Introduction

Rice is a staple food for half of the world’s population and the third most-produced cereal after maize and wheat on a world basis. More than 90% of total production is concentrated in Asian regions, primarily in China, India, and Indonesia, where local production accounts for 66% of global output (^14,45). In Chile, production is concentrated in Maule and Ñuble regions, with an average of 83,368 tons of rice available for human consumption from 2012 to 2022. Historically, this volume has been insufficient to meet 40% - 45% of the domestic demand, with the remainder imported primarily from Argentina, Uruguay, and Paraguay (³⁶). National output has dropped by 30.4% over the last decade, due not only to adverse climatic factors such as frost and water scarcity, but also to current high input prices for fertilizers and pesticides, high land prices, labor shortages, and low market prices, which have significantly reduced output (³⁵). These factors put farmers under pressure to become more efficient in rice production and input utilization to avoid additional costs and make farms profitable. This raises several questions. One of them refers to the study of the characteristics, unique to the farmer, the farm, and the environment, which help understand why one farmer is more cost-efficient than another and, particularly, what role tenure arrangements to exploit the land play. The latter is the focus of this study.

Tenure arrangements, which govern land exploitation, can have an impact on production and cost efficiency. Landlord, fixed rent, and sharecropping are the most common land tenure systems documented in the literature (¹). A large body of literature discusses the factors influencing agricultural production efficiency. However, studies on the impact of various types of land tenure arrangements on production costs are scarce. Works such as ^{Ackerberg and Botticini (2000}), ^{Alem et al. (2018}) and ^{Islam (2018}), conclude that land tenure, either leased or owned, favors technical efficiency levels, but they do not break down production costs into technical inefficiency and input misallocation inefficiency cost. Other papers, decompose and analyze the determinants of technical and allocative efficiencies, but they do not estimate the costs of these inefficiencies, nor analyze differences between land tenure arrangements or the degree of input misallocation and its impact on costs (^{13,19,26,37,44}).

This paper aims to analyze differences in production costs, particularly those due to technical and allocative inefficiencies between ownership, leasing, and mediation arrangements among rice producers in Chile. No other studies deal with this relationship on a cost basis, nor estimate input allocation problems among small rice farmers in Chile. For this purpose, a stochastic frontier model was implemented. Using the primal approach, the degree of input misallocation was estimated and the cost of production was broken down into frontier costs and technical and allocative inefficiencies on a farm basis. The model is applied to a panel data of rice farmers in the Ñuble Region, Chile, collected during the years 2014 and 2015.

This paper is structured as follows: The second part concisely describes rice cultivation and its production chain in Chile. The third section briefly describes the agricultural land tenure system in the country and analyzes its evolution over time. The fourth section introduces the theoretical model and explains the methodology used for this study. The fifth section discusses the data used in the research. In the sixth section, the results obtained are presented and analyzed. Finally, in the seventh section, the main conclusions derived from this study are summarized.

Model

This study uses the primal system approach proposed by ^{Schmidt et al. (1979}) and extended by ^{Kumbhakar et al. (2006}) to identify and measure technical and allocative inefficiencies for a sample of Chilean producers. This approach consists of a production function and first-order conditions of the cost minimization problem. It is algebraically equivalent to the cost system of the self-dual production function (²⁷), but it starts from a parametric production function rather than a cost function.

Consider a Cobb-Douglas production frontier with j inputs, as proposed by ^{Battese et al. (1988}).

where:

y = denotes output

xj = jth input

aj = are technology parameters to be estimated

v = a random error term capturing events beyo nd farmers’ control, which is independently and identically distributed.

u= a non-negative term capturing persistent technical production inefficiency, independently and identically distributed as . Expressing equation (¹) in terms of In x1 we obtain,

where:

are the returns to scale. Equation (²) can be seen as a function of input distance. Following to ^{Kumbhakar et al. (2020}); ^{Musau et al. (2021}) and ^{Schmidt and Lovell (1979}), the first order conditions of the cost minimization problem are2:

where:

PM xj = the marginal product of xj and wj is the price of input j. The term represents the inefficient allocation of input j relative to input 1, the numeraire. Given linear Price homogeneity, it is only possible to estimate negative inefficiency. So, input must be numeraire to identify (⁶). Then, if there will be an underutilization of input j relative to input 1, while if will be overused relative to input 1. Using logarithms for the first-order condition (³),

Then, using the distance function (²), equations (^3,4) derived from the first-order conditions, and solving for xj, the following input demand functions can be obtained logarithmically,

where:

The production cost function can be obtained from the input demands, taking the following form

where:

As pointed out by ^{Kumbhakar et al. (2006}), ^{Musau et al. (2021}) and ^{Vasconcelos (2020}), the impact of technical and allocative inefficiency on production costs can be obtained by comparing the cost function with and without inefficiencies. In the cost function, technical inefficiency increases costs by , while allocative inefficiency increases them by 100(E - Inr)%. When there is no inefficient input allocation, i.e., when , the E and In r terms are equal. Moreover, there is an inverse relationship between the firm’s returns to scale (r) and both inefficiencies. More productive firms should also be more efficient in production and input allocation.

Data

This study uses a balanced panel of 107 rice producers from Ñiquén and San Carlos communes in Ñuble Region, Chile. Data were collected by the Agricultural and Livestock Research Institute (INIA for its acronym in Spanish), particularly, the Technical Assistance Program (SAT, for its acronym in Spanish) from 2014 to 2015. They provide information on yield (kg), output value (CL$), land use (ha), production costs (CL$), public and private infrastructure, and farmer characteristics. Following the methodology described by ^{Alem et al. (2018}) and ^{Henderson (2015}), the prices of the inputs used in this study were collected from secondary sources. Prices per man-day (MD) reflect wages for hired labor, the machinery cost is measured in CLP per hectare, and the price of land (ha) corresponds to the equivalent lease’s market value, representing the opportunity cost. These price data were obtained from the Chilean Ministry of Agriculture’s Office of Agricultural Studies and Policies (ODEPA, for its acronym in Spanish), guaranteeing their reliability and relevance to the country’s agricultural context. For other inputs (seeds, fertilizers, and pesticides), the Consumer Price Index (CPI) was used, as suggested by ^{Musau et al. (2021}). Prices are expressed in Chilean pesos (CL$) for 2014.

Table 1 (page 67), shows summarized statistics of the production cost structure and factor prices per kg of output. Labor costs are the lowest and fluctuate between $5.84 and $70.60, with an average of $20.80.

Table 1 Descriptive statistics of production costs and input prices. Tabla 1. Estadísticas descriptivas de costos de producción y precios de insumos. 

Machinery, other inputs, and land average about $40 and $43 per kg of rice, dominating 86% of the overall cost structure. As expected, the price per hectare of land is the highest, followed by the price per hectare of agricultural machinery and the price per man-day. For estimating the stochastic production frontier, one output and four input variables were used. Total output was measured in kilograms of rice, land in hectares, labor in MD, machinery in hectares, and the other inputs (seeds, fertilizers, and pesticides) in thousands of Chilean pesos as of 2014.

Table 2 shows the summarized statistics of the variables used in the production function. In terms of output, the maximum production level reached 141 tons in 2015, representing a 68% drop, compared to the maximum in 2014.

Table 2 Descriptive statistics of output and inputs. Tabla 2. Estadísticos descriptivos de productos e insumos. 

On average, there was also a significant drop, albeit less pronounced, in the production level, falling back by 9.1%, compared to the previous figure. This result is in line with the decrease in the total area cultivated with rice in Ñuble Region, which fell by 18% in 2015, compared to 2014 (³²). Land use and agricultural machinery also show significant drops of 9.1% and 37.5% on average between periods, respectively. The decrease in machinery use may reflect a capital investment drop, which is in line with the decline in the rice area. In contrast, the number of man-days and the cost of other inputs, considering expenditure on seeds, fertilizers, and pesticides, increased by about 3% in 2015.

Regarding technical and allocative inefficiency cost determinants, annual averages were calculated for each determinant as a model was estimated by assuming persistent technical inefficiency. This arrangement makes sense because the panel is small and few observations demonstrate variation between the relevant years. The estimations were adjusted to account for these observations (⁴¹). Table 3 (page 68), shows descriptive statistics for variables related to farmers’ characteristics, public agricultural infrastructure, and land tenure systems.

Table 3 Descriptive statistics determining allocative and technical inefficiency costs. Tabla 3. Estadísticas descriptivas determinantes de los costos de ineficiencia técnica y de asignación. 

Educational level was represented by a categorical variable, as follows: No education (0), incomplete primary education (1), complete primary education (2), incomplete secondary education (3), complete secondary education (4), incomplete tertiary education (5), and complete tertiary education (6). Only one farmer claimed to have completed college education, whereas more than 75% of the farmers said they had only completed their primary education. The difference between the administration date of the survey and the start of business operations in the rice industry served as the unit of measurement for farmer experience, which was expressed in years. Farmers said they had been producing rice for an average of 12 years; the farmer with the least experience said they had been doing it for two years, while the farmer with the most said they had been doing it for 35 years. The percentage of total agricultural land set aside for rice farming reflects specialization. Farmers in the study devote an average of 50.8% of the land to this crop. Concerning access to water, a dummy variable was created, assuming a value of 1 when the farm is supplied from a rainwater reservoir and 0 otherwise. On average, 43% reported access to water from a pool. Finally, on land tenure systems, 44% of the farmers report working the land by sharecropping and just under 20% report renting the land.

Results and discussion

Table 4 (page 69) shows inefficient allocation parameters for land, labor, and other inputs relative to machinery by land tenure type.

Table 4 Estimates of inefficient allocation by inputs and tenure. Tabla 4. Estimaciones de asignación ineficiente por insumos y tenencia. 

Results suggest that, on average, none of the inputs is used optimally and there is inefficient allocation. On an input basis, land shows the highest inefficiency level, with an three times higher than optimal across all tenure types, revealing a high degree of under-utilization, relative to , thus indicating efficient input allocation. In labor, this situation is also observed, but to a lesser extent, fluctuating between 23% and 33%. On the other hand, other inputs are the only over-utilized factor, with a parameter between 0.617 and 0.638. This result may be associated with the high fertilizer and soil preparation costs incurred by farmers to mitigate the impact on productivity due to weed proliferation. Assessments in the Ñuble Region determined average yield losses of up to 30% due to poor weed control (³⁸).

Concerning land tenure, on average, landlords are the most inefficient input allocators, while sharecroppers are the least inefficient. This finding is generally not supported by empirical literature. ^{Bolhuis et al. (2021}), ^{Chen (2017}) and ^{Chen et al. (2022)}, found that greater access to land rental markets via land titling programs would significantly contribute to reducing the inefficient allocation of productive factors. However, some theoretical and empirical contributions provide insights that may aid in explaining this result. Authors such as ^{At et al. (2019}), ^{Jacoby et al. (2009}), ^{Jamal et al. (2009}), ^{Pi (2013}), argue that sharecropping efficiency, compared to other land tenure arrangements, can be conditioned by the landowner’s monitoring efforts, benefits division, and landholders’ external choices. In other words, sharecropping can be expected to be more efficient because the interests of both sides in sharing benefits make monitoring closer and more effective. These two characteristics are not observed in the sample, but there is educational information from the farmers that could be associated with access to external options for income generation. In our sample, sharecroppers have, on average, a lower schooling level (incomplete secondary) than tenant farmers (complete secondary). This characteristic may be a sign of greater dependence on rice cultivation for income generation, fewer external options, and, thus, greater commitment to devote more time and effort to rice production. This effect does not necessarily hold for other tenure modalities. For example, in cases of lease or land ownership, when the farmer needs to hire workers at a fixed rent, regardless of performance, there may be less incentive for productivity as wage needs to be indexed to performance. This is not the case in a sharecropping arrangement as each party’s income is a fraction of the total benefits, a function of their effort.

From equation (⁷), it is evident that inefficient input allocation will negatively impact production costs. This impact was estimated using these results and technical inefficiency estimates from the input distance function (²). Table 5 (page 70), shows the average cost to produce 1 kg of rice under different inefficiency constraints.

Table 5 Average production cost per kg under different inefficiencies (CLP$). Tabla 5. Costo promedio de producción por kg bajo diferentes ineficiencias (CLP$). 

As expected, sharecropping farms show the lowest production costs on average, i.e., 13.5% lower than leased farms and 3.4% lower than owned farms. Using totelling’s Generalised T-squared tests of means, both the cost of technical inefficiency and allocative inefficiency were found to be significantly different than zero at 1%. Ignoring these costs could lead to underestimating actual farm production costs, regardless of tenure arrangement. Results indicate that economic inefficiency costs exceed frontier costs by 82% in the three tenure arrangements. This percentage is higher, compared to estimates reported for grain production in Norway (³) and China (⁴⁶), and lower than estimates for Indonesia (⁴). On average, 74% of economic inefficiency is attributable to technical inefficiency (61% absolute) and the remaining 26% to allocative inefficiency (21% absolute), i.e., most cost inefficiency is associated with long-term rigidities that are external but affect farm management (^9,29). Both inefficiencies turn into a production cost increase per kg of rice. In line with results in table 4, sharecropping shows the lowest monetary cost inefficiency ($77.8), followed by landowners ($80) and tenants ($88.6). These differences can be partly explained by the fact that sharecroppers have frontier costs that, on average, are 7.5% lower than the other tenure arrangements, but mainly because they have lower inefficient allocation costs due to input misallocation (Table 4). The latter may be related to monitoring efforts, benefit sharing, and sharecroppers’ eventual lower access to external income sources.

This perspective raises an interesting explanation for the potential benefits of sharecropping as a more efficient production organization system compared to land ownership and leasing systems, especially from a wage point of view. One of the critical aspects is that sharecropping is based on a performance-linked incentive system, in contrast to the time-based compensation that is more common in land ownership and leasing systems. In sharecropping, workers have a greater incentive to deploy additional effort and perform all necessary tasks more efficiently, which can reduce or even eliminate the need for supervisory costs typical in wage labor systems. In addition, sharecropping can be a viable alternative when there are labor shortages or financial difficulties in paying wages. This is because sharecropping arrangements often involve a more equitable sharing of risks and rewards between the landowner and the farmer, which can benefit the farmer and the farm from an economic perspective. From a temporal perspective, it is also important to consider that in agricultural production, there are stages or cycles in which the marginal productivity of labor may be lower than the wage paid, which would not be economically optimal. Sharecropping can mitigate this problem by encouraging greater labor intensity relative to other contracting systems, which could improve farm economic performance (⁸).

In summary, sharecropping may offer economic and efficiency advantages in the organization of agricultural production, especially in comparison to land ownership and leasing systems, due to its performance-based incentives and its ability to adapt to variable situations in agriculture.

Table 6 shows the results of Welch’s mean difference test for inefficiencies, according to tenure agreement.

Table 6 Mean difference test. Tabla 6. Prueba de diferencia de medias. 

The first column indicates no statistically significant differences in technical cost inefficiency among lease, sharecropping, and ownership. However, there are significant differences between 1% at allocative inefficiency and total inefficiency (columns 2-3). These results suggest that time-invariant structural and institutional factors affect farm management across farm tenure types. Those differences in efficiency may be related to farmers’ ability to allocate inputs efficiently. At least in this sample, this ability would be related to tenure type.

Figure 1 shows the kernel density distributions of both types of inefficiency.

(a) shows the kernel distribution of technical inefficiency costs; (b) shows allocation inefficiency costs. (a) muestra la distribución kernel de los costos de ineficiencia técnica; (b) muestra los costos de ineficiencia en la asignación.

Figure 1 Cost inefficiency distribution, according to property tenure. Figura 1. Distribución de la ineficiencia de costos, según tenencia de la propiedad. 

In the left-hand panel, the resulting distributions reveal that technical inefficiency scores are skewed to the right for each tenure arrangement. This is confirmed by the 0.403,1.235, and 1.196 skewness coefficients for leasehold, sharecropping, and ownership, respectively. The three distributions look similar, having a high score density, with 92% of the farms located between 0.55 and 0.65. In the right-hand panel, allocation inefficiency distributions for leasing and sharecropping are asymmetric to the right, with coefficients of 0.304 and 0.373. At the same time, owners show an asymmetric distribution to the left with a -0.382 coefficient. Sharecropping shows a high density towards lower inefficiency scores than the other distributions. Particularly, 87% of the farms are between 0.18 and 0.21.

Empirical results for the monetary cost determinants of technical and allocative inefficiency are shown in Table 7 (page 72).

Table 7 Cost determinants of technical and allocative inefficiency. Tabla 7. Costos determinantes de la ineficiencia técnica y de asignación. 

Standard errors in parenthesis. *, **, and *** indicate statistical significance at 10%, 5% and 1%, respectively.

Errores estándar en paréntesis. *, **, y *** indican significancia estadística al 10%, 5% y 1%, respectivamente.

Columns (1) and (4) show that leased land has significantly higher technical and allocative inefficiency costs than owned land (baseline). Regarding sharecropping, the results indicate that this tenure arrangement is statistically more cost-efficient than the ownership system, consistent with previous findings. This efficiency could be related to the fact that sharecropping is based on a contract in which the sharecropper’s salary is linked to the farm’s performance and, in many cases, is made in kind. Therefore, the sharecropper’s earnings are directly related to his performance. This relationship between performance and profits in sharecropping can foster greater efficiency in resource allocation, as both the owner and sharecropper have a shared interest in maximizing farm productivity. Combining the landowner’s experience and knowledge with the sharecropper’s labor could result in greater efficiency than other land tenure systems.

The estimated coefficients for the land variable suggest that more extensive landholdings are more inefficient, the relationship being non-linear, but decreasing. Although not significant, this result is in line with other findings for the agricultural sector (^15,30,43). The specialization coefficient indicates that farmers who allocate a larger proportion of the farm to rice production have significantly lower inefficiency costs. As suggested by ^{Jaime and Salazar (2011}), this result indicates that farmers who specialize in rice cultivation tend to have some advantages in productivity, compared to farmers who diversify and devote their land to other kinds of crops. Education is included in columns (2) and (5) to control for farmer-level heterogeneities. Again, the sharecropping coefficient is only significant in explaining allocative inefficiency costs. The estimated coefficients for leasing and weeding decrease when compared to the results in columns (1) and (4). In the first case, the drop is between 12.7% and 24.9%, while in the second case, it is between 13.7% and 12.7%. This indicates that when controlling for the farmer’s educational level, the tenure arrangement’s effect tends to be more favorable in terms of inefficiency costs. This finding could be related to the fact that better educated farmers have better access to information on good agricultural practices, technical advice and training programs, subsidies, or new production technologies, all of which have a positive impact on efficiency. However, note that the education coefficient is positive and statistically significant for the allocative inefficiency cost, which is not expected but is in line with the findings of ^{Henderson (2015}) and ^{Vasconcelos (2020}). It is reasonable to think that farmers with higher educational attainment face higher opportunity costs in their occupational choice and may see a reduced effort in rice production due to less reliance on farming for income generation.

Columns (3) and (6) include experience as a determinant of inefficiency cost and commune fixed effects. In inefficiency costs, the coefficients for tenure arrangements change slightly, implying that commune-specific market characteristics and imperfections appear to be unimportant in driving the relationship between land tenure and inefficiency costs. This result makes sense given that the communes of Ñiquén and San Carlos are in the Ñuble region and only 33 km apart, implying that there are unlikely to be significant differences in the land market, productive infrastructure, accessibility to inputs, and employment opportunities that contribute significantly to reducing technical and allocative inefficiency costs in each land tenure arrangement.

Finally, it is studied how rice production costs could change with an improvement in the allocation of land input, using current costs as a benchmark. Table 8 (page 73), partially reproduces the results of Table 5 (page 70) and incorporates the estimated costs for different levels of inefficiency.

Table 8 Production costs under different levels of inefficient land allocation. Tabla 8. Costos de producción bajo diferentes niveles de asignación ineficiente de la tierra. 

Relative to benchmark, a 40% efficiency improvement potentially reduces allocation costs by 40.8% for leasehold and ownership and by 41.2% for sharecropping. This leads to an average decrease of 4%-5% in production costs and an increase of 17.8%, 11.2% and 12.9%, and in profits for leasehold, sharecropping, and ownership, respectively. The last three rows of the table show costs when land allocation is efficient relative to cash input. Costs of 1.5%-1.6% due to inefficient allocation of labor and other inputs remain. This finding suggests that about 93% allocation costs are associated with deficiencies in land use, particularly the underutilization of input relative to the numeraire. The potential impact on profits is considerable. The leased land is the most favored with 49.1% increase in earnings. On the other hand, sharecropping and ownership could increase their profits by 25.3% and 29.8%, respectively. These results are intuitive as they demonstrate the monetary impact of efficiency; allow us to understand that there are significant differences depending on the land tenure arrangement; and highlight the need for public policies encouraging the efficient use of productive factors.

Conclusions

This paper empirically investigated how agricultural land ownership, sharecropping, and leasing regimes may affect production cost efficiency. For this purpose, a sample of 107 rice producers from the Ñuble Region in Chile, observed from 2014 to 2015, was used, and a stochastic frontier model of costs was estimated using the primal system approach. This allowed estimating misallocation measures for productive factors, technical and allocative efficiency scores, and decomposing production costs into three components: frontier costs, costs due to technical inefficiency, and costs due to allocative inefficiency.

The results revealed that, on average, inefficiency increases rice production costs by 82%. Of this increase, 61% was attributed to technical inefficiency, while 21% was due to costs due to allocative inefficiency. Regarding the latter costs, statistically significant differences were found among the various land tenure regimes. In particular, the sharecropping system stood out as the most efficient, with production costs 13.5% lower than the rental system and 3.4% lower than those of the ownership system.

The finding may be connected to sharecropping’s potential benefits over land ownership and leasing systems as a production organization system, particularly regarding higher labor productivity and reduced labor and supervision costs. One of the critical factors in this regard is that, in contrast to the time-based wage that is more typical in land ownership and leasing systems, sharecropping in Chile is based on a performance-linked incentive structure. Sharecroppers have a higher incentive to exert more effort and complete all responsibilities more efficiently, which can cut down on or do away with the costs associated with supervisión that are typical in wage labor systems. This is because sharecropping agreements frequently entail a more equitable distribution of risks and benefits between the landowner and the farmer, which can benefit the farmer and the farm from an economic perspective.

An additional relevant finding is that, regardless of the land tenure regime, a public policy that addresses the misallocation of the productive factor of land among farms could potentially reduce up to 93% of the costs associated with inefficient allocation per kilogram of rice. This would substantially impact farmers’ profits and, consequently, wealth generation in the rice industry. According to estimates, improving land use efficiency would result in significant, cross-sectional profit increases for all land tenure types.

This study provides valuable data on the efficiency of rice production. It highlights differences in cost efficiency levels according to land tenure type. It suggests that these differences may be related to the potential of each tenure system to ensure better farm yields. It also highlights the need for public policies that promote a better allocation of productive resources for the whole sector’s benefit. A limitation of this study is assuming that all farmers, regardless of tenure type, have the same skills for working the land. In this sense, relaxing this assumption could solve input misallocation by redistributing them from less to more skilled farmers so that optimum marginal productivities are equated. The latter could be a topic for future research on the particular case of Ñuble Region in Chile.