Abstract

The Econometrics of Agri-Food Value Chains

Agri-food value chains (AFVCs) move food from producers to consumers through multiple stages—farming, trading, processing, transportation, wholesaling, retailing, food service, and ultimately final consumers. These chains move commodities downstream and payments upstream.

Despite their centrality to food security, economic development, and resilience in the face of shocks, AFVCs remain surprisingly underexplored in the statistical and econometric literatures. Research has traditionally concentrated either on (i) primary producers, (ii) consumers, or (iii) dyadic relationships between various pairs of actors that are directly involved with each other (e.g., grower-processor pairs in contract farming), leaving the “midstream” nodes of the chain—where much of the aggregation, value addition, and market coordination occurs—relatively poorly understood.

Value Chains as Networks
We propose a network-based econometric framework to analyze AFVCs, advancing both methodological tools and empirical insights. We begin by conceptualizing AFVCs as directed networks. A network is formally defined as a graph G=(V,E), where V is the set of vertices (i.e., agents such as farmers, traders, or firms) and E is the set of directed edges (i.e., relationships such as sales or contracts). Unlike undirected graphs, AFVCs exhibit clear directionality: commodities flow downstream from producers to consumers, or payments and information flow upstream. This asymmetry means that standard econometric assumptions—most notably independence and identical distribution (i.i.d.) across observational units—fail to hold. Agents are interdependent, interactions are high-dimensional, and the chain involves clustering, bottlenecks, and feedback. Traditional econometric models, which typically treat observations as exchangeable units, are therefore ill-suited to AFVC data. Our contribution is to articulate a network-based statistical framework that respects the directional and relational nature of these chains.

Sampling
We next consider sampling challenges. Unlike in conventional survey design, where one can randomly sample individuals or firms independently, AFVC agents are embedded in relational structures. Selecting one farmer reveals information about their trading partners; sampling a firm indirectly samples all its suppliers and customers. We compare alternative network-based sampling methods, including star sampling, which selects initial nodes and records their connected edges, and snowball sampling, which iteratively includes neighbors through waves.

Using a simulated AFVC population of 100 farmers, 10 traders, and five processors, each with location and demographic attributes, where farmers generate heterogeneous outputs and form links through distance-weighted trade, we show how sampling from different entry points (i.e., farmers, traders, or companies) yields distinct sub-graphs with varying degrees of representativeness. These examples highlight the biases that arise when naively using plug-in estimators from sample data to infer population-level properties, and they motivate the need for careful design and weighting.

Once data are sampled, we demonstrate how to describe AFVC networks statistically. Key measures include degree distributions (e.g., in-degree and out-degree), degree correlations, centrality indices (e.g., closeness, betweenness, eigenvector), and cohesion measures such as density, connectivity, and partitioning.

Modeling
Beyond description, we turn to modeling flows within AFVCs. We adapt the gravity model, long used in trade and transportation studies, to estimate transaction volumes between nodes. In this framework, expected flows between an origin i and a destination j depend multiplicatively on characteristics of the origin (e.g., farmer production), the destination (e.g., trader capacity), and a deterrence function of separation (e.g., geographic distance). A log-linearized form facilitates estimation, though ordinary least squares is biased and inefficient due to heteroskedasticity, zero counts, and Jensen’s inequality. To address these issues, we discuss variance-stabilizing transformations, weighted least squares, and fixed-effects centering. More robustly, we implement maximum likelihood estimation under Poisson and negative binomial specifications which better accommodate count data and overdispersion. Our empirical illustration shows how farmer production and geographic distance jointly determine transaction volumes, with interpretable elasticities.

Broader Considerations
The methodological agenda proposed here situates AFVCs squarely within the domain of statistical analysis of network data, while tailoring models to the unique directional and multi-stage character of food systems. Conceptualizing AFVCs as networks resolves fundamental misalignments between data structure and econometric assumptions. Network-based sampling designs and estimators correct biases inherent in relational data collection. Descriptive measures allow researchers to characterize resilience, centralization, and fragmentation in food chains. And structural modeling, exemplified by gravity specifications, enables inference on the determinants of flows across nodes, with implications for efficiency, equity, and sustainability.

For agricultural statisticians, the framework opens several promising research directions. First, it creates opportunities for better survey design, particularly in low- and middle-income countries where AFVCs mediate both farmer livelihoods and consumer access. Second, it enriches the analysis of shocks—such as pandemics, conflicts, or climate events—by providing tools to study how disruptions propagate through networks. Third, it connects micro-level behavior (e.g., farmer sales decisions) with macro-level outcomes (e.g., food availability and price stability), bridging scales often siloed in research. Finally, the network perspective highlights the roles of midstream actors—traders, transporters, processors—who are crucial but understudied, and whose structural positions may hold the key to improving resilience.