# Causal Effect Estimation

Continuous-time stochastic processes had no instrumental-variable framework, and discrete-time methods place the structural sparsity on finite-step transitions rather than on the actual mechanism. The work writes relevance, exclusion and exogeneity directly at the infinitesimal level of a stochastic differential equation's drift and builds moment conditions from the whole instrument path, giving an identification condition and a consistent estimator in the linear case. On confounded Ornstein-Uhlenbeck simulations, maximum likelihood becomes systematically biased as confounding grows while this estimator stays stable, and a single instrument process identifies multi-dimensional effects.

Continuous-time stochastic processes had no instrumental-variable framework, and discrete-time methods place the structural sparsity on finite-step transitions rather than on the actual mechanism. The work writes relevance, exclusion and exogeneity directly at the infinitesimal level of a stochastic differential equation's drift and builds moment conditions from the whole instrument path, giving an identification condition and a consistent estimator in the linear case. On confounded Ornstein-Uhlenbeck simulations, maximum likelihood becomes systematically biased as confounding grows while this estimator stays stable, and a single instrument process identifies multi-dimensional effects.