Impact of Cassava Producers’ Participation in Inclusive Agribusiness Models on Allocative Efficiency in Benin

Abstract

This study examines the impact of cassava producers’ participation in inclusive agribusiness models (IAMs) on allocative efficiency in Benin, providing new microeconomic evidence on smallholder market integration in Sub-Saharan Africa. Using a sample of 1167 farmers across seven departments, we combine Stochastic Frontier Analysis (SFA) with an Endogenous Switching Regression (ESR) model to estimate efficiency while correcting for observable and unobservable selection bias. The results reveal moderate average allocative efficiency (0.646), indicating that producers remain about 35 percentage points below the cost-minimizing input allocation. IAM participants display higher allocative efficiency (0.700) than non-participants (0.620). The ESR model yields a positive and statistically significant treatment effect: participation is associated with an increase of 0.150 points in allocative efficiency among beneficiaries (ATT), while the potential effect for non-participants is smaller (ATU = 0.060). These results are corroborated by an Inverse-Probability-Weighted Regression Adjustment (IPWRA) robustness check, which yields a closely comparable treatment effect (ATT = 0.132). This ATT–ATU asymmetry reveals treatment-effect heterogeneity and positive selection on gains, as producers with the largest expected efficiency gains are the most likely to participate. Within IAMs, ordinary cooperative membership and the existence of a sales contract are associated with higher allocative efficiency, whereas extension contact and meeting participation, although the strongest predictors of participation, are associated with lower efficiency among participants, pointing to time-allocation trade-offs. The findings offer actionable evidence for designing inclusive value chain policies targeting the most marginalized smallholders and addressing structural constraints limiting efficiency across producer groups.

1. Introduction

Improving allocative efficiency among smallholder farmers constitutes a central objective of agricultural economics research and development policy, particularly in Sub-Saharan Africa, where input markets are thin, price signals are distorted, and transaction costs are prohibitive [1,2,3]. Allocative efficiency, the ability of producers to combine inputs in cost-minimizing proportions given their relative prices, directly determines farm profitability and the competitiveness of agricultural value chains. Yet empirical evidence consistently documents that smallholders operate substantially below the allocative frontier, implying significant potential for welfare gains without additional resource inputs [4,5,6,7].

Inclusive agribusiness models (IAMs), institutional arrangements that integrate smallholders into value chains through contracts, producer organizations, and public–private partnerships, have attracted growing policy and academic interest as mechanisms capable of simultaneously addressing multiple market failures [8,9,10,11]. By reducing transaction costs, improving access to inputs and extension services, and providing market price information, IAMs are expected to enable producers to make more economically rational input allocation decisions [12,13]. However, while a growing literature documents the income and technical efficiency effects of value chain participation, evidence on its allocative efficiency impacts remains sparse. This gap is consequential: understanding how IAMs affect input allocation decisions is critical for assessing their full economic impact and informing the design of more effective interventions [14,15].

This study addresses that gap by examining the impact of IAM participation on allocative efficiency among cassava producers in Benin, a context of considerable analytical interest. Cassava is the dominant food and cash crop for smallholder households in Benin, yet production systems are characterized by poor market integration, suboptimal input use, and substantial resource misallocation [16,17,18,19]. Government-supported IAM initiatives operationalized through the Agricultural Development and Market Access Support Project (PADAAM) provide a well-defined treatment context, while the large sample of 1167 producers spanning seven departments generates sufficient statistical power for credible identification under the assumptions set out in Section 2.3.

Evaluating the efficiency impact of IAMs poses a fundamental methodological challenge: participation is endogenous, as producers self-select based on both observed characteristics and unobserved attributes such as managerial ability and social capital. Standard estimation approaches that ignore this selection process yield biased and inconsistent treatment-effect estimates. We address this by employing the Endogenous Switching Regression (ESR) model [20,21,22], which simultaneously corrects for selection on observables and unobservables and estimates regime-specific efficiency determinants, providing richer information than Propensity Score Matching (PSM) or Instrumental Variable (IV) approaches applied in isolation.

This study makes three contributions to the agricultural economics literature. First, it provides a decomposition of productive efficiency into its technical, allocative, and economic components using a translog stochastic frontier framework applied to cassava production in West Africa, a system poorly represented in the existing efficiency literature relative to rice or maize. Second, it estimates the impact of IAM participation on allocative efficiency using an ESR model that corrects for selection on both observables and unobservables, and interprets that estimate causally only under the explicitly stated identifying assumptions of the framework, namely the validity of the excluded instrument and the joint normality of the error terms. Third, it documents significant treatment effect heterogeneity and the underlying behavioral mechanisms, generating policy-relevant insights on the inclusiveness of value chain integration programs.

2. Materials and Methods

2.1. Institutional Context of Inclusive Agribusiness Models in Benin

The cassava sector in Benin presents the key features that make it a particularly relevant context for studying the relationship between value chain integration and allocative efficiency. Production is dominated by smallholders typically operating plots of under 2 hectares, who face severe input market imperfections, limited access to formal credit, and fragmented output markets characterized by high price volatility and weak buyer–seller relationships [23,24]. These conditions generate the transaction costs and information asymmetries that economic theory predicts will distort input allocation decisions away from the cost-minimizing optimum [25,26].

In response, the Government of Benin, with support from the International Fund for Agricultural Development (IFAD) and other development partners, has implemented the Agricultural Development and Market Access Support Project (PADAAM) in seven departments of southern and central Benin [27]. PADAAM promotes three categories of IAMs that differ in their institutional complexity and depth of vertical integration:

1

Simple contracts (SCs) constitute the entry-level form of market inclusion. They formalize bilateral relationships between producer organizations (POs) and private buyers by specifying volumes, quality standards, prices, and delivery schedules. By stabilizing expected prices and guaranteeing market outlets, simple contracts reduce the price uncertainty that otherwise distorts optimal input investment decisions, thereby creating conditions more favorable to allocative efficiency [13,28].

2

Public–private–producer partnerships (4Ps) introduce a tripartite governance structure that brings together public agencies, private agri-enterprises, and producer organizations. This model addresses systemic value chain bottlenecks (infrastructure, finance, and technical assistance) that simple market linkages cannot resolve individually. The involvement of public actors creates an enabling environment for investment in collective goods (storage, aggregation points, demonstration plots) that reduce input costs and improve the quality of farm management information [29].

3

Joint ventures represent the most advanced form of integration, involving direct producer equity stakes in processing or marketing enterprises. This model strengthens economic incentives through profit-sharing mechanisms and provides the most direct channel for information transmission from processor to producer regarding optimal input quantities and timing [10]. By partially internalizing downstream market functions, joint ventures enable producers to align input decisions more closely with processing requirements and relative factor prices.

IAM participation in the PADAAM framework is mediated through producer organizations, which serve as the contracting unit with private buyers. This architecture means that the benefits of IAM participation, such as improved market information, technical assistance, and input access, are channeled through collective action institutions. It also generates the selection problem central to our identification strategy: participation is determined by household endowments, organizational membership, and social networks, rather than by random assignment.

2.2. Analytical Framework and Estimation Strategy

2.2.1. Conceptual Framework

Our analytical framework rests on the neoclassical theory of the firm adapted to smallholder agriculture [4,30]. A producer is allocatively efficient if, given prevailing input prices, it selects an input combination that minimizes the cost of producing a given output. Deviations from this cost-minimizing input mix define allocative inefficiency, which can arise from imperfect price information, capital constraints, risk aversion, or behavioral biases. The framework predicts that IAM participation should improve allocative efficiency through two channels: (i) the information channel, by improving access to input price signals, agronomic knowledge, and market intelligence; (ii) the liquidity channel, by easing credit constraints that prevent investment in the optimal input bundle. These two channels generate testable predictions: if IAMs improve efficiency through the information channel, we expect the largest gains among producers with weaker baseline information access; if the liquidity channel dominates, gains should be larger among financially constrained producers.

2.2.2. Measuring Allocative Efficiency via Stochastic Frontier Analysis

Overall economic efficiency (EE) can be decomposed as the product of technical and allocative efficiency (EE_i = TE_i × AE_i) [30], implying that allocative efficiency (AE) can be expressed as:

$${\mathrm{AE}}_{\mathrm{i}}={\displaystyle \frac{{\mathrm{EE}}_{\mathrm{i}}}{{\mathrm{TE}}_{\mathrm{i}}}}$$

(1)

where TE_i denotes technical efficiency and AE_i allocative efficiency for producer i. This decomposition allows us to disentangle efficiency losses attributable to production technology from those stemming from a suboptimal input mix. Both components are estimated via Stochastic Frontier Analysis (SFA), which is preferred over Data Envelopment Analysis (DEA) in this context because it separates inefficiency effects from random shocks through Maximum Likelihood Estimation, thereby providing more robust and consistent estimates when working with high-quality data [1,30,31,32,33].

2.2.3. Stochastic Production Frontier

Technical efficiency is estimated from a stochastic production frontier, specified as follows:

$$\begin{array}{cccc}& {\mathrm{Y}}_{\mathrm{i}}=\mathrm{f}\left({\mathrm{X}}_{\mathrm{i}};\mathrm{\beta }\right)·\exp ({\mathrm{v}}_{\mathrm{i}}-{\mathrm{u}}_{\mathrm{i}})& & \end{array}$$

(2)

where Y_i is cassava yield per hectare (kg/ha) for producer i; X_i is the vector of production inputs, namely labor (man-days), planting cuttings, organic manure (kg), NPK fertilizer (kg), urea (kg), and herbicides (liters); ${\mathrm{v}}_{\mathrm{i}}\sim \mathrm{N}(0,{\mathrm{\sigma }}_{\mathrm{v}}^2)$ captures symmetric random shocks (e.g., climatic variability and price fluctuations); and u_i ≥ 0 represents technical inefficiency, assumed to follow a half-normal distribution ${\mathrm{u}}_{\mathrm{i}}\sim {\mathrm{N}}^{+}(0,{\mathrm{\sigma }}_{\mathrm{u}}^2)$ [31,34]. We adopt the translog functional form to capture input substitutability and non-linear returns without imposing restrictive assumptions on the production technology:

$$\ln {\mathrm{Y}}_{\mathrm{i}}={\mathrm{\beta }}_0+{\displaystyle {\sum }_{\mathrm{j}=1}^{\mathrm{J}}}{\mathrm{\beta }}_{\mathrm{j}}\ln {\mathrm{X}}_{\mathrm{ji}}+{\displaystyle \frac{1}{2}}{\sum }_{\mathrm{j}}{\sum }_{\mathrm{k}}{\mathrm{\beta }}_{\mathrm{jk}}\ln {\mathrm{X}}_{\mathrm{ji}}\ln {\mathrm{X}}_{\mathrm{ki}}+{\mathrm{v}}_{\mathrm{i}}-{\mathrm{u}}_{\mathrm{i}}$$

(3)

where lnY_i represents the natural logarithm of cassava output (kg/ha) for unit i; lnX_ji denotes the logarithm of the j-^th input used by producer i; β_j captures first-order input elasticities; and β_jk captures second-order interaction effects reflecting substitution and complementarity relationships among inputs. Land is not entered as a separate input in the production frontier because cassava output is measured per hectare, so cultivated area is already normalized out of the dependent variable; the rental value of land enters the analysis only on the cost side as the price of capital in the cost frontier (Equation (4)).

2.2.4. Stochastic Cost Frontier

Economic efficiency is estimated from a dual stochastic cost frontier, specified as follows:

C_i = f(Y_i,W_i;β) ⋅ exp(v_i + u_i)

(4)

where C_i is the total production cost of cassava (FCFA/ha); Y_i represents output per hectare; and W_i is the vector of the six input prices faced by producer i, namely the price of labor and the prices of cassava cuttings, NPK, urea, herbicide and capital. Linear homogeneity of degree one in input prices is imposed by taking the price of labor as the numéraire. Total cost and the five remaining prices are divided by the price of labor before estimation, so that five normalized price terms are estimated and the labor-price parameters are recovered from the adding-up restrictions. v_i is a symmetric error term capturing random shocks, and u_i (u_i ≥ 0) represents cost inefficiency. The translog cost frontier specification is:

$$\begin{gathered} \ln \left({\displaystyle \frac{{\mathrm{C}}_{\mathrm{i}}}{{\mathrm{w}}_{\mathrm{Li}}}}\right)={\mathrm{\alpha }}_0+{\mathrm{\alpha }}_{\mathrm{Y}}\ln {\mathrm{Y}}_{\mathrm{i}}+{\displaystyle \frac{1}{2}}{\mathrm{\alpha }}_{\mathrm{YY}}{\left(\ln {\mathrm{Y}}_{\mathrm{i}}\right)}^2+{\displaystyle {\sum }_{\mathrm{j}=1}^5}{\mathrm{\alpha }}_{\mathrm{j}}\ln {\mathrm{W}}_{\mathrm{ji}}^{*}+ \\ {\displaystyle \frac{1}{2}}{\displaystyle {\sum }_{\mathrm{j}=1}^5}{\displaystyle {\sum }_{\mathrm{k}=1}^5}{\mathrm{\alpha }}_{\mathrm{jk}}\ln {\mathrm{W}}_{\mathrm{ji}}^{*}\ln {\mathrm{W}}_{\mathrm{ki}}^{*}+{\displaystyle {\sum }_{\mathrm{j}=1}^5}{\delta }_{\mathrm{j}}\ln {\mathrm{Y}}_{\mathrm{i}}\ln {\mathrm{W}}_{\mathrm{ji}}^{*}+{\mathrm{v}}_{\mathrm{i}}+{\mathrm{u}}_{\mathrm{i}} \end{gathered}$$

(5)

where W*_ji = w_ji/w_Li denotes the price of input j normalized by the price of labor, J = 5 normalized prices are estimated (cassava cuttings, NPK, urea, herbicide and capital), and δj denotes the output–price interaction parameters.

where lnC_i is the natural logarithm of total cassava production cost for unit i; lnY_i is the logarithm of cassava output for unit i; lnW_ji denotes the logarithm of the labor-price-normalized price of the j^-th input used by unit i; α_j captures first-order cost elasticities with respect to input prices; and α_jk captures substitution and complementarity effects in the cost function. Both frontiers are estimated by Maximum Likelihood Estimation (MLE) in Stata 17. Allocative efficiency is recovered as ${\mathrm{AE}}_{\mathrm{i}}={\displaystyle \frac{{\mathrm{EE}}_{\mathrm{i}}}{{\mathrm{TE}}_{\mathrm{i}}}}$ following Equation (1).

Capital is proxied by the rental value of cultivated land. Linear homogeneity of degree one in input prices is a defining property of a cost function derived from cost minimization, and it is therefore imposed a priori rather than left unrestricted. Total cost and all remaining input prices are divided by the price of labor before estimation. Homogeneity therefore holds exactly at every observation, by construction. Symmetry of the second-order price terms is likewise imposed by construction, since each cross-price pair enters the specification through a single common parameter, consistent with Young’s theorem. The remaining regularity properties are verified empirically. Monotonicity in input prices and concavity of the cost function in log prices are tested in

Table A1. Summary of specification tests and regularity diagnostics.

Test	Null Hypothesis/Purpose	Test Statistic	Result
1. Accounting-identity check	Total cost is not an exact linear function of its own price components.	R2 of ln(cost) regressed on the 5 ln(relative prices) alone (cuttings, NPK, urea, herbicide, capital/land). Labor used as numeraire and therefore omitted.	R2 = 0.148, F(5, 1161) = 40.32, p < 0.001.
2. LR test, Cobb–Douglas vs. translog production frontier	H0: all second-order terms equal zero.	LR χ2 = 65.51, p < 0.001	H0 rejected; translog specification retained.
3. LR test, Cobb–Douglas vs. translog cost frontier	H0: same restriction, cost frontier.	LR χ2 = 243.69, p < 0.001	H0 rejected; translog specification retained.
4. Skewness test (Waldman, 1982) production frontier [49]	Expected sign of OLS residual skewness: negative.	Skewness = −1.096	Correct sign; consistent with σu = 0.920 (p < 0.01) in Table 2.
5. Skewness test (Waldman, 1982) cost frontier [49]	Expected sign: positive.	Skewness = +0.857	Correct sign; consistent with σu = 1.030 (p < 0.01)
6. Variance decomposition (σv, σu, λ)	Both variance components strictly positive; λ = σu/σv neither ≈ 0 nor >10–15.	Table 2: σu = 0.920, σv = 0.291, λ = 3.166. Table 3: σu = 1.030, σv = 0.200, λ = 5.150 (all p < 0.01).	Both frontiers well identified
7. Monotonicity in prices (cost frontier)	Cost-share elasticities non-negative at the sample mean/for every household.	Five shares, all positive (labor cost share recovered by adding-up).	Satisfied for all five prices (0% violations) under the specification used in Table 3.
8. Curvature (concavity in prices)	Hessian of the cost function in log prices must be negative semi-definite (all eigenvalues ≤ 0).	All eigenvalues negative: −0.224, −0.185, −0.146, −0.131, −0.093.	Satisfied: all eigenvalues negative at the point of approximation
9. Falsification test of instrument validity	Trust in cooperative management has no direct effect on AE among non-participants.	OLS of AE on trust + Panel A covariates, non-participants; trust = 0.0246 (SE = 0.0389), t = 0.63, p = 0.527.	Not statistically significant, providing no evidence of a direct association between trust in cooperative management and AE among non-participants. Combined with the strong relevance evidence reported in Table 5, Panel C (p < 0.01), the result is consistent with the exclusion restriction.

and are satisfied over the whole sample, so the estimated cost frontier is theoretically well behaved.

2.3. Identifying the Causal Impact of IAM Participation: Endogenous Switching Regression (ESR)

Impact evaluation based on observational data poses a major methodological challenge, primarily related to the construction of a credible counterfactual in the presence of self-selection bias. In the context of this study, cassava producers’ participation in inclusive agribusiness models is not random; rather, it results from an endogenous decision influenced by both observable characteristics (education level, farm size, access to inputs) and unobservable factors (managerial ability, motivation, social networks). This endogeneity may generate selection bias if these factors are correlated with allocative efficiency, which constitutes the outcome variable of interest.

Several econometric approaches have been developed to address this bias in cross-sectional data, including Propensity Score Matching (PSM), Inverse Probability Weighting (IPW), and Instrumental Variable (IV) methods. However, both PSM and IPW rely on the Conditional Independence Assumption (CIA) and only account for observable heterogeneity. In contrast, IV-based approaches address endogeneity arising from unobservable factors but depend on strong assumptions regarding the validity and strength of the instruments.

To overcome these limitations, this study employs the Endogenous Switching Regression (ESR) model, which simultaneously corrects for biases arising from both observable and unobservable factors [20,21,22]. Unlike standard treatment-effect models, the ESR framework relaxes the assumption of homogeneous treatment effects by estimating regime-specific outcome functions for participants and non-participants. This approach captures structural heterogeneity in behavior and performance, acknowledging that the determinants of allocative efficiency may differ depending on participation status.

The ESR model is based on a system of three equations jointly estimated using Full Information Maximum Likelihood (FIML). The first equation models the participation decision through a probit specification, incorporating a set of explanatory variables as well as an exclusion restriction to ensure model identification:

D_i = Z_iα + η_i

(6)

where D_i = 1 if the producer participates in an inclusive agribusiness model, and D_i = 0 otherwise. The vector Z_i includes participation determinants and the exclusion restriction. As an instrumental variable, we use producers’ trust in cooperative management (1 = yes; 0 = otherwise), a variable that strongly predicts participation in inclusive agribusiness models, since trust in the managing institution is a precondition for enrolment, but has no plausible direct effect on allocative efficiency conditional on the other covariates (including meeting participation, which is retained as a regular determinant in all three equations), satisfying the relevance condition; a falsification test further supports the exclusion restriction, showing that trust in cooperative management has no significant direct effect on allocative efficiency among non-participants, who have no access to the IAM channel for which this variable serves as a proxy (Table A1, Test 9).

The survey instrument recorded IAM participation as a single indicator (Di = 1 if the producer participates in any inclusive agribusiness model and 0 otherwise) rather than administering separate follow-up questions identifying which of the three arrangement types (simple contracts, 4Ps, or joint ventures) each participating producer was enrolled under; a disaggregated headcount across the three types is therefore not available for the current sample, a data limitation acknowledged in the Limitations Section. Pooling the three arrangements into a single binary participation variable is nonetheless defensible on theoretical grounds: as discussed in the Introduction, the three institutional forms differ in governance depth and the degree of public-sector involvement, but they share the two channels through which our conceptual framework predicts allocative-efficiency gains: price and market-security signals that stabilize expected returns to input use, and information flows on optimal input quantities and timing. Given these common channels and the moderate size of the participant sub-sample (n = 374), a single joint indicator also yields more precise average treatment-effect estimates in the second-stage ESR and IPWRA models than would separate, lower-powered indicators for each arrangement type.

AE_1i = X_iβ₁ + σ₁λ_1i + ϵ_1i (Participants: D_i = 1)

(7)

AE_0i = X_iβ₀ + σ₀λ_0i + ϵ_0i (Non-Participants: D_i = 0)

(8)

where λ_1i and λ_0i are the inverse Mills ratio terms derived from the selection equation, correcting for endogenous selection within each regime. The vector X_i includes farming experience, household size, farm size, gender, cooperative status, education level, participation in meetings, existence of sales contracts, contact with extension agents, and participation in other development projects. Detailed definitions, measurement units, expected signs, and theoretical justifications for all variables included in the model are reported in

Table A2. Variables included in the ESR model, definitions, expected signs, and theoretical justifications.

Variables	Definition/Unit	Justification and Expected Effect on Allocative Efficiency (AE)	Expected Sign	Reference Authors
Participation in inclusive agribusiness models	Dummy (1 = participates, 0 = otherwise)	Improves access to quality inputs, technical training, and contract-based credit, while reducing transaction costs	+	[14,16,19,42]
Gender of household head	Dummy (1 = male, 0 = female)	Ambiguous effect due to differences in access to resources and gender roles	±	[16,19]
Farming experience	Years	Experience enhances mastery of farming practices and leads to more efficient resource allocation	+	[5,14,19]
Education level	Categorical dummies (none, primary, secondary I, secondary II, university; “none” is the reference category), as entered in the regressions reported in Table 5	Facilitates better understanding of relative prices and more rational input allocation	+	[5,16,50]
Household size	Number of individuals	Increases family labor supply but may lead to labor surplus and inefficient allocation	-	[14,51,52]
Farm size	Hectares	Larger holdings may exceed the managerial capacity of the household and complicate the timely, cost-minimising allocation of inputs across parcels	-	[14,53,54,55]
Membership in a cooperative	Dummy (1 = yes, 0 = otherwise)	Facilitates access to information, services, and collective bargaining	+	[14,43]
Participation in training/extension services	Dummy (1 = yes, 0 = otherwise)	Improves technical knowledge and the ability to allocate resources efficiently	+	[19,56,57]
Meeting participation	Dummy (1 = yes, 0 = otherwise)	Attending IAM-related informational meetings increases producers’ exposure to input-use recommendations and market information, improving allocation decisions	+	[19,57]
Existence of sales contract	Dummy (1 = yes, 0 = otherwise)	Provides price and market-security signals that reduce uncertainty in input-investment decisions, encouraging more efficient input use	+	[13,28]
Beneficiary of another development project	Dummy (1 = yes, 0 = otherwise)	Ambiguous effect: complementary external support could ease resource constraints, but attention or resources diverted across multiple simultaneous interventions could dilute the effectiveness of any single program	±	—
Trust in cooperative management (excluded instrument)	Dummy (1 = yes, 0 = otherwise)	Excluded instrument for IAM participation: trust in the managing institution is a precondition for enrollment through the cooperative channel but has no plausible direct effect on allocative efficiency conditional on the other covariates		—

.

The parameters of the full system are estimated using the FIML approach. This framework enables the computation of the Average Treatment Effect on the Treated (ATT), which measures the actual impact of participation on participants, and the Average Treatment Effect on the Untreated (ATU), which captures the potential gains for non-participants.

ATT = E(AE_1i| D_i = 1) − E(AE_0i| D_i = 1)

(9)

ATU = E(AE_1i| D_i = 0) − E(AE_0i| D_i = 0)

(10)

The ATT measures the actual efficiency gain for producers who participated; the ATU measures the hypothetical gain that non-participants would have achieved had they participated. Comparing ATT and ATU reveals treatment-effect heterogeneity and the degree of positive selection into IAMs [21,22,35].

2.4. Diagnostic Tests and Robustness

A series of statistical tests were conducted to validate model specifications and ensure the robustness of the empirical results. For the Stochastic Frontier Analysis (SFA) models, the likelihood-ratio (LR) test compares the translog against the more restrictive Cobb–Douglas specifications [1,30,36]. Multicollinearity is assessed via the Variance Inflation Factor (VIF), with mean values below 3 (

Table A3. Multicollinearity diagnostics (Variance Inflation Factors).

Variable	VIF	1/VIF
Farm size (ha)	2.1	0.475
Household size	2.02	0.496
Farming experience	1.88	0.533
Cooperative status (Executive member)	1.86	0.539
Beneficiary of another project	1.52	0.66
Meeting participation	1.32	0.76
Education level	1.3	0.767
Gender (male)	1.22	0.818
Existence of sales contract	1.14	0.874
Contact with extension (ATDA)	1.12	0.893
Cooperative status (Ordinary member)	1.08	0.927
Mean VIF	1.51	-

), indicating no serious collinearity concerns among the explanatory variables [37]. For the Endogenous Switching Regression (ESR) model, the correlation test of the error terms (Rho test) was applied to assess the presence of endogenous selection bias. The statistical significance of the correlation coefficients provided evidence supporting the existence of selection bias, thereby justifying the use of the ESR framework [21,22]. As a further robustness check that does not rely on the ESR exclusion restriction, Section 3.6 reports treatment effect estimates from an Inverse-Probability-Weighted Regression Adjustment (IPWRA) estimator [38], which identifies the effect of IAM participation under a selection-on-observables assumption instead.

2.5. Data and Sampling Design

Data were collected between January and February 2026 across 38 municipalities in seven departments of southern and central Benin: Atlantique, Couffo, Collines, Mono, Ouémé, Plateau, and Zou (Figure 1 presents a map of the study area). These departments constitute the principal cassava-producing zones in the country [39,40] and host the highest concentration of PADAAM-supported IAM initiatives, making them well suited to studying the efficiency effects of market integration.

A multi-stage sampling design was employed to construct comparable treatment and control groups. In the first stage, administrative databases from PADAAM were used to enumerate all cassava producers registered as IAM participants, constituting the treatment group. In the second stage, an independent list of non-participating producers was compiled from Communal Cell Heads (CCeC) registers, ensuring clean separation between groups. In the third stage, simple random sampling was applied within each municipality, drawing between 25 and 35 producers per municipality from each of the two frames. Because both groups are drawn from the same set of municipalities, participants and non-participants are exposed to broadly similar agroecological and market conditions, which improves the comparability of the two groups. This design concerns the selection of respondents only. It does not randomize participation in IAMs, which remains a self-selected decision, and it does not in itself control for location-specific conditions, since no municipality fixed effects are included in the estimated models. Random selection within municipalities therefore limits the risk of purposive selection of respondents, whereas identification of the treatment effects continues to rest on the assumptions of the ESR and IPWRA frameworks set out in Section 2.3 and Section 3.6.

The final sample comprises 1167 producers, 374 IAM participants (32.1%) and 793 non-participants (67.9%), distributed across 1198 cultivated plots (some producers operating multiple plots). Data were collected via structured questionnaires administered on tablets using KoboToolbox (2.026.33b), covering household socioeconomic characteristics, farming systems, IAM integration level, input quantities and prices at the plot level, market access, and institutional variables. Enumerators received comprehensive training and conducted a pilot survey before the main data collection. All participants were informed of the objectives of the study, participation was entirely voluntary, and free and informed consent was obtained from each respondent prior to data collection. The confidentiality and anonymity of respondents were ensured throughout the study and in accordance with established research ethics standards [40]. To minimize linguistic bias across the multilingual study area, enumerators were selected for proficiency in local languages and trained translators were deployed where necessary.

Input quantities, input prices and output were recorded at the plot level for the 1198 cultivated plots operated by the 1167 sampled producers. Because a minority of producers operate more than one plot, plot-level quantities and costs were first aggregated to the producer level (summing physical quantities and expenditures, and computing cultivated-area-weighted means for unit prices and yields) before any estimation was carried out. Both the stochastic production and cost frontiers reported in Section 3.2 and the Endogenous Switching Regression and treatment-effect models reported in Section 3.4, Section 3.5 and Section 3.6 are therefore estimated on the same unit of observation, the producer, and on the same analysis sample of N = 1167. Because each producer contributes a single observation at every stage of the analysis, the dependence between plots belonging to the same producer is removed by construction and no within-producer clustering correction is required; standard errors are nonetheless estimated using the robust Huber–White method. We do not cluster standard errors by village or other geographic unit; if unobserved shocks are correlated within villages, the reported standard errors could understate the true sampling variability, a limitation acknowledged in the Limitations Section.

3. Results

3.1. Descriptive Statistics

Table 1. Descriptive characteristics of IAM participants and non-participants in cassava production.

Continuous Variables		Non-Participants in IAMs	Participants in IAMs	Total	Statistical Test
		Mean (Std. Dev.)	Mean (Std. Dev.)	Mean (Std. Dev.)	t-Test
Farming experience (years)		21.22 (14.80)	22.05 (15.46)	21.49 (15.02)	−0.88
Household size (members)		2.36 (4.51)	6.73 (3.27)	3.76 (4.63)	3.59 ***
Farm size (ha)		1.73 (0.9)	1.80 (1.78)	1.75 (1.01)	2.31 **
Categorical variables	Categories	Percentage (%)			Chi-square (χ2)
Age group	Mature adults	45.65	45.45	45.59	0.89
	Youth	1.51	1.60	1.54
	Young adults	48.93	47.86	48.59
	Elderly	3.91	5.08	4.28
Cooperative status	Executive member	6.15	56.24	22.20	275.80 ***
	Ordinary member	28.88	9.08	22.54
	Non-member	64.97	34.68	55.26
Gender	Male	74.53	66.84	72.07	7.07 ***
	Female	25.47	33.16	27.93
Access to inputs	No	73.14	24.33	57.49	792.14 ***
	Yes	26.86	75.67	42.51
Collective marketing	No	75.66	24.06	59.13	795.84 ***
	Yes	24.34	75.94	40.87
Existence of sales contract	Yes	16.65	84.22	38.30	488.28 ***
	No	83.35	15.78	61.70
Contact with extension agents (ATDA)	Yes	21.39	71.50	37.45	256.30 ***
	No	78.61	28.50	62.55
Meeting participant	No	90.64	57.38	79.98	129.31 ***
	Yes	9.36	42.62	20.02
Education level	None	56.62	46.79	53.47	11.81 **
	Primary	27.87	34.22	29.91
	Secondary	12.36	14.17	12.94
	Tertiary	2.65	4.55	3.26
	Technical training	0.50	0.27	0.43
Beneficiary of another project	Yes	16.14	70.59	33.59	335.30 ***
	No	83.86	29.41	66.41

Notes: *** p < 0.01; ** p < 0.05. Chi-square tests applied to categorical variables; Student’s t-tests to continuous variables.

presents the descriptive statistics for the estimation sample, which comprises 1167 producers (374 IAM participants; 793 non-participants); full details on sample composition, data collection, and survey protocol are given in Section 2.5.

3.2. Stochastic Frontier Estimation Results

3.2.1. Production Frontier

Table 2. Translog stochastic production frontier estimation results (dependent variable: ln cassava yield, kg/ha).

Log Cassava (Output)	Coefficient	Std. Err.	P > z	[95% Conf. Interval]
Log herbicide	−0.013	0.162	0.934	−0.331	0.304
Log cassava cuttings	0.010	0.050	0.847	−0.089	0.108
Log organic manure	0.209 *	0.116	0.072	−0.018	0.436
Log NPK	0.410	0.264	0.120	−0.107	0.927
Log urea	0.068	0.281	0.810	−0.483	0.619
Log labor	0.048	0.136	0.724	−0.219	0.315
Log herbicide2	−0.020	0.026	0.456	−0.071	0.032
Log cassava cuttings2	0.005	0.006	0.420	−0.007	0.018
Log organic manure2	−0.018	0.017	0.291	−0.053	0.016
Log NPK2	0.102 ***	0.035	0.004	0.033	0.171
Log urea2	0.002	0.045	0.968	−0.087	0.090
Log labor2	0.021 *	0.013	0.096	−0.004	0.046
Log herbicide × cuttings	−0.019	0.016	0.239	−0.050	0.013
Log herbicide × organic manure	−0.022	0.014	0.112	−0.050	0.005
Log herbicide × NPK	0.023 *	0.014	0.091	−0.004	0.050
Log herbicide × urea	0.013	0.014	0.352	−0.014	0.040
Log herbicide × labor	0.057 ***	0.019	0.002	0.020	0.093
Log cuttings × organic manure	−0.004	0.012	0.729	−0.027	0.019
Log cuttings × NPK	0.009	0.025	0.729	−0.040	0.058
Log cuttings × urea	−0.014	0.026	0.593	−0.066	0.037
Log cuttings × labor	−0.018	0.014	0.191	−0.045	0.009
Log organic manure × NPK	−0.010	0.008	0.188	−0.025	0.005
Log organic manure × urea	−0.002	0.008	0.823	−0.018	0.015
Log organic manure × labor	−0.022 **	0.010	0.039	−0.042	−0.001
Log NPK × urea	−0.011	0.008	0.162	−0.027	0.004
Log NPK × labor	0.012	0.018	0.487	−0.023	0.047
Log urea × labor	0.041 **	0.021	0.049	0.000	0.082
Constant	2.894 ***	0.373	0.000	2.164	3.625
Usigma
Constant	−0.166 ***	0.060	0.006	−0.284	−0.048
Vsigma
Constant	−2.471 ***	0.097	0.000	−2.662	−2.280
sigma_u	0.920 ***	0.028	0.000	0.868	0.976
sigma_v	0.291 ***	0.014	0.000	0.264	0.320
lambda (λ = σu/σv)	3.166 ***	0.035	0.000	3.097	3.235
Log likelihood = −1052.7066 Number of obs = 1167 Wald chi2 (27) = 129.02 Prob > chi2 = 0.0000

Notes: *** p < 0.01; ** p < 0.05; * p < 0.10.

reports the translog stochastic production frontier results. The model is globally significant (Wald chi² (27) = 129.02; p < 0.001), and the likelihood ratio test strongly rejects the Cobb–Douglas restriction in favour of the translog specification (LR chi² (21) = 65.51; p < 0.001), confirming the appropriateness of the flexible functional form (Table A1, Test 2). The signal-to-noise ratio λ = σ_u/σ_v = 3.166 is large and highly significant (p < 0.001), indicating that inefficiency effects dominate random noise in explaining output variation.

Among direct input effects, organic manure is the only linear term with a statistically significant positive effect on cassava yield (at the 10% level), underscoring the importance of soil organic matter in cassava production on the generally sandy and nutrient-poor soils of southern Benin. Herbicide, cassava cuttings, NPK, urea, and labor linear terms are not individually significant, suggesting that, at the sample’s prevailing input levels, none of these inputs are unambiguously under- or over-applied on average. However, the significant positive quadratic terms for NPK and labor indicate that returns to these two inputs are non-linear: yield responsiveness increases at higher application intensities, consistent with threshold effects often reported for chemical fertilizer and peak-season labor use in smallholder systems.

Among the interaction terms, the significant positive coefficients on herbicide × NPK and herbicide × labor reveal complementarities: the productivity of weed control is enhanced when combined with nitrogen supply and adequate labor for timely application, with these findings having direct implications for extension advice on optimal input packages. The significant positive urea × labor interaction points to a similar complementarity between fertilization and labor timing. By contrast, the significant negative interaction between organic manure and labor suggests a degree of substitutability between organic soil amendment and labor-intensive practices, consistent with organic manure application reducing the labor otherwise required for in-season weed and fertility management. The remaining interaction terms, including herbicide × cuttings, are not individually significant.

3.2.2. Cost Frontier

Table 3. Translog stochastic cost frontier estimation results (dependent variable: ln total cost, FCFA/ha).

Log Total Cost/Labor Price	Coefficient	Std. Err.	P > z	[95% Conf. Interval]
Log cassava yield (output)	0.952 ***	0.041	0.000	0.872	1.032
Log urea price	0.119 ***	0.018	0.000	0.084	0.154
Log NPK price	0.204 ***	0.024	0.000	0.157	0.251
Log cassava cuttings price	0.178 ***	0.022	0.000	0.135	0.221
Log herbicide price	0.081 ***	0.016	0.000	0.050	0.112
Log capital (land) price	0.121 ***	0.019	0.000	0.084	0.158
Log yield2	0.028 *	0.015	0.062	−0.001	0.057
Log urea price2	−0.033 *	0.017	0.053	−0.066	0.000
Log NPK price2	−0.051 ***	0.019	0.007	−0.088	−0.014
Log cuttings price2	−0.042 **	0.018	0.020	−0.077	−0.007
Log herbicide price2	−0.021	0.015	0.161	−0.050	0.008
Log capital price2	−0.038 **	0.016	0.018	−0.069	−0.007
Log yield × urea price	0.006	0.010	0.548	−0.014	0.026
Log yield × NPK price	0.009	0.012	0.453	−0.015	0.033
Log yield × cuttings price	0.012	0.011	0.275	−0.010	0.034
Log yield × herbicide price	0.004	0.009	0.657	−0.014	0.022
Log yield × capital price	0.007	0.010	0.484	−0.013	0.027
Log urea × NPK price	−0.016	0.014	0.253	−0.043	0.011
Log urea × cuttings price	−0.011	0.013	0.397	−0.036	0.014
Log urea × herbicide price	−0.006	0.011	0.586	−0.028	0.016
Log urea × capital price	−0.010	0.012	0.405	−0.034	0.014
Log NPK × cuttings price	−0.018	0.014	0.199	−0.045	0.009
Log NPK × herbicide price	−0.009	0.012	0.453	−0.033	0.015
Log NPK × capital price	−0.015	0.013	0.249	−0.040	0.010
Log cuttings × herbicide price	−0.008	0.012	0.505	−0.032	0.016
Log cuttings × capital price	−0.014	0.013	0.281	−0.039	0.011
Log herbicide × capital price	−0.007	0.011	0.525	−0.029	0.015
Constant	4.215 ***	0.086	0.000	4.046	4.384
Usigma
Constant	0.060	0.057	0.293	−0.052	0.172
Vsigma
Constant	−3.219 ***	0.118	0.000	−3.450	−2.988
sigma_u	1.030 ***	0.029	0.000	0.974	1.089
sigma_v	0.200 ***	0.012	0.000	0.178	0.225
lambda (λ = σu/σv)	5.150 ***	0.310	0.000	4.542	5.758
Log likelihood = −412.3 Number of obs = 1167 Wald chi2 (27) = 4180.6 Prob > chi2 = 0.000

Notes: *** p < 0.01; ** p < 0.05; * p < 0.10.

presents the translog stochastic cost frontier results, estimated with linear homogeneity of degree one in input prices imposed by taking the price of labor as the numéraire. The model is globally significant (p < 0.001; log likelihood = −412.3), and the estimated variance parameters indicate that cost inefficiency accounts for the dominant share of the composed-error variance (the variance ratio is statistically significant at the 1% level). The small estimated variance of the symmetric error component is consistent with respondents reporting actual transaction prices rather than imputed values.

All prices in Table 3 are expressed relative to the price of labor, so the reported coefficients are elasticities of labor-price-normalized cost with respect to labor-price-normalized prices; the labor-price terms are recovered from the homogeneity restrictions and are not reported separately. The cost elasticity with respect to output is positive and highly significant (0.952, p < 0.01), close to unity and therefore consistent with near-constant returns to scale in the cost structure. All five first-order price elasticities are positive and significant, as required by monotonicity: NPK price (0.204, p < 0.01) and cassava cuttings price (0.178, p < 0.01) are the largest cost drivers, followed by capital (land) price (0.121, p < 0.01), urea price (0.119, p < 0.01) and herbicide price (0.081, p < 0.01). Their sum, 0.703, implies a recovered labor cost share of 0.297, confirming that labor remains the single largest component of production cost in these labor-intensive cassava systems.

The quadratic price terms are negative throughout and significant for NPK (−0.051, p < 0.01), cassava cuttings (−0.042, p < 0.05), capital (−0.038, p < 0.05) and urea (−0.033, p < 0.10), indicating that cost becomes progressively less sensitive to further increases in these prices; only the herbicide term (−0.021, p = 0.161) is not statistically distinguishable from zero. The quadratic output term is positive and weakly significant (0.028, p < 0.10), pointing to a mildly U-shaped cost–output relationship. The cross-price terms are uniformly small and statistically insignificant (all p > 0.19), as are the interactions between output and prices (all p > 0.27), so once homogeneity is imposed, there is no evidence of strong substitution or complementarity between input prices, and no evidence of non-homothetic behaviour in the cost function. The curvature matrix of the cost function in prices, evaluated at the point of approximation, is negative definite, and the regularity conditions required for a well-behaved cost function, monotonicity and concavity in prices, are satisfied over the whole sample (Table A1, Tests 7 and 8).

3.3. Efficiency Score Distribution

Table 4. Efficiency scores of cassava producers by IAM participation status.

	Non-Participants in IAMs				Participants in IAMs				Overall
	Mean	SD	Min	Max	Mean	SD	Min	Max	Mean	SD	Min	Max
Allocative efficiency (AE)	0.620	0.185	0.096	0.896	0.700	0.171	0.293	0.950	0.646	0.162	0.096	0.950
Economic efficiency (EE)	0.430	0.193	0.012	0.856	0.484	0.175	0.020	0.905	0.447	0.185	0.012	0.905
Technical efficiency (TE)	0.693	0.165	0.123	0.955	0.692	0.168	0.067	0.953	0.693	0.166	0.067	0.955

Notes: SD = standard deviation. Allocative efficiency = Economic efficiency/Technical efficiency, derived from jointly estimated translog production and cost frontiers.

reports mean efficiency scores by participation status. Average allocative efficiency across the full sample is 0.646, indicating that the average cassava producer operates about 35 percentage points below the allocative efficiency frontier defined by current output levels and input prices, a substantial gap consistent with prior evidence from smallholder systems in sub-Saharan Africa [6,14,19]. Mean technical efficiency is 0.693 and mean economic efficiency is 0.447.

IAM participants display higher allocative efficiency (AE = 0.700) than non-participants (AE = 0.620), a mean difference of 8.0 percentage points. The gap is concentrated in the allocative dimension: technical efficiency is virtually identical across the two groups (0.692 against 0.693, a difference of one tenth of a percentage point), while economic efficiency differs by 5.4 percentage points (0.484 against 0.430).

Even among IAM participants, allocative efficiency remains well below unity (0.700), so substantial room for improvement persists. Participation is therefore associated not only with a higher average level of allocative efficiency but also with a compression of the lower tail of the distribution, a pattern we examine further through the ESR model.

3.4. Determinants of Allocative Efficiency and Participation

The results reported in

Table 5. Endogenous Switching Regression results: determinants of allocative efficiency and IAM participation.

Variables	Coefficient	Std. Err.
Panel A: Non-participants in IAMs, Outcome equation
Farming experience (years)	−0.0012 *	0.0007
Household size	−0.0093 ***	0.0027
Farm size (ha)	−0.0084 *	0.0049
Gender (1 = male)	0.0016	0.0231
Cooperative status (Ordinary member)	0.0512 *	0.0273
Education level (Primary)	0.0498 **	0.0209
Education level (Secondary I)	−0.0203	0.1284
Contact with extension (ATDA)	−0.0967 ***	0.0296
Meeting participation	0.0171	0.0225
Existence of sales contract	0.0368	0.0308
Beneficiary of another project	−0.1327 ***	0.0299
Constant	0.9127 ***	0.0581
Panel B: Participants in IAMs, Outcome equation
Farming experience (years)	0.0021 **	0.0009
Household size	0.0097 **	0.0043
Farm size (ha)	−0.0029	0.0039
Gender (1 = male)	0.0718 **	0.0342
Cooperative status (Ordinary member)	0.4362 ***	0.0491
Cooperative status (Executive member)	−0.1043 ***	0.0319
Education level (Primary)	−0.0417	0.0348
Education level (Secondary I)	−0.0759	0.0483
Education level (Secondary II)	−0.0946	0.0806
Education level (University)	0.1084	0.4412
Contact with extension (ATDA)	−0.2731 ***	0.0351
Meeting participation	−0.1526 ***	0.0472
Existence of sales contract	0.0951 **	0.0435
Beneficiary of another project	−0.0263	0.0331
Constant	1.1547 ***	0.0671
Panel C: IAM participation, Selection equation
Farming experience (years)	−0.0058 **	0.0029
Household size	−0.0289 **	0.0130
Farm size (ha)	0.0082	0.0114
Gender (1 = male)	−0.2164 **	0.1036
Cooperative status (Ordinary member)	−1.3421 ***	0.1372
Cooperative status (Executive member)	0.1518	0.1123
Education level (Primary)	0.1247	0.1069
Education level (Secondary I)	0.2314	0.1478
Education level (Secondary II)	0.2861	0.2461
Education level (University)	−1.4682 ***	0.4651
Contact with extension (ATDA)	0.8237 ***	0.1094
Meeting participation	0.4619 ***	0.1406
Trust in cooperative management (1 = yes) (instrument)	0.0214 ***	0.0054
Constant	−0.8143 ***	0.2054
/lns0	−1.3574 ***	0.0399
/lns1	−1.0492 ***	0.0512
/r0	−0.0461	0.1287
/r1	−0.4912 ***	0.1523
sigma0	0.2573 ***	0.0103
sigma1	0.3502 ***	0.0179
rho0	−0.0460	0.1284
rho1	−0.4552 ***	0.1207

*** p < 0.01; ** p < 0.05; * p < 0.10. The Variance Inflation Factor (VIF) test yielded a mean value of 1.51. All variables included in the model exhibited VIF values below 3, which is considered acceptable. The detailed VIF values for each variable are reported in Table A3.

from the Endogenous Switching Regression (ESR) model reveal notable differences in the determinants of allocative efficiency between non-participating producers (non-IAMs) and participants in inclusive agribusiness models (IAMs). The model is jointly significant (Wald χ²(14) = 486.3; p < 0.001), and the likelihood-ratio test of independence of the three equations is rejected (χ²(2) = 10.84; p = 0.004), confirming the joint dependence of the outcome and selection equations and thereby justifying the use of this framework rather than separate single-equation estimates. Standard errors are estimated using the robust Huber–White method [41], which corrects for heteroskedasticity of unknown form, a common feature in cross-sectional data, and ensures more reliable significance tests and confidence intervals. It should be noted that the coefficient vectors are allowed to differ freely across regimes, so that the marginal effect of a given characteristic is regime-specific; this is precisely the restriction that a single dummy-variable specification would impose and that the switching framework relaxes.

Among non-participating producers, farm size (−0.0084; p = 0.087), household size (−0.0093; p = 0.001), farming experience (−0.0012; p = 0.087) and contact with extension agents (−0.0967; p = 0.001) all exert significant negative effects on allocative efficiency, while primary education (0.0498; p = 0.017) and, to a lesser extent, ordinary cooperative membership (0.0512; p = 0.061) are associated with significantly higher efficiency. This suggests that farm expansion and larger household size, without corresponding gains in labor-use efficiency or complementary resources, may be accompanied by reduced capacity to optimally allocate inputs. The negative return to experience points in the same direction: outside a structured institutional framework, seniority appears to entrench routine input combinations rather than to refine them. Beneficiary status from another development project is associated with a strong and significant efficiency penalty (−0.1327; p < 0.001), possibly reflecting resource or attention dilution across multiple simultaneous interventions. By contrast, gender, secondary education, meeting participation, and the existence of a sales contract are not statistically significant among non-participants, suggesting that market-linkage variables such as sales contracts only translate into measurable efficiency gains once combined with the fuller institutional package associated with IAM participation.

The estimated coefficients in the participant regime reveal strikingly different dynamics. Farm size retains a negative sign but is no longer statistically significant (−0.0029; p = 0.457), suggesting that IAM membership largely attenuates the scale-related inefficiency observed among non-participants, possibly through collective procurement and shared extension services that help larger farms maintain optimal input ratios. The most notable finding is the sign reversal on farming experience and household size: both carry a significant efficiency penalty among non-participants yet become positive and significant within the IAM regime (0.0021, p = 0.020, and 0.0097, p = 0.024, respectively). This reversal has a coherent economic interpretation: accumulated but unstructured know-how and abundant but under-deployed family labor are converted into productive assets once technical guidance, input access and output timing are standardized by the platform. It also constitutes the clearest empirical justification for the switching specification, since a pooled model would average these opposing effects towards zero and conclude, wrongly, that experience and household size are irrelevant. A second contrast concerns the internal stratification of cooperative status, which is identified only in this regime: ordinary membership is associated with a large and highly significant efficiency gain (0.4362; p < 0.001), whereas executive membership carries a significant penalty (−0.1043; p = 0.001). Within the IAM framework, producers holding leadership positions in cooperatives may prioritize organizational and administrative tasks over farm management, creating time allocation trade-offs that reduce allocative efficiency. This finding challenges the assumption that cooperative leadership uniformly enhances efficiency and suggests that the productivity costs of organizational engagement should be considered in cooperative development programs; it further indicates that the benefits of IAM-linked cooperative affiliation accrue mainly to rank-and-file members rather than to those holding leadership positions. The same time-allocation logic extends to meeting participation, which is neutral among non-participants but significantly negative among participants (−0.1526; p = 0.001), for whom the meeting calendar is considerably denser. Sales contracts, which show no significant effect among non-participants, become significantly positive within the IAM regime (0.0951; p = 0.029), indicating that the market security channel operates only once combined with the broader IAM institutional package. Gender displays a significant positive coefficient among participants (0.0718; p = 0.036), suggesting that male producers achieve higher allocative efficiency within IAMs, potentially reflecting greater access to complementary productive resources or fewer competing time demands from domestic responsibilities among male participants.

The selection equation shows that participation in IAMs is primarily driven by institutional connectivity rather than by cooperative rank or farm-level characteristics as such. Contact with extension agents (0.8237; p < 0.001) and participation in IAM-related meetings (0.4619; p = 0.001) are the strongest positive predictors of enrolment, consistent with information and outreach channels driving selection into the program; trust in cooperative management, the excluded instrument, also strongly and positively predicts participation (0.0214; p < 0.001), as expected. The exclusion restriction is defensible on substantive grounds: trust in cooperative governance plausibly governs the decision to enrol without exerting a direct effect on the technical allocation of inputs conditional on enrolment. By contrast, ordinary cooperative membership is the single strongest negative predictor of participation (−1.3421; p < 0.001), suggesting that IAM outreach has so far under-served rank-and-file cooperative members relative to non-members, even though, once enrolled, it is precisely these ordinary members who capture the largest efficiency gains. This mismatch between who is reached and who benefits is arguably the most policy-relevant result of the model. University education (−1.4682; p = 0.002), larger households (−0.0289; p = 0.026), more experienced farmers (−0.0058; p = 0.046) and male-headed households (−0.2164; p = 0.037) are also significantly associated with a lower probability of participation, a pattern with direct implications for the inclusiveness of future targeting. Executive cooperative status and farm size, by contrast, do not significantly predict participation once these other factors are controlled for.

Finally, the correlation parameters of the error terms confirm the presence of endogenous selection, though only in the participant regime. The correlation coefficient for participants (ρ₁ = −0.4552; p < 0.001) is negative and highly significant, while the corresponding coefficient for non-participants (ρ₀ = −0.0460; p = 0.720) is not statistically distinguishable from zero. The negative and significant sign of ρ₁ indicates negative selection on unobservables in the participant regime. This implies that producers who choose to join IAMs tend, based on unobserved characteristics (such as managerial ability, effort, intrinsic motivation, or organizational capacity), to exhibit lower allocative efficiency than average in the counterfactual scenario (i.e., had they not participated). In other words, relatively less efficient producers, on unobserved dimensions, are more likely to self-select into IAMs, possibly because they stand to gain the most from participation. A direct implication is that naive comparisons of means between participants and non-participants would understate the true effect of the program, since the two groups differ unfavourably for participants on unobservables. The absence of significant selection on unobservables among non-participants suggests that their allocative efficiency outcomes are, by comparison, well explained by the observable characteristics already included in the model. The variance of the error term is also appreciably larger in the participant regime (σ₁ = 0.3502) than in the counterfactual one (σ₀ = 0.2573), pointing to greater dispersion of outcomes and therefore to substantial heterogeneity in the returns to IAM membership.

3.5. Treatment Effects: ATT and ATU

Table 6. Average expected allocative efficiency and treatment effects.

Outcome Variable	Treatment Effects	Decision Stage		Treatment Effects	t-Value	p-Value
		To Participate	Not to Participate
Allocative efficiency	ATT	(a) 0.700	(c) 0.550	0.150 ***	7.85	0.000
	ATU	(d) 0.680	(b) 0.620	0.060 ***	3.92	0.000

Notes: *** p < 0.01. ATT = Average Treatment Effect on the Treated = (a) − (c); ATU = Average Treatment Effect on the Untreated = (d) − (b). Cells (a) and (b) represent observed efficiency for participants and non-participants, respectively; (c) and (d) represent counterfactual efficiency estimates from the ESR model.

reports the Average Treatment Effect on the Treated (ATT) and the Average Treatment Effect on the Untreated (ATU). The ATT is estimated at 0.150 (SE = 0.019; t = 7.85; p < 0.001): actual IAM participants achieve allocative efficiency levels 15.0 percentage points higher than they would have attained in the absence of participation. The relevant counterfactual for the treated is cell (c) of Table 6, which shows the efficiency participants are predicted to have reached had they not participated (0.550); relative to that benchmark, the ATT corresponds to a gain of about 27 percent. This figure describes a change in the allocative efficiency index and must not be read as a proportional reduction in production costs.

The ATU is estimated at 0.060 (SE = 0.015; t = 3.92; p < 0.001): non-participants would gain 6.0 percentage points in allocative efficiency had they participated under current IAM arrangements. The corresponding 95% confidence intervals are [0.113, 0.187] for the ATT and [0.031, 0.089] for the ATU. The ATT–ATU asymmetry, approximately 2.5:1, indicates that the benefits of IAM participation are concentrated among those who actually participate, while current IAM design generates considerably smaller efficiency gains for non-participants. This pattern is consistent with producers who self-select into IAMs being those best positioned to benefit from market integration, through cooperative affiliation, organizational ties, or managerial capacity. The value of cell (c), 0.550, the efficiency IAM participants are predicted to have achieved had they not participated, lies below the actual efficiency of non-participants (b = 0.620); this is directly implied by the negative correlation between the unobserved determinants of participation and of non-participant-regime efficiency (ρ₁ = −0.4552, Table 5): producers with participation-favouring unobserved traits are predicted to have been comparatively inefficient had they remained outside IAM arrangements. This does not contradict the interpretation above, which concerns selection on observable characteristics, whereas ρ₁ captures selection on unobservables specific to the non-participation regime. The two can point in different directions: producers may be observably well positioned to benefit from IAM participation while also carrying unobserved disadvantages that would have depressed their efficiency had they not joined.

3.6. Robustness Check: IPWRA Estimation

To assess whether the ESR treatment-effect estimates are sensitive to the specific parametric and exclusion-restriction assumptions of that framework, we re-estimate the impact of IAM participation on allocative efficiency using an Inverse-Probability-Weighted Regression Adjustment (IPWRA) estimator [38]. IPWRA is a doubly robust estimator: it remains consistent if either the participation (propensity-score) model or the outcome regression is correctly specified, and unlike the ESR model, it does not require an excluded instrument, relying instead on a conditional-independence (selection-on-observables) assumption. The propensity-score model is a probit regression of IAM participation on the same covariates included in the ESR outcome equations (farming experience, household size, farm size, gender, cooperative status, education level, contact with extension agents, meeting participation, existence of a sales contract, and beneficiary status), excluding the trust-in-cooperative-management instrument used for identification in the ESR model.

Table 7. Robustness check: comparison of ESR and IPWRA average treatment effect estimates.

Estimator	Parameter	Coefficient	z	P > z
ESR	ATT	0.150 ***	7.85	0.000
IPWRA	ATT	0.132 ***	6.29	0.000
IPWRA	ATE	0.098 ***	5.44	0.000
IPWRA	POmean(0) 1	0.568 ***	56.80	0.000

Notes: *** p < 0.01. IPWRA = Inverse-Probability-Weighted Regression Adjustment [38], estimated via a probit propensity-score model using the same covariates as the ESR outcome equations, excluding the trust-in-cooperative-management instrument (not required for identification under IPWRA). ATT = Average Treatment Effect on the Treated; ATE = Average Treatment Effect across the full sample. ¹ POmean(0) is the counterfactual mean allocative efficiency for IAM participants had they not participated, used to compute the ATT above.

reports the results. The IPWRA estimate of the ATT is 0.132 (SE = 0.021; p < 0.001), close to the ESR estimate of 0.150: the two estimators, which rely on different identification strategies (exclusion restriction versus selection-on-observables) and different estimation approaches (full-information maximum likelihood versus semi-parametric weighting), converge on materially the same conclusion, namely that IAM participation raises allocative efficiency by roughly 13 to 15 percentage points among participants. That the ESR estimate is the larger of the two is expected: the IPWRA estimator does not correct for selection on unobservables, which the significant ρ₁ reported in Table 5 indicates is present. The population-average treatment effect (ATE = 0.098, SE = 0.018, p < 0.001) is smaller than the ATT, consistent with the positive-selection pattern established via the ATT–ATU asymmetry in Section 3.5: producers who actually select into IAMs benefit more than an average, non-selected producer would. It also recovers almost exactly the ATE implied by the ESR estimates, the participation-weighted average of the ATT and the ATU (0.089). The convergence of two methodologically distinct estimators indicates that the estimated market-integration effect is not an artifact of the specific parametric and exclusion-restriction assumptions of the ESR model. It does not, however, establish causality on its own. IPWRA identifies the effect under a selection-on-observables assumption, while the ESR estimate relies on the validity of the excluded instrument; the two estimates would also agree if the same unobserved determinants of participation were correlated with allocative efficiency in both specifications. The results are therefore best read as consistent with a causal effect of IAM participation under the identifying assumptions stated in Section 2.3 and Section 3.6, rather than as direct evidence of one.

4. Discussion

4.1. IAMs and Allocative Efficiency: Evidence on the Market Integration Hypothesis

The finding that IAM participation significantly improves allocative efficiency (ATT = 0.150) is consistent with the theoretical prediction that market integration reduces transaction costs and information asymmetries that distort input allocation decisions. This result adds to a literature that has documented positive effects of value chain participation on farm income [12,28], technical efficiency [19,42], and productivity [13], while extending the analysis to the specific dimension of allocative efficiency, an angle that has received remarkably little empirical attention despite its direct relevance for cost reduction and farm profitability.

The concentration of efficiency gains in the allocative rather than the technical dimension (the inter-group gap in AE is 8.0 percentage points, against one tenth of a percentage point in TE) is theoretically coherent and policy-relevant. It suggests that the primary pathway through which PADAAM-style IAMs improve farm performance is not the dissemination of new production technologies, but rather the improvement of market information and price incentives that guide input allocation decisions. This interpretation is supported by the institutional design of the interventions examined. PADAAM activities emphasize collective marketing, contract formalization, and input access, all of which directly target the information and transaction cost frictions underlying allocative inefficiency, rather than agronomic extension per se.

These results are consistent with the broader empirical literature connecting market integration to efficiency. Collective action in output markets has been shown to improve the quality of production decisions among smallholders in Kenya [43]. Market links between value chain actors and smallholders have been shown to generate information spillovers that improve resource use [44]. Meta-analytic evidence indicates that contract farming, a key component of the IAMs studied here, enhances efficiency through reduced market risk and improved input supply chains [13]. Our results, obtained from an ESR framework that corrects for selection on both observables and unobservables, are consistent with a causal interpretation of these effects under the identifying assumptions stated in Section 2.3. We note, however, that the information, liquidity, and market-security channels through which we interpret these gains are inferred from the institutional design of PADAAM activities and from the pattern of results (concentration in allocative rather than technical efficiency) rather than directly measured or tested; the survey did not collect data on producers’ information access, liquidity constraints, or perceived market security that would allow these channels to be tested individually, and other unobserved mechanisms consistent with the same pattern cannot be ruled out.

4.2. Treatment-Effect Heterogeneity and the Inclusiveness Challenge

The ATT–ATU asymmetry (0.150 versus 0.060) is one of the most policy-consequential findings of this study. It indicates that current IAM design generates substantial efficiency gains for those who participate, and gains roughly two and a half times smaller for those who remain outside these arrangements. The estimated gain for the treated is also about twice the observed participant/non-participant gap reported in Table 6 (0.080), which means that the raw comparison of the two groups understates the effect of participation for those who take it up. At the same time, it indicates that extending participation to the current non-participant population would generate more modest efficiency gains under current program design.

This ATT–ATU asymmetry has been documented in other contexts of institutional innovation in agriculture. Similar heterogeneity has been found in the returns to climate adaptation in Ethiopia, attributed to differences in adaptive capacity [22]. Evidence on adoption of improved wheat varieties in Ethiopia shows that adopters benefit significantly more than non-adopters would, reflecting complementarities with other endowments [35]. In our context, the most plausible interpretation involves two reinforcing mechanisms. First, in terms of positive selection, the producers who join IAMs, characterized by stronger institutional connectivity and greater engagement with extension services, possess the organizational and managerial capital needed to convert market access into efficiency improvements; notably, this selection operates through engagement with information and outreach channels rather than through cooperative affiliation: contact with extension services and participation in IAM-related meetings are the strongest positive predictors of enrolment, whereas ordinary cooperative membership significantly reduces the likelihood of entry, and farm size plays no role; university education is the only educational category significantly associated with participation, and negatively so. Second, regarding program fit, current IAM structures (collective marketing, sales contracts, and producer organization membership requirements) are designed around producers who already have some degree of market readiness, implicitly excluding producers who lack institutional visibility, including much of the cooperative membership base.

The role of cooperative membership qualifies the first mechanism in an important way. Cooperative affiliation carries opposite signs in the two equations. Ordinary membership is the largest coefficient in the selection equation, but with a negative sign (Table 5, Panel C), so cooperative members are significantly less likely to enter IAMs; within the participant regime, by contrast, ordinary membership is the strongest positive determinant of allocative efficiency, while executive membership carries a significant penalty (Table 5, Panel B). Cooperatives therefore do not function as the recruitment channel for these arrangements, even though they identify precisely the producers who convert market access into efficiency gains once inside. The inclusiveness gap consequently runs through the cooperative structure rather than around it: the producers with the greatest demonstrated capacity to benefit are among the least likely to be reached by current outreach. The selection equation shows that male-headed households, larger households and more experienced farmers are significantly less likely to participate, and that farm size plays no role, with university education being the only educational category significantly associated with participation. Enrolment is therefore driven by exposure to information and outreach channels rather than by individual endowments. From a policy perspective, this argues for adding the cooperative membership base to current recruitment routes rather than for redistributing access within channels that already function.

The discussion above is organized around cooperative membership status rather than other candidate grouping variables such as gender or farm-size quartile, for three reasons. First, cooperative status is the variable that separates capacity to benefit from likelihood of enrolment most sharply in our estimates, which places it at the centre of the inclusiveness question this study addresses. Second, cooperative status is the dimension along which the contrast between the two regimes documented in Section 3.4 is sharpest, making it the natural candidate for a focused discussion. Third, with 374 IAM participants, the sub-sample does not support well-powered treatment-effect splits along multiple additional dimensions simultaneously; further stratifying by gender or farm size on top of participation status would leave individual cells with few observations. We therefore do not report separate ATT estimates by gender or farm size here, and flag disaggregating treatment effects along these additional dimensions, ideally with a larger sample, as a direction for future research.

4.3. The Collective Marketing Channel

The strong positive role of sales contracts within the IAM participant regime, and the institutional centrality of collective marketing in IAM design, point to output market security as a key mechanism through which IAMs improve allocative efficiency. Economic theory provides a clear rationale: when producers face price uncertainty, they make precautionary input decisions that deviate from the cost-minimizing optimum [25,26]. By guaranteeing prices and market outlets, contractual arrangements shift the decision environment toward the conditions required for allocative efficiency: known prices, secured demand, and predictable returns to input investment. Cooperative-mediated collective marketing in Ethiopia has been shown to reduce post-harvest losses and improve input timing, two channels directly relevant to allocative efficiency [45]. Our results extend this evidence to the West African cassava context.

The implication is that programs seeking to improve allocative efficiency among smallholders should prioritize output market security alongside input market improvement. Simply increasing input availability without addressing market uncertainty is unlikely to induce the optimal input allocation behavior that translates physical access into efficiency gains. This argues for the integrated approach characteristic of the PADAAM model, combining contract formalization, collective marketing organization, and input supply facilitation, rather than narrow interventions targeting only input supply or only market linkage.

4.4. Persistent Inefficiency and Binding Structural Constraints

Despite the positive effects of IAM participation, average allocative efficiency among participants remains at 0.700, leaving roughly 30 percentage points of allocative inefficiency. The persistence of substantial inefficiency even under the most favorable institutional arrangement examined here indicates that IAMs, while necessary, are insufficient to close the efficiency gap in the absence of complementary interventions. Three categories of structural constraint appear binding.

First, financial constraints limit the ability of producers to invest in the optimal input bundle even when they know what it is. Liquidity constraints are particularly acute in cassava production, where the 8–12-month crop cycle between planting and harvest creates extended periods of negative cash flow. Innovative financial mechanisms—warehouse receipt systems, value chain financing, and index-based insurance—have shown promise in relaxing these constraints in comparable contexts [46,47]. Second, managerial capacity gaps prevent the efficient implementation of optimal input plans. While returns to extension services have been shown elsewhere to be highest when combined with market integration [48], our own estimates point in the opposite direction within the participant regime, where extension contact is associated with significantly lower allocative efficiency (Table 5, Panel B). As argued in Section 3.4, this most plausibly reflects the time demands of a dense institutional calendar on producers already engaged in IAM activities rather than a negative return to agronomic advice as such. The implication is not that extension should be scaled back, but that its delivery within IAMs should be redesigned to reduce the competing time burden it places on participants. Third, infrastructure deficiencies, particularly storage facilities, feeder roads, and communication networks, increase the cost of accessing inputs and delivering outputs at optimal times, generating input-timing distortions that manifest as allocative inefficiency.

4.5. Policy Implications

Four policy implications follow from these findings. First, the estimated impact of IAMs on allocative efficiency provides justification for continued and expanded investment in value chain integration programs for cassava in Benin and comparable West African agricultural systems. The ATT (0.150) reflects a substantial improvement in allocative efficiency for participating producers. This is a gain in the efficiency score itself, not a direct 15-percentage-point reduction in production costs, since the ATT captures a treatment-induced increase in the efficiency level rather than a percentage change in costs, but it nonetheless implies a marked narrowing of the gap between observed and cost-minimizing input use, with corresponding implications for farm profitability and household welfare.

Second, the markedly smaller ATU (0.060) signals that current program design would generate only limited efficiency gains for non-participants, even in hypothetical scenarios. Expanding coverage without redesigning the program architecture is unlikely to achieve inclusive efficiency improvements. Programs should invest in graduated entry mechanisms, lower-threshold arrangements such as simple contracts for producers not yet ready for full IAM participation, combined with targeted support (input subsidies, cooperative capacity building, extension) to bring marginalized producers up to the threshold of market readiness.

Third, cooperative membership predicts higher allocative efficiency within IAMs but a lower likelihood of entering them, which points to a targeting failure rather than to a delivery success: the producers best able to convert market access into efficiency gains are currently among the least likely to be recruited. Programs should therefore make cooperatives an explicit recruitment channel alongside the extension and meeting channels that already drive enrolment, and should examine why existing cooperative structures have so far channeled their members away from these arrangements rather than into them.

Fourth, the financial constraint binding on even IAM-participating producers argues for integration of agricultural finance instruments into IAM program design. Contract-based financing, where processors provide advance payments secured against delivery contracts, represents a relatively low-cost mechanism for relaxing liquidity constraints within existing program architectures, and it has been shown to improve both efficiency and participation in comparable contexts [46].

5. Conclusions

This study examined the impact of participation in inclusive agribusiness models on the allocative efficiency of cassava producers in Benin, employing an econometric framework that combines Stochastic Frontier Analysis with an Endogenous Switching Regression model. Four key findings emerge.

First, average allocative efficiency in cassava production is moderate (0.646), leaving roughly 35 percentage points of scope for improvement through better input allocation, a large and potentially welfare-improving gain. Second, IAM participation significantly enhances allocative efficiency, with an ATT of 0.150, an estimated effect that remains robust after accounting for selection on both observables and unobservables; this is consistent with, though not definitive proof of, a causal interpretation under the model’s identifying assumptions. Third, the efficiency gains from IAMs are concentrated in the allocative rather than the technical efficiency dimension, pointing to market information and output market security as the primary mechanisms of impact. Fourth, the ATT–ATU asymmetry reveals positive selection on gains: current IAM design captures the largest efficiency gains for those who participate, and generates considerably smaller benefits for those who remain outside these arrangements under current program structures.

These findings contribute to the agricultural economics literature in three ways. They provide quasi-experimental evidence, consistent with a causal interpretation under the model’s identifying assumptions, on the allocative efficiency effects of inclusive agribusiness models in West Africa. They document the mechanism through which value chain integration improves farm performance, operating primarily through input allocation rather than technology adoption. And they reveal the distributional limits of current IAM designs, generating actionable guidance on program redesign to improve inclusiveness.

Several limitations warrant acknowledgment. The cross-sectional design precludes analysis of efficiency dynamics over the course of IAM participation, an important question for future research. Additionally, the absence of panel data prevents us from ruling out all time-invariant confounders, though the ESR approach corrects for unobservable selection in the cross-sectional setting. Identification of the treatment effects also depends on the validity of the excluded instrument (trust in cooperative management); although the falsification test does not reject the exclusion restriction, this is a necessary but not sufficient condition, and the instrument’s validity ultimately rests on an identifying assumption that cannot be directly tested. Input quantities, prices, and cassava output were self-reported by producers rather than independently measured or verified against farm records, which may introduce measurement error; to the extent that such error is non-differential across participation status and attenuates estimated coefficients toward zero, the reported ATT and ATU may understate the true effects, though this cannot be verified without independent validation data. The cost frontier is estimated in translog form with linear homogeneity of degree one in input prices imposed by normalizing by the price of labor, and the remaining regularity conditions, monotonicity and concavity in prices, are satisfied at the observed data points. Finally, the sample is drawn from 38 municipalities across seven departments of southern and central Benin selected for their high concentration of PADAAM-supported IAM initiatives; findings may not generalize to cassava-growing regions with different agroecological conditions, market infrastructure, or program exposure. Future research should exploit longitudinal data or quasi-experimental variation in IAM rollout to examine whether efficiency gains strengthen, weaken, or diffuse over time, and whether expanded participation through redesigned entry mechanisms generates the inclusive efficiency gains that current evidence suggests are currently foreclosed.