The study was conducted in the Matam region, located in northeastern Senegal, 700 km from Dakar, between 14°20 and 16°10 north latitude and 12°40 and 14°60 west longitude (Kabore, 2020) (Fig. 1). It covers an area of 29,616 km², or 15.1% of the national territory, making it the second largest region after Tambacounda (ANSD 2024). The Matam region is located in the middle Senegal River valley. The area has a Sahelian climate with two seasons: a dry season lasting eight months (from November to June) and a wet or rainy season lasting only four months (from July to October). It is located at the isohyet between 300 and 500 mm (Ndiaye et al., 2015), with an average annual temperature of 31.4°C, with the average maximum (44.5°C) recorded in May and the minimum (17°C) in January. The area is subject to two types of winds: the harmattan (a hot, dry wind blowing from the north/northeast) and the monsoon (a hot, humid wind that blows during the rainy season) (ANSD 2024).

There are three distinct agroecological zones: the "Dandé Mayo" or "Walo" or river valley (area under study) consists of depressions and micro-reliefs; the "Ferlo" is a lateritic zone for the most part, and sandy in its western part (Lougré Thiolly and Vélingara); and the "Dieri" or intermediate zone (ANSD 2017). The region has significant water resources, particularly surface water, with the Senegal River running through it for 200 kilometers (km) in the north and east. Agriculture is practiced by 82.4% of households in rural areas and 17.6% of households in urban areas, as the region has an estimated 55,000 hectares (ha) of irrigable land, of which 9,148 are developed by the Société d'Aménagement et d'Exploitation des Terres du Delta du Fleuve Sénégal (SAED), the Matam Agricultural Development Project (PRODAM), and private entities. Agricultural technologies have been introduced in the area, such as the intensive rice cultivation system in 2010, to increase rice productivity.

Basic descriptive statistics, such as mean, frequency, and percentage, were used for the socioeconomic characteristics of producers. The stochastic frontier parametric model was used to estimate the technical efficiency of rice producers and its determinants. In addition, a Multinomial Endogenous Switching Regression (MESR) was used to estimate the impact of the combined adoption of System of Rice Intensification (SRI) on the technical efficiency of rice producers, where the value of technical efficiency (between 0 and 1) was used as the outcome variable. The collected data were analyzed using STATA/SE-17.0 software (StataCorp, 4905 Lake Way Drive, College Station, TX 77845, USA).

The impact of the combined adoption of SRI components (seedlings less than 21 days old, one seedling per hill at transplanting, and 25 cm spacing between seedlings) on the technical efficiency of rice farmers in the study area was analyzed using an econometric model based on Multinomial Endogenous Switching Regression (MESR). This method is used because producers generally adopt a package of technologies, unlike the logit and probit methods, which consider the adoption of a single technology. This method is more appropriate for addressing selection bias issues when the adoption of technology involves more than two options (Kassie et al. 2015; Oparinde 2021; Ahmed 2022; Setsoafia et al. 2022). Observed and unobserved factors (e.g., farmers' innate abilities and motivations) can influence their decisions when choosing to adopt a single SRI or a combination of them. The MESR approach allowed for a two-level estimation. First, there are factors influencing the adoption of a single SRI or a combination of SRI practices. Second, there is the impact of the combined adoption of SRI practices on the technical efficiency of rice farmers. This study focuses on three SRI practices, namely nursery duration (P), number of plants per hill (N), and distance between plants at transplanting (D). These three levels give rise to eight mutually exclusive choices of SRI technology, namely (1) non-adoption (P₀N₀D₀); (2) compliance with nursery duration only (≤ 21 days) (P₁N₀D₀); (3) number of plants per hill only (1 plant per hill) (P₀N₁D₀); (4) distance between plants only (P₀N₀D₁); (5) compliance with nursery duration and number of plants per clump (P₁N₁D₀); (6) compliance with nursery duration and distance between plants (P₁N₀D₁); (7) compliance with the number of plants per pot and the distance between plants (P₀N₁D₁); (8) simultaneous adoption of all three practices (P₁N₁D₁). Farmers choose one of the eight possible options to maximize their expected benefits. Indeed, the theory of McFadden (1972) stipulates that an individual's choice is rational and always oriented toward the option that seems most advantageous among the possible options.

The study assumes that the error terms are identical and independently distributed according to a Gumbel distribution. The probability that rice farmer i, with characteristics X, will choose option j from among the eight possible options is specified using a multinomial logit (MNL) model (McFadden 1972; Teklewold et al. 2013; Zhou et al. 2020). It is specified as follows:

Where: represents the probability that producer i will choose to adopt SRI practice option j; is a vector of observed exogenous variables that capture characteristics at the household, plot, and location levels is a vector of parameters to be estimated.

Maximum likelihood estimation (MLE) is used to estimate the parameters of the latent variable model. In a second step, the ordinary least squares (OLS) model is used to establish the relationship between the outcome variable (technical efficiency) and a set of exogenous variables designated by Z for the chosen SRI combination. Non-adoption of SRI practices (P₀N₀D₀) is designated by j = 1, with the other combinations designated by j = 2, ..., 8. The possible equations for each regime are specified as follows:

Regime 1 : (9)

.

.

Regime j : (10)

Where: I is an index that indicates farmer i's choice to adopt a combination of SRI; is the outcome variable for farmer i; is a vector of exogenous variables; and are parameters to be estimated; and are the error terms; and are selectivity correction terms used to resolve unobserved selection bias issues; and are the covariances between the error terms.

The average treatment effect on treated individuals (ATT) is then calculated in this step. This involves comparing the expected outcome (technical effectiveness) of adopters and non-adopters of SRI practices, with and without adoption. The study estimates the ATT in the actual and counterfactual scenarios using the following equations:

The outcome variable for users of SRI practices who adopted the system (actual scenario):

.

.

The outcome variable for adopters of SRI practices if they had decided not to adopt the system (counterfactual scenario):

.

.

The difference between equations (4a) and (5a) or between equations (4b) and (5b) corresponds to the ATT. For example, the difference between equations (4a) and (5a) is given by:

Table 3 highlights the sociodemographic characteristics of rice farmers in the middle Senegal River valley. Men are in the vast majority in rice farming, accounting for 96.65%, while women account for only 3.35%. In terms of marital status, a large proportion of rice farmers in the study area are married (92.89%), compared to 4.89% who are widowed and 4.44% who are single. Regarding age, almost all rice farmers are over 45 years old (80.80%), followed by those aged 30–45 (17.41%). However, it was noted that young people aged 20 to 30 and under 20 are very poorly represented, with respective frequencies of 1.34% and 0.45%. In terms of education level, more than half of the farmers surveyed (63.11%) had received no formal education, with the remainder having received various types and levels of education, dominated by Qur’anic teaching (25.33%) and primary education (8%). Agriculture is the main activity of 83.56% of the producers surveyed, with more than half (53.33%) being active members of a farmers' organization (FO). The average size of plots dedicated to rice production is 0.96 hectares. However, the majority of these farmers have not been trained in production techniques (72.89%), have not been supervised (81.17%), resulting in a lack of knowledge of SRI (System of Rice Intensification) (79.41%).

Table 4 shows the different levels of technical efficiency. The results show that producers are moderately efficient, with an estimated average technical efficiency of 53.2%, ranging from a minimum of 0.1% to a maximum of 85.4%. This means that the average and most efficient rice farmers need to improve their technical efficiency by 46.8% and 14.6%, respectively, to reach the maximum production frontier. In terms of distribution, only 3.27% have a technical efficiency level above 80%, while the majority (45.33%) have an efficiency level between 61% and 80%.

The stochastic production frontier was estimated for rice-growing households in the study area. Table 5 presents the determinants of technical efficiency. The estimated β coefficients represent production elasticity and indicate, if positive, that an increase in the factor in question leads to an increase in rice production, and the opposite if negative. The results show that only the quantities of seeds and chemical fertilizers used have a highly significant and positive influence on production (p-value < 0.01). On the other hand, the area, the quantity of organic fertilizers, the quantity of pesticides, and the labor components (family and external) proved to be unproductive. Table 5 also highlights the socioeconomic determinants of producers' technical inefficiency. It should be noted that the sign of the coefficients associated with the determinants of technical inefficiency indicates their effect on productive underperformance. In this logic, a negative sign indicates a negative influence on inefficiency and therefore a positive influence on technical efficiency, and vice versa. It appears that having no education has a positive and very significant influence on technical efficiency (β = -0.976; p-value = 0.026; CI: -1.835_-0.116). Also, household size was found to have a positive and significant influence at the 10% threshold (β = -0.095; p-value = 0.053; CI: -0.192_0.001). However, it was noted that age, membership in a farmer’s organization, and marital status (married or widowed) had a negative but insignificant effect on the productive performance of rice farmers (p-value > 10%).

Table 6 shows the frequency with which producers adopt different combinations of SRI practices. The results show that 46.44% of rice farmers in our sample do not adopt any SRI practices. The proportion of rice farmers adopting only one component of SRI is 16.32% for the number of plants per hill only (P₀N₁D₀), 12.13% for monitoring compliance with nursery duration (P₁N₀D₀), and 1.67% for compliance with plant spacing during sowing. Similarly, the highest rate (11.33%) is for the combined adoption of compliance with nursery duration and plant spacing in combination with SRI categories. Very few producers adopt both compliance with plant spacing only (P₀N₀D₁) and the number of plants per hill and plant spacing (P₀N₁D₁). Approximately 7.11% of rice farmers simultaneously adopt all three components of SRI (P₁N₁D₁).

Table 7 presents the results estimated by the multinomial logistic model (MNL), which highlight the factorial analysis of the determinants influencing the decision of rice farmers in the study area to adopt one or more SRI practices. Farmers who have not adopted any type of SRI (P₀N₀D₀) are used as the reference group in the empirical estimates of the MLM model.

First, the results show that only membership in a farmer’s organization (FO) significantly promotes the exclusive adoption of the recommended nursery duration (P₁N₀D₀). Second, household size, membership in an FO, and having a Koranic education positively and significantly influence the exclusive adoption of the recommended number of seedlings per hole (P₀N₁D₀). However, knowledge of SRI seems to negatively affect this adoption.

Furthermore, lack of education has a negative influence on the exclusive adoption of the recommended plant spacing (P₀N₀D₁). On the other hand, knowledge of SRI has a very significant and positive effect on the adoption of this category.

With regard to the P₁N₁D₀ combination, the results indicate that household size, knowledge of SRI, and lack of education have a significant and positive influence. In addition, the fact that agriculture is the respondent's main activity, membership in a PO, and household size positively influence the adoption of the P₁N₀D₁ category. However, family labor negatively impacts the adoption of this combination.

Furthermore, no parameter significantly influences the combined adoption of the specified number of plants per hole and the recommended distance between plants (P₀N₁D₁). Finally, being married significantly and negatively influences the simultaneous adoption of the three SRI practices (P₁N₁D₁). Conversely, being male, knowledge of SRI practices, and household size positively influence the adoption of this category (P₁N₁D₁).

Table 8 shows the impact of the combined adoption of SRI practices on the technical efficiency (TE) of rice farmers. The adoption of the P₀N₁D₀ category, corresponding to compliance with the number of plants per hill only, has a positive and very significant impact on technical efficiency. The ATT estimate also shows that adopting the package that combines all three practices (adherence to the recommended nursery duration, adherence to the number of plants per hill, and adherence to the recommended distance between plants (P₁N₁D₁)) significantly increases technical efficiency.

Rice farming in the study area is mainly practiced by married men. This is because, in line with the logic of specialization in society, rural women are more active in household activities and market gardening. Indeed, according to Ndiaye & Kabou (2021), rural women spend more time on household tasks than on farm work. Our results confirm those of Fall (2016) and Sane (2019), according to whom 94% and 88.72% of rice farmers in the Senegal River Valley are men, respectively. The majority of rice farmers are aged 45 or over, which could be explained by the fact that this age group has important responsibilities as heads of households, with needs to be met. It is normal for them to be more involved in rice farming activities. These results are consistent with those of Sane (2019), where the average age was 52.70 years. It was noted that the majority of rice farmers are not familiar with SRI, have not been trained in agriculture, and have no technical support, despite the fact that agriculture is their main activity.

This study shows that, on average, rice farmers in the study area are operating at only 53.2% of their maximum production capacity. This translates into a potential for improving production performance by 46.8% without necessarily increasing inputs. Our results are consistent with those of Diallo & Garba (2023), who found an average technical efficiency score of 54.5% among rice farmers in Senegal. According to the distribution, there was a low representation of the highest efficiency levels (81–100%). This could be linked to a poor understanding of technical production methods, which would reduce producers' ability to increase their production without simultaneously increasing their inputs (seeds, fertilizers, etc.).

The estimation of the production function showed that the use of chemical fertilizers increases producer performance. This can be explained by the fact that the application of large quantities of fertilizer increases the immediate availability of the nutrients that plants need for their development. In addition, according to Ahmadou et al. (2023), the use of high doses of fertilizer promotes a drop in soil pH and, consequently, the growth of rice plants. At the same time, the quantity of seeds used promotes the performance of rice farmers, as seeds are the basic element of production. This observation is consistent with that of Coulibaly et al. (2017), who noted a 0.40% increase in production for a 1% variation in seed quantity. However, our results are not consistent with those of Diallo & Garba (2023), who found that increasing the quantity of seeds does not influence efficiency, as quality is more important than quantity. However, the quantity of organic fertilizer used was found not to influence production. This can be explained by the fact that rice farmers in the area do not have livestock that would provide them with unlimited organic fertilizer for rice production. Similarly, the size of the plot does not influence technical efficiency. This result corroborates the work of Mendy (2019), which found that increasing plot size had a negligible effect on efficiency.

The technical inefficiency model estimate showed that having no education has a negative effect on inefficiency, and therefore, uneducated rice farmers had better technical efficiency. This could be related to the fact that they have more time to gain experience in rice production than those with advanced schooling, as they become involved at a very early age. Indeed, according to Diallo & Garba (2023), lack of education reduces the technical inefficiency of rice farmers by 12.2%. Our results are corroborated by those of Ndiaye & Kabou (2021), according to which the lack of formal education has a positive impact on the technical efficiency of 21.7%. In addition, household size has a negative influence on technical inefficiency, reflecting the better productive performance of large households. This is linked to the fact that larger households have a larger workforce and can meet all the requirements of rice production. And in a context of low mechanization, the large size of households makes it possible to carry out farming operations in accordance with the farming calendar, particularly in the study area, where rice cultivation requires a significant amount of labor. This observation is at odds with that of Ndiaye & Kabou (2021), according to which household size has a negative impact on the technical efficiency of rice farmers. Other studies, such as those by Mendy (2019), report that an increase in household size reduces efficiency.

The results show that the majority of rice farmers in the middle Senegal River valley do not adopt the intensive rice cultivation system (P₀N₀D₀). Furthermore, a very small proportion of rice farmers (7.11%) adopt all three SRI practices simultaneously. This is a consequence of the lack of training on SRI and, therefore, the limited knowledge of SRI principles and practices, as well as the lack of technical support for farmers. Indeed, according to the results of Dione (2019), the fact that households are aware of the SRI may encourage its adoption.

The exclusive adoption of the P₁N₀D₀ category, corresponding to compliance with the recommended nursery duration (less than 21 days), is more prevalent in the study area. This could be explained by the fact that farmers are aware that nurseries exceeding this duration were less productive and more fragile. To this end, according to Andriankaja (2001), the SRI recommends transplanting young plants in order to limit the consequences of transplant shock and the resulting yield losses. In addition, before tillering begins, a stage that coincides with the start of photosynthetic activity, the plant feeds on the reserves in the grain and can withstand the brief stress caused by transplanting.

Male rice farmers who are members of an FO, familiar with SRI, and living in large households are more likely to adopt all three SRI practices simultaneously (P₁N₁D₁). This is because men are more involved in rice production and because training and awareness-raising sessions are often held in FO with a view to building members' capacities. In addition, knowledge of a technology promotes its adoption and therefore its implementation. Similarly, household size facilitates the application of new rice cultivation technologies without the risk of loss of performance due to a lack of labor.

Our results are similar to those of Dione (2019), which show that membership in a PO facilitates access to information about the SRI. In addition, according to Ouédraogo & Dakouo (2017), large families have more labor available for production, which generally encourages the adoption of new technologies.

The impact assessment of the combined adoption of SRI practices using the Multinomial Endogenous Switching Regression (MESR) model revealed that the adoption of the P₀N₁D₀ category, corresponding to transplanting with one seedling per hole, has a significant impact on technical efficiency. This practice prevents root crowding and competition between plants for light and soil nutrients. Indeed, according to Andriankaja (2001), adopting this SRI practice allows farmers to fully exploit the yield potential of the transplanted shoot, which alone can produce more than 80 tillers under optimal conditions. This increases the rice farmer's productivity.

At the same time, the simultaneous adoption of the three SRI practices (seedlings less than 21 days old, one seedling per hole when transplanting, and 25 cm between seedlings) has a very strong and positive impact on the technical efficiency of rice farmers. This impact is linked to the fact that transplanting young rice plants, with a lower planting density, has a greater capacity for development due to the virtual absence of competition between plants and the unlimited availability of nutrients and growing space. According to the study conducted by Andriankaja (2001), the combination of these three practices works synergistically: young rice plants (reduced nursery time) retain their potential, transplanting a single plant unlocks this potential, and spacing maximizes access to resources (soil nutrients, light, etc.). Together, they promote strong tillering capacity, more efficient photosynthesis, better seed economy, and therefore higher technical efficiency. Indeed, according to the study conducted by Barah (2009)Farmers who practice SRI use 5 to 8 kg of seeds, compared to 40 to 50 kg in conventional practices. Our results are consistent with those of Dione (2019), who noted a significant impact of the adoption of SRI practices on the yields of rice farmers in the Senegal River Valley.

The objective of this study was to assess the technical efficiency of rice farmers in the middle Senegal River valley and the impact of adopting the intensive rice cultivation system (SRI) practices on efficiency. The main finding of the study was that the level of efficiency of rice farmers in the middle Senegal River valley is relatively low. It was also noted that factors such as household size, level of education, and the amount of fertilizer and seeds used influence technical efficiency. At the same time, the adoption of SRI practices has a positive impact on the technical efficiency of rice farmers. This adoption is itself strongly influenced by training in SRI, membership in a producer organization, and household size. Thus, training farmers in good rice cultivation practices and the principles and practices of SRI, as well as providing ongoing technical support, are all levers that can be used to improve the adoption of SRI practices and enhance the technical efficiency of rice farmers in the middle Senegal River valley. As part of a strategic approach to improving technical efficiency and, therefore, the productive performance of rice farmers, it is also important to strengthen producer organizations institutionally. National rice self-sufficiency policies should also focus more on making quality seeds and fertilizers accessible through subsidies and credit. In light of this study, it would be interesting to assess the sustainability of rice production systems in the study area in the face of climate change challenges.