Modeling Agricultural Risk Dependencies: A Comparison of Copula and Kernel Density Methods for Farm-Level Risk Management

Accurately modeling multivariate distributions is crucial for understanding variable dependencies and supporting informed decision-making in fields such as risk management. This study compares two approaches, Multivariate kernel density estimation (MV-KDE) and copulas, to determine which approach, when specified using a data sample, generally most closely captures an unknown true joint probability distribution. Simulated data generated from diverse distributions are used to evaluate the performance of each method across different sample sizes. Empirical data on crop yields and prices are also incorporated to test a real-world scenario to inform better risk assessment. Goodness-of-fit is assessed using the maximum mean discrepancy aggregated two-sample test. With large sample sizes, copulas outperform MV-KDE when an appropriate distributional form exists to capture the underlying dependence structure. With small sample sizes, MV-KDE consistently outperforms data-driven functional form selection for copulas and parametric marginal distributions by avoiding misspecification risks. This makes MV-KDE a safer choice under limited sample sizes and unknown underlying distributions, particularly when the dimensionality remains moderate.