiders. Therefore, enhancing social trust (especially institutional trust) plays a critical role in promoting land transfer and contract formalization [64].

In summary, farmers’ actual optimal farmland scale is the result of a dynamic tradeoff between production economies of scale and transaction costs. Transaction costs in the labor market can explain why the smallest farms are more efficient in low-income countries, while the increase in machine capacity with scale explains the productivity improvements of large farms globally [47]. However, some empirical studies indicate that economies of scale in Chinese agriculture are relatively small, and the benefits farmers gain from expanding farmland scale are limited [65]. Calculations based on Indian data show that if all farms reached the minimum efficient scale, the number of farms would decrease by 82%, and average agricultural income would increase by 68% [47]. If transaction costs cannot be effectively reduced during scale expansion, the increased land and labor investments required to meet higher output demands will partially undermine returns to scale, thereby slowing the growth rate of farmland scale. If smaller producers can utilize advanced technologies to offset the scale advantages of large farms, they can benefit disproportionately from their higher transaction cost-saving potential [66]. China’s recent practices also show that organized land transfer models significantly improve farmland allocative efficiency by enhancing transfer stability and expanding the scale of land transfers [67]. This highlights the constraining effect of high transaction costs on scale expansion during spontaneous transfers. Therefore, the marginal cost of land transfer is not a constant. Its dynamic changes prematurely offset the marginal production benefits of scale expansion at the micro level, forcing farmers’ actual farmland scale to remain at a suboptimal equilibrium below the technical optimum.

2.3. Summary of the Literature

Synthesizing the aforementioned literature, farmers’ decisions regarding farmland scale are essentially the result of a dynamic interplay between the production cost savings brought by economies of scale and increasing transaction costs. Although existing studies have widely confirmed that land fragmentation and informal contracts lead to agricultural efficiency losses, most empirical investigations focus on evaluating the overall impact of these frictions on agricultural productivity. Few studies have delved into how transfer costs dynamically constrain and shift the turning point of the optimal farmland scale for farmers. This literature gap provides the motivation for this paper to explore the nonlinear relationship between farmland scale and production efficiency.

Consequently, this study attempts to introduce the marginal cost of land transfer into the theoretical framework and incorporate proxy variables into the empirical testing. We quantitatively examine the specific impact of transaction cost constraints on the turning point of farmers’ optimal farmland scale. This aims to provide micro-level empirical evidence for understanding the current slowdown in the land transfer process.

3. Theoretical Analysis

Based on microeconomic production theory, a farmer’s optimal farmland scale is determined by profit maximization behavior. Accordingly, we construct the farmer’s profit function $\mathrm{\Pi }\left(L\right)$ where L represents the farmland scale:

$$\max \mathrm{\Pi }\left(L\right) = \mathit{TR}\left(L\right)-\mathit{TC}\left(L\right) = P·Q\left(L\right)-\left[C_p\right(L\left) + C_t\right(L,F)]$$

(1)

where $\mathit{TR}\left(L\right)$ is total revenue and $\mathit{TC}\left(L\right)$ is total cost. $P$ represents the exogenous market price of agricultural products in a perfectly competitive smallholder market. $Q\left(L\right)$ is the agricultural production function. Total cost $\mathit{TC}\left(L\right)$ comprises two components: direct agricultural production costs $C_p\left(L\right)$ (e.g., fertilizer, labor, and machinery) and the transaction cost of land transfer $C_t(L,F)$. Here, $F$ represents physical land fragmentation and market frictions.

To maximize profit, we take the first-order partial derivative of the profit function with respect to farmland scale $L$ and set it to zero, yielding the First-Order Condition (FOC) for profit maximization:

$${\displaystyle \frac{\partial \mathrm{\Pi }\left(L\right)}{\partial L}} = P·Q\prime (L)-{\displaystyle \frac{\partial C_p\left(L\right)}{\partial L}}-{\displaystyle \frac{\partial C_t(L,F)}{\partial L}} = 0$$

(2)

This implies that the equilibrium condition for the farmer to achieve the optimal farmland scale $L^{\ast }$ is that marginal revenue ($\mathit{MR}$) equals total marginal cost, which is the sum of the marginal production cost and the marginal transfer transaction cost:

$$\mathit{MR}\left(L) = M{C}_p\right(L\left) + M{C}_t\right(L,F)$$

(3)

Given the inherent nature of agricultural production, household labor and management capacity impose rigid constraints. Consequently, within the rational stage of production, marginal output decreases as farmland scale $L$ expands ($Q″\left(L\right)<0$). This leads to a gradual decline in marginal revenue $\mathit{MR}\left(L\right)$. Meanwhile, marginal production cost $M{C}_p\left(L\right)$—comprising inputs such as fertilizer, machinery, and labor—is primarily constrained by a given technological baseline. Therefore, under similar technological and price conditions, the core variable causing significant differences in the optimal farmland scale among farmers is the marginal cost of land transfer $M{C}_t(L,F)$, driven by topographical features and market frictions.

This study posits that the marginal cost of land transfer primarily arises from the additional transaction costs incurred for each extra plot leased in. This increase is driven by three main factors. First, information asymmetry exists between transacting parties. In highly fragmented regions, obtaining accurate information on the quality and cropping history of numerous individual plots is difficult, particularly for external lessees [68,69]. Second, informal contracts (e.g., verbal agreements) dominate the land rental market; consequently, managing a larger number of plots increases the probability of default [70,71]. Third, fragmentation prolongs the transaction process. To transfer an equivalent area of land, highly fragmented regions require more individual transactions, directly escalating transaction costs. Therefore, achieving a specific farmland scale in severely fragmented areas requires leasing a larger number of plots. This exacerbates market frictions stemming from information asymmetry and contract instability, ultimately driving a sharper increase in the marginal cost of land transfer.

Based on differences in physical land fragmentation and market frictions ($F$), we define two comparative scenarios. These scenarios illustrate the dynamic constraints of the marginal cost of land transfer on the optimal farmland scale (Figure 1).

The “Ideal Scenario” assumes completely contiguous land and a frictionless land rental market. Farmers leasing in land only pay a fixed rent without incurring additional search or default prevention costs. In this case, the marginal cost of land transfer is constant ($M{C}_{t,\mathit{ideal}} = c$). The slope of the total cost ($TC$) curve is mainly determined by stable production costs, showing a relatively gentle upward trend.

Conversely, the “Realistic Scenario” features severe land fragmentation and information asymmetry. Farmers must negotiate with multiple lessors. Furthermore, the default risk of informal verbal agreements rises significantly with the number of plots. Consequently, the implicit transaction cost required for each additional unit of leased land continuously increases. Mathematically, this manifests as an increasing marginal cost of land transfer as farmland scale expands (${\displaystyle \frac{\partial M{C}_t}{\partial L}} = {\displaystyle \frac{{\partial }^2{C}_t}{\partial L^2}} > 0$). Therefore, the marginal cost under the realistic scenario ($M{C}_{\mathit{real}}$) is higher and steeper than that under the ideal baseline. This drives the realistic total cost (TC) curve to increase at an increasing rate.

Determining the farmer’s optimal farmland scale is an endogenous process that adjusts dynamically with the marginal cost of land transfer. Based on the total revenue ($TR$) and total cost ($TC$) curves (Figure 2), profit maximization occurs when their tangents are parallel. At this point, marginal revenue equals marginal cost ($\mathit{MR} = \mathit{MC}$). The corresponding horizontal coordinate represents the optimal farmland scale. Agricultural product prices are exogenous, and marginal output diminishes. Consequently, the TR curve is concave with a decreasing slope. Under this constraint, we shift the TC curves of the realistic and ideal scenarios to establish tangency with the TR curve. In the realistic scenario, the marginal cost increases rapidly. Thus, its TC curve satisfies the equal-slope condition ($\mathit{MR} = M{C}_{\mathit{real}}$) at a smaller farmland scale (Point A). Conversely, the slow growth of the marginal cost in the ideal scenario allows equilibrium ($\mathit{MR} = M{C}_{\mathit{ideal}}$) at a larger farmland scale (Point B).

Mathematical derivations and graphical analysis corroborate a core corollary: given that $M{C}_{\mathit{real}}>M{C}_{\mathit{ideal}}$ and that marginal revenue $\mathit{MR}$ monotonically decreases, the equilibrium condition is inevitably satisfied at a smaller scale in the realistic scenario. Specifically, the optimal farmland scale at Point A must be strictly smaller than that at Point B ($L_A^{\ast }<L_B^{\ast }$). This implies that, under the realistic constraints of land fragmentation and market frictions, spontaneous land transfers can only achieve a suboptimal equilibrium. The nonlinear increase in the transaction cost of land transfer directly caps the upper limit of the optimal farmland scale.

Based on the theoretical analysis, the optimal farmland scale adjusts dynamically with changes in the marginal cost of land transfer. This dynamic process can be summarized into three scenarios. First, factors increasing marginal costs reduce the optimal farmland scale. The land fragmentation issue discussed in this study exemplifies this. Second, factors that do not change marginal costs have no effect on the optimal farmland scale. As shown in Figure 2, the point of tangency between the total cost and total revenue curves determines the optimal farmland scale; therefore, factors not affecting marginal costs will not alter this optimum. However, various production inputs—such as pesticides, fertilizers, and labor—still influence the overall process, as they constitute the marginal production cost ($M{C}_p$) in the earlier formula. Third, factors decreasing marginal costs can expand the optimal farmland scale. Practices in China’s land rental market demonstrate many such factors, including the implementation of land titling policies, the establishment of land trading platforms, and the formation of land cooperatives. These initiatives effectively reduce information asymmetry and transaction time. Consequently, they lower the marginal cost of land transfer and expand the optimal farmland scale.

To analyze the impact mechanism of the marginal cost of land transfer on the optimal farmland scale, the previous mathematical derivations rely on two key simplifying assumptions: price exogeneity and land homogeneity. Given the complex micro-environment of Chinese agriculture, relaxing these assumptions provides a deeper explanation for the dynamic changes in the optimal farmland scale. This also highlights the limitations and potential extensions of this theoretical model.

On the one hand, the ideal scenario assumes uniform and completely contiguous land (homogeneity), thereby isolating the net effect of transaction costs on farmland scale. However, in the real land rental market, land quality often exhibits high spatial heterogeneity. As farmland scale expands, farmers are often forced to lease in marginal plots located farther from the village, with poorer infrastructure or lower soil fertility. This decay of physical attributes not only increases the difficulty of field management but also serves as a key objective driver behind the steep rise in the marginal cost ($M{C}_{\mathit{real}}$) curve in the realistic scenario. This implies that if land heterogeneity is endogenized, the constraining effect of fragmentation on the optimal farmland scale would be even more severe than the theoretical expectation in Figure 2.

On the other hand, this model treats farmers as price takers in a perfectly competitive market, assuming constant prices for agricultural products and inputs. Although this aligns with the market reality for most Chinese smallholders today, a farmer’s bargaining power in input procurement and product sales increases significantly once their farmland scale crosses a certain threshold (e.g., transitioning into large household farms). In this situation, the price parameter shifts from a constant to an increasing function of farmland scale, thereby slowing the decline in the slope of the total revenue (TR) curve. This suggests that if the market pricing mechanism grants a scale premium, the ceiling for the optimal farmland scale in the ideal scenario (Point B) could expand even further.

Based on micro-level household survey data from 10 Chinese provinces, this paper employs the Stochastic Frontier Analysis (SFA) model to empirically test the theoretical hypotheses. The SFA model measures the distance between farmers’ actual output and the production frontier (i.e., technical inefficiency). Empirically, this indicator captures the efficiency loss caused by deviating from the optimal farmland scale defined in the theoretical model. Following our theoretical derivations, the empirical analysis proceeds in two steps. First, we test for an inverted U-shaped relationship between farmland scale and technical efficiency to verify the existence of an optimal farmland scale. Second, we utilize proxy variables for the marginal cost of land transfer (relief degree of land surface, slope degree, and village-level land transfer rate). Using grouped and interaction term models, we examine how the turning point of the optimal farmland scale dynamically shifts under varying physical resistances and market frictions. Through this design, we leverage micro-survey data to empirically test the nonlinear relationship between farmland scale and technical efficiency, alongside the moderating effect of the marginal cost of land transfer.

4. Method and Model Specification

Since the introduction of the stochastic frontier production function [72], it has been widely used to assess farmers’ technical efficiency. Various methods exist to measure technical efficiency, depending on data type (cross-sectional or panel) and inefficiency term specifications [73]. Generally, analyzing the heterogeneity of technical efficiency follows two main approaches. The first approach is a two-step strategy that initially estimates technical efficiency using a production function and subsequently evaluates the impact of exogenous factors via regression. However, Wang and Schmidt [74] and Belotti et al. [73] demonstrate that this approach introduces severe estimation biases. The second approach employs a flexible simultaneous estimation method, directly incorporating exogenous factors into the distribution parameters of the inefficiency term ${\mu }_{\mathrm{h}i}$ (Equation (7)). Because ${\mu }_{\mathrm{h}i}$ follows a truncated normal distribution, its variance is a function of both ${\mathsf{\varpi }}_{\mathrm{h}i}$ and ${\sigma }_u^2$. Thus, the heteroskedasticity of ${\mu }_{\mathrm{h}i}$ can be modeled using a non-constant ${\mathsf{\varpi }}_{\mathrm{h}i}$, a non-constant ${\sigma }_u^2$, or both [75]. This study primarily focuses on the exogenous factors influencing technical efficiency rather than its inherent uncertainty. Therefore, following Kumbhakar et al. [76], Huang and Liu [77], and Battese and Coelli [78], we specify the mean of the inefficiency term (${\mathsf{\varpi }}_{\mathrm{h}i})$ as observation-specific while keeping ${\sigma }_u^2$ constant.

$$\mathrm{l}\mathrm{n}{Y}_{hi}={\beta }_0+\sum _{j=1}^4{\beta }_j\mathrm{l}\mathrm{n}{X}_{hij}+{\displaystyle \frac{1}{2}}\sum _{j=1}^4\sum _{k=1}^4{\beta }_{jk}\mathrm{l}\mathrm{n}{X}_{hij}\mathrm{l}\mathrm{n}{X}_{hik}+C_i+D_c+{\nu }_{hi}-{\mu }_{hi}$$

(4)

$${\nu }_{hi}\sim i.i.d.N(0,{\sigma }_{\nu }^2)$$

(5)

$${\mathrm{\mu }}_{\mathrm{h}\mathrm{i}}\sim {\mathrm{N}}^{+}({\mathsf{\varpi }}_{\mathrm{h}\mathrm{i}},{\mathrm{\sigma }}_{\mathrm{u}}^2)$$

(6)

$${\mathsf{\varpi }}_{hi}={\delta }_0 +{\delta }_1{l}_{hi} +{ \delta }_2{l}_{hi}^2 +{\delta }_3{f}_{hi}$$

(7)

$$Op=e^{-{\displaystyle \frac{{\delta }_1}{2{\delta }_2}}}$$

(8)

Equations (4)–(7) detail the specific model, where subscripts $h$, $i,$ and $j$ denote households, crops, and input variables, respectively. Compared to the Cobb–Douglas (C-D) production function, which imposes constant output elasticities, the translog production function relaxes the assumption of a constant elasticity of substitution. This allows it to more flexibly capture interactions and nonlinear relationships among inputs. Therefore, we employ the translog production function to estimate technical efficiency. To further verify the statistical validity of this functional specification, we conduct a Likelihood Ratio (LR) test in the empirical analysis to compare it against the C-D model.

Regarding variable selection, this study follows the microeconomic theory of agricultural production. In Equation (4), $\ln Y_{\mathrm{h}i}$ denotes the logarithmic yield of crop $i$ (wheat, rice, or maize) for household $h$. $X_{\mathrm{h}\mathrm{ij}}$ represents core production inputs, encompassing land (sown area), capital and technology (material costs and purchased mechanization services), and labor (labor costs). $C_i$ and $D_c$ are crop and regional fixed effects, respectively, controlling for unobservable heterogeneity. ${\nu }_{\mathrm{h}i}$ is an independent and identically distributed (i.i.d.) white noise error term. ${\mu }_{\mathrm{h}i}$ is the technical inefficiency term, modeled as a non-negative truncated normal random variable with an observation-specific mean ${\mathsf{\varpi }}_{\mathrm{h}i}$ and a fixed variance ${\sigma }_u^2$.

In the inefficiency equation, $l_{\mathrm{h}i}$ denotes the logarithm of the household’s farmland scale. The model includes the quadratic term of $l_{\mathrm{h}i}$ to capture the potential optimum of the farmland scale. The variable $f_{\mathrm{h}i}$ indicates the number of plots, controlling for land fragmentation. The coefficients ${\delta }_1$ and ${\delta }_2$ in Equation (7) are the parameters of primary interest. Significant coefficients indicate a nonlinear quadratic relationship between farmland scale and technical efficiency. Consequently, the optimal farmland scale can be calculated using Equation (8). Because $l_{\mathrm{h}i}$ is logarithmically transformed, we apply an exponential function to derive the actual optimal farmland scale in Equation (8).

To refine the model identification and estimation strategy, this study further addresses potential endogeneity biases and model specification dependencies. First, a household’s farmland scale ($l_{\mathrm{h}i}$) may not be strictly exogenous. Unobservable heterogeneity, such as a farmer’s farming aptitude and management ability, simultaneously affects their land transfer decisions and technical efficiency. Direct estimation may induce simultaneity bias, thereby confounding the empirical estimates. To address this, we introduce the average farmland scale of other surveyed farmers in the same village as an instrumental variable. Employing the Control Function (CF) approach, we incorporate the first-stage residuals of the endogenous explanatory variable into the main regression to control for and isolate the endogeneity bias caused by unobservable factors. Second, to rule out interference from outliers and the sensitivity of the frontier model to distributional assumptions, we conduct multiple robustness checks alongside the baseline regression. These include altering the distributional assumption of the inefficiency term (e.g., using a half-normal distribution) and removing outliers, thereby ensuring the overall reliability of the empirical results.

5. Data and Description of Variables

5.1. Data

This study utilizes data from the China Rural Revitalization Survey (CRRS), conducted in 2020 by the Rural Development Institute of the Chinese Academy of Social Sciences. The survey employed a stratified random sampling method to select rural households nationwide. First, based on provincial economic development levels and spatial distribution, 10 provinces representing eastern, central, and western China were selected: Heilongjiang in the northeast; Zhejiang, Shandong, and Guangdong in the east; Anhui and Henan in the central region; and Guizhou, Sichuan, Shaanxi, and Ningxia in the west. Second, within each province, all counties were stratified into five groups based on per capita GDP, with one county randomly selected from each group. Next, following a similar procedure, three towns were randomly selected from each sampled county, and two villages from each town. Finally, 12 to 14 rural households were randomly drawn from each village (Figure 3). The survey yielded a total sample of 3833 rural households, 64% of which were engaged in agricultural production. To accurately match household characteristics with crop-level production information, we merged the main household database with the crop cultivation sub-database, retaining only households engaged in staple crop production.

The survey data contain crop-level information (e.g., inputs, outputs, sown area, and number of plots) and household-level information (e.g., farmland scale and household characteristics). These data form the basis for calculating crop-level technical efficiency and analyzing its determinants. Based on a stratified random sampling design according to provincial economic development and spatial distribution, the survey covers multi-level administrative units across eastern, central, and western China. The final sample objectively reflects the fundamental landscape of contemporary Chinese agriculture—dominated by smallholder farmers while incorporating a certain degree of scale operations—in terms of farmland scale, crop structure, factor inputs, and household characteristics. This provides a highly representative micro-level observational sample for this study.

5.2. Variable Description

Prior to the empirical analysis, we rigorously cleaned the raw data. First, we excluded observations with logical contradictions (e.g., instances where the sum of the three largest plots’ areas exceeded the total farmland scale, or where core economic indicators were non-positive). Second, at the crop level, we winsorized all continuous variables (including yield, farmland scale, number of plots, and various input costs) at the 1st and 99th percentiles. This mitigates potential estimation bias caused by extreme values and unusually large farms. Finally, we retained only the three major staple crops (wheat, rice, and maize) and removed observations with missing values for model variables. This yielded a final dataset of 1988 valid observations (see

Table 2. Sample screening path and distribution of valid observations.

Screening Step	Sample Size	Description
Initial total sample	4933	Initial multi-crop observations from 3833 households.
Excluding logical contradictions	4856	Excluded observations where the three largest plots exceeded the total farmland scale, or where area/yield/plot counts were non-positive.
1% winsorization	4856	Winsorized yield, farmland scale, number of plots, household size, material costs, labor costs, machinery services, and sown area at the 1st and 99th percentiles.
Retaining staple crops	2749	Retained only wheat, rice, and maize.
Excluding missing values	1988	Removed observations with missing values for key variables (e.g., output, inputs, and farmland scale).

for the sample screening path).

Table 3. Descriptive statistics and variable definition.

Variable	Definition or Unit	Mean	Std. Dev.	Min	Max
Farm and Plot characteristics
Farmland scale	All arable land managed by the household (mu)	25.90	53.90	0.80	420.00
Plots	Number of plots	3.95	3.80	1.00	29.00
Variables of crop-level
Yield	kg/mu	440.41	173.70	38.14	1000.00
Material cost	Fertilizer, seed, pesticide, water/electricity (Yuan/mu)	282.66	140.18	50.00	1060.00
Cropland	Area planted with a specific crop (mu)	16.69	39.14	0.50	310.00
Labor cost	Employment and opportunity cost (Yuan/mu)	265.07	360.49	0.00	2132.00
Machinery service	Purchase machinery service (Yuan/mu)	102.68	89.19	0.00	516.92
Head of household characteristics
Gender	1 = male; 0 = female	0.96	0.19	0.00	1.00
Education level
Illiteracy	1 = yes; 0 = otherwise	0.07	0.25	0.00	1.00
<=Primary school	1 = yes; 0 = otherwise	0.31	0.46	0.00	1.00
Junior high school	1 = yes; 0 = otherwise	0.50	0.50	0.00	1.00
Senior high school	1 = yes; 0 = otherwise	0.12	0.32	0.00	1.00
>=College	1 = yes; 0 = otherwise	0.01	0.11	0.00	1.00
Village cadre	1 = yes; 0 = otherwise	0.14	0.35	0.00	1.00
Non-agricultural employment	1 = yes; 0 = otherwise	0.05	0.22	0.00	1.00
Household and Risk characteristics
Household size	Total number of permanent household members	3.26	1.41	1.00	10.00
Disaster	1 = Not suffered natural disasters; 0 = otherwise	0.66	0.47	0.00	1.00
Insurance	1 = The crop is insured; 0 = otherwise	0.50	0.50	0.00	1.00
Market and Natural endowments
Relief	Relief degree of land surface	0.68	0.78	0.00	5.08
Slope	Slope degree of the land	1.04	1.82	0.01	13.86
Transfer rate	Village land transfer rate (0–1)	0.14	0.17	0.00	1.00
Avg. farmland scale	Leave-one-out mean farmland scale of the village	25.98	39.68	0.80	288.33
Extended and Robustness variables
Avg. plot size	Cropland/Number of plots	4.24	11.48	0.13	310.00
Crop diversity	Number of crops planted	3.95	2.85	1.00	21.00
Labor cost (Half)	Opportunity cost calculated at half wage	138.01	196.21	0.00	2437.50
Actual land rent	Yuan/mu	102.44	181.27	0.00	1028.57
Idle season wage	Village avg. wage in idle season	95.95	35.50	0.00	200.00
Crop-specific variables
Wheat dummy	1 = Wheat; 0 = otherwise	0.26	0.44	0.00	1.00
Rice dummy	1 = Rice; 0 = otherwise	0.23	0.42	0.00	1.00
Maize dummy	1 = Maize; 0 = otherwise	0.51	0.50	0.00	1.00
Cropland (Wheat)	Area planted with wheat (mu)	10.51	25.88	0.60	250.00
Cropland (Rice)	Area planted with rice (mu)	22.71	53.26	0.50	310.00
Cropland (Maize)	Area planted with maize (mu)	17.09	36.68	0.50	260.00
Farmland scale (Wheat)	Total farmland scale of wheat-planting households (mu)	17.16	33.98	1.00	270.00
Farmland scale (Rice)	Total farmland scale of rice-planting households (mu)	31.32	62.90	1.00	340.00
Farmland scale (Maize)	Total farmland scale of maize-planting households (mu)	27.87	57.15	0.80	420.00

Note: 1 Mu ≈ 1/15 Ha; Yuan is the currency of China (1 USD = 6.90 Yuan in 2019).

reports the summary statistics for all variables in the final sample.

Production frontier variables: The baseline stochastic frontier model includes one output and four factor inputs. The dependent variable is the logarithmic yield per unit area. Regarding factor inputs, material capital input is expressed as the logarithm of the total cost for fertilizer, pesticide, seeds, and water/electricity (mean = 282.66 Yuan/mu). Labor input comprises actual hired labor costs and the opportunity cost of household labor (calculated using the village’s average non-agricultural wage), measured as the logarithm of their sum. Machinery input is measured as the logarithm of purchased mechanization service fees per unit area. Land input is measured as the logarithm of the actual sown area for a specific crop.

Core explanatory variables: The core explanatory variables for exploring the impact mechanism on technical efficiency are the logarithm of the household’s farmland scale and its squared term. Descriptive statistics show that the average farmland scale of the sampled households is 25.90 mu, ranging from a minimum of 0.8 mu to a maximum of 420 mu. Concurrently, the average sown area at the single-crop level is 16.69 mu, which is significantly lower than the total household farmland scale. Given that 69.1% of the sampled households planted two or more types of crops (an average of 3.95 crop types), this objectively reflects the mixed-cropping practices widely adopted by current smallholder farmers.

Control variables: Based on the household decision-making model, we selected additional control variables at the household and household head levels for inclusion in both the inefficiency equation and the production function. Regarding cropping structure, the number of plots (mean = 3.95) is introduced to control for physical land fragmentation. Regarding household head characteristics, the vast majority are male (96%), with education concentrated at the primary and junior high school levels (81%). Additionally, 14% serve as village cadres, and only 5% are engaged in non-agricultural employment. Regarding household and risk characteristics, the average household size is 3.26; 66% of households were unaffected by natural disasters; and 50% purchased agricultural insurance. Furthermore, the model incorporates crop and regional fixed effects to absorb unobservable heterogeneity.

Mechanism and robustness check variables: To support subsequent empirical identification and extended analysis, we selected three categories of auxiliary indicators. First, to address endogeneity, we employed the average farmland scale of other surveyed farmers in the same village as an instrumental variable (IV). This indicator reflects the overall village land rental environment, thereby indirectly affecting individual farmers’ land transfer decisions without directly impacting their agricultural production processes. Second, for mechanism verification, we selected the relief degree of land surface, the slope degree, and the village-level land transfer rate as proxy indicators for the marginal cost of land transfer. These physical attributes capture the physical resistance constraining plot consolidation and mechanized operations, while the transfer rate reflects the development level of the local market and information frictions. Due to micro-survey data limitations, these objective indicators, while unable to directly quantify individual implicit transaction costs, effectively map the core constraints on farmland scale expansion, providing a valid empirical substitute. Third, for robustness checks, we extracted the actual number of crop types (mean = 3.95) to measure crop diversification and utilized the village-level average off-farm wage during the idle season to recalculate labor opportunity costs.

6. Results and Discussion

6.1. Baseline Regression Results

The technical efficiency calculated using Stochastic Frontier Analysis (SFA) is presented in

Table 4. Technical efficiency of different crops.

Variable	Mean	Std. Dev.	Min	Max
Full samples	0.677	0.199	0.057	0.954
Wheat	0.708	0.205	0.063	0.967
Rice	0.733	0.164	0.080	0.955
Maize	0.669	0.207	0.053	0.949

. The average technical efficiency for the full sample is 0.677. This indicates that the technical efficiency loss in China’s staple crop production is approximately 32.3%, leaving substantial room for improvement. Disaggregated by crop, the technical efficiencies for wheat, rice, and maize are 0.708, 0.733, and 0.669, respectively. These estimates are highly consistent with recent SFA studies on Chinese agriculture. Specifically, our full-sample average (0.677) closely matches the 0.675 efficiency reported by Zeng and Hu [79] for major grain-producing regions. Furthermore, our crop-specific findings align well with Shi and Paudel [80], who found a 0.74 efficiency for rice, and remain consistent with the broader 0.78 frontier for independent family farms observed by Gong et al. [81]. This cross-validation firmly corroborates the robustness of our empirical approach. The differences in technical efficiency among crops primarily stem from the objective constraints of China’s multiple-cropping systems and the differentiated resource allocation behaviors of farmers. In major grain-producing regions, a double-cropping rotation system is widely adopted. Wheat and rice mostly serve as preceding or prioritized primary crops, with relatively sufficient farming preparation periods. This enables farmers to invest sufficient agricultural inputs and implement refined and intensive field management. In contrast, maize is predominantly planted as a succeeding crop. Constrained by tight planting windows, soil fertility depletion from preceding crops, and dispersed managerial efforts, the production and operation processes of maize tend to be relatively extensive. Furthermore, in terms of economic positioning, rice and wheat are core staple crops, which attract greater production priority from farmers. Conversely, maize exhibits distinct commercial characteristics, possesses a lower cultivation threshold, and is highly compatible with part-time farming. Driven by the opportunity costs of off-farm employment, labor inputs and field maintenance during the maize growing season are relatively insufficient. The aforementioned rotation constraints and differences in labor allocation jointly lead to the overall technical efficiency of maize being lower than that of rice and wheat. Furthermore, the technical efficiency across the full sample ranges from a minimum of 0.057 to a maximum of 0.954. This wide variation indirectly reveals substantial disparities among Chinese smallholder farmers in terms of agricultural production methods and managerial capacity, indicating that standardized modern agricultural practices have not been widely adopted.

Table 5. Effect of farmland scale on technical inefficiency.

Variable	Model (1)	Model (2)	Model (3)	Model (4)
	All Samples	Wheat	Rice	Maize
Frontier (Panel A)
lnX1	−0.1562	2.7636 ***	1.5379 ***	−0.9443 **
	(0.299)	(0.603)	(0.593)	(0.400)
lnX2	−0.1046	0.2847	0.5828*	−0.2295
	(0.100)	(0.195)	(0.334)	(0.152)
lnX3	−0.2039 **	−0.4524 **	0.2179	−0.3382 **
	(0.099)	(0.196)	(0.251)	(0.141)
lnX4	−0.0694	0.1771	0.0652	−0.1268
	(0.062)	(0.207)	(0.115)	(0.089)
lnX1 × lnX1	0.0124	−0.2253 ***	−0.0876 **	0.0669 *
	(0.025)	(0.050)	(0.042)	(0.035)
lnX2 × lnX2	−0.0022	−0.0002	−0.0200	−0.0069
	(0.004)	(0.007)	(0.014)	(0.007)
lnX3 × lnX3	0.0104 **	0.0191 **	−0.0003	0.0167 **
	(0.004)	(0.008)	(0.009)	(0.007)
lnX4 × lnX4	0.0019	0.0285 ***	0.0015	0.0001
	(0.004)	(0.007)	(0.007)	(0.006)
lnX1 × lnX2	0.0152	−0.0261	−0.0673	0.0417 *
	(0.017)	(0.037)	(0.042)	(0.023)
lnX1 × lnX3	0.0219	0.0555 *	−0.0311	0.0394 *
	(0.015)	(0.029)	(0.033)	(0.021)
lnX1 × lnX4	0.0015	−0.0387	−0.0220	0.0126
	(0.009)	(0.035)	(0.013)	(0.013)
lnX2 × lnX3	−0.0014	0.0046	−0.0083	−0.0022
	(0.006)	(0.014)	(0.018)	(0.010)
lnX2 × lnX4	0.0116 **	−0.0277 *	0.0084	0.0159 **
	(0.005)	(0.015)	(0.010)	(0.007)
lnX3 × lnX4	0.0085 **	0.0076	0.0056	0.0073
	(0.004)	(0.012)	(0.007)	(0.006)
Gender	0.1056 ***	0.0493	0.0488	0.0892
	(0.039)	(0.061)	(0.090)	(0.058)
Education level
≤Primary school	−0.0410	0.0740	0.0187	−0.0777 *
	(0.034)	(0.057)	(0.070)	(0.044)
Junior high school	−0.0279	0.1029 *	0.0283	−0.0696
	(0.033)	(0.055)	(0.070)	(0.044)
Senior high school	0.0531	0.1002	0.0721	0.0264
	(0.039)	(0.062)	(0.086)	(0.053)
≥College	−0.0950	0.0084	0.1034	−0.1971 *
	(0.073)	(0.122)	(0.134)	(0.108)
Village cadre	0.0643 ***	−0.0112	0.1726 ***	0.0401
	(0.023)	(0.037)	(0.046)	(0.032)
Non-agricultural employment	0.0626	0.1590 ***	0.0365	0.0593
	(0.038)	(0.058)	(0.071)	(0.056)
Household characteristics
Household size	0.0040	−0.0090	0.0175	0.0109
	(0.006)	(0.008)	(0.011)	(0.008)
Disaster	0.2073 ***	0.1513 ***	0.1482 ***	0.2147 ***
	(0.018)	(0.026)	(0.035)	(0.025)
Insurance	0.0515 ***	0.0141	−0.0315	0.0948 ***
	(0.016)	(0.025)	(0.033)	(0.024)
Crop controls	Yes	-	-	-
Region controls	Yes	Yes	Yes	Yes
Inefficiency term (Panel B)
Log (farmland scale)	−1.3531 ***	−1.5564 **	−1.2485 **	−1.6560 ***
	(0.287)	(0.688)	(0.567)	(0.456)
Square of log (farmland scale)	0.2353 ***	0.2982 **	0.2214 **	0.2352 ***
	(0.050)	(0.131)	(0.096)	(0.076)
The number of plots	−0.1174 ***	−0.2231 *	−0.0524	−0.0592
	(0.035)	(0.118)	(0.050)	(0.047)
${\sigma }_u$	0.2740 **	0.3128	−0.2706	0.4688 ***
	(0.134)	(0.300)	(0.298)	(0.179)
${\sigma }_v$	−3.4914 ***	−4.5392 ***	−3.3941 ***	−3.4893 ***
	(0.093)	(0.223)	(0.174)	(0.134)
Constant	6.8889 ***	−2.8909	−0.3116	9.8256 ***
	(1.003)	(2.040)	(2.491)	(1.332)
Observations	1965	507	455	1003
Optimal scale (mu)	17.7413	13.5987	16.7592	33.7890

Note: Standard errors are in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01. lnX1, lnX2, lnX3, and lnX4 represent the natural logarithm of the material cost, labor cost, sown area, and purchase machinery service variables at the crop level.

reports the baseline regression results. Model (1) presents the estimates for the full sample, while Models (2) through (4) report the results for the wheat, rice, and maize subsamples, respectively. Overall, the estimates align with theoretical expectations. Given our primary focus on the impact of farmland scale on technical efficiency, we concentrate our analysis on the estimates in Panel B (the inefficiency term).

Across both the full sample and the three staple crop subsamples, the linear term coefficients for farmland scale are significantly negative at the 1% or 5% level, while the quadratic term coefficients are all significantly positive. This implies a U-shaped relationship between household farmland scale and technical inefficiency. Given the strict inverse mapping between technical efficiency and technical inefficiency, this strongly corroborates an inverted U-shaped relationship between farmland scale and technical efficiency. Economically, in the initial stage of farmland scale expansion, farmers can more effectively spread the fixed costs of machinery purchases and purchased mechanization services. This achieves optimal factor allocation (economies of scale), thereby driving technical efficiency upward. However, as the farmland scale crosses the optimal turning point, the inherent biological characteristics of agricultural production become pronounced. Constrained by tight time windows during peak farming seasons and physical land fragmentation, farmers’ supervision costs for hired labor and production processes rise significantly. Constraints on managerial capacity ultimately lead to diseconomies of scale, causing technical efficiency to decline.

Notably, after controlling for total farmland scale, the coefficient for the number of plots is significantly negative in the full sample and some subsamples. This indicates that more plots correlate with lower technical inefficiency (i.e., higher technical efficiency). Combined with the objective data in Section 5 showing an average of 3.95 crops per household, this finding reveals a distinctive logic within the Chinese smallholder production model: moderate land fragmentation provides smallholder farmers with a short-term efficiency compensation mechanism. Farmers employ crop diversification to mitigate agricultural risks. They match specific crops to plot-specific soil characteristics and fully utilize household labor for intensive farming. Consequently, under current constraints, plot diversity translates into a production advantage.

Calculated from the regression coefficients, the theoretical optimal farmland scale for the full sample is 17.74 mu, while the actual average scale is 25.90 mu, exceeding the theoretical optimum. While technical efficiency optimization corresponds to maximum efficiency per unit of output, farmers’ actual farmland scale is jointly determined by profit-maximization motives, production technology characteristics, cost structures, and factor market conditions. This deviation aligns with the current realities of Chinese agricultural production. Disaggregated by crop, the theoretical optimal scale for wheat is 13.60 mu, while the actual average farmland scale is 17.16 mu, exceeding the optimal level. Wheat production is significantly affected by land fragmentation. Dispersed plots drive up the transaction costs for machinery coordination and field management, lowering the ceiling for the optimal scale. Concurrently, to spread the fixed costs of machinery inputs, farmers have an intrinsic motivation to expand their farmland scale, resulting in an actual scale higher than the theoretical optimum. For rice, the theoretical optimal farmland scale is 16.76 mu, while the actual average scale reaches 31.32 mu, exhibiting a more pronounced deviation. As a typical paddy crop, rice production demands strict precision in water and fertilizer management, as well as pest control. Scale expansion significantly increases management and supervision costs, thereby restricting the optimal scale. However, higher profit margins per unit area, coupled with the widespread adoption of purchased mechanization services (e.g., machine transplanting and drying), mitigate labor constraints. Consequently, the actual scale expands significantly. For maize, the theoretical optimal farmland scale is 33.79 mu, and the actual average scale is 27.87 mu, falling short of the optimal level. As a dryland crop, maize is highly amenable to mechanization and requires relatively extensive management. Management costs rise slowly with scale expansion, leading to a relatively higher optimal scale. In reality, however, the insufficient supply of contiguous land suitable for mechanized operations, coupled with high land rental and transaction costs, objectively constrains the expansion of scale. This results in unrealized scale potential.

Importantly, because farmers generally engage in mixed-cropping practices, the estimation results in this section reflect an overall trend. Although we are confident in confirming the inverted U-shaped relationship between farmland scale and technical efficiency—which is consistent with the theoretical analysis in Section 3—the theoretical optimal farmland scale is not a fixed value. As emphasized by Kumbhakar et al. [82], efficiency estimates and parameter results are highly sensitive to unobserved heterogeneity and distributional assumptions of the functional specification. First, with varying land availability and the dynamic development of the land rental market, the optimal farmland scale will shift accordingly. Second, potential endogeneity and measurement biases in the empirical model may compromise the reliability of the baseline results. Therefore, in Section 6.2 and Section 6.3, we employ an instrumental variable (IV) approach to address potential endogeneity and comprehensively test the robustness of these findings using a series of alternative indicators and model specifications.

6.2. Addressing Endogeneity

The estimation of the relationship between farmland scale and technical efficiency may be confounded by potential endogeneity. Typically, unobservable heterogeneity, such as households’ field management experience and farming aptitude, simultaneously affects their land rental decisions and technical efficiency. Failing to account for this endogeneity may lead to biased estimates in the baseline model. Given that the stochastic frontier model in this study includes a quadratic nonlinear term for farmland scale, the traditional Two-Stage Least Squares (2SLS) method is invalid. Therefore, we employ the Control Function (CF) approach for endogeneity correction. We select the average farmland scale of other surveyed households in the same village as an instrumental variable (IV). Economically, the average farmland scale of other households in the same village represents the overall land endowment and rental market development environment of the village. This constitutes an exogenous objective condition affecting a specific household’s decision to lease land in or out. Furthermore, this aggregate village-level environment does not directly interfere with the micro-agricultural production process within a specific household, thereby strictly satisfying the exclusion restriction of an instrumental variable.

Table 6. Endogeneity test: two-stage control function approach.

Variable	Model (1)	Model (2)	Model (3)	Model (4)
	All Samples	Wheat	Rice	Maize
Log (farmland scale)	−1.8332 ***	−2.3496 *	−1.5201 *	−2.6143 ***
	(0.445)	(1.219)	(0.823)	(0.895)
Square of log (farmland scale)	0.2867 ***	0.3487 *	0.2642 **	0.3162 **
	(0.069)	(0.192)	(0.134)	(0.123)
The number of plots	−0.1042 ***	−0.1749	−0.0536	−0.0038
	(0.039)	(0.131)	(0.055)	(0.057)
Residual (1st stage)	0.6472 ***	1.4057 *	0.1488	1.3677 **
	(0.232)	(0.777)	(0.296)	(0.555)
${\sigma }_u$	0.4743 ***	0.6179	−0.1618	0.7920 ***
	(0.169)	(0.392)	(0.379)	(0.254)
${\sigma }_v$	−3.4817 ***	−4.4919 ***	−3.3633 ***	−3.4887 ***
	(0.092)	(0.215)	(0.167)	(0.132)
Constant	6.8710 ***	−3.4473 *	−0.7263	9.9984 ***
	(1.005)	(1.884)	(2.444)	(1.319)
Observations	1955	506	450	999
Optimal scale (mu)	24.4693	29.0531	17.7638	62.4539
1st-stage IV Coef.	0.2703 ***	0.1620 ***	0.3306 ***	0.2876 ***
1st-stage IV Std. Err.	(0.021)	(0.040)	(0.050)	(0.030)
1st-stage F-statistic	251.39	50.04	72.14	153.15
1st-stage R-squared	0.802	0.746	0.833	0.821

Note: Standard errors are in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01. The first-stage residual is included in Panel B to address endogeneity. The variables in the translog production frontier are omitted for brevity. All models control for regional fixed effects.

reports the two-stage estimation results of the CF approach. The first-stage regression shows that the instrumental variable is significantly positive at the 1% level across the full sample and all subsamples. Furthermore, the first-stage F-statistics (ranging from 50.04 to 251.39) far exceed the empirical critical value for weak instruments, indicating that the IV satisfies the relevance condition. Additionally, the first-stage residuals are significant in the second stage for most models. This confirms the existence of endogeneity bias in farmland scale and justifies the necessity of using the CF approach. After effectively accounting for endogeneity, the signs and significance of the coefficients for the logarithm of farmland scale and its squared term remain robust, once again corroborating the inverted U-shaped relationship between farmland scale and technical efficiency.

Notably, after correcting for endogeneity bias, the theoretical optimal farmland scale for each crop shifted rightward compared to the baseline regression (the optimal scale for the full sample increased from 17.74 mu to 24.47 mu, while wheat and maize expanded to 29.05 mu and 62.45 mu, respectively). As shown in Table 6, the coefficients for the first-stage residuals in the inefficiency function are mostly significantly positive. This indicates that the unobservable factors driving households to endogenously expand their farmland scale actually exacerbate technical inefficiency. Contextualized within Chinese agriculture, this often reflects an extensive expansion model prioritizing land accumulation over intensive management. Such behavior is frequently driven by non-productive motives, such as capturing scale subsidies, or occurs under conditions of insufficient complementary capital and modern managerial capacity. By failing to effectively isolate the inefficiency increase caused by this suboptimal expansion, the baseline model underestimated the potential of the optimal farmland scale. Importantly, the theoretical optima derived from the CF approach reflect the long-term scale potential under ideal factor matching. In reality, the actual optimal farmland scale achievable by households remains constrained by capital endowments and topographical conditions. In contrast, the theoretical optimal farmland scale for rice exhibits strong relative rigidity (rising slightly from 16.76 mu to 17.76 mu). This further highlights the stringent constraints imposed by the intensive farming practices of paddy fields on households’ managerial capacity, making its optimal farmland scale relatively less susceptible to endogeneity bias.

6.3. Robustness Checks

To verify the reliability of the baseline conclusions, we conducted multiple robustness checks addressing outlier sensitivity, distributional assumptions, functional specifications, variable measurement, and potential omitted variables. The estimation results are summarized in

Table 7. Estimation results of robustness checks.

Variable	Model (1)	Model (2)	Model (3)	Model (4)	Model (5)	Model (6)
	Baseline	Drop Top 1%	Half-Normal	C-D Function	Half-Wage	Add Diversity
Log (farmland scale)	−1.3531 ***	−1.5167 ***	−0.4780 ***	−1.2069 ***	−1.3508 ***	−1.5667 ***
	(0.287)	(0.320)	(0.051)	(0.261)	(0.287)	(0.378)
Square of log (farmland scale)	0.2353 ***	0.2799 ***	0.0966 ***	0.2071 ***	0.2350 ***	0.2940 ***
	(0.050)	(0.059)	(0.012)	(0.045)	(0.050)	(0.069)
The number of plots	−0.1174 ***	−0.1160 ***	−0.0356 ***	−0.1120 ***	−0.1176 ***	−0.1549 ***
	(0.035)	(0.036)	(0.009)	(0.033)	(0.035)	(0.048)
Crop diversity						−0.1446 ***
						(0.052)
${\sigma }_u$	0.2740 **	0.2936 **		0.2200 *	0.2735 **	0.4939 ***
	(0.134)	(0.138)		(0.130)	(0.134)	(0.167)
${\sigma }_v$	−3.4914 ***	−3.4694 ***	−3.7815 ***	−3.4613 ***	−3.4954 ***	−3.4409 ***
	(0.093)	(0.093)	(0.118)	(0.089)	(0.094)	(0.092)
Constant	6.8889 ***	6.8435 ***	6.6999 ***	5.5480 ***	6.7978 ***	6.8924 ***
	(1.003)	(1.012)	(1.017)	(0.119)	(0.965)	(1.009)
Observations	1965	1946	1965	1965	1965	1929
Optimal scale	17.74	15.02	11.87	18.44	17.70	14.37
LR Test Stat				20.99
LR Test p-value				0.021

Note: Standard errors are in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01. The variables in the translog production frontier are omitted for brevity. Farmland scale variables in Model (3) affect the inefficiency variance rather than its mean, but are aligned here for formatting. All models control for region fixed effects.

. Overall, across all model adjustments, the linear coefficient for farmland scale remains significantly negative, and the quadratic coefficient remains significantly positive. This indicates that the inverted U-shaped relationship between farmland scale and technical efficiency has strong empirical robustness.

First, considering that a small fraction of ultra-large farms might exert a disproportionate leverage effect on the fitted curve, Model (2) excludes observations in the top 1% of the farmland scale distribution. The re-estimation results show that the signs and significance of the core variables remain unaffected. Furthermore, the derived optimal farmland scale is 15.02 mu, which is highly consistent in magnitude with the baseline full-sample estimate, ruling out the possibility that the empirical conclusions are driven by extreme outliers.

Second, to address the sensitivity of the stochastic frontier model to distributional assumptions and functional forms, we conducted alternative specification tests. Model (3) replaces the baseline truncated-normal distribution assumption for the inefficiency term with a half-normal distribution. The significance of the farmland scale variables remains robust, with the optimal scale stabilizing at 11.87 mu. Model (4) restricts the frontier function from the translog form to the Cobb–Douglas (C-D) specification, yielding consistent scale effect characteristics. Meanwhile, the Likelihood Ratio (LR) test statistic is 20.99 (p = 0.021), rejecting the C-D functional form at the 5% level. This statistically confirms the necessity and validity of adopting the translog functional specification in our baseline regression.

Finally, we supplemented the analysis with tests for variable measurement errors and potential omitted variables. In empirical agricultural microeconomics, due to rural labor market imperfections, directly using full off-farm wages to estimate the opportunity cost of household labor carries a risk of overestimation. Therefore, Model (5) recalculates the total cost of labor input using half of the village-level average off-farm wage during the idle season. The optimal farmland scale derived from this regression (17.70 mu) is highly consistent with the baseline result. Furthermore, as shown earlier, surveyed households generally engage in mixed-cropping practices. To avoid omitted variable bias in efficiency evaluation caused by differences in cropping patterns, Model (6) directly introduces crop diversity as a control variable into the inefficiency function. The results show that, after controlling for crop diversity, the inverted U-shaped effect of farmland scale remains highly significant. Additionally, the coefficient for crop diversity is significantly negative at the 1% level (−0.1446). This empirical finding corroborates the analysis regarding the number of plots in Section 6.1. It confirms that moderate crop diversification helps reduce technical inefficiency, serving as an effective mechanism to mitigate risks and improve efficiency under the current smallholder production model.

7. Further Analysis: Dynamic Evolution of the Optimal Scale

7.1. Impact of Natural Resource Endowments on the Optimal Farmland Scale

This study selects village-level relief degree of land surface (RDLS) and slope degree as measurement indicators to examine the dynamic impact of natural resource endowments on the relationship between farmland scale and technical efficiency. Both indicators are calculated using elevation data with a 1 km spatial resolution, sourced from the Resource and Environment Science and Data Center (https://www.resdc.cn/). RDLS measures the elevation difference between the highest and lowest points within a specific area. We calculate it following the DEM-based measurement model proposed by Feng et al. [83]:

$$RDLS=ALT/1000 + \left\{\left[Max\right(H)-Min(H\left)\right]\times [1-P(A)/A]\right\}/500$$

(9)

where $\mathit{RDLS}$ denotes the relief degree of land surface; $Max\left(H\right)$ and $Min\left(H\right)$ denote the highest and lowest elevations (m), respectively, within a specific area centered on a given grid cell; $P\left(A\right)$ denotes the area of flat ground within this region (${\mathrm{km}}^2$); and $A$ denotes the total area.

Slope degree data are extracted using the 3D Analyst tool in ArcGIS 10.2. To derive village-level indicators, we spatially overlaid the geographic coordinates of the sampled villages with national-level relief and slope raster data, matching the values using the “Extract Values to Points” tool in ArcGIS.

To set the group boundaries for the spatial variables, referring to the statistical analysis of the distribution characteristics of China’s RDLS by Feng et al. [83], we use a threshold of 0.5 to divide the relief degree into low-relief and high-relief areas. For the micro-level plot slope degree indicator, considering its significantly right-skewed sample distribution, this study determines the empirical boundary by combining sensitivity tests with sample distribution characteristics. The results indicate that when using the 75th percentile of the sample (slope degree > 0.75) as the boundary for the high-slope group, the sample sizes of both groups meet the requirements for statistical inference, and the topographic moderating effect is most significant. These two spatial variables are strongly exogenous, can objectively reflect the physical resistance and marginal costs of land transfer and mechanized operations under different endowments, and are not directly affected by households’ current production decisions.

Table 8. Grouped regression by natural endowment.

Variable	Model (1)	Model (2)	Model (3)	Model (4)
	Low Relief	High Relief	Low Slope	High Slope
Log (farmland scale)	−2.5469 **	−1.4158 ***	−2.6801 ***	−0.4675 *
	(0.994)	(0.514)	(1.000)	(0.246)
Square of log (farmland scale)	0.4237 ***	0.2706 ***	0.4534 ***	0.0893 *
	(0.163)	(0.104)	(0.165)	(0.048)
The number of plots	−0.1932	−0.0686	−0.1695 *	−0.0580
	(0.128)	(0.082)	(0.094)	(0.082)
${\sigma }_u$	0.5928 *	0.1441	0.6508 **	−0.2110
	(0.336)	(0.251)	(0.308)	(0.238)
${\sigma }_v$	−4.0276 ***	−3.0055 ***	−3.7923 ***	−3.1622 ***
	(0.157)	(0.123)	(0.138)	(0.170)
Constant	6.2272 ***	5.9069 ***	6.1777 ***	6.4374 ***
	(0.086)	(0.096)	(0.087)	(0.159)
Observations	1072	885	1306	651
Optimal Scale	20.19	13.68	19.22	13.70

Note: Cluster-robust standard errors at the village level are in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01. The variables in the translog production frontier are omitted for brevity. All models control for regional fixed effects.

reports the stochastic frontier estimation results grouped by natural resource endowment. The estimation results show that in the models grouped by either relief or slope degree, the quadratic coefficients of farmland scale in the inefficiency equation are all significantly positive, and the linear coefficients are significantly negative. This indicates that an inverted U-shaped relationship is maintained between technical efficiency and farmland scale. Calculations based on the extremum formula reveal that the greater the topographic resistance, the smaller the household’s optimal scale. Specifically, in villages with high relief, the optimal scale is 13.68 mu, whereas in villages with low relief, the optimal scale expands to 20.19 mu. The slope degree grouping presents a consistent trend: the optimal scale in high-slope areas is 13.70 mu, while in low-slope areas it is 19.22 mu. This suggests that in flat terrain areas, differences between plots are small and contiguous integration is easier, resulting in lower marginal costs for households to expand their farmland scale. In contrast, in rugged terrain areas, natural topographic conditions pose objective limitations on the substitution of large agricultural machinery and the contiguous integration of land.

To further examine the moderating effect of topographic resistance on the optimal scale, while avoiding multicollinearity and curvature overfitting issues in high-dimensional nonlinear SFA models, we construct a restricted interaction model (

Table 9. Restricted interaction models of natural resource endowment and farmland scale.

Variable	Model (1)	Model (2)
	Relief Interaction	Slope Interaction
Log (farmland scale)	−1.9090 ***	−1.5222 ***
	(0.600)	(0.492)
Square of log (farmland scale)	0.3014 ***	0.2369 ***
	(0.096)	(0.082)
The number of plots	−0.1352 *	−0.1122 *
	(0.077)	(0.066)
High relief (Dummy)	−0.5592
	(0.651)
Log (farmland scale) × High relief	0.6440 **
	(0.279)
High slope (Dummy)		−0.4272
		(0.557)
Log (farmland scale) × High slope		0.4219 **
		(0.214)
${\sigma }_u$	0.4368	0.3431
	(0.273)	(0.243)
${\sigma }_v$	−3.5388 ***	−3.5127 ***
	(0.132)	(0.122)
Constant	6.1673 ***	6.1695 ***
	(0.073)	(0.076)
Observations	1957	1957
Optimal scale (Low Group)	23.74	24.84
Optimal scale (High Group)	8.15	10.20

Note: Cluster-robust standard errors at the village level are in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01. The variables in the translog production frontier are omitted for brevity. This model employs a restricted interaction specification by introducing interaction terms between farmland scale and topography dummies in the inefficiency equation to measure the horizontal shift in the optimal scale. All models control for regional fixed effects.

). While controlling for regional fixed effects and absorbing frontier heterogeneity, this model introduces an interaction term between the linear term of farmland scale and the topographic grouping dummy into the inefficiency equation. The regression results show that both the relief interaction term (0.6440) and the slope degree interaction term (0.4219) are significantly positive at the 5% level. The interaction terms have the opposite sign to the main effect of farmland scale, indicating that topographic resistance exerts an offsetting effect on economies of scale. Calculations of the horizontal shift in the optimum reveal that high-relief and high-slope degree environments cause the theoretical optimal scale to shift leftward from 23.74 mu and 24.84 mu in the low-resistance groups to 8.15 mu and 10.20 mu, respectively. This result quantifies the degree to which differences in natural resource endowments constrain the upper limit of the optimal farmland scale.

To evaluate the dynamic relationship between farmland scale and technical efficiency, we employ locally weighted scatterplot smoothing (Lowess) to plot non-parametric fitted curves (Figure 4). The Lowess algorithm relaxes specific functional form specifications, allowing us to capture the nonlinear patterns between farmland scale and technical efficiency. Panels (A) and (B) in Figure 4 display the evolutionary trajectories under different relief and slope degree conditions, respectively. Observing the relative levels and turning points of the fitted curves reveals that the overall technical efficiency in low-resistance areas is relatively higher, and the optimal scale corresponding to the efficiency peak shifts rightward compared to high-resistance areas. These non-parametric fitted trajectories align with the optimum calculations from our previous parametric regressions, further corroborating the dynamic impact mechanism of resource endowments on the optimal farmland scale.

7.2. Impact of Land Rental Market Development on the Optimal Farmland Scale

The village-level land transfer rate reflects the development level of the local rental market and possesses a strong exogenous attribute for micro-level households. Using the median of the village-level land transfer rate as the boundary, we divide the sample into two groups: “well-developed land rental market” and “less-developed land rental market”. The former indicates that more households in the village participate in land transfer, land transfers are relatively active, and the market is mature; the latter is precisely the opposite. Theoretically, in regions with well-developed rental markets, the degree of information asymmetry is lower, and transfer prices are more transparent. This objectively reduces the marginal transaction costs for households to lease in land. Based on these two market scenarios, we re-estimate the parametric relationship between farmland scale and technical inefficiency, with the estimation results shown in

Table 10. Grouped regression by land rental market development.

Variable	Model (1)	Model (2)
	Less-Developed Land Rental Market	Well-Developed Land Rental Market
Log (farmland scale)	−0.9911 **	−2.0429 ***
	(0.441)	(0.672)
Square of log (farmland scale)	0.1894 **	0.3435 ***
	(0.084)	(0.109)
The number of plots	−0.0485	−0.1948
	(0.057)	(0.119)
${\sigma }_u$	0.0698	0.4550
	(0.256)	(0.278)
${\sigma }_v$	−3.3535 ***	−3.8121 ***
	(0.162)	(0.170)
Constant	6.0512 ***	6.2291 ***
	(0.167)	(0.086)
Observations	971	953
Optimal scale	13.68	19.57

Note: Cluster-robust standard errors at the village level are in parentheses. ** p < 0.05, *** p < 0.01. The variables in the translog production frontier are omitted for brevity. All models control for regional fixed effects.

. Concurrently, we plot fitted curves using the non-parametric locally weighted scatterplot smoothing method (Figure 5).

The results in Table 10 show that in both well-developed and less-developed rental market scenarios, the linear coefficient of farmland scale is significantly negative, and the quadratic coefficient is significantly positive. This indicates that the inverted U-shaped relationship between farmland scale and technical efficiency does not change with differences in market development. Furthermore, the theoretical optimum derived from the coefficients differs significantly between the two groups. Specifically, in the well-developed rental market, the optimal scale corresponding to the household’s peak technical efficiency is 19.57 mu; in the less-developed rental market, this optimal scale shrinks to 13.68 mu. This demonstrates that the improvement of the land rental market helps reduce the marginal costs of land transactions and transfers. It confirms that a decrease in market transaction costs can cause the household’s optimal farmland scale to shift horizontally to the right.

The non-parametric estimation curves in Figure 5 also corroborate this result. In the figure, the top dashed line represents the well-developed rental market sample, the middle solid line represents the full sample, and the bottom dash-dot line represents the less-developed rental market sample. It can be observed from the figure that under well-developed rental market conditions, the log farmland scale corresponding to the technical efficiency peak is around 3.5; the log optimal scale for the full sample is approximately 3.0; and under less-developed rental market conditions, the peak of the log optimal scale shifts significantly to the left to around 1.0. The parametric regression and non-parametric fitting results are consistent with each other. This indicates that when a household’s production reaches maximum technical efficiency, the optimal farmland scale for households in a well-developed rental market is significantly larger than that for households in a less-developed rental market.

8. Conclusions and Policy Implications

8.1. Main Conclusions

This study explores the relationship between farmers’ farmland scale and technical efficiency through theoretical and empirical analyses, and further examines this relationship from the perspective of the marginal cost of land transfer. The results show an inverted U-shaped relationship between farmland scale and technical efficiency; that is, technical efficiency first increases and then decreases as the farmland scale expands. After correcting for the endogeneity bias of farmland scale, the theoretical optima of farmland scale for all staple crops shift rightward. Furthermore, there is significant crop heterogeneity in the optimal farmland scale; the theoretical optimal scales for wheat and rice are lower than that for maize, which possesses stronger suitability for mechanization.

This study further verifies the dynamic adjustment mechanism of the optimal farmland scale. The inverted U-shaped relationship determines the existence of a theoretical optimal scale for household agricultural production. However, this scale is not a fixed value; it adjusts dynamically with changes in the marginal cost of land transfer. The smaller the marginal cost of land transfer, the larger the household’s optimal scale. Empirical tests using farmland topography and the land rental market as exogenous indicators show that flatter relief and slope degrees, along with a more developed land rental market, correspond to lower physical resistance and transaction costs faced by households, resulting in a correspondingly larger optimal farmland scale.

Additionally, the research reveals the intrinsic logic underlying the current smallholder production mode. After controlling for the total farmland scale, an increase in the number of plots and crop diversification actually reduce technical inefficiency. This indicates that under realistic production constraints, moderate land fragmentation and mixed-cropping practices serve as effective short-term compensation mechanisms for households to mitigate natural and market risks and smooth labor utilization.

8.2. Policy Implications

Accelerating land transfer and improving the mechanization and modernization levels of agricultural production are realistic paths for China’s agricultural development. However, in recent years, the growth of the land transfer rate has slowed down, and households’ farmland scales have remained relatively stable. This indicates that current land transfers may have reached a suboptimal equilibrium under realistic constraints. To break this equilibrium and improve overall efficiency, public policymaking needs to shift from a pure aggregate expansion orientation to targeted policies based on objective constraints. The focus can be advanced from three dimensions:

First, implement differentiated land transfer strategies and avoid a one-size-fits-all approach to scale expansion. Topographical features exert a significant constraining effect on the optimal farmland scale. In flat areas, policies can continue to encourage land transfer and contiguous integration to fully realize economies of scale. However, in restricted areas with high relief or slope degrees, policy planning must respect the objective reality that the optimal farmland scale is relatively small. For such regions, the policy focus should shift to promoting small and micro agricultural machinery suitable for complex terrain and cultivating specialty high-value-added agriculture, rather than the uncritical pursuit of large-scale land transfers.

Second, cultivate service-oriented third-party organizations and trading platforms to reduce the marginal transaction costs of land transfer. Optimizing the institutional environment can effectively expand the upper limit of the optimal farmland scale. The government should encourage the development of non-profit third-party institutions, such as grassroots agricultural cooperatives, village collective economic organizations, and standardized land trading platforms. By leveraging the coordinating role of such organizations, fragmented and dispersed plots can be consolidated first and then uniformly leased out to large grain farmers with genuine operational capacity. This approach can substantially reduce the transaction costs for large-scale farmers in information searching, bargaining, and contract signing, thereby promoting the rational expansion of farmland scale.

Third, coordinate short-term realistic tolerance with long-term modernization goals to steadily advance contiguous land consolidation. Currently, moderate land fragmentation and crop diversification are rational choices for smallholder farmers to mitigate natural and market risks and optimize labor allocation. This also forms a suboptimal equilibrium that maintains stable efficiency in agricultural production at the present stage. In advancing land consolidation initiatives, such as “merging small plots into large ones” and constructing high-standard farmland, mandatory measures like forced consolidation and mandatory mono-cropping should be avoided. Before the agricultural insurance system and purchased mechanization service networks can fully hedge the risks of mono-cropping operations, adequate flexibility for moderate crop diversification must be reserved for smallholder farmers, fully accommodating their realistic production and operational needs. From the perspective of long-term agricultural development trends, the outflow of rural labor is irreversible. Mechanization and scale expansion are the fundamental pathways to China’s agricultural modernization. The dispersed operation model, which relies heavily on intensive human labor, objectively constrains the popularization and application of large-scale modern agricultural machinery, making it difficult to adapt to the requirements of modern agricultural development. Public policies need to precisely grasp the balance between short-term tolerance and long-term guidance. Premised on respecting households’ willingness and protecting their legal rights, contiguous land consolidation should be advanced step by step. This will gradually break the long-term constraints of the persistent suboptimal equilibrium, clear spatial obstacles for large-scale agricultural operations and mechanized farming, achieve an organic connection between smallholder production and modern agricultural development, and create foundational conditions for cultivating new agricultural business entities.

8.3. Limitations and Outlook

This study still has certain limitations in data dimensions and indicator measurement, which need to be further addressed in future research. First, the empirical inferences in this paper are based on cross-sectional data, which have inherent limitations in controlling for time-invariant unobservable heterogeneity (such as a household’s inherent management endowment and the long-term quality of micro-plots). Future research could construct high-quality, large-sample micro-level panel data to further isolate individual fixed effects, thereby identifying the causal relationship between farmland scale and technical efficiency more rigorously. Second, when measuring the marginal cost of land transfer, this study selected exogenous proxy variables such as the relief degree, slope degree, and village-level transfer rate. These indicators focus on reflecting the physical resistance and market environment of scale expansion. They fail to directly observe the implicit transaction costs actually borne by micro-level farmers during processes like transfer negotiations, information searching, and default prevention. Future research could design targeted survey instruments to directly quantify these implicit transaction costs. Incorporating these quantified costs into the frontier efficiency model would further improve the testing of the dynamic evolution mechanism of the optimal farmland scale.