The Causal Effect of BMI on Hypertension: A Copula Model Approach with Genetic Risk Instruments

This paper estimates the causal effect of body mass index (BMI) on hypertension risk using data from the Young Finns Study. The empirical framework combines genetic instruments for BMI with a triangular copula model that accommodates a binary outcome and a continuous endogenous treatment, allowing unobserved determinants of BMI and hypertension to be correlated through alternative symmetric and asymmetric copula specifications. Sensitivity analyses examine alternative copula families and nested BMI genetic-score constructions to address pleiotropy concerns. The results show that higher BMI increases hypertension risk across ordered blood-pressure severity categories. Probability-scale treatment effects reveal a nonlinear pattern: marginal risk is concentrated in clinically relevant regions of the BMI distribution and shifts from early blood-pressure elevation toward more severe hypertension as body mass increases. The findings illustrate how genetic instruments and copula-based triangular models can be combined to study endogenous continuous treatments with nonlinear health outcomes, while identifying where along the BMI distribution marginal increases in body mass are most consequential for blood-pressure risk.