Neuroscientists have become increasingly interested in exploring dynamic relationships among brain regions. Such a relationship, when directed from one region toward another, is denoted by ``effective connectivity.'' An fMRI experimental paradigm which is well-suited for examination of effective connectivity is the slow event-related design. This design presents stimuli at sufficient temporal spacing for determining within-trial trajectories of BOLD activation. However, while several analytic methods for determining effective connectivity in fMRI studies have been devised, few are adapted to the characteristics of event-related designs, which include non-stationary BOLD responses and nesting of responses within trials and subjects. We propose a model tailored for exploring effective connectivity of multiple brain regions in event-related fMRI designs - a semi-parametric adaptation of vector autoregressive (VAR) models, termed "stimulus-locked VAR" (SloVAR). Connectivity coefficients vary as a function of time relative to stimulus onset, are regularized via basis expansions, and vary randomly across subjects. SloVAR obtains flexible, data-driven estimates of effective connectivity and hence is useful for building connectivity models when prior information on dynamic regional relationships is sparse. Indices derived from the coefficient estimates can also be used to relate effective connectivity estimates to behavioral or clinical measures. We demonstrate the SloVAR model on a sample of clinically depressed and normal controls, showing that early but not late cortico-amygdala connectivity appears crucial to emotional control and early but not late cortico-cortico connectivity predicts depression severity in the depressed group, relationships that would have been missed in a more traditional VAR analysis.